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+The Project Gutenberg eBook, A Budget of Paradoxes, Volume II (of II), by
+Augustus de Morgan, Edited by David Eugene Smith
+
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+
+
+
+Title: A Budget of Paradoxes, Volume II (of II)
+
+
+Author: Augustus de Morgan
+
+Editor: David Eugene Smith
+
+Release Date: August 23, 2008  [eBook #26408]
+
+Language: English
+
+Character set encoding: ISO-646-US (US-ASCII)
+
+
+***START OF THE PROJECT GUTENBERG EBOOK A BUDGET OF PARADOXES, VOLUME II
+(OF II)***
+
+
+E-text prepared by David Starner, Keith Edkins, and the Project Gutenberg
+Online Distributed Proofreading Team (http://www.pgdp.net)
+
+
+
+Transcriber's note:
+
+      A few typographical errors have been corrected: they are
+      listed at the end of the text.
+
+      In mathematical formulae the carat (^) and underscore (_)
+      introduce superscripts or subscripts respectively, of one
+      character or a group enclosed in curly braces ({xyz}).
+      Elsewhere underscores delimit italics in the text, and
+      braces enclose the original page numbers thus {123}.
+
+
+
+
+
+BY AUGUSTUS DE MORGAN
+
+A BUDGET OF
+PARADOXES
+
+REPRINTED WITH THE AUTHOR'S ADDITIONS FROM THE ATHENAEUM
+
+SECOND EDITION EDITED BY DAVID EUGENE SMITH
+
+WITH A NEW INTRODUCTION BY ERNEST NAGEL
+
+PROFESSOR OF PHILOSOPHY, COLUMBIA UNIVERSITY
+
+UNABRIDGED EDITION--TWO VOLUMES BOUND AS ONE
+
+Volume II
+
+
+
+
+
+
+
+DOVER PUBLICATIONS, INC., NEW YORK
+
+       *       *       *       *       *
+
+_This new Dover Edition, published in 1954,
+is an unabridged republication of the Second Edition
+of 1915, with a new introduction by Professor Ernest Nagel._
+
+_Copyright 1954 by Dover Publications, Inc.
+Manufactured in the United States of America_
+
+       *       *       *       *       *
+
+
+{1}
+
+A BUDGET OF PARADOXES.
+
+VOLUME II.
+
+ON SOME PHILOSOPHICAL ATHEISTS.
+
+With the general run of the philosophical atheists of the last century the
+notion of a God was an hypothesis. There was left an admitted possibility
+that the vague somewhat which went by more names than one, might be
+personal, intelligent, and superintendent. In the works of Laplace,[1] who
+is sometimes called an atheist from his writings, there is nothing from
+which such an inference can be drawn: unless indeed a Reverend Fellow of
+the Royal Society may be held to be the fool who said in his heart, etc.,
+etc., if his contributions to the _Philosophical Transactions_ go no higher
+than _nature_. The following anecdote is well known in Paris, but has never
+been printed entire. Laplace once went in form to present some edition of
+his "Systeme du Monde" to the First Consul, or Emperor. Napoleon, whom some
+wags had told that this book contained no mention of the name of God, and
+who was fond of putting embarrassing questions, received it with--"M.
+Laplace, they tell me you have written this large book on the system of the
+universe, and have never even mentioned its Creator." Laplace, who, though
+the most supple of politicians, was as stiff as a martyr on every point of
+his philosophy or religion (e. g., even under Charles X he never concealed
+his dislike of the priests), drew himself up and answered {2} bluntly, "Je
+n'avais pas besoin de cette hypothese-la."[2] Napoleon, greatly amused,
+told this reply to Lagrange, who exclaimed, "Ah! c'est une belle hypothese;
+ca explique beaucoup de choses."[3]
+
+It is commonly said that the last words of Laplace were, "Ce que nous
+connaissons est peu de chose; ce que nous ignorons est immense."[4] This
+looks like a parody on Newton's pebbles:[5] the following is the true
+account; it comes to me through one remove from Poisson.[6] After the
+publication (in 1825) of the fifth volume of the _Mecanique Celeste_,
+Laplace became gradually weaker, and with it musing and abstracted. He
+thought much on the great problems of existence, and often muttered to
+himself, _Qu'est ce que c'est que tout cela!_[7] After many alternations,
+he appeared at last so permanently prostrated that his family applied to
+his favorite pupil, M. Poisson, to try to get a word from him. Poisson paid
+a visit, and after a few words of salutation, said, "J'ai une bonne
+nouvelle a vous annoncer: on a recu au Bureau des Longitudes une lettre
+d'Allemagne annoncant que M. Bessel a verifie par l'observation vos
+decouvertes theoriques sur les satellites de Jupiter."[8] Laplace opened
+his eyes and answered with deep {3} gravity, "_L'homme ne poursuit que des
+chimeres_."[9] He never spoke again. His death took place March 5, 1827.
+
+The language used by the two great geometers illustrates what I have said:
+a supreme and guiding intelligence--apart from a blind rule called _nature
+of things_--was an _hypothesis_. The absolute denial of such a ruling power
+was not in the plan of the higher philosophers: it was left for the smaller
+fry. A round assertion of the non-existence of anything which stands in the
+way is the refuge of a certain class of minds: but it succeeds only with
+things subjective; the objective offers resistance. A philosopher of the
+appropriative class tried it upon the constable who appropriated _him_: I
+deny your existence, said he; Come along all the same, said the
+unpsychological policeman.
+
+Euler[10] was a believer in God, downright and straightforward. The
+following story is told by Thiebault,[11] in his _Souvenirs de vingt ans de
+sejour a Berlin_,[12] published in his old age, about 1804. This volume was
+fully received as trustworthy; and Marshall Mollendorff[13] told the Duc de
+Bassano[14] in 1807 that it was the most veracious of books written by the
+most honest of men. Thiebault says that he has no personal knowledge of the
+truth of the story, but {4} that it was believed throughout the whole of
+the north of Europe. Diderot[15] paid a visit to the Russian Court at the
+invitation of the Empress. He conversed very freely, and gave the younger
+members of the Court circle a good deal of lively atheism. The Empress was
+much amused, but some of her councillors suggested that it might be
+desirable to check these expositions of doctrine. The Empress did not like
+to put a direct muzzle on her guest's tongue, so the following plot was
+contrived. Diderot was informed that a learned mathematician was in
+possession of an algebraical demonstration of the existence of God, and
+would give it him before all the Court, if he desired to hear it. Diderot
+gladly consented: though the name of the mathematician is not given, it was
+Euler. He advanced towards Diderot, and said gravely, and in a tone of
+perfect conviction: _Monsieur,_ (a + b^{n}) / n = x, _donc Dieu existe;
+repondez!_[16] Diderot, to whom algebra was Hebrew, was embarrassed and
+disconcerted; while peals of laughter rose on all sides. He asked
+permission to return to France at once, which was granted.
+
+
+
+ROTATION OF THE MOON.
+
+    An examination of the Astronomical doctrine of the Moon's rotation. By
+    J. L.[17] Edinburgh, 1847, 8vo.
+
+A systematic attack of the character afterwards made with less skill and
+more notice by Mr. Jellinger Symons.
+
+July 1866, J. L. appears as Mr. James Laurie, with a new pamphlet "The
+Astronomical doctrines of the Moon's rotation ..." Edinburgh. Of all the
+works I have seen on the question, this is the most confident, and the
+sorest. {5} A writer on astronomy said of Mr. Jellinger Symons,[18] "Of
+course he convinced no one who knew anything of the subject." This
+"ungenerous slur" on the speculator's memory appears to have been keenly
+felt; but its truth is admitted. Those who knew anything of the subject are
+"the so-called men of science," whose three P's were assailed; prestige,
+pride, and prejudice: this the author tries to effect for himself with
+three Q's; quibble, quirk, and quiddity. He explains that the Scribes and
+Pharisees would not hear Jesus, and that the lordly bishop of Rome will not
+cast his tiara and keys at the feet of the "humble presbyter" who now plays
+the part of pope in Scotland. I do not know whom he means: but perhaps the
+friends of the presbyter-pope may consider this an ungenerous slur. The
+best proof of the astronomer is just such "as might have been expected from
+the merest of blockheads"; but as the giver is of course not a blockhead,
+this circumstance shows how deeply blinded by prejudice he must be.
+
+Of course the paradoxers do not persuade any persons who know their
+subjects: and so these Scribes and Pharisees reject the Messiah. We must
+suppose that the makers of this comparison are Christians: for if they
+thought the Messiah an enthusiast or an impostor, they would be absurd in
+comparing those who reject what they take for truth with others who once
+rejected what they take for falsehood. And if Christians, they are both
+irreverent and blind to all analogy. The Messiah, with His Divine mission
+proved by miracles which all might see who chose to look, is degraded into
+a prototype of James Laurie, ingeniously astronomizing upon ignorant
+geometry and false logic, and comparing to blockheads those who expose his
+nonsense. Their comparison is as foolish as--supposing {6} them
+Christians--it is profane: but, like errors in general, its other end
+points to truth. There were Pseudochrists and Antichrists; and a
+Concordance would find the real forerunners of all the paradoxers. But they
+are not so clever as the old false prophets: there are none of whom we
+should be inclined to say that, if it were possible, they would deceive the
+very educated. Not an Egyptian among them all can make uproar enough to
+collect four thousand men that are murderers--of common sense--to lead out
+into the wilderness. Nothing, says the motto of this work, is so difficult
+to destroy as the errors and false facts propagated by illustrious men
+whose words have authority. I deny it altogether. There are things much
+more difficult to destroy: it is much more difficult to destroy the truths
+and real facts supported by such men. And again, it is much more difficult
+to prevent men of no authority from setting up false pretensions; and it is
+much more difficult to destroy assertions of fancy speculation. Many an
+error of thought and learning has fallen before a gradual growth of
+thoughtful and learned opposition. But such things as the quadrature of the
+circle, etc., are never put down. And why? Because thought can influence
+thought, but thought cannot influence self-conceit: learning can annihilate
+learning: but learning cannot annihilate ignorance. A sword may cut through
+an iron bar; and the severed ends will not reunite: let it go through the
+air, and the yielding substance is whole again in a moment.
+
+
+
+    Miracles _versus_ Nature: being an application of certain propositions
+    in the theory of chances to the Christian miracles. By
+    Protimalethes.[19] Cambridge, 1847, 8vo.
+
+The theory, as may be supposed, is carried further than most students of
+the subject would hold defensible.
+
+{7}
+
+
+
+    An astronomical Lecture. By the Rev. R. Wilson.[20] Greenock, 1847,
+    12mo.
+
+Against the moon's rotation on her axis.
+
+
+
+    [Handed about in the streets in 1847: I quote the whole:] Important
+    discovery in astronomy, communicated to the Astronomer Royal, December
+    21st, 1846. That the Sun revolve round the Planets in 25748-2/5 years,
+    in consequence of the combined attraction of the planets and their
+    satellites, and that the Earth revolve round the Moon in 18 years and
+    228 days. D. T. GLAZIER [altered with a pen into GLAZION.] Price one
+    penny.
+
+1847. In the _United Service Magazine_ for September, 1847, Mrs.
+Borron,[21] of Shrewsbury, published some remarks tending to impeach the
+fact that Neptune, the planet found by Galle,[22] really was the planet
+which Le Verrier and Adams[23] had a right to claim. This was followed
+(September 14) by two pages, separately circulated, of "Further
+Observations upon the Planets Neptune and Uranus, with a Theory of
+Perturbations"; and (October 19, 1848) by three pages of "A Review of M.
+Leverrier's Exposition." Several persons, when the remarkable discovery was
+made, contended that the planet actually discovered was an intruder; and
+the future histories of the discovery must contain some account of this
+little afterpiece. Tim Linkinwater's theory that there is no place like
+London for coincidences, would have been utterly overthrown in favor of
+what they used to call the celestial spaces, if there had been a planet
+which by chance was put {8} near the place assigned to Neptune at the time
+when the discovery was made.
+
+
+
+EARLY IDEAS OF AVIATION.
+
+    Aerial Navigation; containing a description of a proposed flying
+    machine, on a new principle. By Daedalus Britannicus. London, 1847, 8vo.
+
+In 1842-43 a Mr. Henson[24] had proposed what he called an aeronaut
+steam-engine, and a Bill was brought in to incorporate an "Aerial Transit
+Company." The present plan is altogether different, the moving power being
+the explosion of mixed hydrogen and air. Nothing came of it--not even a
+Bill. What the final destiny of the balloon may be no one knows: it may
+reasonably be suspected that difficulties will at last be overcome.
+Darwin,[25] in his "Botanic Garden" (1781), has the following prophecy:
+
+ "Soon shall thy arm, unconquered Steam! afar
+  Drag the slow barge, or drive the rapid car;
+  Or, on wide-waving wings expanded, bear
+  The flying chariot through the fields of air."
+
+Darwin's contemporaries, no doubt, smiled pity on the poor man. It is worth
+note that the two true prophecies have been fulfilled in a sense different
+from that of the predictions. Darwin was thinking of the suggestion of
+Jonathan Hulls,[26] when he spoke of dragging the slow barge: it is only
+very recently that the steam-tug has been employed on the canals. The car
+was to be driven, not drawn, and on the common roads. Perhaps, the flying
+chariot will {9} be something of a character which we cannot imagine, even
+with the two prophecies and their fulfilments to help us.[27]
+
+
+
+THE SECRET OF THE UNIVERSE DIVULGED.
+
+    A book for the public. New Discovery. The causes of the circulation of
+    the blood; and the true nature of the planetary system. London, 1848,
+    8vo.
+
+Light is the sustainer of motion both in the earth and in the blood. The
+natural standard, the pulse of a person in health, four beats to one
+respiration, gives the natural second, which is the measure of the earth's
+progress in its daily revolution. The Greek fable of the Titans is an
+elaborate exposition of the atomic theory: but any attempt to convince
+learned classics would only meet their derision; so much does long-fostered
+prejudice stand in the way of truth. The author complains bitterly that men
+of science will not attend to him and others like him: he observes, that
+"in the time occupied in declining, a man of science might test the
+merits." This is, alas! too true; so well do applicants of this kind know
+how to stick on. But every rule has its exception: I have heard of one. The
+late Lord Spencer[28]--the Lord Althorp of the House of Commons--told me
+that a speculator once got access to him at the Home Office, and was
+proceeding to unfold his way of serving the public. "I do not understand
+these things," said Lord Althorp, "but I happen to have ---- (naming an
+eminent engineer) upstairs; suppose you talk to him on the subject." The
+discoverer went up, and in half-an-hour returned, and said, "I am very much
+obliged to your Lordship for introducing me to Mr. ----; he has convinced
+me {10} that I am quite wrong." I supposed, when I heard the story--but it
+would not have been seemly to say it--that Lord A. exhaled candor and
+sense, which infected those who came within reach: he would have done so,
+if anybody.
+
+
+
+THE TRISECTION AND QUADRATURE AGAIN.
+
+    A method to trisect a series of angles having relation to each other;
+    also another to trisect any given angle. By James Sabben. 1848 (two
+    quarto pages).
+
+"The consequence of years of intense thought": very likely, and very sad.
+
+1848. The following was sent to me in manuscript. I give the whole of it:
+
+"_Quadrature of the Circle_.--A quadrant is a curvilinear angle traversing
+round and at an equal distance from a given point, called a center, no two
+points in the curve being at the same angle, but irreptitiously graduating
+from 90 to 60. It is therefore a mean angle of 90 and 60, which is 75,
+because it is more than 60, and less than 90, approximately from 60 to 90,
+and from 90 to 60, with equal generation in each irreptitious
+approximation, therefore meeting in 75, and which is the mean angle of the
+quadrant.
+
+"Or suppose a line drawn from a given point at 90, and from the same point
+at 60. Let each of these lines revolve on this point toward each other at
+an equal ratio. They will become one line at 75, and bisect the curve,
+which is one-sixth of the entire circle. The result, taking 16 as a
+diameter, gives an area of 201.072400, and a circumference of 50.2681.
+
+"The original conception, its natural harmony, and the result, to my own
+mind is a demonstrative truth, which I presume it right to make known,
+though perhaps at the hazard of unpleasant if not uncourteous remarks."
+
+I have added punctuation: the handwriting and spelling {11} are those of an
+educated person; the word _irreptitious_ is indubitable. The whole is a
+natural curiosity.
+
+
+
+    The quadrature and exact area of the circle demonstrated. By Wm.
+    Peters. 8vo. _n. d._ (circa 1848).[29]
+
+    Suggestions as to the necessity for a revolution in philosophy; and
+    prospectus for the establishment of a new quarterly, to be called the
+    _Physical Philosopher and Heterodox Review_. By Q. E. D. 8vo. 1848.
+
+These works are by one author, who also published, as appears by
+advertisement,
+
+"Newton rescued from the precipitancy of his followers through a century
+and a half,"[30] and "Dangers along a coast by correcting (as it is called)
+a ship's reckoning by bearings of the land at night fall, or in a fog,
+nearly out of print. Subscriptions are requested for a new edition."
+
+The area of a circle is made four-fifths of the circumscribed square:
+proved on an assumption which it is purposed to explain in a longer
+essay.[31] The author, as Q. E. D., was in controversy with the _Athenaeum_
+journal, and criticised a correspondent, D., who wrote against a certain
+class of discoverers. He believed the common theories of hydrostatics to be
+wrong, and one of his questions was:
+
+"Have you ever taken into account anent gravity and gravitation the fact
+that a five grain cube of cork will of itself half sink in the water,
+whilst it will take 20 grains of brass, which will sink of itself, to pull
+under the other half? Fit this if you can, friend D., to your notions of
+gravity and specific gravity, as applied to the construction of a universal
+law of gravitation."
+
+This the _Athenaeum_ published--but without some Italics, for which the
+editor was sharply reproved, as a sufficient {12} specimen of the _quod
+erat_ D. _monstrandum_: on which the author remarks--"D,--Wherefore the e
+caret? is it D apostrophe? D', D'M, D'Mo, D'Monstrandum; we cannot find the
+_wit_ of it." This I conjecture to contain an illusion to the name of the
+supposed author; but whether De Mocritus, De Mosthenes, or De Moivre was
+intended, I am not willing to decide.
+
+
+
+    The Scriptural Calendar and Chronological Reformer, for the statute
+    year 1849. Including a review of recent publications on the Sabbath
+    question. London, 1849, 12mo.[32]
+
+This is the almanac of a sect of Christians who keep the Jewish Sabbath,
+having a chapel at Mill Yard, Goodman's Fields. They wrote controversial
+works, and perhaps do so still; but I never chanced to see one.
+
+
+
+    Geometry _versus_ Algebra; or the trisection of an angle geometrically
+    solved. By W. Upton, B.A.[33] Bath (circa 1849). 8vo.
+
+The author published two tracts under this title, containing different
+alleged proofs: but neither gives any notice of the change. Both contain
+the same preface, complaining of the British Association for refusing to
+examine the production. I suppose that the author, finding his first proof
+wrong, invented the second, of which the Association never had the offer;
+and, feeling sure that they would have equally refused to examine the
+second, thought it justifiable to {13} present that second as the one which
+they had refused. Mr. Upton has discovered that the common way of finding
+the circumference is wrong, would set it right if he had leisure, and, in
+the mean time, has solved the problem of the duplication of the cube.
+
+_The trisector of an angle, if he demand attention from any mathematician,
+is bound to produce, from his construction, an expression for the sine or
+cosine of the third part of any angle, in terms of the sine or cosine of
+the angle itself, obtained by help of no higher than the square root._ The
+mathematician knows that such a thing cannot be; but the trisector
+virtually says it can be, and is bound to produce it, to save time. This is
+the misfortune of most of the solvers of the celebrated problems, that they
+have not knowledge enough to present those consequences of their results by
+which they can be easily judged. Sometimes they have the knowledge and
+quibble out of the use of it. In many cases a person makes an honest
+beginning and presents what he is sure is a solution. By conference with
+others he at last feels uneasy, fears the light, and puts self-love in the
+way of it. Dishonesty sometimes follows. The speculators are, as a class,
+very apt to imagine that the mathematicians are in fraudulent confederacy
+against them: I ought rather to say that each one of them consents to the
+mode in which the rest are treated, and fancies conspiracy against himself.
+The mania of conspiracy is a very curious subject. I do not mean these
+remarks to apply to the author before me.
+
+One of Mr. Upton's trisections, if true, would prove the truth of the
+following equation:
+
+  3 cos ([theta] / 3) = 1 + [root](4 - sin^2[theta])
+
+which is certainly false.[34]
+
+{14}
+
+In 1852 I examined a terrific construction, at the request of the late Dr.
+Wallich,[35] who was anxious to persuade a poor countryman of his, that
+trisection of the angle was waste of time. One of the principles was, that
+"magnitude and direction determine each other." The construction was
+equivalent to the assertion that, [theta] being any angle, the cosine of
+its third part is
+
+  sin 3[theta] . cos(5[theta]/2) + sin^2 [theta] sin (5[theta]/2)
+
+divided by the square root of
+
+  sin^2 3[theta] . cos^2 (5[theta]/2) + sin^4 [theta] + sin 3[theta] . sin
+      5[theta] . sin^2 [theta].
+
+This is from my rough notes, and I believe it is correct.[36] It is so
+nearly true, unless the angle be very obtuse, that common drawing, applied
+to the construction, will not detect the error. There are many formulae of
+this kind: and I have several times found a speculator who has discovered
+the corresponding construction, has seen the approximate success of his
+drawing--often as great as absolute truth could give in graphical
+practice,--and has then set about his demonstration, in which he always
+succeeds to his own content.
+
+There is a trisection of which I have lost both cutting and reference: I
+think it is in the _United Service Journal_. I could not detect any error
+in it, though certain there must {15} be one. At least I discovered that
+two parts of the diagram were incompatible unless a certain point lay in
+line with two others, by which the angle to be trisected--and which was
+trisected--was bound to be either 0 deg. or 180 deg..
+
+Aug. 22, 1866. Mr. Upton sticks to his subject. He has just published "The
+Uptonian Trisection. Respectfully dedicated to the schoolmasters of the
+United Kingdom." It seems to be a new attempt. He takes no notice of the
+sentence I have put in italics: nor does he mention my notice of him,
+unless he means to include me among those by whom he has been "ridiculed
+and sneered at" or "branded as a brainless heretic." I did neither one nor
+the other: I thought Mr. Upton a paradoxer to whom it was likely to be
+worth while to propound the definite assertion now in italics; and Mr.
+Upton does not find it convenient to take issue on the point. He prefers
+general assertions about algebra. So long as he cannot meet algebra on the
+above question, he may issue as many "respectful challenges" to the
+mathematicians as he can find paper to write: he will meet with no
+attention.
+
+
+
+There is one trisection which is of more importance than that of the angle.
+It is easy to get half the paper on which you write for margin; or a
+quarter; but very troublesome to get a third. Show us how, easily and
+certainly, to fold the paper into three, and you will be a real benefactor
+to society.
+
+Early in the century there was a Turkish trisector of the angle, Hussein
+Effendi, who published two methods. He was the father of Ameen Bey, who was
+well known in England thirty years ago as a most amiable and cultivated
+gentleman and an excellent mathematician. He was then a student at
+Cambridge; and he died, years ago, in command of the army in Syria. Hussein
+Effendi was instructed in mathematics by Ingliz Selim Effendi, who
+translated a work {16} of Bonnycastle[37] into Turkish.[38] This Englishman
+was Richard Baily, brother of Francis Baily[39] the astronomer, who
+emigrated to Turkey in his youth, and adopted the manners of the Turks, but
+whether their religion also I never heard, though I should suppose he did.
+
+I now give the letters from the agricultural laborer and his friend,
+described on page 12, Vol. I. They are curiosities; and the history of the
+quadrature can never be well written without some specimens of this kind:
+
+"Doctor Morgan, Sir. Permit me to address you
+
+"Brute Creation may perhaps enjoy the faculty of beholding visible things
+with a more penitrating eye than ourselves. But Spiritual objects are as
+far out of their reach as though they had no being
+
+"Nearest therefore to the brute Creation are those men who Suppose
+themselves to be so far governed by external objects as to believe nothing
+but what they See and feel And Can accomedate to their Shallow
+understanding and Imaginations
+
+"My Dear Sir Let us all Consult ourselves by the wise proverb.
+
+"I believe that evry man^s merit & ability aught to be appreciated and
+valued In proportion to its worth & utility
+
+"In whatever State or Circumstances they may fortunately or unfortunately
+be placed
+
+"And happy it is for evry man to know his worth and place
+
+"When a Gentleman of your Standing in Society Clad with those honors Can
+not understand or Solve a problem That is explicitly explained by words and
+Letters and {17} mathematically operated by figuers He had best consult the
+wise proverd
+
+"Do that which thou Canst understand and Comprehend for thy good.
+
+"I would recommend that Such Gentleman Change his business
+
+"And appropriate his time and attention to a Sunday School to Learn what he
+Could and keep the Litle Children form durting their Close
+
+"With Sincere feelings of Gratitude for your weakness and Inability I am
+
+ "Sir your Superior in Mathematics ----"
+
+"1849 June th29."
+
+
+
+"Dor Morgin Sir
+
+"I wrote and Sent my work to Professor ---- of ---- State of ---- United
+States
+
+"I am now in the possession of the facts that he highly approves of my
+work. And Says he will Insure me Reward in the States
+
+"I write this that you may understand that I have knowledge of the unfair
+way that I am treated In my own nati County
+
+"I am told and have reasons to believe that it is the Clergy that treat me
+so unjust.
+
+"I am not Desirous of heaping Disonors upon my own nation. But if I have to
+Leave this kingdom without my Just dues. The world Shall know how I am and
+have been treated.
+
+ "I am Sir Desirous of my
+             "Just dues ----"
+
+"1849 July 3."
+
+
+
+"July 7th, 1849.
+
+"Sir, I have been given to understand that a friend of mine one whom I
+shall never be ashamed to acknowledge as {18} such tho' lowly his origine;
+nay not only not ashamed but proud of doing so for I am one of those who
+esteem and respect a man according to his ability and probity, deeming with
+Dr. Watts 'that the mind is the standard of the man,'[40] has laid before
+you and asked your opinion of his extraordinary performance, viz. the
+quadrature of the circle, he did this with the firmest belief that you
+would not only treat the matter in a straightforward manner but with the
+conviction that from your known or supposed knowledge of mathematicks would
+have given an upright and honorable decision upon the subject; but the
+question is have you done so? Could I say yes I would with the greatest of
+pleasure and have congratulated you upon your decision whatever it might
+have been but I am sorry to say that I cannot your letter is a paltry
+evasion, you say 'that it is a great pity that you (Mr. ----) should have
+attempted this (the quadrature of the circle) for your mathematical
+knowledge is not sufficient to make you know in what the problem consists,'
+you don't say in what it does consist _according to your ideas_, oh! no
+nothing of the sort, you enter into no disquisition upon the subject in
+order to show where you think Mr. ---- is wrong and why you have not is
+simply--_because you cannot_--you know that he has done it and what is if I
+am not wrongly informed _you have been heard to say so_. He has done what
+you nor any other mathematician as those who call themselves such have
+done. And what is the reason that you will not candidly acknowledge to him
+as you have to others that he has squared the circle shall I tell you? it
+is because he has performed the feat to obtain the glory of which
+mathematicians have battled from time immemorial that they might encircle
+their brows with a wreath of laurels far more glorious than ever conqueror
+won it is simply this that it is a poor man a {19} humble artisan who has
+gained that victory that you don't like to acknowledge it you don't like to
+be beaten and worse to acknowledge that you have miscalculated, you have in
+short too small a soul to acknowledge that he is right.
+
+"I was asked my opinion and _I_ gave it unhesitatingly in the affirmative
+and I am backed in my opinion not only by Mr. ---- a mathematician and
+watchmaker residing in the boro of Southwark but by no less an authority
+than the Professor of mathematics of ---- College ---- ---- United States
+Mr. ---- and I presume that he at least is your equal as an authority and
+Mr. ---- says that the government of the U.S. will recompense M. D. for the
+discovery he has made if so what a reflection upon Old england the boasted
+land of freedom the nursery of arts and sciences that her sons are obliged
+to go to a foreign country to obtain that recompense to which they are
+justly entitled
+
+"In conclusion I had to contradict an assertion you made to the effect that
+'there is not nor ever was any reward offered by the government of this
+country for the discovery of the quadrature of the circle.' I beg to inform
+you that there _was_ but that it having been deemed an impossibility the
+government has withdrawn it. I do this upon no less an authority than the
+Marquis of Northampton.[41]
+
+ "I am, sir, yours ----"
+
+"Dr. Morgan."
+
+
+
+THE MOON'S ROTATION.
+
+    Notes on the Kinematic Effects of Revolution and Rotation, with
+    reference to the Motions of the Moon and of the earth. By Henry
+    Perigal, Jun. Esq. London, 1846-1849, 8vo.
+
+    On the misuse of technical terms. Ambiguity of the terms _Rotation_ and
+    _Revolution_, owing to the double meaning improperly {20} attributed to
+    each of the words. (No date nor place, but by Mr. Perigal,[42] I have
+    no doubt, and containing letters of 1849 and 1850.)
+
+    The moon controversy. Facts _v._ Definitions. By H. P., Jun. London,
+    1856, 8vo. (pp. 4.)
+
+Mr. Henry Perigal helped me twenty years ago with the diagrams, direct from
+the lathe to the wood, for the article "Trochoidal Curves," in the _Penny
+Cyclopaedia_: these cuts add very greatly to the value of the article,
+which, indeed, could not have been made intelligible without them. He has
+had many years' experience, as an amateur turner, in combination of double
+and triple circular motions, and has published valuable diagrams in
+profusion. A person to whom the double circular motion is familiar in the
+lathe naturally looks upon one circle moving upon another as in _simple_
+motion, if the second circle be fixed to the revolving radius, so that one
+and the same point of the moving circle travels upon the fixed circle. Mr.
+Perigal commenced his attack upon the moon for moving about her axis, in
+the first of the tracts above, ten years before Mr. Jellinger Symons;[43]
+but he did not think it necessary to make it a subject for the _Times_
+newspaper. His familiarity with combined motions enabled him to handle his
+arguments much better than Mr. J. Symons could do: in fact, he is the
+clearest assailant of the lot which turned out with Mr. J. Symons. But he
+is as wrong as the rest. The assault is now, I suppose, abandoned, until it
+becomes epidemic again. This it will do: it is one of those fallacies which
+are very tempting. There was a dispute on the subject in 1748, between
+James Ferguson[44] and an anonymous opponent; and I think there have been
+others.
+
+{21}
+
+A poet appears in the field (July 19, 1863) who calls himself Cyclops, and
+writes four octavo pages. He makes a distinction between _rotation_ and
+_revolution_; and his doctrines and phrases are so like those of Mr.
+Perigal that he is a follower at least. One of his arguments has so often
+been used that it is worth while to cite it:
+
+ "Would Mathematicals--forsooth--
+  If true, have failed to prove its truth?
+  Would not they--if they could--submit
+  Some overwhelming proofs of it?
+  But still it totters _proofless_! Hence
+  There's strong presumptive evidence
+  None do--or can--such proof profound
+  Because _the dogma is unsound_.
+  For, were there means of doing so,
+  They would have proved it long ago."
+
+This is only one of the alternatives. Proof requires a person who can give
+and a person who can receive. I feel inspired to add the following:
+
+ "A blind man said, As to the Sun,
+  I'll take my Bible oath there's none;
+  For if there had been one to show
+  They would have shown it long ago.
+  How came he such a goose to be?
+  Did he not know he couldn't see?
+                  Not he!"
+
+The absurdity of the verses is in the argument. The writer was not so
+ignorant or so dishonest as to affirm that nothing had been offered by the
+other side as proof; accordingly, his syllogism amounts to this: If your
+proposition were true, you could have given proof satisfactory to _me_; but
+this you have not done, therefore, your proposition is not true.
+
+The echoes of the moon-controversy reached Benares in 1857, in which year
+was there published a pamphlet "Does the Moon Rotate?" in Sanskrit and
+English. The {22} arguments are much the same as those of the discussion at
+home.
+
+
+
+ON THE NAMES OF RELIGIOUS BODIES.
+
+We see that there are paradoxers in argument as well as in assertion of
+fact: my plan does not bring me much into contact with these; but another
+instance may be useful. Sects, whether religious or political, give
+themselves names which, in meaning, are claimed also by their opponents;
+loyal, liberal, conservative (of good), etc. have been severally
+appropriated by parties. _Whig_ and _Tory_ are unobjectionable names: the
+first--which occurs in English ballad as well as in Scotland--is sour
+milk;[45] the second is a robber. In theology, the Greek Church is
+_Orthodox_, the Roman is _Catholic_, the modern Puritan is _Evangelical_,
+etc.
+
+The word _Christian_ (Vol. I, p. 248[46]) is an instance. When words begin,
+they carry their meanings. The Jews, who had their Messiah to come, and the
+followers of Jesus of Nazareth, who took _Him_ for their Messiah, were both
+_Christians_ (which means _Messianites_): the Jews would never have
+invented the term to signify _Jesuans_, nor would the disciples have
+invented such an ambiguous term for themselves; had they done so, the Jews
+would have disputed it, as they would have done in later times if they had
+had fair play. The Jews of our day, I see by their newspapers, speak of
+Jesus Christ as the _Rabbi Joshua_. But the {23} heathens, who knew little
+or nothing about the Jewish hope, would naturally apply the term
+_Christians_ to the only followers of a _Messiah_ of whom they had heard.
+For the _Jesuans_ invaded them in a missionary way; while the Jews did not
+attempt, at least openly, to make proselytes.
+
+All such words as Catholic, etc., are well enough as mere nomenclature; and
+the world falls for the most part, into any names which parties choose to
+give themselves. Silly people found inferences on this concession; and, as
+usually happens, they can cite some of their betters. St. Augustine,[47] a
+freakish arguer, or, to put it in the way of an old writer, _lectorem ne
+multiloquii taedio fastidiat, Punicis quibusdam argutiis recreare
+solet_,[48] asks, with triumph, to what chapel a stranger would be
+directed, if he inquired the way to the _Catholic assembly_. But the best
+exhibition of this kind in our own century is that made by the excellent
+Dr. John Milner,[49] in a work (first published in 1801 or 1802) which I
+suppose still circulates, "The End of Religious Controversy": a startling
+title which, so far as its truth is concerned, might as well have been "The
+floor of the bottomless pit." This writer, whom every one of his readers
+will swear to have been a worthy soul, though many, even of his own sect,
+will not admire some of his logic, speaks as follows:
+
+"Letter xxv. _On the true Church being Catholic._ In treating of this third
+mark of the true Church, as expressed in our common creed, I feel my
+spirits sink within me, and I am almost tempted to throw away my pen in
+despair. For what chance is there of opening the eyes of candid Protestants
+to the other marks of the Church, if they are capable of keeping them shut
+to this? Every time they address the {24} God of Truth, either in solemn
+worship or in private devotion [stretch of rhetoric], they are forced, each
+of them, to repeat: _I believe in_ THE CATHOLIC _Church_, and yet if I ask
+any of them the question: _Are you a_ CATHOLIC? he is sure to answer me,
+_No, I am a_ PROTESTANT! Was there ever a more glaring instance of
+inconsistency and self-condemnation among rational beings!"
+
+ "John Milner, honest and true,
+  Did what honest people still may do,
+  If they write for the many and not for the few,
+  But what by and bye they must eschew."
+
+He _shortened his clause_; and for a reason. If he had used the whole
+epithet which he knew so well, any one might have given his argument a
+half-turn. Had he written, as he ought, "the _Holy_ Catholic Church" and
+then argued as above, some sly Protestant would have parodied him with "and
+yet if I ask any of them the question: _Are you_ HOLY? he is sure to answer
+me _No, I am a_ SINNER." To take the adjective from the Church, and apply
+it to the individual partisan, is recognized slipslop, but not ground of
+argument. If Dr. M. had asked his Protestant whether he belonged to the
+Catholic _Church_, the answer would have been Yes, but not to the Roman
+branch. When he put his question as he did, he was rightly answered and in
+his own division. This leaving out words is a common practice, especially
+when the omitter is in authority, and cannot be exposed. A year or two ago
+a bishop wrote a snubbing letter to a poor parson, who had complained that
+he was obliged, in burial, to send the worst of sinners to everlasting
+happiness. The bishop sternly said, "_hope_[50] is not _assurance_." {25}
+Could the clergyman have dared to answer, he would have said, "No, my Lord!
+but '_sure and certain_ hope' is as like assurance as a _minikin_ man is
+like a dwarf." Sad to say, a theologian must be illogical: I feel sure that
+if you took the clearest headed writer on logic that ever lived, and made a
+bishop of him, he would be shamed by his own books in a twelvemonth.
+
+Milner's sophism is glaring: but why should Dr. Milner be wiser than St.
+Augustine, one of his teachers? I am tempted to let out the true derivation
+of the word _Catholic, as exclusively applied to the Church of Rome_. All
+can find it who have access to the _Rituale_ of Bonaventura Piscator[51]
+(lib. i. c. 12, _de nomine Sacrae Ecclesiae_, p. 87 of the Venice {26} folio
+of 1537). I am told that there is a _Rituale_ in the Index Expurgatorius,
+but I have not thought it worth while to examine whether this be the one: I
+am rather inclined to think, as I have heard elsewhere, that the book was
+held too dangerous for the faithful to know of it, even by a prohibition:
+it would not surprise me at all if Roman Christians should deny its
+existence.[52]
+
+It amuses me to give, at a great distance of time, a small Rowland for a
+small Oliver,[53] which I received, _de par l'Eglise_,[54] so far as lay in
+the Oliver-carrier more than twenty years ago. The following contribution
+of mine to _Notes and Queries_ (3d Ser. vi. p. 175, Aug. 27, 1864) will
+explain what I say. There had been a complaint that a contributor had used
+the term _Papist_, which a very excellent dignitary of the Papal system
+pronounced an offensive term:
+
+
+
+PAPIST.
+
+The term _papist_ should be stripped of all except its etymological
+meaning, and applied to those who give the higher and final authority to
+the declaration _ex cathedra_[55] of the Pope. See Dr. Wiseman's[56]
+article, _Catholic Church_, in the _Penny Cyclopaedia_.
+
+What is one to do about these names? First, it is clear that offence
+should, when possible, be avoided: secondly, no one must be required to
+give a name which favors _any_ assumption made by those to whom it is
+given, and not {27} granted by those who give it. Thus the subdivision
+which calls itself distinctly _Evangelical_ has no right to expect others
+to concede the title. Now the word _Catholic_, of course, falls under this
+rule; and even _Roman Catholic_ may be refused to those who would restrict
+the word _Catholic_ to themselves. _Roman Christian_ is unobjectionable,
+since the Roman Church does not deny the name of Christian to those whom
+she calls heretics. No one is bound in this matter by Acts of Parliament.
+In many cases, no doubt, names which have offensive association are used
+merely by habit, sometimes by hereditary transmission. Boswell records of
+Johnson that he always used the words "dissenting teacher," refusing
+_minister_ and _clergyman_ to all but the recipients of episcopal
+ordination.
+
+This distinctive phrase has been widely adopted: it occurs in the Index of
+3d S. iv. [_Notes and Queries_]. Here we find "Platts (Rev. John),
+Unitarian teacher, 412;" the article indexed has "Unitarian minister."
+
+This, of course is habit: an intentional refusal of the word _minister_
+would never occur in an index. I remember that, when I first read about Sam
+Johnson's little bit of exclusiveness, I said to myself: "Teacher? Teacher?
+surely I remember One who is often called _teacher_, but never _minister_
+or _clergyman_: have not the dissenters got the best of it?"
+
+When I said that the Roman Church concedes the epithet Christians to
+Protestants, I did not mean that all its adherents do the same. There is,
+or was, a Roman newspaper, the _Tablet_, which, seven or eight years ago,
+was one of the most virulent of the party journals. In it I read, referring
+to some complaint of grievance about mixed marriages, that if _Christians_
+would marry _Protestants_ they must take the consequences. My memory notes
+this well; because I recollected, when I saw it, that there was in the
+stable a horse fit to run in the curricle with this one. About seventeen
+years ago an Oxford M. A., who hated {28} mathematics like a genuine
+Oxonian of the last century, was writing on education, and was compelled to
+give some countenance to the nasty subject. He got out cleverly; for he
+gave as his reason for the permission, that man is an arithmetical,
+geometrical, and mechanical _animal_, as well as a rational _soul_.
+
+The _Tablet_ was founded by an old pupil of mine, Mr. Frederic Lucas,[57]
+who availed himself of his knowledge of me to write some severe
+articles--even abusive, I was told, but I never saw them--against me, for
+contributing to the _Dublin Review_, and poking my heretic nose into
+orthodox places. Dr. Wiseman, the editor, came in for his share, and ought
+to have got all. Who ever blamed the pig for intruding himself into the
+cabin when the door was left open? When Mr. Lucas was my pupil, he was of
+the Society of Friends--in any article but this I should say _Quaker_--and
+was quiet and gentlemanly, as members of that Church--in any article but
+this I should, from mere habit, say _sect_--usually are. This is due to his
+memory; for, by all I heard, when he changed his religion he ceased to be
+Lucas couchant, and became Lucas rampant, fanged and langued gules. (I
+looked into Guillim[58] to see if my terms were right: I could not find
+them; but to prove I have been there, I notice that he calls a violin a
+_violent_. How comes the word to take this form?) I met with several Roman
+Christians, born and bred, who were very much annoyed at Mr. Lucas and his
+doings; and said some severe things about new converts needing
+kicking-straps.
+
+{29}
+
+The mention of Dr. Wiseman reminds me of another word, appropriated by
+Christians to themselves: _fides_;[59] the Roman faith is _fides_, and
+nothing else; and the adherents are _fideles_.[60] Hereby hangs a retort.
+When Dr. Wiseman was first in England, he gave a course of lectures in
+defence of his creed, which were thought very convincing by those who were
+already convinced. They determined to give him a medal, and there was a
+very serious discussion about the legend. Dr. Wiseman told me himself that
+he had answered to his subscribers that he would not have the medal at all
+unless--(naming some Italian authority, whom I forget) approved of the
+legend. At last _pro fide vindicata_[61] was chosen: this may be read
+either in a Popish or heretical sense. The feminine substantive _fides_
+means confidence, trust, (it is made to mean _belief_), but _fidis_, with
+the same ablative, _fide_, and also feminine, is a _fiddle-string_.[62] If
+a Latin writer had had to make a legend signifying "For the defence of the
+fiddle-string," he could not have done it otherwise, in the terseness of a
+legend, than by writing _pro fide vindicata_. Accordingly, when a Roman
+Christian talks to you of the _faith_, as a thing which is his and not
+yours, you may say _fiddle_. I have searched Bonaventura Piscator in vain
+for notice of this ambiguity. But the Greeks said fiddle; according to
+Suidas,[63] [Greek: skindapsos][64]--a word meaning a four stringed
+instrument played with a quill--was an exclamation of contemptuous dissent.
+How the wits of different races jump!
+
+{30}
+
+I am reminded of a case of _fides vindicata_, which, being in a public
+letter, responding to a public invitation, was not meant to be
+confidential. Some of the pupils of University College, in which all
+subdivisions of religion are (1866; _were_, 1867) on a level, have of
+course changed their views in after life, and become adherents of various
+high churches. On the occasion of a dinner of old students of the College,
+convened by circular, one of these students, whether then Roman or
+Tractarian Christian I do not remember, not content with simply giving
+negative answer, or none at all, concocted a jorum of theological rebuke,
+and sent it to the Dinner Committee. Heyday! said one of them, this man got
+out of bed backwards! How is that? said the rest. Why, read his name
+backwards, and you will see. As thus read it was--_No grub_![65]
+
+
+
+THE WORD CHURCH.
+
+To return to _Notes and Queries_. The substitution in the (editorial) index
+of "Unitarian teacher," for the contributor's "Unitarian minister," struck
+me very much. I have seldom found such things unmeaning. But as the journal
+had always been free from editorial sectarianisms,--and very apt to check
+the contributorial,--I could not be sure in this case. True it was, that
+the editor and publisher had been changed more than a year before; but this
+was not of much force. Though one swallow does not make a summer, I have
+generally found it show that summer is coming. However, thought I to
+myself, if this be Little Shibboleth, we shall have Big Shibboleth
+by-and-bye. At last it came. About a twelvemonth afterwards, (3d S. vii. p.
+36) the following was the _editorial_ answer to the question when the
+establishment was first called the "Church of England and Ireland":
+
+{31}
+
+"That unmeaning clause, 'The United Church of England and Ireland,' which
+occurs on the title-page of _The Book of Common Prayer_, was first used at
+the commencement of the present century. The authority for this phrase is
+the fifth article of the Union of 1800: 'That the Churches of England and
+Ireland be united into one _Protestant_ (!) episcopal Church, to be called
+"The United Church of England and Ireland."' Of course, churchmen are not
+responsible for the theology of Acts of Parliament, especially those passed
+during the dark ages of the Georgian era."
+
+That is to say, the journal gives its adhesion to the party which--under
+the assumed title of _the_ Church of England--claims for the endowed
+corporation for the support of religion rights which Parliament cannot
+control, and makes it, in fact, a power above the State. The State has
+given an inch: it calls this corporation by the name of the "United
+_Church_ of England and Ireland," as if neither England nor Ireland had any
+other Church. The corporation, accordingly aspires to an ell. But this the
+nation will only give with the aspiration prefixed. To illustrate my
+allusion in a delicate way to polite ears, I will relate what happened in a
+Johnian lecture-room at Cambridge, some fifty years ago, my informant being
+present. A youth of undue aspirations was giving a proposition, and at last
+said, "Let E F be produced to 'L':" "Not quite so far, Mr. ----," said the
+lecturer, quietly, to the great amusement of the class, and the utter
+astonishment of the aspirant, who knew no more than a Tractarian the
+tendency of his construction.
+
+This word _Church_ is made to have a very mystical meaning. The following
+dialogue between Ecclesiastes and Haereticus, which I cannot vouch for, has
+often taken place in spirit, if not in letter: E. The word _Church_
+([Greek: ekklesia])[66] is never used in the New Testament except generally
+or locally for that holy and mystical body to which the sacraments and the
+ordinances of Christianity are entrusted. {32} H. Indeed! E. It is beyond a
+doubt (here he quoted half a dozen texts in support). H. Do you mean that
+any doctrine or ordinance which was solemnly practised by the [Greek:
+ekklesia] is binding upon you and me? E. Certainly, unless we should be cut
+off from the congregation of the faithful. H. Have you a couple of hours to
+spare? E. What for? H. If you have, I propose we spend them in crying,
+Great is Diana of the Ephesians! E. What do you mean? H. You ought to know
+the solemn service of the [Greek: ekklesia] (Acts xix. 32, 41), at Ephesus;
+which any one might take to be true Church, by the more part not knowing
+wherefore they were come together, and which was dismissed, after one of
+the most sensible sermons ever preached, by the Recorder. E. I see your
+meaning: it is true, there is that one exception! H. Why, the Recorder's
+sermon itself contains another, the [Greek: ennomos ekklesia],[67]
+legislative assembly. E. Ah! the New Testament can only be interpreted by
+the Church! H. I see! the Church interprets itself into existence out of
+the New Testament, and then interprets the New Testament out of existence
+into itself!
+
+I look upon all the Churches as fair game which declare of me that _absque
+dubio in aeternum peribo_;[68] not for their presumption towards God, but
+for their personal insolence towards myself. I find that their sectaries
+stare when I say this. Why! they do not speak of you in _particular_! These
+poor reasoners seem to think that there could be no meaning, as against me,
+unless it should be propounded that "without doubt he shall perish
+everlastingly, especially A. De Morgan." But I hold, with the schoolmen,
+that "_Omnis_ homo est animal" in conjunction with "Sortes est homo"
+amounts to "_Sortes_ est animal."[69] But they do not mean it _personally_!
+Every universal proposition is {33} personal to every instance of the
+subject. If this be not conceded, then I retort, in their own sense and
+manner, "Whosoever would serve God, before all things he must not pronounce
+God's decision upon his neighbor. Which decision, except every one leave to
+God himself, without doubt he is a bigoted noodle."
+
+The reasoning habit of the educated community, in four cases out of five,
+permits universal propositions to be stated at one time, and denied, _pro
+re nata_,[70] at another. "Before we proceed to consider any question
+involving physical principles, we should set out with _clear ideas_ of the
+naturally possible and impossible." The eminent man who said this, when
+wanting it for his views of mental education (!) never meant it for more
+than what was in hand, never assumed it in the researches which will give
+him to posterity! I have heard half-a-dozen defences of his having said
+this, not one of which affirmed the truth of what was said. A worthy
+clergyman wrote that if A. B. had said a certain thing the point in
+question would have been established. It was shown to him that A. B. _had_
+said it, to which the reply was a refusal to admit the point because A. B.
+said it in a second pamphlet and in answer to objections. And I might give
+fifty such instances with very little search. Always assume more than you
+want; because you cannot tell how much you may want: put what is over into
+the didn't-mean-that basket, or the extreme case what-not.
+
+
+
+PROTESTANT AND PAPAL CHRISTENDOM.
+
+Something near forty years of examination of the theologies on and
+off--more years very much on than quite off--have given me a good title--to
+myself, I ask no one else for leave--to make the following remarks: A
+conclusion has _premises_, facts or doctrines from proof or authority, and
+_mode of inference_. There may be invention or {34} falsehood of premise,
+with good logic; and there may be tenable premise, followed by bad logic;
+and there may be both false premise _and_ bad logic. The Roman system has
+such a powerful manufactory of premises, that bad logic is little wanted;
+there is comparatively little of it. The doctrine-forge of the Roman Church
+is one glorious compound of everything that could make Heraclitus[71] sob
+and Democritus[72] snigger. But not the only one. The Protestants, in
+tearing away from the Church of Rome, took with them a fair quantity of the
+results of the Roman forge, which they could not bring themselves to give
+up. They had more in them of Martin than of Jack. But they would have no
+premises, except from the New Testament; though some eked out with a few
+general Councils. The consequence is that they have been obliged to find
+such a logic as would bring the conclusions they require out of the
+canonical books. And a queer logic it is; nothing but the Roman forge can
+be compared with the Protestant loom. The picking, the patching, the
+piecing, which goes to the Protestant _termini ad quem_,[73] would be as
+remarkable to the general eye, as the Roman manufacture of _termini a
+quo_,[74] if it were not that the world at large seizes the character of an
+asserted fact better than that of a mode of inference. A grand step towards
+the deification of a lady, made by alleged revelation 1800 years after her
+death, is of glaring evidence: two or three additional shiffle-shuffles
+towards defence of saying the Athanasian curse in church and unsaying it
+out of church, are hardly noticed. Swift has bungled his satire where he
+makes Peter a party to finding out what he wants, _totidem syllabis_ and
+_totidem literis_, {35} when he cannot find it _totidem verbis_[75] This is
+Protestant method: the Roman plan is _viam faciam_; the Protestant plan is
+_viam inveniam_.[76] The public at large begins to be conversant with the
+ways of _wriggling out_, as shown in the interpretations of the damnatory
+parts of the Athanasian Creed, the phrases of the Burial Service, etc. The
+time will come when the same public will begin to see the ways of
+_wriggling in_. But one thing at a time: neither Papal Rome nor Protestant
+Rome was built--nor will be pulled down--in a day.
+
+The distinction above drawn between the two great antitheses of Christendom
+may be illustrated as follows. Two sets of little general dealers lived
+opposite to one another: all sold milk. Each vaunted its own produce: one
+set said that the stuff on the other side the way was only chalk and water;
+the other said that the opposites sold all sorts of filth, of which calves'
+brain was the least nasty. Now the fact was that both sets sold milk, and
+from the same dairy: but adulterated with different sorts of dirty water:
+and both honestly believed that the mixture was what they were meant to
+sell and ought to sell. The great difference between them, about which the
+apprentices fought each other like Trojans, was that the calves' brain men
+poured milk into the water, and the chalk men poured water into the milk.
+The Greek and Roman sects on one side, the Protestant sects on the other,
+must all have _churches_: the Greek and Roman sects pour the New Testament
+into their churches; the Protestant sects pour their churches into the New
+Testament. The Greek and Roman insist upon the New Testament being no more
+than part and parcel of their churches: the Protestant insist upon their
+churches being as much part and parcel of the New Testament. All dwell
+vehemently upon the doctrine that there must be milk {36} somewhere; and
+each says--I have it. The doctrine is true: and can be verified by any one
+who can and will go to the dairy for himself. Him will the several traders
+declare to have no milk at all. They will bring their own wares, and
+challenge a trial: they want nothing but to name the judges. To vary the
+metaphor, those who have looked at Christianity in open day, know that all
+who see it through painted windows shut out much of the light of heaven and
+color the rest; it matters nothing that the stains are shaped into what are
+meant for saints and angels.
+
+But there is another side to the question. To decompose any substance, it
+must be placed between the poles of the battery. Now theology is but one
+pole; philosophy is the other. No one can make out the combinations of our
+day unless he read the writings both of the priest and the philosopher: and
+if any one should hold the first word offensive, I tell him that I mean
+_both_ words to be _significant_. In reading these writings, he will need
+to bring both wires together to find out what it is all about. Time was
+when most priests were very explicit about the fate of philosophers, and
+most philosophers were very candid about their opinion of priests. But
+though some extremes of the old sorts still remain, there is now, in the
+middle, such a fusion of the two pursuits that a plain man is wofully
+puzzled. The theologian writes a philosophy which seems to tell us that the
+New Testament is a system of psychology; and the philosopher writes a
+Christianity which is utterly unintelligible as to the question whether the
+Resurrection be a fact or a transcendental allegory. What between the
+theologian who assents to the Athanasian denunciation in what seems the
+sense of no denunciation, and the philosopher who parades a Christianity
+which looks like no revelation, there is a maze which threatens to have the
+only possible clue in the theory that everything is something else, and
+nothing is anything at all. But this is a paradox far beyond my handling:
+it is a Budget of itself. {37}
+
+
+
+RELIGION AND PHILOSOPHY.
+
+Religion and Philosophy, the two best gifts of Heaven, set up in opposition
+to each other at the revival of letters; and never did competing tradesmen
+more grossly misbehave. Bad wishes and bad names flew about like swarms of
+wasps. The Athanasian curses were intended against philosophers; who, had
+they been a corporation, with state powers to protect them, would have
+formulized a _per contra_. But the tradesmen are beginning to combine: they
+are civil to each other; too civil by half. I speak especially of Great
+Britain. Old theology has run off to ritualism, much lamenting, with no
+comfort except the discovery that the cloak Paul left at Troas was a
+chasuble. Philosophy, which always had a little sense sewed up in its
+garments--to pay for its funeral?--has expended a trifle in accommodating
+itself to the new system. But the two are poles of a battery; and a
+question arises.
+
+  If Peter Piper picked a peck of pepper,
+  Where is the peck of pepper Peter Piper picked?
+
+If Religion and Philosophy be the two poles of a battery, whose is the
+battery Religion and Philosophy have been made the poles of? Is the change
+in the relation of the wires any presumption of a removal of the managers?
+We know pretty well who handled the instrument: has he resigned or been[77]
+turned out? Has he been put under {38} restriction? A fool may ask more
+questions than twenty sages can answer: but there is hope; for twenty sages
+cannot ask more questions than one reviewer can answer. I should like to
+see the opposite sides employed upon the question, What are the _commoda_,
+and what the _pericula_,[78] of the current approximation of Religion and
+Philosophy?
+
+All this is very profane and irreverent! It has always been so held by
+those whose position demands such holding. To describe the Church as it is
+passes for assailing the Church as it ought to be with all who cannot do
+without it. In Bedlam[79] a poor creature who fancied he was St. Paul, was
+told by another patient that he was an impostor; the first maniac lodged a
+complaint against the second for calling St. Paul an impostor, which, he
+argued, with much appearance of sanity, ought not to be permitted in a well
+regulated madhouse. Nothing could persuade him that he had missed the
+question, which was whether _he_ was St. Paul. The same thing takes place
+in the world _at large_. And especially must be noted the refusal to permit
+to the _profane_ the millionth part of the licence assumed by the _sacred_.
+I give a sound churchman the epitaph of St. John Long; the usual
+pronunciation of whose name must be noted--
+
+ "Behold! ye quacks, the vengeance strong
+    On deeds like yours impinging:
+  For here below lies St. John Long[80]
+    Who now must be _long singeing_."
+
+How shameful to pronounce this of the poor man! What, Mr. Orthodox! may I
+not do in joke to one pretender what {39} you do in earnest--unless you
+quibble--to all the millions of the Greek Church, and a great many others.
+Enough of you and your reasoning! Go and square the circle!
+
+The few years which end with 1867 have shown, not merely the intermediate
+fusion of Theology and Philosophy of which I have spoken, but much
+concentration of the two extremes, which looks like a gathering of forces
+for some very hard fought Armageddon. Extreme theology has been aiming at a
+high Church in England, which is to show a new front to all heresy: and
+extreme philosophy is contriving a physical organization which is to
+_think_, and to show that mind is a consequence of matter, or thought a
+recreation of brain. The physical speculators begin with a possible
+hypothesis, in which they aim at explanation: and so the bold aspirations
+of the author of the _Vestiges_ find standing-ground in the variation of
+species by "natural selection." Some relics--so supposed--of extremely
+ancient men are brought to help the general cause. Only distant hints are
+given that by possibility it may end in the formation of all living
+organisms from a very few, if not from one. The better heads above
+mentioned know that their theory, if true, does not bear upon morals. The
+formation of solar systems from a nebular hypothesis, followed by
+organizations gradually emerging from some curious play of particles, nay,
+the very evolution of mind and thought from such an apparatus, are all as
+consistent with a Personal creative power to whom homage and obedience are
+due, and who has declared himself, as with a blind Nature of Things. A pure
+materialist, as to all things visible, may be even a bigotted Christian:
+this is not frequent, but it is possible. There is a proverb which says, A
+pig may fly, but it isn't a likely bird. But when the psychological
+speculator comes in, he often undertakes to draw inferences from the
+physical conclusions, by joining on his tremendous apparatus of _a priori_
+knowledge. He deduces that he can _do without_ a God: he can deduce all
+things {40} without any such necessity. With Occam[81] and Newton he will
+have no more causes than are necessary to explain phenomena _to him_: and
+if by pure head-work combined with results of physical observation he can
+construct his universe, he must be a very _unphilosophical_ man who would
+encumber himself with a useless Creator! There is something tangible about
+my method, says he; yours is vague. He requires it to be granted that his
+system is _positive_ and that yours is _impositive_. So reasoned the stage
+coachman when the railroads began to depose him--"If you're upset in a
+stage-coach, why, there you are! but if you're upset on the railroad, where
+are you?" The answer lies in another question, Which is most positive
+knowledge, God deduced from man and his history, or the postulates of the
+few who think they can reason _a priori_ on the tacit assumption of
+unlimited command of data?
+
+We are not yet come to the existence of a school of philosophers who
+explicitly deny a Creator: but we are on the way, though common sense may
+interpose. There are always straws which show the direction of the wind. I
+have before me the printed letter of a medical man--to whose professional
+ability I have good testimony--who finds the vital principle in highly
+rarefied oxygen. With the usual logic of such thinkers, he dismisses the
+"eternal personal identity" because "If soul, spirit, mind, which are
+merely modes of sensation, be the attribute or function of nerve-tissue, it
+cannot possibly have any existence apart from its material organism!" How
+does he know this _impossibility_? If all the mind _we_ know be from
+nerve-tissue, how does it appear that mind in other planets may not be
+another thing? Nay, when we come to _possibilities_, does not his own
+system give a queer one? If highly rarefied oxygen be vital power, more
+highly rarefied oxygen {41} may be more vital and more powerful. Where is
+this to stop? Is it _impossible_ that a finite quantity, rarefied _ad
+infinitum_, may be an Omnipotent? Perhaps the true Genesis, when written,
+will open with "In the beginning was an imperial quart of oxygen at 60
+deg. of Fahrenheit, and the pressure of the atmosphere; and this oxygen
+was infinitely rarefied; and this oxygen became God." For myself, my
+aspirations as to this system are Manichaean. The quart of oxygen is the
+Ormuzd, or good principle: another quart, of hydrogen, is the Ahriman, or
+evil principle! My author says that his system explains Freewill and
+Immortality so obviously that it is difficult to read previous speculations
+with becoming gravity. My deduction explains the conflict of good and evil
+with such clearness that no one can henceforward read the New Testament
+with becoming reverence. The surgeon whom I have described is an early bud
+which will probably be nipped by the frost and wither on the ground: but
+there is a good crop coming. Material pneuma is destined to high functions;
+and man is to read by gas-light.
+
+
+
+THE SUN AN ELECTRIC SPACE.
+
+    The solar system truly solved; demonstrating by the perfect harmony of
+    the planets, founded on the four universal laws, the Sun to be an
+    electric space; and a source of every natural production displayed
+    throughout the solar system. By James Hopkins.[82] London, 1849, 8vo.
+
+The author says:
+
+"I am satisfied that I have given the true _laws_ constituting the _Sun_ to
+be _space_; and I call upon those disposed to maintain the contrary, to
+give true _laws_ showing him to be a body: until such can be satisfactorily
+established, I have an undoubted claim to the credit of my theory,--That
+the Sun is an _Electric Space_, fed and governed by the {42} planets, which
+have the property of attracting heat from it; and the means of supplying
+the necessary _pabulum_ by their degenerated air driven off towards the
+central space--the wonderful alembic in which it becomes transmuted to the
+revivifying necessities of continuous action; and the central space or Sun
+being perfectly electric, has the counter property of repulsing the bodies
+that attract it. How wonderful a conception! How beautiful, how magnificent
+an arrangement!
+
+"O Centre! O Space! O Electric Space!"
+
+
+
+JOSEPH ADY.
+
+1849. _Joseph Ady_[83] is entitled to a place in this list of discoverers:
+his great fault, like that of some others, lay in pushing his method too
+far. He began by detecting unclaimed dividends, and disclosing them to
+their right owners, exacting his fee before he made his communication. He
+then generalized into trying to get fees from all of the _name_ belonging
+to a dividend; and he gave mysterious hints of danger impending. For
+instance, he would write to a clergyman that a legal penalty was hanging
+over him; and when the alarmed divine forwarded the sum required for
+disclosure, he was favored with an extract from some old statute or canon,
+never repealed, forbidding a clergyman to be a member of a corporation, and
+was reminded that he had insured his life in the ---- Office, which had a
+royal charter. He was facetious, was Joseph: he described himself in his
+circulars as "personally known to Sir Peter Laurie[84] and all other
+aldermen"; which was nearly true, {43} as he had been before most of them
+on charges of false pretence; but I believe he was nearly always within the
+law. Sir James Duke, when Lord Mayor, having particularly displeased him by
+a decision, his circulars of 1849 contain the following:
+
+"Should you have cause to complain of any party, Sir J. Duke has contrived
+a new law of evidence, viz., write to him, he will consider your letter
+sufficient proof, and make the parties complained of pay without judge or
+jury, and will frank you from every expense."
+
+I strongly suspect that Joseph Ady believed in himself.
+
+He sometimes issued a second warning, of a Sibylline character:
+
+"Should you find cause to complain of anybody, my voluntary referee, the
+Rt. Hon. Sir Peter Laurie, Kt., perpetual Deputy Lord Mayor, will see
+justice done you without any charge whatever: he and his toady, -- ----
+----. The accursed of Moses can hang any man: thus, by catching him alone
+and swearing Naboth spake evil against God and the King. Therefore (!) I
+admit no strangers to a personal conference without a prepayment of 20s.
+each. Had you attended to my former notice you would have received twice as
+much: neglect this and you will lose all."
+
+
+
+ON MODERN ASTROLOGY.
+
+    Zadkiel's Almanac for 1849. Nineteenth number.
+
+    Raphael's Prophetic Almanac for 1849. Twenty-ninth number.
+
+    Reasons for belief in judicial astrology, and remarks on the dangerous
+    character of popish priestcraft. London, 1849, 12mo.
+
+    Astronomy in a nutshell: or the leading problems of the solar system
+    solved by simple proportion only, on the theory of magnetic attraction.
+    By Lieut. Morrison,[85] N. N. London (_s. a._) 12mo.
+
+{44}
+
+Lieut. Morrison is Zadkiel Tao Sze, and declares himself in real earnest an
+astrologer. There are a great many books on astrology, but I have not felt
+interest enough to preserve many of them which have come in my way. If
+anything ever had a fair trial, it was astrology. The idea itself is
+natural enough. A human being, set down on this earth, without any
+tradition, would probably suspect that the heavenly bodies had something to
+do with the guidance of affairs. I think that any one who tries will
+ascertain that the planets do not prophesy: but if he should find to the
+contrary, he will of course go on asking. A great many persons class
+together belief in astrology and belief in apparitions: the two things
+differ in precisely the way in which a science of observation differs from
+a science of experiment. Many make the mistake which M. le Marquis made
+when he came too late, and hoped M. Cassini[86] would do the eclipse over
+again for his ladies. The apparition chooses its own time, and comes as
+seldom or as often as it pleases, be it departed spirit, nervous
+derangement, or imposition. Consequently it can only be observed, and not
+experimented upon. But the heavens, if astrology be true, are prophesying
+away day and night all the year round, and about every body. Experiments
+can be made, then, except only on rare phenomena, such as eclipses: anybody
+may choose his time and his question. This is the great difference: and
+experiments were made, century after century. If astrology had been true,
+it must have lasted in an ever-improving state. If it be true, it is a
+truth, and a useful truth, which had experience and prejudice both in its
+favor, and yet lost ground as soon as astronomy, its working tool, began to
+improve.
+
+
+
+1850. A letter in the handwriting of an educated man, dated from a street
+in which it must be taken that educated persons live, is addressed to the
+Secretary of the {45} Astronomical Society about a matter on which the
+writer says "his professional pursuit will enable him to give a
+satisfactory reply." In a question before a court of law it is sworn on one
+side that the moon was shining at a certain hour of a certain night on a
+certain spot in London; on the other side it is affirmed that she was
+clouded. The Secretary is requested to decide. This is curious, as the
+question is not astrological. Persons still send to Greenwich, now and
+then, to have their fortunes told. In one case, not very many years ago, a
+young gentleman begged to know who his wife was to be, and what fee he was
+to remit.
+
+Sometimes the astronomer turns conjurer for fun, and his prophesies are
+fulfilled. It is related of Flamsteed[87] that an old woman came to know
+the whereabouts of a bundle of linen which had strayed. Flamsteed drew a
+circle, put a square into it, and gravely pointed out a ditch, near her
+cottage, in which he said it would be found. He meant to have given the
+woman a little good advice when she came back: but she came back in great
+delight, with the bundle in her hand, found in the very place. The late
+Baron Zach[88] received a letter from Pons,[89] a successful finder of
+comets, complaining that for a certain period he had found no comets,
+though he had searched diligently. Zach, a man of much sly humor, told him
+that no spots had been seen on the sun for about the same time--which was
+true,--and assured him that when the spots came back, the comets would come
+with them. Some time after he got a letter {46} from Pons, who informed him
+with great satisfaction that he was quite right, that very large spots had
+appeared on the sun, and that he had found a fine comet shortly after. I do
+not vouch for the first story, but I have the second in Zach's handwriting.
+It would mend the joke exceedingly if some day a real relation should be
+established between comets and solar spots: of late years good reason has
+been shown for advancing a connection between these spots and the earth's
+magnetism.[90] If the two things had been put to Zach, he would probably
+have chosen the comets. Here is a hint for a paradox: the solar spots are
+the dead comets, which have parted with their light and heat to feed the
+sun, as was once suggested. I should not wonder if I were too late, and the
+thing had been actually maintained. My list does not contain the twentieth
+part of the possible whole.
+
+The mention of coincidences suggests an everlasting source of explanations,
+applicable to all that is extraordinary. The great paradox of coincidence
+is that of Leibnitz, known as the _pre-established harmony_, or _law of
+coincidences_, by which, separately and independently, the body receives
+impressions, and the mind proceeds as if it had perceived them from
+without. Every sensation, and the consequent state of the soul, are
+independent things coincident in time by the pre-established law. The
+philosopher could not otherwise _account for_ the connection of mind and
+matter; and he never goes by so vulgar a rule as _Whatever is, is_; to him
+that which is not clear as to how, is not at all. Philosophers in general,
+who tolerate each other's theories much better than Christians do each
+other's failings, seldom revive Leibnitz's fantasy: they seem to act upon
+the maxim quoted by Father Eustace[91] from the {47} Decretals, _Facinora
+ostendi dum puniuntur, flagitia autem abscondi debent_.[92]
+
+The great _ghost-paradox_, and its theory of _coincidences_, will rise to
+the surface in the mind of every one. But the use of the word _coincidence_
+is here at variance with its common meaning. When A is constantly
+happening, and also B, the occurrence of A and B at the same moment is the
+mere coincidence which may be casualty. But the case before us is that A is
+constantly happening, while B, when it does happen, almost always happens
+with A, and very rarely without it. That is to say, such is the phenomenon
+asserted: and all who rationally refer it to casualty, affirm that B is
+happening very often as well as A, but that it is not thought worthy of
+being recorded except when A is simultaneous. Of course A is here a death,
+and B the spectral appearance of the person who dies. In talking of this
+subject it is necessary to put out of the question all who play fast and
+loose with their secret convictions: these had better give us a reason,
+when they feel internal pressure for explanation, that there is no
+weathercock at Kilve; this would do for all cases. But persons of real
+inquiry will see that first, experience does not bear out the asserted
+frequency of the spectre, without the alleged coincidence of death: and
+secondly, that if the crowd of purely casual spectres were so great that it
+is no wonder that, now and then the person should have died at or near the
+moment, we ought to expect a much larger proportion of cases in which the
+spectre should come at the moment of the death of one or another of all the
+cluster who are closely connected with the original of the spectre. But
+this, we know, is almost without example. It remains then, for all, who
+speculate at all, to look upon the asserted phenomenon, think what they may
+of it, the thing which is to be explained, as a _connection_ in time of the
+death, and the {48} simultaneous appearance of the dead. Any person the
+least used to the theory of probabilities will see that purely casual
+coincidence, the _wrong spectre_ being comparatively so rare that it may be
+said never to occur, is not within the rational field of possibility.
+
+The purely casual coincidence, from which there is no escape except the
+actual doctrine of special providences, carried down to a very low point of
+special intention, requires a junction of the things the like of each of
+which is always happening. I will give three instances which have occurred
+to myself within the last few years: I solemnly vouch for the literal truth
+of every part of all three:
+
+In August 1861, M. Senarmont,[93] of the French Institute, wrote to me to
+the effect that Fresnel[94] had sent to England, in or shortly after 1824,
+a paper for translation and insertion in the _European Review_, which
+shortly afterwards expired. The question was what had become of that paper.
+I examined the _Review_ at the Museum, found no trace of the paper, and
+wrote back to that effect at the Museum, adding that everything now
+depended on ascertaining the name of the editor, and tracing his papers: of
+this I thought there was no chance. I posted this letter on my way home, at
+a Post Office in the Hampstead Road at the junction with Edward Street, on
+the opposite side of which is a bookstall. Lounging for a moment over the
+exposed books, _sicut meus est mos_,[95] I saw, within a few minutes of the
+posting of the letter, a little catch-penny book of anecdotes of Macaulay,
+which I bought, and ran over for a minute. My eye was soon caught by this
+sentence: "One of the young fellows immediately wrote to the editor (Mr.
+Walker) {49} of the _European Review_." I thus got the clue by which I
+ascertained that there was no chance of recovering Fresnel's paper. Of the
+mention of current reviews, not one in a thousand names the editor.
+
+In the summer of 1865 I made my first acquaintance with the tales of
+Nathaniel Hawthorne, and the first I read was about the siege of Boston in
+the War of Independence. I could not make it out: everybody seemed to have
+got into somebody else's place. I was beginning the second tale, when a
+parcel arrived: it was a lot of old pamphlets and other rubbish, as he
+called it, sent by a friend who had lately sold his books, had not thought
+it worth while to send these things for sale, but thought I might like to
+look at them and possibly keep some. The first thing I looked at was a
+sheet which, being opened, displayed "A plan of Boston and its environs,
+shewing the true situation of his Majesty's army and also that of the
+rebels, drawn by an engineer, at Boston Oct. 1775." Such detailed plans of
+current sieges being then uncommon, it is explained that "The principal
+part of this plan was surveyed by Richard Williams, Lieutenant at Boston;
+and sent over by the son of a nobleman to his father in town, by whose
+permission it was published." I immediately saw that my confusion arose
+from my supposing that the king's troops were besieging the rebels, when it
+was just the other way.
+
+April 1, 1853, while engaged in making some notes on a logical point, an
+idea occurred which was perfectly new to me, on the mode of conciliating
+the notions _omnipresence_ and _indivisibility into parts_. What it was is
+no matter here: suffice it that, since it was published elsewhere (in a
+paper on _Infinity_, _Camb. Phil. Trans._ vol. xi. p. 1) I have not had it
+produced to me. I had just finished a paragraph on the subject, when a
+parcel came in from a bookseller containing Heywood's[96] _Analysis of
+Kant's Critick_, 1844.
+
+{50} On turning over the leaves I found (p. 109) the identical thought
+which up to this day, I only know as in my own paper, or in Kant. I feel
+sure I had not seen it before, for it is in Kant's first edition, which was
+never translated to my knowledge; and it does not appear in the later
+editions. Mr. Heywood gives some account of the first edition.
+
+In the broadsheet which gave account of the dying scene of Charles II, it
+is said that the Roman Catholic priest was introduced by P. M. A. C. F. The
+chain was this: the Duchess of Portsmouth[97] applied to the Duke of York,
+who may have consulted his Cordelier confessor, Mansuete, about procuring a
+priest, and the priest was smuggled into the king's room by the Duchess and
+Chiffinch.[98] Now the letters are a verbal acrostic of _Pere Mansuete a
+Cordelier Friar_, and a syllabic acrostic of _PortsMouth and ChifFinch_.
+This is a singular coincidence. Macaulay adopted the first interpretation,
+preferring it to the second, which I brought before him as the conjecture
+of a near relative of my own. But Mansuete is not mentioned in his
+narrative: it may well be doubted whether the writer of a broadside for
+English readers would use _Pere_ instead of _Father_. And the person who
+really "reminded" the Duke of "the duty he owed to his brother," was the
+Duchess and not Mansuete. But my affair is only with the coincidence.
+
+But there are coincidences which are really connected without the
+connection being known to those who find in them matter of astonishment.
+Presentiments furnish marked cases: sometimes there is no mystery to those
+who have the clue. In the _Gentleman's Magazine_ (vol. 80, part 2, p. 33)
+we read, the subject being presentiment of death, as follows: "In 1778, to
+come nearer the recollection of {51} survivors, at the taking of
+Pondicherry, Captain John Fletcher, Captain De Morgan, and Lieutenant
+Bosanquet, each distinctly foretold his own death on the morning of his
+fate." I have no doubt of all three; and I knew it of my grandfather long
+before I read the above passage. He saw that the battery he commanded was
+unduly exposed: I think by the sap running through the fort when produced.
+He represented this to the engineer officers, and to the
+commander-in-chief; the engineers denied the truth of the statement, the
+commander believed them, my grandfather quietly observed that he must make
+his will, and the French fulfilled his prediction. His will bore date the
+day of his death; and I always thought it more remarkable than the
+fulfilment of the prophecy that a soldier should not consider any danger
+short of one like the above, sufficient reason to make his will. I suppose
+the other officers were similarly posted. I am told that military men very
+often defer making their wills until just before an action: but to face the
+ordinary risks intestate, and to wait until speedy death must be the all
+but certain consequence of a stupid mistake, is carrying the principle very
+far. In the matter of coincidences there are, as in other cases, two
+wonderful extremes with every intermediate degree. At one end we have the
+confident people who can attribute anything to casual coincidence; who
+allow Zadok Imposture and Nathan Coincidence to anoint Solomon Selfconceit
+king. At the other end we have those who see something _very curious_ in
+any coincidence you please, and whose minds yearn for a deep reason. A
+speculator of this class happened to find that Matthew viii. 28-33 and Luke
+viii. 26-33 contain the same account, that of the demons entering into the
+swine. Very odd! chapters tallying, and verses so nearly: is the
+versification rightly managed? Examination is sure to show that there are
+monstrous inconsistencies in the mode of division, which being corrected,
+the verses tally as well as the chapters. And then how comes it? I cannot
+go on, {52} for I have no gift at torturing a coincidence, but I would lay
+twopence, if I could make a bet--which I never did in all my life--that
+some one or more of my readers will try it. Some people say that the study
+of chances tends to awaken a spirit of gambling: I suspect the contrary. At
+any rate, I myself, the writer of a mathematical book and a comparatively
+popular book, have never laid a bet nor played for a stake, however small:
+not one single time.
+
+It is useful to record such instances as I have given, with precision and
+on the solemn word of the recorder. When such a story as that of Flamsteed
+is told, _a priori_ assures us that it could not have been: the story may
+have been a _ben trovato_,[99] but not the bundle. It is also useful to
+establish some of the good jokes which all take for inventions. My friend
+Mr. J. Bellingham Inglis,[100] before 1800, saw the tobacconist's carriage
+with a sample of tobacco in a shield, and the motto _Quid rides_[101] (_N._
+& _Q._, 3d S. i. 245). His father was able to tell him all about it. The
+tobacconist was Jacob Brandon, well known to the elder Mr. Inglis, and the
+person who started the motto, the instant he was asked for such a thing,
+was Harry Calender of Lloyd's, a scholar and a wit. My friend Mr. H. Crabb
+Robinson[102] remembers the King's Counsel (Samuel Marryat) who took the
+motto _Causes produce effects_, when his success enabled him to start a
+carriage.
+
+The coincidences of errata are sometimes very remarkable: it may be that
+the misprint has a sting. The death of Sir W. Hamilton[103] of Edinburgh
+was known in London on a Thursday, and the editor of the _Athenaeum_ wrote
+to {53} me in the afternoon for a short obituary notice to appear on
+Saturday. I dashed off the few lines which appeared without a moment to
+think: and those of my readers who might perhaps think me capable of
+contriving errata with meaning will, I am sure, allow the hurry, the
+occasion, and my own peculiar relation to the departed, as sufficient
+reasons for believing in my entire innocence. Of course I could not see a
+proof: and two errata occurred. The words "addition to Stewart"[104]
+require "_for_ addition to _read_ edition of." This represents what had
+been insisted on by the Edinburgh publisher, who, frightened by the edition
+of Reid,[105] had stipulated for a simple reprint without notes. Again
+"principles of logic and mathematics" required "_for_ mathematics _read_
+metaphysics." No four words could be put together which would have so good
+a title to be Hamilton's motto.
+
+
+
+April 1850, found in the letter-box, three loose leaves, well printed and
+over punctuated, being
+
+    Chapter VI. Brethren, lo I come, holding forth the word of life, for so
+    I am commanded.... Chapter VII. Hear my prayer, O generations! and walk
+    by the way, to drink the waters of the river.... Chapter VIII. Hearken
+    o earth, earth, earth, and the kings of the earth, and their armies....
+
+A very large collection might be made of such apostolic writings. They go
+on well enough in a misty--meant for mystical--imitation of St. Paul or the
+prophets, until at last some prodigious want of keeping shows the education
+of the writer. For example, after half a page which might {54} pass for
+Irving's[106] preaching--though a person to whom it was presented as such
+would say that most likely the head and tail would make something more like
+head and tail of it--we are astounded by a declaration from the _Holy
+Spirit_, speaking of himself, that he is "not ashamed of the Gospel of
+Christ." It would be long before we should find in _educated_ rhapsody--of
+which there are specimens enough--such a thing as a person of the Trinity
+taking merit for moral courage enough to stand where St. Peter fell. The
+following declaration comes next--"I will judge between cattle and cattle,
+that use their tongues."
+
+
+
+THE FIGURE OF THE EARTH.
+
+    The figure of the earth. By J. L. Murphy,[107] of Birmingham. (London
+    and Birmingham, 4 pages, 12mo.) (1850?)
+
+Mr. Murphy invites attention and objection to some assertions, as that the
+earth is prolate, not oblate. "If the philosopher's conclusion be right,
+then the pole is the center of a valley (!) thirteen miles deep." Hence it
+would be very warm. It is answer enough to ask--Who knows that it is not?
+
+
+
+    *** A paragraph in the MS. appears to have been inserted in this place
+    by mistake. It will be found in the Appendix at the end of this
+    volume.--S. E. De M.
+
+
+
+PERPETUAL MOTION.
+
+1851. The following letter was written by one of a class of persons whom,
+after much experience of them, I {55} do _not_ pronounce insane. But in
+this case the second sentence gives a suspicion of actual delusion of the
+senses; the third looks like that eye for the main chance which passes for
+sanity on the Stock Exchange and elsewhere:
+
+15th Sept. 1851.
+
+"Gentlemen,--I pray you take steps to make known that yesterday I completed
+my invention which will give motion to every country on the Earth;--to move
+Machinery!--the long sought in vain 'Perpetual Motion'!!--I was supported
+at the time by the Queen and H.R.H. Prince Albert. If, Gentlemen, you can
+advise me how to proceed to claim the reward, if any is offered by the
+Government, or how to secure the PATENT for the machine, or in any way
+assist me by advice in this great work, I shall most graciously acknowledge
+your consideration.
+
+These are my convictions that my SEVERAL discoveries will be realized: and
+this great one can be at once acted upon: although at this moment it only
+exists in my mind, from my knowledge of certain fixed principles in
+nature:--the Machine I have not made, as I only completed the discovery
+YESTERDAY, Sunday!
+
+          I have, etc. ---- ----"
+
+  To the Directors of the
+  London University, Gower Street.
+
+
+
+ON SPIRITUALISM.
+
+    The Divine Drama of History and Civilisation. By the Rev. James Smith,
+    M.A.[108] London, 1854, 8vo.
+
+I have several books on that great paradox of our day, _Spiritualism_, but
+I shall exclude all but three. The bibliography of this subject is now very
+large. The question is one both of evidence and speculation;--Are the facts
+{56} true? Are they caused by spirits? These I shall not enter upon: I
+shall merely recommend this work as that of a spiritualist who does not
+enter on the subject, which he takes for granted, but applies his derived
+views to the history of mankind with learning and thought. Mr. Smith was a
+man of a very peculiar turn of thinking. He was, when alive, the editor, or
+_an_ editor, of the _Family Herald_: I say when alive, to speak according
+to knowledge; for, if his own views be true, he may have a hand in it
+still. The answers to correspondents, in his time, were piquant and
+original above any I ever saw. I think a very readable book might be made
+out of them, resembling "Guesses at Truth:" the turn given to an inquiry
+about morals, religion, or socials, is often of the highest degree of
+_unexpectedness_; the poor querist would find himself right in a most
+unpalatable way.
+
+Answers to correspondents, in newspapers, are very often the fag ends of
+literature. I shall never forget the following. A person was invited to
+name a rule without exception, if he could: he answered "A man _must_ be
+present when he is shaved." A lady--what right have ladies to decide
+questions about shaving?--said this was not properly a rule; and the oracle
+was consulted. The editor agreed with the lady; he said that "a man _must_
+be present when he is shaved" is not a _rule_, but a _fact_.
+
+
+
+[Among my anonymous communicants is one who states that I have done
+injustice to the Rev. James Smith in "referring to him as a spiritualist,"
+and placing his "Divine Drama" among paradoxes: "it is no paradox, nor do
+_spiritualistic_ views mar or weaken the execution of the design." Quite
+true: for the design is to produce and enforce "spiritualistic views"; and
+leather does not mar nor weaken a shoemaker's plan. I knew Mr. Smith well,
+and have often talked to him on the subject: but more testimony from me is
+unnecessary; his book will speak for itself. {57} His peculiar style will
+justify a little more quotation than is just necessary to prove the point.
+Looking at the "battle of opinion" now in progress, we see that Mr. Smith
+was a prescient:
+
+(P. 588.) "From the general review of parties in England, it is evident
+that no country in the world is better prepared for the great Battle of
+Opinion. Where else can the battle be fought but where the armies are
+arrayed? And here they all are, Greek, Roman, Anglican, Scotch, Lutheran,
+Calvinist, Established and Territorial, with Baronial Bishops, and
+Nonestablished of every grade--churches with living prophets and apostles,
+and churches with dead prophets and apostles, and apostolical churches
+without apostles, and philosophies without either prophets or apostles, and
+only wanting one more, 'the Christian Church,' like Aaron's rod, to swallow
+up and digest them all, and then bud and flourish. As if to prepare our
+minds for this desirable and inevitable consummation, different parties
+have been favored with a revival of that very spirit of revelation by which
+the Church itself was originally founded. There is a complete series of
+spiritual revelations in England and the United States, besides mesmeric
+phenomena that bear a resemblance to revelation, and thus gradually open
+the mind of the philosophical and infidel classes, as well as the professed
+believers of that old revelation which they never witnessed in living
+action, to a better understanding of that Law of Nature (for it is a Law of
+Nature) in which all revelation originates and by which its spiritual
+communications are regulated."
+
+Mr. Smith proceeds to say that there are _only_ thirty-five incorporated
+churches in England, all formed from the New Testament except five, to each
+of which five he concedes a revelation of its own. The five are the
+Quakers, the Swedenborgians, the Southcottians, the Irvingites, and the
+Mormonites. Of Joanna Southcott he speaks as follows: {58}
+
+(P. 592.) "Joanna Southcott[109] is not very gallantly treated by the
+gentlemen of the Press, who, we believe, without knowing anything about
+her, merely pick up their idea of her character from the rabble. We once
+entertained the same rabble idea of her; but having read her works--for we
+really have read them--we now regard her with great respect. However, there
+is a great abundance of chaff and straw to her grain; but the grain is
+good, and as we do not eat either the chaff or straw if we can avoid it,
+nor even the raw grain, but thrash it and winnow it, and grind it and bake
+it, we find it, after undergoing this process, not only very palatable, but
+a special dainty of its kind. But the husk is an insurmountable obstacle to
+those learned and educated gentlemen who judge of books entirely by the
+style and the grammar, or those who eat grain as it grows, like the cattle.
+Such men would reject all prological revelation; for there never was and
+probably never will be a revelation by voice and vision communicated in
+classical manner. It would be an invasion of the rights and prerogatives of
+Humanity, and as contrary to the Divine and Established order of mundane
+government, as a field of quartern loaves or hot French rolls."
+
+
+
+Mr. Smith's book is spiritualism from beginning to end; and my anonymous
+gainsayer, honest of course, is either ignorant of the work he thinks he
+has read, or has a most remarkable development of the organ of
+imperception.]
+
+
+
+A CONDENSED HISTORY OF MATHEMATICS.
+
+I cut the following from a Sunday paper in 1849:
+
+"X. Y.--The Chaldeans began the mathematics, in which the Egyptians
+excelled. Then crossing the sea, by means {59} of Thales,[110] the
+Milesian, they came into Greece, where they were improved very much by
+Pythagoras,[111] Anaxagoras,[112] and Anopides[113] of Chios. These were
+followed by Briso,[114] Antipho, [two circle-squarers; where is Euclid?]
+and Hippocrates,[115] but the excellence of the algebraic art was begun by
+Geber,[116] an Arabian astronomer, and was carried on by Cardanus,[117]
+Tartaglia,[118] Clavius,[119], Stevinus,[120] Ghetaldus,[121]
+Herig_e_nius,[122] Fran. Van Schooten [meaning Francis Van Schooten[123]],
+Florida de Beau_m_e,[124] etc."
+
+Bryso was a mistaken man. Antipho had the disadvantage of being in advance
+of his age. He had the notion of which the modern geometry has made so
+much, that of {60} a circle being the polygon of an infinitely great number
+of sides. He could make no use of it, but the notion itself made him a
+sophist in the eyes of Aristotle, Eutocius,[125] etc. Geber, an Arab
+astronomer, and a reputed conjurer in Europe, seems to have given his name
+to unintelligible language in the word _gibberish_. At one time _algebra_
+was traced to him; but very absurdly, though I have heard it suggested that
+_algebra_ and _gibberish_ must have had one inventor.
+
+Any person who meddles with the circle may find himself the crane who was
+netted among the geese: as Antipho for one, and Olivier de Serres[126] for
+another. This last gentleman ascertained, by weighing, that the area of the
+circle is very nearly that of the square on the side of the inscribed
+equilateral triangle: which it is, as near as 3.162 ... to 3.141.... He did
+not pretend to more than approximation; but Montucla and others
+misunderstood him, and, still worse, misunderstood their own
+misunderstanding, and made him say the circle was exactly double of the
+equilateral triangle. He was let out of limbo by Lacroix, in a note to his
+edition of Montucla's _History of Quadrature_.
+
+
+
+ST. VITUS, PATRON OF CYCLOMETERS.
+
+    Quadratura del cerchio, trisezione dell' angulo, et duplicazione del
+    cubo, problemi geometricamente risolute e dimostrate dal Reverendo
+    Arciprete di San Vito D. Domenico Anghera,[127] Malta, 1854, 8vo.
+
+    {61}
+
+    Equazioni geometriche, estratte dalla lettera del Rev. Arciprete ... al
+    Professore Pullicino[128] sulla quadratura del cerchio. Milan, 1855 or
+    1856, 8vo.
+
+    Il Mediterraneo gazetta di Malta, 26 Decembre 1855, No. 909: also 911,
+    912, 913, 914, 936, 939.
+
+    The Malta Times, Tuesday, 9th June 1857.
+
+    Misura esatta del cerchio, dal Rev. D. Anghera. Malta, 1857, 12mo.
+
+    Quadrature of the circle ... by the Rev. D. Anghera, Archpriest of St.
+    Vito. Malta, 1858, 12mo.
+
+I have looked for St. Vitus in catalogues of saints, but never found his
+legend, though he figures as a day-mark in the oldest almanacs. He must be
+properly accredited, since he was an archpriest. And I pronounce and
+ordain, by right accruing from the trouble I have taken in this subject,
+that he, St. Vitus, who leads his votaries a never-ending and unmeaning
+dance, shall henceforth be held and taken to be the patron saint of the
+circle-squarer. His day is the 15th of June, which is also that of St.
+Modestus,[129] with whom the said circle-squarer often has nothing to do.
+And he must not put himself under the first saint with a slantendicular
+reference to the other, as is much to be feared was done by the Cardinal
+who came to govern England with a title containing St. Pudentiana,[130] who
+shares a day with _St. Dunstan_. The Archpriest of St. Vitus will have it
+that the square inscribed in a semicircle is half of the semicircle, or the
+circumference 3-1/5 diameters. He is active and able, with {62} nothing
+wrong about him except his paradoxes. In the second tract named he has
+given the testimonials of crowned heads and ministers, etc. as follows.
+Louis-Napoleon gives thanks. The minister at Turin refers it to the Academy
+of Sciences, and hopes so much labor will be judged _degna di pregio_.[131]
+The Vice-Chancellor of Oxford--a blunt Englishman--begs to say that the
+University has never proposed the problem, as some affirm. The Prince
+Regent of Baden has received the work with lively interest. The Academy of
+Vienna is not in a position to enter into the question. The Academy of
+Turin offers the most _distinct_ thanks. The Academy della Crusca attends
+only to literature, but gives thanks. The Queen of Spain has received the
+work with the highest appreciation. The University of Salamanca gives
+infinite thanks, and feels true satisfaction in having the book. Lord
+Palmerston gives thanks, by the hand of "William San." The Viceroy of
+Egypt, not being yet up in Italian, will spend his first moments of leisure
+in studying the book, when it shall have been translated into French: in
+the mean time he congratulates the author upon his victory over a problem
+so long held insoluble. All this is seriously published as a rate in aid of
+demonstration. If these royal compliments cannot make the circumference of
+a circle about 2 per cent. larger than geometry will have it --which is all
+that is wanted--no wonder that thrones are shaky.
+
+I am informed that the legend of St. Vitus is given by Ribadeneira[132] in
+his lives of Saints, and that Baronius,[133] in {63} his _Martyrologium
+Romanum_, refers to several authors who have written concerning him. There
+is an account in Mrs. Jameson's[134] _History of Sacred and Legendary Art_
+(ed. of 1863, p. 544). But it seems that St. Vitus is the patron saint of
+_all_ dances; so that I was not so far wrong in making him the protector of
+the cyclometers. Why he is represented with a cock is a disputed point,
+which is now made clear: next after _gallus gallinaceus_[135] himself,
+there is no crower like the circle-squarer.
+
+
+
+CELEBRATED APPROXIMATIONS OF [pi].
+
+The following is an extract from the _English Cyclopaedia_, Art. TABLES:
+
+"1853. William Shanks,[136] _Contributions to Mathematics, comprising
+chiefly the Rectification of the Circle to 607 Places of Tables_, London,
+1853. (QUADRATURE OF THE CIRCLE.) Here is a _table_, because it tabulates
+the results of the subordinate steps of this enormous calculation as far as
+527 decimals: the remainder being added as results only during the
+printing. For instance, one step is the calculation of the reciprocal of
+601.5^{601}; and the result is given. The number of pages required to
+describe these results is 87. Mr. Shanks has also thrown off, as chips or
+splinters, the values of the base of Napier's logarithms, and of its
+logarithms of 2, 3, 5, 10, to 137 decimals; and the value of the modulus
+.4342 ... to 136 decimals: with the 13th, 25th, 37th ... up to the 721st
+powers of 2. These tremendous stretches of calculation--at least we so call
+them in our day--are useful in several respects; they prove more than {64}
+the capacity of this or that computer for labor and accuracy; they show
+that there is in the community an increase of skill and courage. We say in
+the community: we fully believe that the unequalled turnip which every now
+and then appears in the newspapers is a sufficient presumption that the
+average turnip is growing bigger, and the whole crop heavier. All who know
+the history of the quadrature are aware that the several increases of
+numbers of decimals to which [pi] has been carried have been indications of
+a general increase in the power to calculate, and in courage to face the
+labor. Here is a comparison of two different times. In the day of
+Cocker,[137] the pupil was directed to perform a common subtraction with a
+voice-accompaniment of this kind: '7 from 4 I cannot, but add 10, 7 from 14
+remains 7, set down 7 and carry 1; 8 and 1 which I carry is 9, 9 from 2 I
+cannot, etc.' We have before us the announcement of the following _table_,
+undated, as open to inspection at the Crystal Palace, Sydenham, in two
+diagrams of 7 ft. 2 in, by 6 ft. 6 in.: 'The figure 9 involved into the
+912th power, and antecedent powers or involutions, containing upwards of
+73,000 figures. Also, the proofs of the above, containing upwards of
+146,000 figures. By Samuel Fancourt, of Mincing Lane, London, and completed
+by him in the year 1837, at the age of sixteen. N.B. The whole operation
+performed by simple arithmetic.' The young operator calculated by
+successive squaring the 2d, 4th, 8th, etc., powers up to the 512th, with
+proof by division. But 511 multiplications by 9, in the short (or 10-1)
+way, would have been much easier. The 2d, 32d, 64th, 128th, 256th, and
+512th powers are given at the back of the announcement. The powers of 2
+have been calculated for many purposes. In Vol. II of his _Magia
+Universalis Naturae et Artis_, Herbipoli, 1658, 4to, the Jesuit Gaspar
+Schott[138] having discovered, on some grounds of theological {65} magic,
+that the degrees of grace of the Virgin Mary were in number the 256th power
+of 2, calculated that number. Whether or no his number correctly
+represented the result he announced, he certainly calculated it rightly, as
+we find by comparison with Mr. Shanks."
+
+
+
+There is a point about Mr. Shanks's 608 figures of the value of [pi] which
+attracts attention, perhaps without deserving it. It might be expected
+that, in so many figures, the nine digits and the cipher would occur each
+about the same number of times; that is, each about 61 times. But the fact
+stands thus: 3 occurs 68 times; 9 and 2 occur 67 times each; 4 occurs 64
+times; 1 and 6 occur 62 times each; 0 occurs 60 times; 8 occurs 58 times; 5
+occurs 56 times; and 7 occurs only 44 times. Now, if all the digits were
+equally likely, and 608 drawings were made, it is 45 to 1 against the
+number of sevens being as distant from the probable average (say 61) as 44
+on one side or 78 on the other. There must be some reason why the number 7
+is thus deprived of its fair share in the structure. Here is a field of
+speculation in which two branches of inquirers might unite. There is but
+one number which is treated with an unfairness which is incredible as an
+accident; and that number is the mystic number _seven_! If the cyclometers
+and the apocalyptics would lay their heads together until they come to a
+unanimous verdict on this phenomenon, and would publish nothing until they
+are of one mind, they would earn the gratitude of their race.--I was wrong:
+it is the Pyramid-speculator who should have been appealed to. A
+correspondent of my friend Prof. Piazzi Smyth[139] notices that 3 is the
+number of most frequency, and that 3-1/7 is the nearest approximation to it
+in simple digits. Professor Smyth himself, whose word on Egypt is paradox
+of a very high order, backed by a great quantity of useful labor, the
+results which will be made available by those who do not receive {66} the
+paradoxes, is inclined to see confirmation for some of his theory in these
+phenomena.
+
+
+
+CURIOUS CALCULATIONS.
+
+These paradoxes of calculation sometimes appear as illustrations of the
+value of a new method. In 1863, Mr. G. Suffield,[140] M.A., and Mr. J. R.
+Lunn,[141] M.A., of Clare College and of St. John's College, Cambridge,
+published the whole quotient of 10000 ... divided by 7699, throughout the
+whole of one of the recurring periods, having 7698 digits. This was done in
+illustration of Mr. Suffield's method of _Synthetic division_.
+
+Another instance of computation carried to paradoxical length, in order to
+illustrate a method, is the solution of x^3 - 2x = 5, the example given of
+Newton's method, on which all improvements have been tested. In 1831,
+Fourier's[142] posthumous work on equations showed 33 figures of solution,
+got with enormous labor. Thinking this a good opportunity to illustrate the
+superiority of the method of W. G. Horner,[143] not yet known in France,
+and not much known in {67} England, I proposed to one of my classes, in
+1841, to beat Fourier on this point, as a Christmas exercise. I received
+several answers, agreeing with each other, to 50 places of decimals. In
+1848, I repeated the proposal, requesting that 50 places might be exceeded:
+I obtained answers of 75, 65, 63, 58, 57, and 52 places. But one answer, by
+Mr. W. Harris Johnston,[144] of Dundalk, and of the Excise Office, went to
+101 decimal places. To test the accuracy of this, I requested Mr. Johnston
+to undertake another equation, connected with the former one in a way which
+I did not explain. His solution verified the former one, but he was unable
+to see the connection, even when his result was obtained. My reader may be
+as much at a loss: the two solutions are:
+
+  2.0945514815423265...
+  9.0544851845767340...
+
+The results are published in the _Mathematician_, Vol. III, p. 290. In
+1851, another pupil of mine, Mr. J. Power Hicks,[145] carried the result to
+152 decimal places, without knowing what Mr. Johnston had done. The result
+is in the _English Cyclopaedia_, article INVOLUTION AND EVOLUTION.
+
+I remark that when I write the initial of a Christian name, the most usual
+name of that initial is understood. I never saw the name of W. G. Horner
+written at length, until I applied to a relative of his, who told me that
+he was, as I supposed, Wm. _George_, but that he was named after a relative
+of that _surname_.
+
+The square root of 2, to 110 decimal places, was given {68} me in 1852 by
+my pupil, Mr. William Henry Colvill, now (1867) Civil Surgeon at Baghdad.
+It was
+
+  1.4142135623730950488016887242096980785696
+    7187537694807317667973799073247846210703
+    885038753432764157273501384623
+
+Mr. James Steel[146] of Birkenhead verified this by actual multiplication,
+and produced
+
+  2 - 2580413 / 10^{117}
+
+as the square.
+
+
+
+    Calcolo decidozzinale del Barone Silvio Ferrari. Turin, 1854, 4to.
+
+This is a serious proposal to alter our numeral system and to count by
+twelves. Thus 10 would be twelve, 11 thirteen, etc., two new symbols being
+invented for ten and eleven. The names of numbers must of course be
+changed. There are persons who think such changes practicable. I thought
+this proposal absurd when I first saw it, and I think so still:[147] but
+the one I shall presently describe beats it so completely in that point,
+that I have not a smile left for this one.
+
+
+
+ON COMETS.
+
+    The successful and therefore probably true theory of Comets. London,
+    1854. (4pp. duodecimo.)
+
+The author is the late Mr. Peter Legh,[148] of Norbury Booths Hall,
+Knutsford, who published for eight or ten {69} years the _Ombrological
+Almanac_, a work of asserted discovery in meteorology. The theory of comets
+is that the joint attraction of the new moon and several planets in the
+direction of the sun, draws off the gases from the earth, and forms these
+cometic meteors. But how these meteors come to describe orbits round the
+sun, and to become capable of having their returns predicted, is not
+explained.
+
+
+
+A NEW PHASE OF MORMONISM.
+
+    The Mormon, New York, Saturday, Oct. 27, 1855.
+
+A newspaper headed by a grand picture of starred and striped banners,
+beehive, and eagle surmounting it. A scroll on each side: on the left,
+"Mormon creed. Mind your own business. Brigham Young;"[149] on the right,
+"Given by inspiration of God. Joseph Smith."[150] A leading article on the
+discoveries of Prof. Orson Pratt[151] says, "Mormonism has long taken the
+lead in religion: it will soon be in the van both in science and politics."
+At the beginning of the paper is Professor Pratt's "Law of Planetary
+Rotation." The cube roots of the densities of the planets are as the square
+roots of their periods of rotation. The squares of the cube roots of the
+masses divided by the squares of the diameters are as the periods of
+rotation. Arithmetical verification attempted, and the whole very modestly
+stated {70} and commented on. Dated G. S. L. City, Utah Ter., Aug. 1, 1855.
+If the creed, as above, be correctly given, no wonder the Mormonites are in
+such bad odor.
+
+
+
+MATHEMATICAL ILLUSTRATIONS OF DOCTRINE.
+
+    The two estates; or both worlds mathematically considered. London,
+    1855, small (pp. 16).
+
+The author has published mathematical works with his name. The present
+tract is intended to illustrate mathematically a point which may be guessed
+from the title. But the symbols do very little in the way of illustration:
+thus, x being the _present value_ of the future estate (eternal happiness),
+and a of all that this world can give, the author impresses it on the
+mathematician that, x being infinitely greater than a, x + a = x, so that a
+need not be considered. This will not act much more powerfully on a
+mathematician by virtue of the symbols than if those same symbols had been
+dispensed with: even though, as the author adds, "It was this method of
+neglecting infinitely small quantities that Sir Isaac Newton was indebted
+to for his greatest discoveries."
+
+There has been a moderate quantity of well-meant attempt to enforce,
+sometimes motive, sometimes doctrine, by arguments drawn from mathematics,
+the proponents being persons unskilled in that science for the most part.
+The ground is very dangerous: for the illustration often turns the other
+way with greater power, in a manner which requires only a little more
+knowledge to see. I have, in my life, heard from the pulpit or read, at
+least a dozen times, that all sin is infinitely great, proved as follows.
+The greater the being, the greater the sin of any offence against him:
+therefore the offence committed against an infinite being is infinitely
+great. Now the mathematician, of which the proposers of this argument are
+not aware, is perfectly familiar with quantities which increase together,
+and never cease increasing, but so that one of them remains finite when
+{71} the other becomes infinite. In fact, the argument is a perfect _non
+sequitur_.[152] Those who propose it have in their minds, though in a
+cloudy and indefinite form, the idea of the increase of guilt being
+_proportionate_ to the increase of greatness in the being offended. But
+this it would never do to state: for by such statement not only would the
+argument lose all that it has of the picturesque, but the asserted premise
+would have no strong air of exact truth. How could any one undertake to
+appeal to conscience to declare that an offence against a being 4-7/10
+times as great as another is exactly, no more and no less, 4-7/10 times as
+great an offence against the other?
+
+The infinite character of the offence against an infinite being is laid
+down in Dryden's _Religio Laici_,[153] and is, no doubt, an old argument:
+
+ "For, granting we have sinned, and that th' offence
+  Of man is made against Omnipotence,
+  Some price that bears proportion must be paid,
+  And infinite with infinite be weighed.
+  See then the Deist lost; remorse for vice
+  Not paid; or, paid, inadequate in price."
+
+Dryden, in the words "bears proportion" is in verse more accurate than most
+of the recent repeaters in prose. And this is not the only case of the kind
+in his argumentative poetry.
+
+My old friend, the late Dr. Olinthus Gregory,[154] who was a sound and
+learned mathematician, adopted this dangerous kind of illustration in his
+_Letters on the Christian Religion_. {72} He argued, by parallel, from what
+he supposed to be the necessarily mysterious nature of the _impossible_
+quantity of algebra to the necessarily mysterious nature of certain
+doctrines of his system of Christianity. But all the difficulty and mystery
+of the impossible quantity is now cleared away by the advance of
+algebraical thought: and yet Dr. Gregory's book continues to be sold, and
+no doubt the illustration is still accepted as appropriate.
+
+The mode of argument used by the author of the tract above named has a
+striking defect. He talks of reducing this world and the next to "present
+value," as an actuary does with successive lives or next presentations.
+Does value make interest? and if not, why? And if it do, then the present
+value of an eternity is _not_ infinitely great. Who is ignorant that a
+perpetual annuity at five per cent is worth only twenty years' purchase?
+This point ought to be discussed by a person who treats heaven as a
+deferred perpetual annuity. I do not ask him to do so, and would rather he
+did not; but if he _will_ do it, he must either deal with the question of
+discount, or be asked the reason why.
+
+When a very young man, I was frequently exhorted to one or another view of
+religion by pastors and others who thought that a mathematical argument
+would be irresistible. And I heard the following more than once, and have
+since seen it in print, I forget where. Since eternal happiness belonged to
+the particular views in question, a benefit infinitely great, then, even if
+the probability of their arguments were small, or even infinitely small,
+yet the product of the chance and benefit, according to the usual rule,
+might give a result which no one ought in prudence to pass over. They did
+not see that this applied to all systems as well as their own. I take this
+argument to be the most perverse of all the perversions I have heard or
+read on the subject: there is some high authority for it, whom I forget.
+
+The moral of all this is, that such things as the preceding should be kept
+out of the way of those who are not {73} mathematicians, because they do
+not understand the argument; and of those who are, because they do.
+
+[The high authority referred to above is Pascal, an early cultivator of
+mathematical probability, and obviously too much enamoured of his new
+pursuit. But he conceives himself bound to wager on one side or the other.
+To the argument (_Pensees_, ch. 7)[155] that "le juste est de ne point
+parier," he answers, "Oui: mais il faut parier: vous etes embarque; et ne
+parier point que Dieu est, c'est parier qu'il n'est pas."[156] Leaving
+Pascal's argument to make its way with a person who, _being a sceptic_, is
+yet positive that the issue is salvation or perdition, if a God there
+be,--for the case as put by Pascal requires this,--I shall merely observe
+that a person who elects to believe in God, as the best chance of gain, is
+not one who, according to Pascal's creed, or any other worth naming, will
+really secure that gain. I wonder whether Pascal's curious imagination ever
+presented to him in sleep his convert, in the future state, shaken out of a
+red-hot dice-box upon a red-hot hazard-table, as perhaps he might have
+been, if Dante had been the later of the two. The original idea is due to
+the elder Arnobius,[157] who, as cited by Bayle,[158] speaks thus:
+
+"Sed et ipse [Christus] quae pollicetur, non probat. Ita est. Nulla enim, ut
+dixi, futurorum potest existere comprobatio. Cum ergo haec sit conditio
+futurorum, ut teneri et comprehendi nullius possint anticipationis attactu;
+nonne {74} purior ratio est, ex duobus incertis, et in ambigua expectatione
+pendentibus, id potius credere, quod aliquas spes ferat, quam omnino quod
+nullas? In illo enim periculi nihil est, si quod dicitur imminere, cassum
+fiat et vacuum: in hoc damnum est maximum, id est salutis amissio, si cum
+tempus advenerit aperiatur non fuisse mendacium."[159]
+
+Really Arnobius seems to have got as much out of the notion, in the third
+century, as if he had been fourteen centuries later, with the arithmetic of
+chances to help him.]
+
+
+
+NOVUM ORGANUM MORALIUM.
+
+    The Sentinel, vol. ix. no. 27. London, Saturday, May 26, 1855.
+
+This is the first London number of an Irish paper, Protestant in politics.
+It opens with "Suggestions on the subject of a _Novum Organum Moralium_,"
+which is the application of algebra and the differential calculus to
+morals, socials, and politics. There is also a leading article on the
+subject, and some applications in notes to other articles. A separate
+publication was afterwards made, with the addition of a long Preface; the
+author being a clergyman who I presume must have been the editor of the
+_Sentinel_.
+
+    Suggestions as to the employment of a _Novum Organum Moralium_. Or,
+    thoughts on the nature of the Differential Calculus, and on the
+    application of its principles to metaphysics, with a view to the
+    attainment of demonstration and certainty in moral, {75} political and
+    ecclesiastical affairs. By Tresham Dames Gregg,[160] Chaplain of St.
+    Mary's, within the church of St. Nicholas intra muros, Dublin. London,
+    1859, 8vo. (pp. xl + 32).
+
+I have a personal interest in this system, as will appear from the
+following extract from the newspaper:
+
+    "We were subsequently referred to De Morgan's _Formal Logic_ and
+    Boole's _Laws of Thought_[161] both very elaborate works, and greatly
+    in the direction taken by ourselves. That the writers amazingly surpass
+    us in learning we most willingly admit, but we venture to pronounce of
+    both their learned treatises, that they deal with the subject in a mode
+    that is scholastic to an excess.... That their works have been for a
+    considerable space of time before the world and effected nothing, would
+    argue that they have overlooked the vital nature of the theme.... On
+    the whole, the writings of De Morgan and Boole go to the full
+    justification of our principle without in any wise so trenching upon
+    our ground as to render us open to reproach in claiming our Calculus as
+    a great discovery.... But we renounce any paltry jealousy as to a
+    matter so vast. If De Morgan and Boole have had a priority in the case,
+    to them we cheerfully shall resign the glory and honor. If such be the
+    truth, they have neither done justice to the discovery, nor to
+    themselves [quite true]. They have, under the circumstances, acted like
+    'the foolish man, who roasteth not that which he taketh {76} in
+    hunting.... It will be sufficient for us, however, to be the Columbus
+    of these great Americi, and popularize what they found, _if_ they found
+    it. We, as from the mountain top, will then become _their_ trumpeters,
+    and cry glory to De Morgan and glory to Boole, under Him who is the
+    source of all glory, the only good and wise, to Whom be glory for ever!
+    _If_ they be our predecessors in this matter, they have, under Him,
+    taken moral questions out of the category of probabilities, and
+    rendered them perfectly certain. In that case, let their books be read
+    by those who may doubt the principles this day laid before the world as
+    a great discovery, by our newspaper. Our cry shall be [Greek:
+    eurekasi]![162] Let us hope that they will join us, and henceforth keep
+    their light [_sic_] from under their bushel."
+
+For myself, and for my old friend Mr. Boole, who I am sure would join me, I
+disclaim both priority, simultaneity, and posteriority, and request that
+nothing may be trumpeted from the mountain top except our abjuration of all
+community of thought or operation with this _Novum Organum_.
+
+To such community we can make no more claim than Americus could make to
+being the forerunner of Columbus who popularized his discoveries. We do not
+wish for any [Greek: eurekasi] and not even for [Greek: heurekasi]. For
+self and Boole, I point out what would have convinced either of us that
+this house is divided against itself.
+
+[Alpha] being an apostolic element, [delta] the doctrinal element, and
+[Chi] the body of the faithful, the church is [Alpha] [delta] [Chi], we are
+told. Also, that if [Alpha] become negative, or the Apostolicity become
+Diabolicity [my words]; or if [delta] become negative, and doctrine become
+heresy; or if [Chi] become negative, that is, if the faithful become
+unfaithful; the church becomes negative, "the very opposite to what it
+ought to be." For self and Boole, I admit this. But--which is not
+noticed--if [Alpha] and [delta] should _both_ become negative, diabolical
+origin {77} and heretical doctrine, then the church, [Alpha] [delta] [Chi],
+is still positive, what it ought to be, unless [Chi] be also negative, or
+the people unfaithful to it, in which case it is a bad church. Now, self
+and Boole--though I admit I have not asked my partner--are of opinion that
+a diabolical church with false doctrine does harm when the people are
+faithful, and can do good only when the people are unfaithful. We may be
+wrong, but this is what we _do_ think. Accordingly, we have caught nothing,
+and can therefore roast nothing of our own: I content myself with roasting
+a joint of Mr. Gregg's larder.
+
+These mathematical vagaries have uses which will justify a large amount of
+quotation: and in a score of years this may perhaps be the only attainable
+record. I therefore proceed.
+
+After observing that by this calculus juries (heaven help them! say I) can
+calculate damages "almost to a nicety," and further that it is made
+abundantly evident that c e x is "the general expression for an
+individual," it is noted that the number of the Beast is not given in the
+Revelation in words at length, but as [Greek: chxw'].[163] On this the
+following remark is made:
+
+"Can it be possible that we have in this case a specimen given to us of the
+arithmetic of heaven, and an expression revealed, which indicates by its
+function of addibility, the name of the church in question, and of each
+member of it; and by its function of multiplicability the doctrine, the
+mission, and the members of the great Synagogue of Apostacy? We merely
+propound these questions;--we do not pretend to solve them."
+
+After a translation in blank verse--a very pretty one--of the 18th Psalm,
+the author proceeds as follows, to render it into differential calculus:
+
+{78}
+
+"And the whole tells us just this, that David did what he could. He
+augmented those elements of his constitution which were (_exceptis
+excipiendis_)[164] subject to himself, and the Almighty then augmented his
+personal qualities, and his vocational _status_. Otherwise, to throw the
+matter into the expression of our notation, the variable e was augmented,
+and c x rose proportionally. The law of the variation, according to our
+theory, would be thus expressed. The resultant was David the king c e x [c
+= r?] (who had been David the shepherd boy), and from the conditions of the
+theorem we have
+
+  du/de = ce(dx/de) + ex(dc/de)x + cx
+
+which, in the terms of ordinary language, just means, the increase of
+David's educational excellence or qualities--his piety, his prayerfulness,
+his humility, obedience, etc.--was so great, that when multiplied by his
+original talent and position, it produced a product so great as to be equal
+in its amount to royalty, honor, wealth, and power, etc.: in short, to all
+the attributes of majesty."[165]
+
+The "solution of the family problem" is of high interest. It is to
+determine the effect on the family in general from a change [of conduct] in
+one of them. The person chosen is one of the maid-servants.
+
+"Let c e x be the father; c_1e_1x_1 the mother, etc. The family then
+consists of the maid's master, her mistress, her young master, her young
+mistress, and fellow servant. Now the master's calling (or c) is to
+exercise his share of control over this servant, and mind the rest of his
+business: call this remainder a, and let his calling generally, or all his
+affairs, be to his maid-servant as m : y, i.e., y = (mz/c); ... {79} and
+this expression will represent his relation to the servant. Consequently,
+
+  c e x = (a + mz/c)e x; otherwise (a + mz/c)e x
+
+is the expression for the father when viewed as the girl's master."
+
+I have no objection to repeat so far; but I will not give the formula for
+the maid's relation to her young master; for I am not quite sure that all
+young masters are to be trusted with it. Suffice it that the son will be
+affected directly as his influence over her, and inversely as his
+vocational power: if then he should have some influence and no vocational
+power, the effect on him would be infinite. This is dismal to think of.
+Further, the formula brings out that if one servant improve, the other must
+deteriorate, and _vice versa_. This is not the experience of most families:
+and the author remarks as follows:
+
+"That is, we should venture to say, a very beautiful result, and we may say
+it yielded us no little astonishment. What our calculation might lead to we
+never dreamt of; that it should educe a conclusion so recondite that our
+unassisted power never could have attained to, and which, if we could have
+conjectured it, would have been at best the most distant probability, that
+conclusion being itself, as it would appear, the quintessence of truth,
+afforded us a measure of satisfaction that was not slight."
+
+That the writings of Mr. Boole and myself "go to the full justification of"
+this "principle," is only true in the sense in which the Scotch use, or did
+use, the word _justification_.
+
+
+
+A TRIBUTE TO BOOLE.
+
+[The last number of this Budget had stood in type for months, waiting until
+there should be a little cessation of correspondence more connected with
+the things of the day. {80} I had quite forgotten what it was to contain;
+and little thought, when I read the proof, that my allusions to my friend
+Mr. Boole, then in life and health, would not be printed till many weeks
+after his death. Had I remembered what my last number contained, I should
+have added my expression of regret and admiration to the numerous obituary
+testimonials, which this great loss to science has called forth.
+
+The system of logic alluded to in the last number of this series is but one
+of many proofs of genius and patience combined. I might legitimately have
+entered it among my _paradoxes_, or things counter to general opinion: but
+it is a paradox which, like that of Copernicus, excited admiration from its
+first appearance. That the symbolic processes of algebra, invented as tools
+of numerical calculation, should be competent to express every act of
+thought, and to furnish the grammar and dictionary of an all-containing
+system of logic, would not have been believed until it was proved. When
+Hobbes,[166] in the time of the Commonwealth, published his _Computation or
+Logique_, he had a remote glimpse of some of the points which are placed in
+the light of day by Mr. Boole. The unity of the forms of thought in all the
+applications of reason, however remotely separated, will one day be matter
+of notoriety and common wonder: and Boole's name will be remembered in
+connection with one of the most important steps towards the attainment of
+this knowledge.]
+
+
+
+DECIMALS RUN RIOT.
+
+    The Decimal System as a whole. By Dover Statter.[167] London and
+    Liverpool, 1856, 8vo.
+
+{81}
+
+The proposition is to make everything decimal. The day, now 24 hours, is to
+be made 10 hours. The year is to have ten months, Unusber, Duober, etc.
+Fortunately there are ten commandments, so there will be neither addition
+to, nor deduction from, the moral law. But the twelve apostles! Even
+rejecting Judas, there is a whole apostle of difficulty. These points the
+author does not touch.
+
+
+
+ON PHONETIC SPELLING.
+
+    The first book of Phonetic Reading. London, Fred. Pitman,[168] Phonetic
+    Depot, 20, Paternoster Row, 1856, 12mo.
+
+    The Phonetic Journal. Devoted to the propagation of phonetic reading,
+    phonetic longhand, phonetic shorthand, and phonetic printing. No. 46.
+    Saturday, 15 November 1856. Vol. 15.
+
+I write the titles of a couple out of several tracts which I have by me.
+But the number of publications issued by the promoters of this spirited
+attempt is very large indeed.[169] The attempt itself has had no success
+with the mass of the public. This I do not regret. Had the world found that
+the change was useful, I should have gone contentedly with the stream; but
+not without regretting our old language. I admit the difficulties which our
+unpronounceable spelling puts in the way of learning to read: and I have no
+doubt that, as affirmed, it is easier to teach children phonetically, and
+afterwards to introduce them to our common system, than to proceed in the
+usual way. But by the usual way I mean proceeding by letters from the very
+beginning. If, which I am sure is a better plan, children be taught at the
+commencement very much by _complete words_, as if they were learning
+Chinese, and be gradually accustomed to {82} resolve the known words into
+letters, a fraction, perhaps a considerable one, of the advantage of the
+phonetic system is destroyed. It must be remembered that a phonetic system
+can only be an approximation. The differences of pronunciation existing
+among educated persons are so great, that, on the phonetic system,
+different persons ought to spell differently.
+
+But the phonetic party have produced something which will immortalize their
+plan: I mean their _shorthand_, which has had a fraction of the success it
+deserves. All who know anything of shorthand must see that nothing but a
+phonetic system can be worthy of the name: and the system promulgated is
+skilfully done. Were I a young man I should apply myself to it
+systematically. I believe this is the only system in which books were ever
+published. I wish some one would contribute to a public journal a brief
+account of the dates and circumstances of the phonetic movement, not
+forgetting a list of the books published in shorthand.
+
+A child beginning to read by himself may owe terrible dreams and waking
+images of horror to our spelling, as I did when six years old. In one of
+the common poetry-books there is an admonition against confining little
+birds in cages, and the child is asked what if a great giant, amazingly
+strong, were to take you away, shut you up,
+
+  And feed you with vic-tu-als you ne-ver could bear.
+
+The book was hyphened for the beginner's use; and I had not the least idea
+that _vic-tu-als_ were _vittles_: by the sound of the word I judged they
+must be of iron; and it entered into my soul.
+
+The worst of the phonetic shorthand book is that they nowhere, so far as I
+have seen, give _all_ the symbols, in every stage of advancement, together,
+in one or following pages. It is symbols and talk, more symbols and more
+talk, etc. A universal view of the signs ought to begin the works. {83}
+
+
+
+A HANDFUL OF LITTLE PARADOXERS.
+
+    Ombrological Almanac. Seventeenth year. An essay on Anemology and
+    Ombrology. By Peter Legh,[170] Esq. London, 1856, 12mo.
+
+Mr. Legh, already mentioned, was an intelligent country gentleman, and a
+legitimate speculator. But the clue was not reserved for him.
+
+    The proof that the three angles of a triangle are equal to two right
+    angles looked for in the inflation of the circle. By Gen. Perronet
+    Thompson. London, 1856, 8vo. (pp. 4.)
+
+Another attempt, the third, at this old difficulty, which cannot be put
+into few words of explanation.[171]
+
+    Comets considered as volcanoes, and the cause of their velocity and
+    other phenomena thereby explained. London (_circa_ 1856), 8vo.
+
+The title explains the book better than the book explains the title.
+
+
+
+1856. A stranger applied to me to know what the ideas of a friend of his
+were worth upon the magnitude of the earth. The matter being one involving
+points of antiquity, I mentioned various persons whose speculations he
+seemed to have ignored; among others, Thales. The reply was, "I am
+instructed by the author to inform you that he is perfectly acquainted with
+the works of Thales, Euclid, Archimedes, ..." I had some thought of asking
+whether he had used the Elzevir edition of Thales,[172] which is known to
+be very incomplete, or that of Professor Niemand with the lections,
+Nirgend, 1824, 2 vols. folio; just to see whether the {84} last would not
+have been the very edition he had read. But I refrained, in mercy.
+
+
+
+    The moon is the image of the Earth, and is not a solid body. By T^{he}
+    Longitude.[173] (Private Circulation.) In five parts. London, 1856,
+    1857, 1857; Calcutta, 1858, 1858, 8vo.
+
+The earth is "brought to a focus"; it describes a "looped orbit round the
+sun." The eclipse of the sun is thus explained: "At the time of eclipses,
+the image is more or less so directly before or behind the earth that, in
+the case of new moon, bright rays of the sun fall and bear upon the spot
+where the figure of the earth is brought to a focus, that is, bear upon the
+image of the earth, when a darkness beyond is produced reaching to the
+earth, and the sun becomes more or less eclipsed." How the earth is
+"brought to a focus" we do not find stated. Writers of this kind always
+have the argument that some things which have been ridiculed at first have
+been finally established. Those who put into the lottery had the same kind
+of argument; but were always answered by being reminded how many blanks
+there were to one prize. I am loath to pronounce against anything: but it
+does force itself upon me that the author of these tracts has drawn a
+blank.
+
+
+
+LUNAR MOTION AGAIN.
+
+    _Times_, April 6 or 7, 1856. The moon has no rotary motion.
+
+A letter from Mr. Jellinger Symons,[174] inspector of schools, which
+commenced a controversy of many letters and pamphlets. This dispute comes
+on at intervals, and will continue to do so. It sometimes arises from
+inability to understand the character of simple rotation, geometrically;
+sometimes from not understanding the mechanical doctrine of rotation.
+
+{85}
+
+
+
+    Lunar Motion. The whole argument stated, and illustrated by diagrams;
+    with letters from the Astronomer Royal. By Jellinger C. Symons. London,
+    1856, 8vo.
+
+The Astronomer Royal endeavored to disentangle Mr. J. C. Symons, but
+failed. Mr. Airy[175] can correct the error of a ship's compasses, because
+he can put her head which way he pleases: but this he cannot do with a
+speculator.
+
+Mr. Symons, in this tract, insinuated that the rotation of the moon is one
+of the silver shrines of the craftsmen. To see a thing so clearly as to be
+satisfied that all who say they do not see it are telling wilful falsehood,
+is the nature of man. Many of all sects find much comfort in it, when they
+think of the others; many unbelievers solace themselves with it against
+believers; priests of old time founded the right of persecution upon it,
+and of our time, in some cases, the right of slander: many of the
+paradoxers make it an argument against students of science. But I must say
+for men of science, for the whole body, that they are fully persuaded of
+the honesty of the paradoxers. The simple truth is, that all those I have
+mentioned, believers, unbelievers, priests, paradoxers, are not so sure
+they are right in their points of difference that they can safely allow
+themselves to be persuaded of the honesty of opponents. Those who know
+demonstration are differently situated. I suspect a train might be laid for
+the formation of a better habit in this way. We know that Suvaroff[176]
+taught his Russians at Ismail not to fear the Turks by accustoming them to
+charge bundles of faggots dressed in turbans, etc.
+
+  At which your wise men sneered in phrases witty,
+  He made no answer--but he took the city!
+
+Would it not be a good thing to exercise boys, in pairs, in the following
+dialogue:--Sir, you are quite wrong!--Sir, {86} I am sure you honestly
+think so! This was suggested by what used to take place at Cambridge in my
+day. By statute, every B.A. was obliged to perform a certain number of
+disputations, and the _father_ of the college had to affirm that it had
+been done. Some were performed in earnest: the rest were huddled over as
+follows. Two candidates occupied the places of the respondent and the
+opponent: _Recte statuit Newtonus_, said the respondent: _Recte non statuit
+Newtonus_,[177] said the opponent. This was repeated the requisite number
+of times, and counted for as many _acts_ and _opponencies_. The parties
+then changed places, and each unsaid what he had said on the other side of
+the house: I remember thinking that it was capital drill for the House of
+Commons, if any of us should ever get there. The process was repeated with
+every pair of candidates.
+
+The real disputations were very severe exercises. I was badgered for two
+hours with arguments given and answered in Latin,--or what we called
+Latin--against Newton's first section, Lagrange's[178] derived functions,
+and Locke[179] on innate principles. And though I _took off_ everything,
+and was pronounced by the moderator to have disputed _magno honore_,[180] I
+never had such a strain of thought in my life. For the inferior opponents
+were made as sharp as their betters by their tutors, who kept lists of
+queer objections, drawn from all quarters. The opponents used to meet the
+day before to compare their arguments, that the same might not come twice
+over. But, after I left Cambridge, it became the fashion to invite the
+respondent to be present, who therefore learnt all that was to be brought
+against him. This made the whole thing a farce: and the disputations were
+abolished.
+
+{87}
+
+
+
+    The Doctrine of the Moon's Rotation, considered in a letter to the
+    Astronomical Censor of the _Athenaeum_. By Jones L. MacElshender.[181]
+    Edinburgh, 1856, 8vo.
+
+This is an appeal to those cultivated persons who will read it "to overrule
+the _dicta_ of judges who would sacrifice truth and justice to professional
+rule, or personal pique, pride, or prejudice"; meaning, the great mass of
+those who have studied the subject. But how? Suppose the "cultivated
+persons" were to side with the author, would those who have conclusions to
+draw and applications to make consent to be wrong because the "general body
+of intelligent men," who make no special study of the subject, are against
+them? They would do no such thing: they would request the general body of
+intelligent men to find their own astronomy, and welcome. But the truth is,
+that this intelligent body knows better: and no persons know better that
+they know better than the speculators themselves.
+
+But suppose the general body were to combine, in opposition to those who
+have studied. Of course all my list must be admitted to their trial; and
+then arises the question whether both sides are to be heard. If so, the
+general body of the intelligent must hear all the established side have to
+say: that is, they must become just as much of students as the inculpated
+orthodox themselves. And will they not then get into _professional rule_,
+pique, pride, and prejudice, as the others did? But if, which I suspect,
+they are intended to judge as they are, they will be in a rare difficulty.
+All the paradoxers are of like pretensions: they cannot, as a class, be
+right, for each one contradicts a great many of the rest. There will be the
+puzzle which silenced the crew of the cutter in Marryat's novel of the Dog
+Fiend.[182] "A tog is a tog," said Jansen.--"Yes," replied another, "we all
+know a dog is a dog; but the question is--Is _this_ dog {88} a dog?" And
+this question would arise upon every dog of them all.
+
+
+
+ZETETIC ASTRONOMY.
+
+    Zetetic Astronomy: Earth not a globe. 1857 (Broadsheet).
+
+Though only a traveling lecturer's advertisement, there are so many
+arguments and quotations that it is a little pamphlet. The lecturer gained
+great praise from provincial newspapers for his ingenuity in proving that
+the earth is a flat, surrounded by ice. Some of the journals rather incline
+to the view: but the _Leicester Advertiser_ thinks that the statements
+"would seem very seriously to invalidate some of the most important
+conclusions of modern astronomy," while the _Norfolk Herald_ is clear that
+"there must be a great error on one side or the other." This broadsheet is
+printed at Aylesbury in 1857, and the lecturer calls himself _Parallax_:
+but at Trowbridge, in 1849, he was S. Goulden.[183] In this last
+advertisement is the following announcement: "A paper on the above subjects
+was read before the Council and Members of the Royal Astronomical Society,
+Somerset House, Strand, London (Sir John F. W. Herschel,[184] President),
+Friday, Dec. 8, 1848." No account of such a paper appears in the _Notice_
+for that month: I suspect that the above is Mr. S. Goulden's way of
+representing the following occurrence: Dec. 8, 1848, the Secretary of the
+Astronomical Society (De Morgan by name) said, at the close of the
+proceedings,--"Now, gentlemen, if you will promise not to tell the Council,
+I will read something for your amusement": and he then read a few of the
+arguments which had been transmitted by the lecturer. The fact is worth
+noting that from 1849 to 1857, arguments on the roundness or flatness of
+the earth did itinerate. I have {89} no doubt they did much good: for very
+few persons have any distinct idea of the evidence for the rotundity of the
+earth. The _Blackburn Standard_ and _Preston Guardian_ (Dec. 12 and 16,
+1849) unite in stating that the lecturer ran away from his second lecture
+at Burnley, having been rather too hard pressed at the end of his first
+lecture to explain why the large hull of a ship disappeared before the
+sails. The persons present and waiting for the second lecture assuaged
+their disappointment by concluding that the lecturer had slipped off the
+icy edge of his flat disk, and that he would not be seen again till he
+peeped up on the opposite side.
+
+But, strange as it may appear, the opposer of the earth's roundness has
+more of a case--or less of a want of case--than the arithmetical squarer of
+the circle. The evidence that the earth is round is but cumulative and
+circumstantial: scores of phenomena ask, separately and independently, what
+other explanation can be imagined except the sphericity of the earth. The
+evidence for the earth's figure is tremendously powerful of its kind; but
+the proof that the circumference is 3.14159265... times the diameter is of
+a higher kind, being absolute mathematical demonstration.
+
+The Zetetic system still lives in lectures and books; as it ought to do,
+for there is no way of teaching a truth comparable to opposition. The last
+I heard of it was in lectures at Plymouth, in October, 1864. Since this
+time a prospectus has been issued of a work entitled "The Earth not a
+Globe"; but whether it has been published I do not know. The contents are
+as follows:
+
+
+
+"The Earth a Plane--How circumnavigated.--How time is lost or gained.--Why
+a ship's hull disappears (when outward bound) before the mast head.--Why
+the Polar Star sets when we proceed Southward, etc.--Why a pendulum
+vibrates with less velocity at the Equator than {90} at the Pole.--The
+allowance for rotundity _supposed_ to be made by surveyors, not made in
+practice.--Measurement of Arcs of the Meridian unsatisfactory.--Degrees of
+Longitude North and South of the Equator considered.--Eclipses and Earth's
+form considered.--The Earth no motion on axis or in orbit.--How the Sun
+moves above the Earth's surface concentric with the North Pole.--Cause of
+Day and Night, Winter and Summer; the long alternation of light and
+darkness at the Pole.--Cause of the Sun rising and setting.--Distance of
+the Sun from London, 4,028 miles--How measured.--_Challenge to
+Mathematicians._--Cause of Tides.--Moon self-luminous, NOT a
+reflector.--Cause of Solar and Lunar eclipses.--Stars _not worlds_; their
+distance.--Earth, the _only material_ world; its true position in the
+universe; its condition and ultimate destruction by fire (2 Peter iii.),
+etc."
+
+I wish there were geoplatylogical lectures in every town; in England
+(_platylogical_, in composition, need not mean _babbling_). The late Mr.
+Henry Archer[185] would, if alive, be very much obliged to me for recording
+his vehement denial of the roundness of the earth: he was excited if he
+heard any one call it a globe. I cannot produce his proof from the
+Pyramids, and from some caves in Arabia. He had other curious notions, of
+course: I should no more believe that a flat earth was a man's only
+paradox, than I should that Dutens,[186] the editor of Leibnitz, was
+eccentric only in supplying a tooth which he had lost by one which he found
+in an Italian tomb, and fully believed that it had once belonged to Scipio
+Africanus, whose family vault was discovered, it is supposed, in 1780. Mr.
+Archer is of note as {91} the suggester of the perforated border of the
+postage-stamps, and, I think, of the way of doing it; for this he got
+4000l. reward. He was a civil engineer.
+
+(_August 28, 1865._) The _Zetetic Astronomy_ has come into my hands. When,
+in 1851, I went to see the Great Exhibition, I heard an organ played by a
+performer who seemed very desirous to exhibit one particular stop. "What do
+you think of that stop?" I was asked.--"That depends on the name of it,"
+said I.--"Oh! what can the name have to do with the sound? 'that which we
+call a rose,' etc."--"The name has everything to do with it: if it be a
+flute-stop, I think it very harsh; but if it be a railway-whistle-stop, I
+think it very sweet." So as to this book: if it be childish, it is clever;
+if it be mannish, it is unusually foolish. The flat earth, floating
+tremulously on the sea; the sun moving always over the flat, giving day
+when near enough, and night when too far off; the self-luminous moon, with
+a semi-transparent invisible moon, created to give her an eclipse now and
+then; the new law of perspective, by which the vanishing of the hull before
+the masts, usually thought to prove the earth globular, really proves it
+flat;--all these and other things are well fitted to form exercises for a
+person who is learning the elements of astronomy. The manner in which the
+sun dips into the sea, especially in tropical climates, upsets the whole.
+Mungo Park,[187] I think, gives an African hypothesis which explains
+phenomena better than this. The sun dips into the western ocean, and the
+people there cut him in pieces, fry him in a pan, and then join him
+together again, take him round the underway, and set him up in the east. I
+hope this book will be read, and that many will be puzzled by it: for there
+are many whose notions of astronomy deserve no better fate. There is no
+subject on which there is so little {92} accurate conception as that of the
+motions of the heavenly bodies. The author, though confident in the
+extreme, neither impeaches the honesty of those whose opinions he assails,
+nor allots them any future inconvenience: in these points he is worthy to
+live on a globe, and to revolve in twenty-four hours.
+
+
+
+(_October, 1866._) A follower appears, in a work dedicated to the preceding
+author: it is _Theoretical Astronomy examined and exposed by Common Sense_.
+The author has 128 well-stuffed octavo pages. I hope he will not be the
+last. He prints the newspaper accounts of his work: the _Church Times_
+says--not seeing how the satire might be retorted--"We never began to
+despair of Scripture until we discovered that 'Common Sense' had taken up
+the cudgels in its defence." This paper considers our author as the type of
+a _Protestant_. The author himself, who gives a summary of his arguments in
+verse, has one couplet which is worth quoting:
+
+ "How is't that sailors, bound to sea, with _a 'globe'_ would never start,
+  But in its place will always take _Mercator's_[188] LEVEL _chart_!"
+
+To which I answer:
+
+  Why, really Mr. Common Sense, you've never got so far
+  As to think Mercator's planisphere shows countries as they are;
+  It won't do to measure distances; it points out how to steer,
+  But this distortion's not for you; another is, I fear.
+  The earth must be a cylinder, if seaman's charts be true,
+  Or else the boundaries, right and left, are one as well as two;
+  They contradict the notion that we dwell upon a plain,
+  For straight away, without a turn, will bring you home again.
+  There are various plane projections; and each one has its use:
+  I wish a milder word would rhyme--but really you're a goose!
+
+The great wish of persons who expose themselves as above, is to be argued
+with, and to be treated as reputable {93} and refutable opponents. "Common
+Sense" reminds us that no amount of "blatant ridicule" will turn right into
+wrong. He is perfectly correct: but then no amount of bad argument will
+turn wrong into right. These two things balance; and we are just where we
+were: but you should answer our arguments, for whom, I ask? Would reason
+convince this kind of reasoner? The issue is a short and a clear one. If
+these parties be what I contend they are, then ridicule is made for them:
+if not, for what or for whom? If they be right, they are only passing
+through the appointed trial of all good things. Appeal is made to the
+future: and my Budget is intended to show samples of the long line of
+heroes who have fallen without victory, each of whom had his day of
+confidence and his prophecy of success. Let the future decide: they say
+roundly that the earth is flat; I say flatly that it is round.
+
+The paradoxers all want reason, and not ridicule: they are all accessible,
+and would yield to conviction. Well then, let them reason with one another!
+They divide into squads, each with a subject, and as many different
+opinions as persons in each squad. If they be really what they say they
+are, the true man of each set can put down all the rest, and can come
+crowned with glory and girdled with scalps, to the attack on the orthodox
+misbelievers. But they know, to a man, that the rest are not fit to be
+reasoned with: they pay the regulars the compliment of believing that the
+only chance lies with them. They think in their hearts, each one for
+himself, that ridicule is of fit appliance to the rest.
+
+
+
+    Miranda. A book divided into three parts, entitled Souls, Numbers,
+    Stars, on the Neo-Christian Religion ... Vol. i. London, 1858, 1859,
+    1860. 8vo.
+
+The name of the author is Filopanti.[189] He announces himself as the 49th
+and last Emanuel: his immediate {94} predecessors were Emanuel Washington,
+Emanuel Newton, and Emanuel Galileo. He is to collect nations into one
+family. He knows the transmigrations of the whole human race. Thus
+Descartes became William III of England: Roger Bacon became Boccaccio. But
+Charles IX,[190] in retribution for the massacre of St. Bartholomew, was
+hanged in London under the name of Barthelemy for the murder of Collard:
+and many of the Protestants whom he killed as King of France were shouting
+at his death before the Old Bailey.
+
+
+
+THE SABBATH--THE GREAT PYRAMID
+
+    A Letter to the members of the Anglo-Biblical Institute, dated Sept. 7,
+    1858, and signed 'Herman Heinfetter.'[191] (Broadsheet.)
+
+This gentleman is well known to the readers of the _Athenaeum_, in which,
+for nearly twenty years, he has inserted, as advertisements, long arguments
+in favor of Christians keeping the Jewish Sabbath, beginning on Friday
+Evening. The present letter maintains that, by the force of the definite
+article, the _days_ of creation may not be consecutive, but may have any
+time--millions of years--between them. This ingenious way of reconciling
+the author of Genesis and the indications of geology is worthy to be added
+to the list, already pretty numerous. Mr. Heinfetter has taken such pains
+to make himself a public agitator, that {95} I do not feel it to be any
+invasion of private life if I state that I have heard he is a large
+corn-dealer. No doubt he is a member of the congregation whose almanac has
+already been described.
+
+
+
+    The great Pyramid. Why was it built? And who built it? By John Taylor,
+    1859,[192] 12mo.
+
+This work is very learned, and may be referred to for the history of
+previous speculations. It professes to connect the dimensions of the
+Pyramid with a system of metrology which is supposed to have left strong
+traces in the systems of modern times; showing the Egyptians to have had
+good approximate knowledge of the dimensions of the earth, and of the
+quadrature of the circle. These are points on which coincidence is hard to
+distinguish from intention. Sir John Herschel[193] noticed this work, and
+gave several coincidences, in the _Athenaeum_, Nos. 1696 and 1697, April 28
+and May 5, 1860: and there are some remarks by Mr. Taylor in No. 1701, June
+2, 1860.
+
+Mr. Taylor's most recent publication is--
+
+    The battle of the Standards: the ancient, of four thousand years,
+    against the modern, of the last fifty years--the less perfect of the
+    two. London, 1864, 12mo.
+
+This is intended as an appendix to the work on the Pyramid. Mr. Taylor
+distinctly attributes the original system to revelation, of which he says
+the Great Pyramid is the record. We are advancing, he remarks, towards the
+end of the Christian dispensation, and he adds that it is satisfactory to
+see that we retain the standards which were given by unwritten revelation
+700 years before Moses. This is lighting the candle at both ends; for
+myself, I shall not undertake to deny or affirm either what is said about
+the dark past or what is hinted about the dark future.
+
+{96}
+
+My old friend Mr. Taylor is well known as the author of the argument which
+has convinced many, even most, that Sir Philip Francis[194] was Junius:
+pamphlet, 1813; supplement, 1817; second edition "The Identity of Junius
+with a distinguished living character established," London, 1818, 8vo. He
+told me that Sir Philip Francis, in a short conversation with him, made
+only this remark, "You may depend upon it you are quite mistaken:" the
+phrase appears to me remarkable; it has an air of criticism on the book,
+free from all personal denial. He also mentioned that a hearer told him
+that Sir Philip said, speaking of writers on the question,--"Those fellows,
+for half-a-crown, would prove that Jesus Christ was Junius."
+
+Mr. Taylor implies, I think, that he is the first who started the
+suggestion that Sir Philip Francis was Junius, which I have no means either
+of confirming or refuting. If it be so [and I now know that Mr. Taylor
+himself never heard of any predecessor], the circumstance is very
+remarkable: it is seldom indeed that the first proposer of any solution of
+a great and vexed question is the person who so nearly establishes his
+point in general opinion as Mr. Taylor has done.
+
+As to the Junius question in general, there is a little bit of the
+philosophy of horse-racing which may be usefully applied. A man who is so
+confident of his horse that he places him far above any other, may
+nevertheless, and does, refuse to give odds against all in the field: for
+many small adverse chances united make a big chance for one or other of the
+opponents. I suspect Mr. Taylor has made it at least 20 to 1 for Francis
+against any one competitor who has been named: but what the odds may be
+against the {97} whole field is more difficult to settle. What if the real
+Junius should be some person not yet named?
+
+Mr. Jopling, _Leisure Hour_, May 23, 1863, relies on the porphyry coffer of
+the Great Pyramid, in which he finds "the most ancient and accurate
+standard of measure in existence."
+
+I am shocked at being obliged to place a thoughtful and learned writer, and
+an old friend, before such a successor as he here meets with. But
+chronological arrangement defies all other arrangement.
+
+(I had hoped that the preceding account would have met Mr. Taylor's eye in
+print: but he died during the last summer. For a man of a very thoughtful
+and quiet temperament, he had a curious turn for vexed questions. But he
+reflected very long and very patiently before he published: and all his
+works are valuable for their accurate learning, whichever side the reader
+may take.)
+
+
+
+MRS. ELIZABETH COTTLE.
+
+1859. _The Cottle Church._--For more than twenty years printed papers have
+been sent about in the name of Elizabeth Cottle.[195] It is not so
+remarkable that such papers should be concocted as that they should
+circulate for such a length of time without attracting public attention.
+Eighty years ago Mrs. Cottle might have rivalled Lieut. Brothers or Joanna
+Southcott.[196] Long hence, when the now current volumes of our journals
+are well-ransacked works of reference, those who look into them will be
+glad to see this {98} feature of our time: I therefore make a few extracts,
+faithfully copied as to type. The Italic is from the New Testament; the
+Roman is the requisite interpretation:
+
+"Robert Cottle '_was numbered_ (5196) _with the transgressors_' at the back
+of the Church in Norwood Cemetery, May 12, 1858--Isa. liii. 12. The Rev.
+J. G. Collinson, Minister of St. James's Church, Chapham, the then district
+church, before All Saints was built, read the funeral service _over the
+Sepulchre wherein never before man was laid_.
+
+"_Hewn on the stone_, 'at the mouth of the Sepulchre,' is his name,--Robert
+Cottle, born at Bristol, June 2, 1774; died at Kirkstall Lodge, Clapham
+Park, May 6, 1858. _And that day_ (May 12, 1858) _was the preparation_ (day
+and year for 'the PREPARED place for you'--Cottleites---by the widowed
+mother of the Father's house, at Kirkstall Lodge--John xiv. 2, 3). _And the
+Sabbath_ (Christmas Day, Dec. 25, 1859) _drew on_ (for the resurrection of
+the Christian body on 'the third [Protestant Sun]-day'--1 Cor. xv. 35).
+_Why seek ye the living_ (God of the New Jerusalem--Heb. xii. 22; Rev. iii.
+12) _among the dead_ (men): _he_ (the God of Jesus) _is not here_ (in the
+grave), _but is risen_ (in the person of the Holy Ghost, from the supper of
+'the dead in the second death' of Paganism). _Remember how he spake unto
+you_ (in the church of the Rev. George Clayton,[197] April 14, 1839). _I
+will not drink henceforth_ (at this last Cottle supper) _of the fruit of
+this_ (Trinity) _vine, until that day_ (Christmas Day, 1859), _when I_
+(Elizabeth Cottle) _drink it new with you_ (Cottleites) _in my Father's
+kingdom_--John xv. _If this_ (Trinitarian) _cup may not pass away from me_
+(Elizabeth Cottle, April 14, 1839), _except I drink it_ ('new with you
+Cottleites, in my Father's Kingdom'), _thy will be done_--Matt. xxvi. 29,
+42, 64. 'Our Father which art (God) in Heaven,' _hallowed be thy name, thy_
+(Cottle) _kingdom_ {99} _come, thy will be done in earth, as it is_ (done)
+_in_ (the new) _Heaven_ (and new earth of the new name of Cottle--Rev. xxi.
+1; iii. 12).
+
+"... Queen Elizabeth, from A.D. 1558 to 1566. _And this_ WORD _yet once
+more_ (by a second Elizabeth--the WORD of his oath) _signifieth_ (at John
+Scott's baptism of the Holy Ghost) _the removing of those things_ (those
+Gods and those doctrines) _that are made_ (according to the Creeds and
+Commandments of men) _that those things_ (in the moral law of God) _which
+cannot be shaken_ (as a rule of faith and practice) _may remain, wherefore
+we receiving_ (from Elizabeth) _a kingdom_ (of God,) _which cannot be
+moved_ (by Satan) _let us have grace_ (in his Grace of Canterbury) _whereby
+we may serve God acceptably_ (with the acceptable sacrifice of Elizabeth's
+body and blood of the communion of the Holy Ghost) _with reverence_ (for
+truth) _and godly fear_ (of the unpardonable sin of blasphemy against the
+Holy Ghost) _for our God_ (the Holy Ghost) _is a consuming fire_ (to the
+nation that will not serve him in the Cottle Church). We cannot defend
+ourselves against the Almighty, and if He is our defence, no nation can
+invade us.
+
+"In verse 4 the Church of St. Peter is _in prison between four quaternions
+of soldiers_--the Holy Alliance of 1815. Rev. vii. i. Elizabeth, _the Angel
+of the Lord_ Jesus _appears_ to the Jewish and Christian body with _the
+vision_ of prophecy to the Rev. Geo. Clayton and his clerical brethren,
+April 8th, 1839. _Rhoda_ was the name of her maid at Putney Terrace who
+used _to open the door to her Peter_, the Rev. Robert Ashton,[198] the
+Pastor of 'the little flock' 'of 120 names together, assembled in an upper
+(school) room' at Putney Chapel, to which little flock she gave the
+revelation (Acts. i. 13, 15) _of Jesus the same_ King of the Jews
+_yesterday_ at the prayer meeting, Dec. 31, 1841, _and to-day_, {100} Jan.
+1, 1842, _and for ever_. See book of Life, page 24. Matt. xviii. 19, xxi.
+13-16. In verse 6 the Italian body of St. Peter _is sleeping_ 'in the
+second death' _between the two_ Imperial _soldiers_ of France and Austria.
+The Emperor of France from Jan. 1, to July 11, 1859, causes the Italian
+_chains of St. Peter to fall off from his_ Imperial _hands_.
+
+"_I say unto thee_, Robert Ashton, _thou art Peter_, a stone, _and upon
+this rock_, of truth, _will I_ Elizabeth, the angel of Jesus, _build my_
+Cottle _Church, and the gates of hell_, the doors of St. Peter, at Rome,
+shall not prevail against it--Matt. xvi. 18. Rev. iii. 7-12."
+
+This will be enough for the purpose. When any one who pleases can circulate
+new revelations of this kind, uninterrupted and unattended to, new
+revelations will cease to be a good investment of excentricity. I take it
+for granted that the gentlemen whose names are mentioned have nothing to do
+with the circulars or their doctrines. Any lady who may happen to be
+intrusted with a revelation may nominate her own pastor, or any other
+clergyman, one of her apostles; and it is difficult to say to what court
+the nominees can appeal to get the commission abrogated.
+
+_March 16, 1865._ During the last two years the circulars have continued.
+It is hinted that funds are low: and two gentlemen who are represented as
+gone "to Bethlehem asylum in despair" say that Mrs. Cottle "will spend all
+that she hath, while Her Majesty's Ministers are flourishing on the wages
+of sin." The following is perhaps one of the most remarkable passages in
+the whole:
+
+"_Extol and magnify Him_ (Jehovah, the Everlasting God, see the Magnificat
+and Luke i. 45, 46--68--73--79), _that rideth_ (by rail and steam over land
+and sea, from his holy habitation at Kirkstall Lodge, Psa. lxxvii. 19, 20),
+_upon the_ (Cottle) _heavens, as it were_ (Sept. 9, 1864, see pages 21,
+170), _upon an_ (exercising, Psa. cxxxi. 1), _horse_-(chair, bought of Mr.
+John Ward, Leicester-square)." {101}
+
+I have pretty good evidence that there is a clergyman who thinks Mrs.
+Cottle a very sensible woman.
+
+[_The Cottle Church._ Had I chanced to light upon it at the time of
+writing, I should certainly have given the following. A printed letter to
+the _Western Times_, by Mr. Robert Cottle, was accompanied by a manuscript
+letter from Mrs. Cottle, apparently a circular. The date was Nov^{r}. 1853,
+and the subject was the procedure against Mr. Maurice[199] at King's
+College for doubting that God would punish human sins by an existence of
+torture lasting through years numbered by millions of millions of millions
+of millions (repeat the word _millions_ without end,) etc. The memory of
+Mr. Cottle has, I think, a right to the quotation: he seems to have been no
+participator in the notions of his wife:
+
+"The clergy of the Established Church, taken at the round number of 20,000,
+may, in their first estate, be likened to 20,000 gold blanks, destined to
+become sovereigns, in succession,--they are placed between the matrix of
+the Mint, when, by the pressure of the screw, they receive the impress that
+fits them to become part of the current coin of the realm. In a way
+somewhat analogous this great body of the clergy have each passed through
+the crucibles of Oxford and Cambridge,--have been assayed by the Bishop's
+chaplain, touching the health of their souls, and the validity of their
+call by the Divine Spirit, and then the gentle pressure of a prelate's hand
+upon their heads; and the words--'Receive the Holy Ghost,' have, in a brief
+space of time, wrought a {102} change in them, much akin to the miracle of
+transubstantiation--the priests are completed, and they become the current
+ecclesiastical coin of our country. The whole body of clergy, here spoken
+of, have undergone the preliminary induction of baptism and confirmation;
+and all have been duly ordained, _professing_ to hold one faith, and to
+believe in the selfsame doctrines! In short, to be as identical as the
+20,000 sovereigns, if compared one with the other. But mind is not
+malleable and ductile, like gold; and all the preparations of tests,
+creeds, and catechisms will not insure uniformity of belief. No stamp of
+orthodoxy will produce the same impress on the minds of different men.
+Variety is manifest, and patent, upon everything mental and material. The
+Almighty has not created, nor man fashioned, two things alike! How futile,
+then, is the attempt to shape and mould man's apprehension of divine truth
+by one fallible standard of man's invention! If proof of this be required,
+an appeal might be made to history and the experience of eighteen hundred
+years."
+
+This is an argument of force against the reasonableness of expecting tens
+of thousands of educated readers of the New Testament to find the doctrine
+above described in it. The lady's argument against the doctrine itself is
+very striking. Speaking of an outcry on this matter among the Dissenters
+against one of their body, who was the son of "the White Stone (Rev. ii.
+17), or the Roman cement-maker," she says--
+
+"If the doctrine for which they so wickedly fight were true, what would
+become of the black gentlemen for whose redemption I have been sacrificed
+from April 8 1839."
+
+There are certainly very curious points about this revelation. There have
+been many surmises about the final restoration of the infernal spirits,
+from the earliest ages of Christianity until our own day: a collection of
+them would be worth making. On reading this in proof, I see a possibility
+that by "black gentlemen" may be meant the clergy: {103} I suppose my first
+interpretation must have been suggested by context: I leave the point to
+the reader's sagacity.]
+
+
+
+JAMES SMITH, ARCH-PARADOXER.
+
+    The Problem of squaring the circle solved; or, the circumference and
+    area of the circle discovered. By James Smith.[200] London, 1859, 8vo.
+
+    On the relations of a square inscribed in a circle. Read at the British
+    Association, Sept. 1859, published in the Liverpool Courier, Oct. 8,
+    1859, and reprinted in broadsheet.
+
+    The question: Are there any commensurable relations between a circle
+    and other Geometrical figures? Answered by a member of the British
+    Association ... London, 1860, 8vo.--[This has been translated into
+    French by M. Armand Grange, Bordeaux, 1863, 8vo.]
+
+    The Quadrature of the Circle. Correspondence between an eminent
+    mathematician and James Smith, Esq. (Member of the Mersey Docks and
+    Harbour Board), London, 1861, 8vo. (pp. 200).
+
+    Letter to the ... British Association ... by James Smith, Esq.
+    Liverpool, 1861, 8vo.
+
+    Letter to the ... British Association ... by James Smith, Esq.
+    Liverpool, 1862, 8vo.--[These letters the author promised to continue.]
+
+    A Nut to crack for the readers of Professor De Morgan's 'Budget of
+    Paradoxes.' By James Smith, Esq. Liverpool, 1863, 8vo.
+
+    Paper read at the Liverpool Literary and Philosophical Society,
+    reported in the Liverpool Daily Courier, Jan. 26, 1864. Reprinted as a
+    pamphlet.
+
+    The Quadrature of the circle, or the true ratio between the diameter
+    and circumference geometrically and mathematically demonstrated. By
+    James Smith, Esq. Liverpool, 1865, 8vo.
+
+    {104}
+
+    [On the relations between the dimensions and distances of the Sun,
+    Moon, and Earth; a paper read before the Literary and Philosophical
+    Society of Liverpool, Jan. 25, 1864. By James Smith, Esq.
+
+    The British Association in Jeopardy, and Dr. Whewell, the Master of
+    Trinity, in the stocks without hope of escape. Printed for the authors
+    (J. S. confessed, and also hidden under _Nauticus_). (No date, 1865).
+
+    The British Association in Jeopardy, and Professor De Morgan in the
+    Pillory without hope of escape. London, 1866, 8vo.]
+
+When my work appeared in numbers, I had not anything like an adequate idea
+of Mr. James Smith's superiority to the rest of the world in the points in
+which he is superior. He is beyond a doubt the ablest head at unreasoning,
+and the greatest hand at writing it, of all who have tried in our day to
+attach their names to an error. Common cyclometers sink into puny orthodoxy
+by his side.
+
+The behavior of this singular character induces me to pay him the
+compliment which Achilles paid Hector, to drag him round the walls again
+and again. He was treated with unusual notice and in the most gentle
+manner. The unnamed mathematician, E. M. bestowed a volume of mild
+correspondence upon him; Rowan Hamilton[201] quietly proved him wrong in a
+way accessible to an ordinary schoolboy; Whewell,[202] as we shall see,
+gave him the means of seeing himself wrong, even more easily than by
+Hamilton's method. Nothing would do; it was small kick and silly fling at
+all; and he exposed his conceit by alleging that he, James Smith, had
+placed Whewell in the stocks. He will therefore be universally pronounced a
+proper object of the severest literary punishment: but the opinion of all
+who can put two propositions together will be that of the many strokes I
+have given, the hardest and most telling are my republications of his own
+attempts to reason.
+
+He will come out of my hands in the position he ought {105} to hold, the
+Supreme Pontiff of cyclometers, the vicegerent of St. Vitus upon earth, the
+Mamamouchi of burlesque on inference. I begin with a review of him which
+appeared in the _Athenaeum_ of May 11, 1861. Mr. Smith says I wrote it: this
+I neither affirm nor deny; to do either would be a sin against the
+editorial system elsewhere described. Many persons tell me they know me by
+my style; let them form a guess: I can only say that many have declared as
+above while fastening on me something which I had never seen nor heard of.
+
+
+
+    The Quadrature of the Circle: Correspondence between an Eminent
+    Mathematician and James Smith, Esq. (Edinburgh, Oliver & Boyd; London,
+    Simpkin, Marshall & Co.)
+
+"A few weeks ago we were in perpetual motion. We did not then suppose that
+anything would tempt us on a circle-squaring expedition: but the
+circumstances of the book above named have a peculiarity which induces us
+to give it a few words.
+
+"Mr. James Smith, a gentleman residing near Liverpool, was some years ago
+seized with the _morbus cyclometricus_.[203] The symptoms soon took a
+defined form: his circumference shrank into exactly 3-1/8 times his
+diameter, instead of close to 3-16/113, which the mathematician knows to be
+so near to truth that the error is hardly at the rate of a foot in 2,000
+miles. This shrinking of the circumference remained until it became
+absolutely necessary that it should be examined by the British Association.
+This body, which as Mr. James Smith found to his sorrow, has some interest
+in 'jealously guarding the mysteries of their profession,' refused at first
+to entertain the question. On this Mr. Smith changed his 'tactics' and the
+name of his paper, and smuggled in the subject under the form of 'The
+Relations of a Circle inscribed in a Square'! The paper was thus forced
+upon the Association, for Mr. Smith informs us that he {106} 'gave the
+Section to understand that he was not the man that would permit even the
+British Association to trifle with him.' In other words, the Association
+bore with and were bored with the paper, as the shortest way out of the
+matter. Mr. Smith also circulated a pamphlet. Some kind-hearted man, who
+did not know the disorder as well as we do, and who appears in Mr. Smith's
+handsome octavo as E. M.--the initials of 'eminent mathematician'--wrote to
+him and offered to show him in a page that he was all wrong. Mr. Smith
+thereupon opened a correspondence, which is the bulk of the volume. When
+the correspondence was far advanced, Mr. Smith announced his intention to
+publish. His benevolent instructor--we mean in intention--protested against
+the publication, saying 'I do not wish to be gibbeted to the world as
+having been foolish enough to enter upon what I feel now to have been a
+ridiculous enterprise.'
+
+"For this Mr. Smith cared nothing: he persisted in the publication, and the
+book is before us. Mr. Smith has had so much grace as to conceal his kind
+adviser's name under E. M., that is to say, he has divided the wrong among
+all who may be suspected of having attempted so hopeless a task as that of
+putting a little sense into his head. He has violated the decencies of
+private life. Against the will of the kind-hearted man who undertook his
+case, he has published letters which were intended for no other purpose
+than to clear his poor head of a hopeless delusion. He deserves the
+severest castigation; and he will get it: his abuse of confidence will
+stick by him all his days. Not that he has done his benefactor--in
+intention, again--any harm. The patience with which E. M. put the blunders
+into intelligible form, and the perseverance with which he tried to find a
+cranny-hole for common reasoning to get in at, are more than respectable:
+they are admirable. It is, we can assure E. M., a good thing that the
+nature of the circle-squarer should be so completely exposed as in this
+volume. The benefit which he intended Mr. James Smith may be {107}
+conferred upon others. And we should very much like to know his name, and
+if agreeable to him, to publish it. As to Mr. James Smith, we can only say
+this: he is not mad. Madmen reason rightly upon wrong premises: Mr. Smith
+reasons wrongly upon no premises at all.
+
+"E. M. very soon found out that, to all appearance, Mr. Smith got a circle
+of 3-1/8 times the diameter by making it the supposition to set out with
+that there was such a circle; and then finding certain consequences which,
+so it happened, were not inconsistent with the supposition on which they
+were made. Error is sometimes self-consistent. However, E. M., to be quite
+sure of his ground, wrote a short letter, stating what he took to be Mr.
+Smith's hypothesis, containing the following: 'On AC as diameter, describe
+the circle D, which by hypothesis shall be equal to three and one-eighth
+times the length of AC.... I beg, before proceeding further, to ask whether
+I have rightly stated your argument.' To which Mr. Smith replied: 'You have
+stated my argument with perfect accuracy.' Still E. M. went on, and we
+could not help, after the above, taking these letters as the initials of
+Everlasting Mercy. At last, however, when Mr. Smith flatly denied that the
+area of the circle lies between those of the inscribed and circumscribed
+polygons, E. M. was fairly beaten, and gave up the task. Mr. Smith was left
+to write his preface, to talk about the certain victory of truth--which,
+oddly enough, is the consolation of all hopelessly mistaken men; to compare
+himself with Galileo; and to expose to the world the perverse behavior of
+the Astronomer Royal, on whom he wanted to fasten a conversation, and who
+replied, 'It would be a waste of time, Sir, to listen to anything you could
+have to say on such a subject.'
+
+"Having thus disposed of Mr. James Smith, we proceed to a few remarks on
+the subject: it is one which a journal would never originate, but which is
+rendered necessary from time to time by the attempts of the autopseustic to
+become {108} heteropseustic. To the mathematician we have nothing to say:
+the question is, what kind of assurance can be given to the world at large
+that the wicked mathematicians are not acting in concert to keep down their
+superior, Mr. James Smith, the current Galileo of the quadrature of the
+circle.
+
+"Let us first observe that this question does not stand alone:
+independently of the millions of similar problems which exist in higher
+mathematics, the finding of the diagonal of a square has just the same
+difficulty, namely, the entrance of a pair of lines of which one cannot be
+definitely expressed by means of the other. We will show the reader who is
+up to the multiplication-table how he may go on, on, on, ever nearer, never
+there, in finding the diagonal of a square from the side.
+
+"Write down the following rows of figures, and more, if you like, in the
+way described:
+
+  1   2   5   12   29   70   169   408     985
+  1   3   7   17   41   99   239   577   1393
+
+After the second, each number is made up of double the last increased by
+the last but one: thus, 5 is 1 more than twice 2, 12 is 2 more than twice
+5, 239 is 41 more than twice 99. Now, take out two adjacent numbers from
+the upper line, and the one below the first from the lower: as
+
+  70   169
+  99.
+
+Multiply together 99 and 169, giving 16,731. If, then, you will say that 70
+diagonals are exactly equal to 99 sides, you are in error about the
+diagonal, but an error the amount of which is not so great as the 16,731st
+part of the diagonal. Similarly, to say that five diagonals make exactly
+seven sides does not involve an error of the 84th part of the diagonal.
+
+"Now, why has not the question of _crossing the square_ been as celebrated
+as that of _squaring the circle_? Merely because Euclid demonstrated the
+impossibility of the first {109} question, while that of the second was not
+demonstrated, completely, until the last century.
+
+"The mathematicians have many methods, totally different from each other,
+of arriving at one and the same result, their celebrated approximation to
+the circumference of the circle. An intrepid calculator has, in our own
+time, carried his approximation to what they call 607 decimal places: this
+has been done by Mr. Shanks,[204] of Houghton-le-Spring, and Dr.
+Rutherford[205] has verified 441 of these places. But though 607 looks
+large, the general public will form but a hazy notion of the extent of
+accuracy acquired. We have seen, in Charles Knight's[206] _English
+Cyclopaedia_, an account of the matter which may illustrate the
+unimaginable, though rationally conceivable, extent of accuracy obtained.
+
+"Say that the blood-globule of one of our animalcules is a millionth of an
+inch in diameter. Fashion in thought a globe like our own, but so much
+larger that our globe is but a blood-globule in one of its animalcules:
+never mind the microscope which shows the creature being rather a bulky
+instrument. Call this the first globe _above_ us. Let the first globe above
+us be but a blood-globule, as to size, in the animalcule of a still larger
+globe, which call the second globe above us. Go on in this way to the
+twentieth globe above us. Now go down just as far on the other side. Let
+the blood-globule with which we started be a globe peopled with animals
+like ours, but rather smaller: {110} and call this the first globe below
+us. Take a blood-globule out of this globe, people it, and call it the
+second globe below us: and so on to the twentieth globe below us. This is a
+fine stretch of progression both ways. Now give the giant of the twentieth
+globe _above_ us the 607 decimal places, and, when he has measured the
+diameter of his globe with accuracy worthy of his size, let him calculate
+the circumference of his equator from the 607 places. Bring the little
+philosopher from the twentieth globe _below_ us with his very best
+microscope, and set him to see the small error which the giant must make.
+He will not succeed, unless his microscopes be much better for his size
+than ours are for ours.
+
+"Now it must be remembered by any one who would laugh at the closeness of
+the approximation, that the mathematician generally goes _nearer_; in fact
+his theorems have usually no error at all. The very person who is
+bewildered by the preceding description may easily forget that if there
+were _no error at all_, the Lilliputian of the millionth globe below us
+could not find a flaw in the Brobdingnagian of the millionth globe above.
+The three angles of a triangle, of perfect accuracy of form, are
+_absolutely_ equal to two right angles; no stretch of progression will
+detect _any_ error.
+
+"Now think of Mr. Lacomme's mathematical adviser (_ante_, Vol. I, p. 46)
+making a difficulty of advising a stonemason about the quantity of pavement
+in a circular floor!
+
+"We will now, for our non-calculating reader, put the matter in another
+way. We see that a circle-squarer can advance, with the utmost confidence,
+the assertion that when the diameter is 1,000, the circumference is
+accurately 3,125: the mathematician declaring that it is a trifle more than
+3,141-1/2. If the squarer be right, the mathematician has erred by about a
+200th part of the whole: or has not kept his accounts right by about 10s.
+in every 100l. Of course, if he set out with such an error he will
+accumulate blunder upon blunder. Now, if there be a process in which {111}
+close knowledge of the circle is requisite, it is in the prediction of the
+moon's place--say, as to the time of passing the meridian at Greenwich--on
+a given day. We cannot give the least idea of the complication of details:
+but common sense will tell us that if a mathematician cannot find his way
+round the circle without a relative error four times as big as a
+stockbroker's commission, he must needs be dreadfully out in his attempt to
+predict the time of passage of the moon. Now, what is the fact? His error
+is less than a second of time, and the moon takes 27 days odd to revolve.
+That is to say, setting out with 10s. in 100l. of error in his
+circumference, he gets within the fifth part of a farthing in 100l. in
+predicting the moon's transit. Now we cannot think that the respect in
+which mathematical science is held is great enough--though we find it not
+small--to make this go down. That respect is founded upon a notion that
+right ends are got by right means: it will hardly be credited that the
+truth can be got to farthings out of data which are wrong by shillings.
+Even the celebrated Hamilton[207] of Edinburgh, who held that in
+mathematics there was no way of going wrong, was fully impressed with the
+belief that this was because error was avoided from the beginning. He never
+went so far as to say that a mathematician who begins wrong must end right
+somehow.
+
+"There is always a difficulty about the mode in which the thinking man of
+common life is to deal with subjects he has not studied to a professional
+extent. He must form opinions on matters theological, political, legal,
+medical, and social. If he can make up his mind to choose a guide, there
+is, of course, no perplexity: but on all the subjects mentioned the
+direction-posts point different ways. Now why should he not form his
+opinion upon an abstract mathematical question? Why not conclude that, as
+to the circle, it is possible Mr. James Smith may be the man, just {112} as
+Adam Smith[208] was the man of things then to come, or Luther, or Galileo?
+It is true that there is an unanimity among mathematicians which prevails
+in no other class: but this makes the chance of their all being wrong only
+different in degree. And more than this, is it not generally thought among
+us that priests and physicians were never so much wrong as when there was
+most appearance of unanimity among them? To the preceding questions we see
+no answer except this, that the individual inquirer may as rationally
+decide a mathematical question for himself as a theological or a medical
+question, so soon as he can put himself into a position in mathematics,
+level with that in which he stands in theology or medicine. The every-day
+thought and reading of common life have a certain resemblance to the
+thought and reading demanded by the learned faculties. The research, the
+balance of evidence, the estimation of probabilities, which are used in a
+question of medicine, are closely akin in character, however different the
+matter of application, to those which serve a merchant to draw his
+conclusions about the markets. But the mathematicians have methods of their
+own, to which nothing in common life bears close analogy, as to the nature
+of the results or the character of the conclusions. The logic of
+mathematics is certainly that of common life: but the data are of a
+different species; they do not admit of doubt. An expert arithmetician,
+such as is Mr. J. Smith, may fancy that calculation, merely as such, is
+mathematics: but the value of his book, and in this point of view it is not
+small, is the full manner in which it shows that a practised arithmetician,
+venturing into the field of mathematical demonstration, may show himself
+utterly destitute of all that distinguishes the reasoning geometrical
+investigator from the calculator.
+
+{113}
+
+"And further, it should be remembered that in mathematics the power of
+verifying results far exceeds that which is found in anything else: and
+also the variety of distinct methods by which they can be attained. It
+follows from all this that a person who desires to be as near the truth as
+he can will not judge the results of mathematical demonstration to be open
+to his criticism, in the same degree as results of other kinds. Should he
+feel compelled to decide, there is no harm done: his circle may be 3-1/8
+times its diameter, if it please him. But we must warn him that, in order
+to get this circle, he must, as Mr. James Smith has done, _make it at
+home_: the laws of space and thought beg leave respectfully to decline the
+order."
+
+
+
+I will insert now at length, from the _Athenaeum_ of June 8, 1861, the easy
+refutation given by my deceased friend, with the remarks which precede.
+
+"Mr. James Smith, of whose performance in the way of squaring the circle we
+spoke some weeks ago in terms short of entire acquiescence, has advertised
+himself in our columns, as our readers will have seen. He has also
+forwarded his letter to the Liverpool _Albion_, with an additional
+statement, which he did not make in _our_ journal. He denies that he has
+violated the decencies of private life, since his correspondent revised the
+proofs of his own letters, and his 'protest had respect only to making his
+name public.' This statement Mr. James Smith precedes by saying that we
+have treated as true what we well knew to be false: and he follows by
+saying that we have not read his work, or we should have known the above
+facts to be true. Mr. Smith's pretext is as follows. His correspondent
+E. M. says, 'My letters were not intended for publication, and I protest
+against their being published,' and he subjoins 'Therefore I must desire
+that my name may not be used.' The obvious meaning is that E. M. protested
+against the publication altogether, but, judging that Mr. Smith was {114}
+determined to publish, desired that his name should not be used. That he
+afterwards corrected the proofs merely means that he thought it wiser to
+let them pass under his own eyes than to leave them entirely to Mr. Smith.
+
+"We have received from Sir W. Rowan Hamilton[209] a proof that the
+circumference is more than 3-1/8 diameters, requiring nothing but a
+knowledge of four books of Euclid. We give it in brief as an exercise for
+our juvenile readers to fill up. It reminds us of the old days when real
+geometers used to think it worth while seriously to demolish pretenders.
+Mr. Smith's fame is now assured: Sir W. R. Hamilton's brief and easy
+exposure will procure him notice in connection with this celebrated
+problem.
+
+"It is to be shown that the perimeter of a regular polygon of 20 sides is
+greater than 3-1/8 diameters of the circle, and still more, of course, is
+the circumference of the circle greater than 3-1/8 diameters.
+
+"1. It follows from the 4th Book of Euclid, that the rectangle under the
+side of a regular decagon inscribed in a circle, and that side increased by
+the radius, is equal to the square of the radius. But the product 791 (791
++ 1280) is less than 1280 x 1280; if then the radius be 1280 the side of
+the decagon is greater than 791.
+
+"2. When a diameter bisects a chord, the square of the chord is equal to
+the rectangle under the doubles of the segments of the diameter. But the
+product 125 (4 x 1280 - 125) is less than 791 x 791. If then the bisected
+chord be a side of the decagon, and if the radius be still 1280, the double
+of the lesser segment exceeds 125.
+
+"3. The rectangle under this doubled segment and the radius is equal to the
+square of the side of an inscribed regular polygon of 20 sides. But the
+product 125 x 1280 is equal to 400 x 400; therefore, the side of the
+last-mentioned polygon is greater than 400, if the radius be still 1280. In
+other words, if the radius be represented by the new {115} member 16, and
+therefore the diameter by 32, this side is greater than 5, and the
+perimeter exceeds 100. So that, finally, if the diameter be 8, the
+perimeter of the inscribed regular polygon of 20 sides, and still more the
+circumference of the circle, is greater than 25: that is, the circumference
+is more than 3-1/8 diameters."
+
+The last work in the list was thus noticed in the _Athenaeum_, May 27, 1865.
+
+"Mr. James Smith appears to be tired of waiting for his place in the Budget
+of Paradoxes, and accordingly publishes a long letter to Professor De
+Morgan, with various prefaces and postscripts. The letter opens by a hint
+that the Budget appears at very long intervals, and 'apparently without any
+sufficient reason for it.' As Mr. Smith hints that he should like to see
+Mr. De Morgan, whom he calls an 'elephant of mathematics,' 'pumping his
+brains' 'behind the scenes'--an odd thing for an elephant to do, and an odd
+place to do it in--to get an answer, we think he may mean to hint that the
+Budget is delayed until the pump has worked successfully. Mr. Smith is
+informed that we have had the whole manuscript of the Budget, excepting
+only a final summing-up, in our hands since October, 1863. [This does not
+refer to the Supplement.] There has been no delay: we knew from the
+beginning that a series of historical articles would be frequently
+interrupted by the things of the day. Mr. James Smith lets out that he has
+never been able to get a private line from Mr. De Morgan in answer to his
+communications: we should have guessed it. He says, 'The Professor is an
+old bird and not to be easily caught, and by no efforts of mine have I been
+able, up to the present moment, either to induce or twit him into a
+discussion....' Mr. Smith curtails the proverb: old birds are not to be
+caught with _chaff_, nor with _twit_, which seems to be Mr. Smith's word
+for his own chaff, and, so long as the first letter is sounded, a very
+proper word. Why does he not try a little grain of sense? Mr. Smith
+evidently {116} thinks that, in his character as an elephant, the Professor
+has not pumped up brain enough to furnish forth a bird. In serious earnest,
+Mr. Smith needs no answer. In one thing he excites our curiosity: what is
+meant by demonstrating 'geometrically _and_ mathematically?'"
+
+I now proceed to my original treatment of the case.
+
+
+
+Mr. James Smith will, I have no doubt, be the most uneclipsed
+circle-squarer of our day. He will not owe this distinction to his being an
+influential and respected member of the commercial world of Liverpool, even
+though the power of publishing which his means give him should induce him
+to issue a whole library upon one paradox. Neither will he owe it to the
+pains taken with him by a mathematician who corresponded with him until the
+joint letters filled an octavo volume. Neither will he owe it to the notice
+taken of him by Sir William Hamilton, of Dublin, who refuted him in a
+manner intelligible to an ordinary student of Euclid, which refutation he
+calls a remarkable paradox easily explainable, but without explaining it.
+What he will owe it to I proceed to show.
+
+Until the publication of the _Nut to Crack_ Mr. James Smith stood among
+circle-squarers in general. I might have treated him with ridicule, as I
+have done others: and he says that he does not doubt he shall come in for
+his share at the tail end of my Budget. But I can make a better job of him
+than so, as Locke would have phrased it: he is such a very striking example
+of something I have said on the use of logic that I prefer to make an
+example of his writings. On one point indeed he well deserves the
+_scutica_,[210] if not the _horribile flagellum_.[211] He tells me that he
+will bring his solution to me in such a form as shall compel me to admit it
+as _un fait accompli_ [_une faute accomplie?_][212] {117} or leave myself
+open to the humiliating charge of mathematical ignorance and folly. He has
+also honored me with some private letters. In the first of these he gives
+me a "piece of information," after which he cannot imagine that I, "as an
+honest mathematician," can possibly have the slightest hesitation in
+admitting his solution. There is a tolerable reservoir of modest assurance
+in a man who writes to a perfect stranger with what he takes for an
+argument, and gives an oblique threat of imputation of dishonesty in case
+the argument be not admitted without hesitation; not to speak of the minor
+charges of ignorance and folly. All this is blind self-confidence, without
+mixture of malicious meaning; and I rather like it: it makes me understand
+how Sam Johnson came to say of his old friend Mrs. Cobb,[213]--"I love Moll
+Cobb for her impudence." I have now done with my friend's _suaviter in
+modo_,[214] and proceed to his _fortiter in re_[215]: I shall show that he
+_has_ convicted himself of ignorance and folly, with an honesty and candor
+worthy of a better value of [pi].
+
+Mr. Smith's method of proving that every circle is 3-1/8 diameters is to
+assume that it is so,--"if you dislike the term datum, then, by hypothesis,
+let 8 circumferences be exactly equal to 25 diameters,"--and then to show
+that every other supposition is thereby made absurd. The right to this
+assumption is enforced in the "Nut" by the following analogy:
+
+"I think you (!) will not dare (!) to dispute my right to this hypothesis,
+when I can prove by means of it that every other value of [pi] will lead to
+the grossest absurdities; unless indeed, you are prepared to dispute the
+right of Euclid to adopt a false line hypothetically for the purpose {118}
+of a '_reductio ad absurdum_'[216] demonstration, in pure geometry."
+
+
+
+Euclid assumes what he wants to _disprove_, and shows that his _assumption_
+leads to absurdity, and so _upsets itself_. Mr. Smith assumes what he wants
+to _prove_, and shows that _his_ assumption makes _other propositions_ lead
+to absurdity. This is enough for all who can reason. Mr. James Smith cannot
+be argued with; he has the whip-hand of all the thinkers in the world.
+Montucla would have said of Mr. Smith what he said of the gentleman who
+squared his circle by giving 50 and 49 the same square root, _Il a perdu le
+droit d'etre frappe de l'evidence_.[217]
+
+It is Mr. Smith's habit, when he finds a conclusion agreeing with its own
+assumption, to regard that agreement as proof of the assumption. The
+following is the "piece of information" which will settle me, if I be
+honest. Assuming [pi] to be 3-1/8, he finds out by working instance after
+instance that the mean proportional between one-fifth of the area and
+one-fifth of eight is the radius. That is,
+
+  if [pi] = 25/8, sqrt(([pi]r^2)/5 . 8/5) = r.
+
+This "remarkable general principle" may fail to establish Mr. Smith's
+quadrature, even in an honest mind, if that mind should happen to know
+that, a and b being any two numbers whatever, we need only assume--
+
+  [pi] = a^2/b, to get at sqrt(([pi]r^2)/a . b/a) = r.
+
+We naturally ask what sort of glimmer can Mr. Smith have of the subject
+which he professes to treat? On this point he has given satisfactory
+information. I had mentioned the old problem of finding two mean
+proportionals, {119} as a preliminary to the duplication of the cube. On
+this mention Mr. Smith writes as follows. I put a few words in capitals;
+and I write rq[218] for the sign of the square root, which embarrasses
+small type:
+
+"This establishes the following _infallible_ rule, for finding two mean
+proportionals OF EQUAL VALUE, and is more than a preliminary, to the famous
+old problem of 'Squaring the circle.' Let any finite number, say 20, and
+its fourth part = (1/4)(20) = 5, be given numbers. Then rq(20 x 5) = rq 100 =
+10, is their mean proportional. Let this be a given mean proportional TO
+FIND ANOTHER MEAN PROPORTIONAL OF EQUAL VALUE. Then
+
+  20 x [pi]/4 = 20 x 3.125/4 = 20 x .78125 = 15.625
+
+will be the first number; as
+
+  25 : 16 :: rq 20 : rq 8.192: and (rq 8.192)^2 x [pi]/4 = 8.192 x .78125 =
+      6.4
+
+will be the second number; therefore rq(15.625 x 6.4) = rq 100 = 10, is the
+required mean proportional.... Now, my good Sir, however competent you may
+be to prove every man a fool [not _every_ man, Mr. Smith! only _some_; pray
+learn logical quantification] who now thinks, or in times gone by has
+thought, the 'Squaring of the Circle' _a possibility_; I doubt, and, on the
+evidence afforded by your Budget, I cannot help doubting, whether you were
+ever before competent to find two mean proportionals _by my unique
+method_."--(_Nut_, pp. 47, 48.) [That I never was, I solemnly declare!]
+
+All readers can be made to see the following exposure. When 5 and 20 are
+given, x is a mean proportional when in 5, x, 20, 5 is to x as x to 20. And
+x must be 10. But x and y are two mean proportionals when in 5, x, y, 20, x
+{120} is a mean proportional between 5 and y, and y is a mean proportional
+between x and 20. And these means are x = 5 [cuberoot]4, y = 5
+[cuberoot]16. But Mr. Smith finds _one_ mean, finds it _again_ in a
+roundabout way, and produces 10 and 10 as the two (equal!) means, in
+solution of the "famous old problem." This is enough: if more were wanted,
+there is more where this came from. Let it not be forgotten that Mr. Smith
+has found a translator abroad, two, perhaps three, followers at home,
+and--most surprising of all--a real mathematician to try to set him right.
+And this mathematician did not discover the character of the subsoil of the
+land he was trying to cultivate until a goodly octavo volume of letters had
+passed and repassed. I have noticed, in more quarters than one, an apparent
+want of perception of the _full_ amount of Mr. Smith's ignorance: persons
+who have not been in contact with the non-geometrical circle-squarers have
+a kind of doubt as to whether anybody can carry things so far. But I am an
+"old bird" as Mr. Smith himself calls me; a Simorg, an "all-knowing Bird of
+Ages" in matters of cyclometry.
+
+The curious phenomena of thought here exhibited illustrate, as above said,
+a remark I have long ago made on the effect of proper study of logic. Most
+persons reason well enough on matter to which they are accustomed, and in
+terms with which they are familiar. But in unaccustomed matter, and with
+use of strange terms, few except those who are practised in the
+abstractions of pure logic can be tolerably sure to keep their feet. And
+one of the reasons is easily stated: terms which are not quite familiar
+partake of the vagueness of the X and Y on which the student of logic
+learns to see the formal force of a proposition independently of its
+material elements.
+
+I make the following quotation from my fourth paper on logic in the
+_Cambridge Transactions_:
+
+"The uncultivated reason proceeds by a process almost entirely material.
+Though the necessary law of thought {121} must determine the conclusion of
+the ploughboy as much as that of Aristotle himself, the ploughboy's
+conclusion will only be tolerably sure when the matter of it is such as
+comes within his usual cognizance. He knows that geese being all birds does
+not make all birds geese, but mainly because there are ducks, chickens,
+partridges, etc. A beginner in geometry, when asked what follows from
+'Every A is B,' answers 'Every B is A.' That is, the necessary laws of
+thought, except in minds which have examined their tools, are not very sure
+to work correct conclusions except upon familiar matter.... As the
+cultivation of the individual increases, the laws of thought which are of
+most usual application are applied to familiar matter with tolerable
+safety. But difficulty and risk of error make a new appearance with a new
+subject; and this, in most cases, until new subjects are familiar things,
+unusual matter common, untried nomenclature habitual; that is, until it is
+a habit to be occupied upon a novelty. It is observed that many persons
+reason well in some things and badly in others; and this is attributed to
+the consequence of employing the mind too much upon one or another subject.
+But those who know the truth of the preceding remarks will not have far to
+seek for what is often, perhaps most often, the true reason.... I maintain
+that logic tends to make the power of reason over the unusual and
+unfamiliar more nearly equal to the power over the usual and familiar than
+it would otherwise be. The second is increased; but the first is almost
+created."
+
+Mr. James Smith, by bringing ignorance, folly, dishonesty into contact with
+my name, in the way of conditional insinuation, has done me a good turn: he
+has given me right to a freedom of personal remark which I might have
+declined to take in the case of a person who is useful and respected in
+matters which he understands.
+
+Tit for tat is logic all the world over. By the way, what has become of the
+rest of the maxim: we never hear it {122} now. When I was a boy, in some
+parts of the country at least, it ran thus:
+
+ "Tit for tat;
+  Butter for fat:
+  If you kill my dog,
+  I'll kill your cat."
+
+He is a glaring instance of the truth of the observations quoted above. I
+will answer for it that, at the Mersey Dock Board, he never dreams of
+proving that the balance at the banker's is larger than that in the book by
+assuming that the larger sum is there, and then proving that the other
+supposition--the smaller balance--is upon that assumption, an absurdity. He
+never says to another director, How can you dare to refuse me a right to
+assume the larger balance, when you yourself, the other day,
+said,--Suppose, for argument's sake, we had 80,000l. at the banker's,
+though you knew the book only showed 30,000l.? This is the way in which he
+has supported his geometrical paradox by Euclid's example: and this is not
+the way he reasons at the board; I know it by the character of him as a man
+of business which has reached my ears from several quarters. But in
+geometry and rational arithmetic he is a smatterer, though expert at
+computation; at the board he is a trained man of business. The language of
+geometry is so new to him that he does not know what is meant by "two mean
+proportionals:" but all the phrases of commerce are rooted in his mind. He
+is most unerasably booked in the history of the squaring of the circle, as
+the speculator who took a right to assume a proposition for the destruction
+of other propositions, on the express ground that Euclid assumes a
+proposition to show that it destroys itself: which is as if the curate
+should demand permission to throttle the squire because St. Patrick drove
+the vermin to suicide to save themselves from slaughter. He is conspicuous
+as a speculator who, more visibly than almost any other known to history,
+reasoned in a circle by way of reasoning on a circle. But {123} what I have
+chiefly to do with is the force of instance which he has lent to my
+assertion that men who have not had real training in pure logic are unsafe
+reasoners in matter which is not familiar. It is hard to get first-rate
+examples of this, because there are few who find the way to the printer
+until practice and reflection have given security against the grossest
+slips. I cannot but think that his case will lead many to take what I have
+said into consideration, among those who are competent to think of the
+great mental disciplines. To this end I should desire him to continue his
+efforts, to amplify and develop his great principle, that of proving a
+proposition by assuming it and taking as confirmation every consequence
+that does not contradict the assumption.
+
+Since my Budget commenced, Mr. Smith has written me notes: the portion
+which I have preserved--I suppose several have been mislaid--makes a
+hundred and seven pages of note-paper, closely written. To all this I have
+not answered one word: but I think I cannot have read fewer than forty
+pages. In the last letter the writer informs me that he will not write at
+greater length until I have given him an answer, according to the "rules of
+good society." Did I not know that for every inch I wrote back he would
+return an ell? Surely in vain the net is spread in the eyes of anything
+that hath a wing. There were several good excuses for not writing to Mr. J.
+Smith: I will mention five. First, I distinctly announced at the beginning
+of this Budget that I would not communicate with squarers of the circle.
+Secondly, any answer I might choose to give might with perfect propriety be
+reserved for this article; had the imputation of incivility been made after
+the first note, I should immediately have replied to this effect: but I
+presumed it was quite understood. Thirdly, Mr. Smith, by his publication of
+E. M.'s letters against the wish of the writer, had put himself out of the
+pale of correspondence. Fourthly, he had also gone beyond the rules of good
+society in sending {124} letter after letter to a person who had shown by
+his silence an intention to avoid correspondence. Fifthly, these same rules
+of good society are contrived to be flexible or frangible in extreme cases:
+otherwise there would be no living under them; and good society would be
+bad. Father Aldrovand has laid down the necessary distinction--"I tell
+thee, thou foolish Fleming, the text speaketh but of promises made unto
+Christians, and there is in the rubric a special exemption of such as are
+made to Welchmen." There is also a rubric to the rules of good society; and
+squarers of the circle are among those whom there is special permission not
+to answer: they are the wild Welchmen of geometry, who are always
+assailing, but never taking, the Garde Douloureuse[219] of the circle. "At
+this commentary," proceeds the story, "the Fleming grinned so broadly as to
+show his whole case of broad strong white teeth." I know not whether the
+Welchman would have done the like, but I hope Mr. James Smith will: and I
+hope he has as good a case to show as Wilkin Flammock. For I wish him long
+life and long health, and should be very glad to see so much energy
+employed in a productive way. I hope he wishes me the same: if not, I will
+give him what all his judicious friends will think a good reason for doing
+so. His pamphlets and letters are all tied up together, and will form a
+curious lot when death or cessation of power to forage among book-shelves
+shall bring my little library to the hammer. And this time may not be far
+off: for I was X years old in A.D. X^2; not 4 in A.D. 16, nor 5 in A.D. 25,
+but still in one case under that law. And now I have made my own age a
+problem of quadrature, and Mr. J. Smith may solve it. But I protest against
+his method of assuming a result, and making itself prove itself: he might
+in this way, as sure as eggs is eggs (a corruption of X is X), make me
+1,864 years old, which is a great deal too much.
+
+{125}
+
+_April 5, 1864._--Mr. Smith continues to write me long letters, to which he
+hints that I am to answer. In his last, of 31 closely written sides of
+note-paper, he informs me, with reference to my obstinate silence, that
+though I think myself and am thought by others to be a mathematical
+Goliath, I have resolved to play the mathematical snail, and keep within my
+shell. A mathematical _snail_! This cannot be the thing so called which
+regulates the striking of a clock; for it would mean that I am to make Mr.
+Smith sound the true time of day, which I would by no means undertake upon
+a clock that gains 19 seconds odd in every hour by false quadrature. But he
+ventures to tell me that pebbles from the sling of simple truth and common
+sense will ultimately crack my shell, and put me _hors de combat_.[220] The
+confusion of images is amusing: Goliath turning himself into a snail to
+avoid [pi] = 3-1/8, and James Smith, Esq., of the Mersey Dock Board: and
+put _hors de combat_--which should have been _cache_[221]--by pebbles from
+a sling. If Goliath had crept into a snail-shell, David would have cracked
+the Philistine with his foot. There is something like modesty in the
+implication that the crack-shell pebble has not yet taken effect; it might
+have been thought that the slinger would by this time have been singing--
+
+ "And thrice [and one-eighth] I routed all my foes,
+  And thrice [and one-eighth] I slew the slain."
+
+But he promises to give the public his nut-cracker if I do not, before the
+Budget is concluded, "unravel" the paradox, which is the
+mathematico-geometrical nut he has given me to crack. Mr. Smith is a crack
+man: he will crack his own nut; he will crack my shell; in the mean time he
+cracks himself up. Heaven send he do not crack himself into lateral
+contiguity with himself.
+
+On June 27 I received a letter, in the handwriting of Mr. James Smith,
+signed Nauticus. I have ascertained {126} that one of the letters to the
+_Athenaeum_ signed Nauticus is in the same handwriting. I make a few
+extracts:
+
+"... The important question at issue has been treated by a brace of
+mathematical birds with too much levity. It may be said, however, that
+sarcasm and ridicule sometimes succeed, where reason fails.... Such a
+course is not well suited to a discussion.... For this reason I shall for
+the future [this implies there has been a past, so that Nauticus is not
+before me for the first time] endeavor to confine myself to dry reasoning
+from incontrovertible premises.
+
+... It appears to me that so far as his theory is concerned he comes off
+unscathed. You might have found "a hole in Smith's circle" (have you seen a
+pamphlet bearing this title? [I never heard of it until now]), but after
+all it is quite possible the hole may have been left by design, for the
+purpose of entrapping the unwary."
+
+[On the publication of the above, the author of the pamphlet obligingly
+forwarded a copy to me of _A Hole in Smith's Circle_--by a Cantab: Longman
+and Co., 1859, (pp. 15). "It is pity to lose any fun we can get out of the
+affair," says my almamaternal brother: to which I add that in such a case
+warning without joke is worse than none at all, as giving a false idea of
+the nature of the danger. The Cantab takes some absurdities on which I have
+not dwelt: but there are enough to afford a Cantab from every college his
+own separate hunting ground.]
+
+Does this hint that his mode of proof, namely, assuming the thing to be
+proved, was a design to entrap the unwary? if so, it bangs Banagher. Was
+his confounding two mean proportionals with one mean proportional found
+twice over a trick of the same intent? if so, it beats cockfighting. That
+Nauticus is Mr. Smith appears from other internal evidence. In 1819, Mr.
+J. C. Hobhouse[222] was sent to Newgate for a {127} libel on the House of
+Commons which was only intended for a libel on Lord Erskine.[223] The
+ex-Chancellor had taken Mr. Hobhouse to be thinking of him in a certain
+sentence; this Mr. Hobhouse denied, adding, "There is but one man in the
+country who is always thinking of Lord Erskine." I say that there is but
+one man of our day who would couple me and Mr. James Smith as a "brace of
+mathematical birds."
+
+Mr. Smith's "theory" is unscathed by me. Not a doubt about it: but how does
+he himself come off? I should never think of refuting a theory proved by
+assumption of itself. I left Mr. Smith's [pi] untouched: or, if I put in my
+thumb and pulled out a plum, it was to give a notion of the cook, not of
+the dish. The "important question at issue" was not the circle: it was,
+wholly and solely, whether the abbreviation of _James_ might be spelled
+_Jimm_.[224] This is personal to the verge of scurrility: but in literary
+controversy the challenger names the weapons, and Mr. Smith begins with
+charge of ignorance, folly, and dishonesty, by conditional implication. So
+that the question is, not the personality of a word, but its applicability
+to the person designated: it is enough if, as the Latin grammar has it,
+_Verbum personale concordat cum nominativo_.[225]
+
+I may plead precedent for taking a liberty with the orthography of _Jem_.
+An instructor of youth was scandalized at the abrupt and irregular--but
+very effective--opening of Wordsworth's little piece:
+
+{128}
+
+         "A simple child
+  That lightly draws its breath,
+  And feels its life in every limb,
+  What should it know of death?"
+
+So he mended the matter by instructing his pupils to read the first line
+thus:
+
+ "A simple child, dear brother ----."
+
+The brother, we infer from sound, was to be James, and the blank must
+therefore be filled up with _Jimb_.
+
+I will notice one point of the letter, to make a little more distinction
+between the two birds. Nauticus lays down--quite correctly--that the sine
+of an angle is less than its circular measure. He then takes 3.1416 for
+180 deg., and finds that 36' is .010472. But this is exactly what he finds
+for the sine of 36' in tables: he concludes that either 3.1416 or the
+tables must be wrong. He does not know that sines, as well as [pi], are
+interminable decimals, of which the tables, to save printing, only take in
+a finite number. He is a six-figure man: let us go thrice again to make up
+nine, and we have as follows:
+
+  Circular measure of 36'         .010471975...
+  Sine of 36'                     .010471784...
+  Excess of measure over sine     .000000191...
+
+Mr. Smith invites me to say which is wrong, the quadrature, or the tables:
+I leave him to guess. He says his assertions "arise naturally and
+necessarily out of the arguments of a circle-squarer:" he might just as
+well lay down that all the pigs went to market because it is recorded that
+"_This_ pig went to market." I must say for circle-squarers that very few
+bring their pigs to so poor a market. I answer the above argument because
+it is, of all which Mr. James Smith has produced, the only one which rises
+to the level of a schoolboy: to meet him halfway I descend to that level.
+
+Mr. Smith asks me to solve a problem in the _Athenaeum_: {129} and I will do
+it, because the question will illustrate what is _below_ schoolboy level.
+
+"Let x represent the circular measure of an angle of 15 deg., and y half
+the sine of an angle of 30 deg. = area of the square on the radius of a
+circle of diameter unity = .25. If x - y = xy, firstly, what is the
+arithmetical value of xy? secondly, what is the angle of which xy
+represents the circular measure?"
+
+If x represent 15 deg. and y be 1/4, xy represents 3 deg. 45', whether
+x - y be xy or no. But, y being 1/4, x - y is _not_ xy unless x be 1/3,
+that is, unless 12x or [pi] be 4, which Mr. Smith would not admit. How
+could a person who had just received such a lesson as I had given
+immediately pray for further exposure, furnishing the stuff so liberally
+as this? Is it possible that Mr. Smith, because he signs himself
+Nauticus, means to deny his own very regular, legible, and peculiar
+hand? It is enough to make the other members of the Liverpool Dock Board
+cry, Mersey on the man!
+
+Mr. Smith says that for the future he will give up what he calls sarcasm,
+and confine himself, "as far as possible," to what he calls dry reasoning
+from incontrovertible premises. If I have fairly taught him that _his_
+sarcasm will not succeed, I hope he will find that his wit's end is his
+logic's beginning.
+
+I now reply to a question I have been asked again and again since my last
+Budget appeared: Why do you take so much trouble to expose such a reasoner
+as Mr. Smith? I answer as a deceased friend of mine used to answer on like
+occasions--A man's capacity is no measure of his power to do mischief. Mr.
+Smith has untiring energy, which does something; self-evident honesty of
+conviction, which does more; and a long purse, which does most of all. He
+has made at least ten publications, full of figures which few readers can
+criticize. A great many people are staggered to this extent, that they
+imagine there must be {130} the indefinite _something_ in the mysterious
+_all this_. They are brought to the point of suspicion that the
+mathematicians ought not to treat "all this" with such undisguised
+contempt, at least. Now I have no fear for [pi]: but I do think it possible
+that general opinion might in time demand that the crowd of
+circle-squarers, etc. should be admitted to the honors of opposition; and
+this would be a time-tax of five per cent., one man with another, upon
+those who are better employed. Mr. James Smith may be made useful, in hands
+which understand how to do it, towards preventing such opinion from
+growing. A speculator who expressly assumes what he wants to prove, and
+argues that all which contradicts it is absurd, _because_ it cannot stand
+side by side with his assumption, is a case which can be exposed to all.
+And the best person to expose it is one who has lived in the past as well
+as the present, who takes misthinking from points of view which none but a
+student of history can occupy, and who has something of a turn for the
+business.
+
+Whether I have any motive but public good must be referred to those who can
+decide whether a missionary chooses his pursuit solely to convert the
+heathen. I shall certainly be thought to have a little of the spirit of
+Col. Quagg, who delighted in strapping the Grace-walking Brethren. I must
+quote this myself: if I do not, some one else will, and then where am I?
+The Colonel's principle is described as follows:
+
+"I licks ye because I kin, and because I like, and because ye'se critters
+that licks is good for. Skins ye have on, and skins I'll have off; hard or
+soft, wet or dry, spring or fall. Walk in grace if ye like till pumpkins is
+peaches; but licked ye must be till your toe-nails drop off and your noses
+bleed blue ink. And--licked--they--were--accordingly."
+
+I am reminded of this by the excessive confidence with which Mr. James
+Smith predicted that he would treat me as Zephaniah Stockdolloger (Sam
+Slick calls it _slockdollager_) treated Goliah Quagg. He has announced his
+{131} intention of bringing me, with a contrite heart, and clean
+shaved,--4159265... razored down to 25,--to a camp-meeting of
+circle-squarers. But there is this difference: Zephaniah only wanted to
+pass the Colonel's smithy in peace; Mr. James Smith sought a fight with me.
+As soon as this Budget began to appear, he oiled his own strap, and
+attempted to treat me as the terrible Colonel would have treated the
+inoffensive brother.
+
+He is at liberty to try again.
+
+
+
+THE MOON HOAX.
+
+    The Moon-hoax; or the discovery that the moon has a vast population of
+    human beings. By Richard Adams Locke.[226] New York, 1859, 8vo.
+
+This is a reprint of the hoax already mentioned. I suppose R. A. Locke is
+the name assumed by M. Nicollet.[227] The publisher informs us that when
+the hoax first appeared day by day in a morning paper, the circulation
+increased fivefold, and the paper obtained a permanent footing. Besides
+this, an edition of 60,000 was sold off in less than one month.
+
+The discovery was also published under the name of A. R. Grant.[228]
+Sohncke's[229] _Bibliotheca Mathematica_ confounds this Grant with Prof. R.
+Grant[230] of Glasgow, the author of the _History of Physical Astronomy_,
+who is accordingly made to guarantee the discoveries in the moon. I hope
+Adams Locke will not merge in J. C. Adams,[231] the co-discoverer of
+Neptune. Sohncke gives the titles of {132} three French translations of the
+Moon hoax at Paris, of one at Bordeaux, and of Italian translations at
+Parma, Palermo, and Milan.
+
+A Correspondent, who is evidently fully master of details, which he has
+given at length, informs me that the Moon hoax appeared first in the _New
+York Sun_, of which R. A. Locke was editor. It so much resembled a story
+then recently published by Edgar A. Poe, in a Southern paper, "Adventures
+of Hans Pfaal," that some New York journals published the two side by side.
+Mr. Locke, when he left the _New York Sun_, started another paper, and
+discovered the manuscript of Mungo Park;[232] but this did not deceive. The
+_Sun_, however, continued its career, and had a great success in an account
+of a balloon voyage from England to America, in seventy-five hours, by Mr.
+Monck Mason,[233] Mr. Harrison Ainsworth,[234] and others. I have no doubt
+that M. Nicollet was the author of the Moon hoax,[235] written in a way
+which marks the practised observatory astronomer beyond all doubt, and by
+evidence seen in the most minute details. Nicollet had an eye to Europe. I
+suspect that he took Poe's story, and made it a basis for his own. Mr.
+Locke, it would seem, when he attempted a fabrication for himself, did not
+succeed.
+
+
+
+    The Earth we inhabit, its past, present, and future. By Capt.
+    Drayson.[236] London, 1859, 8vo.
+
+The earth is growing; absolutely growing larger: its diameter increases
+three-quarters of an inch per mile every year. The foundations of our
+buildings will give way in {133} time: the telegraph cables break, and no
+cause ever assigned except ships' anchors, and such things. The book is for
+those whose common sense is unwarped, who can judge evidence as well as the
+ablest philosopher. The prospect is not a bad one, for population increases
+so fast that a larger earth will be wanted in time, unless emigration to
+the Moon can be managed, a proposal of which it much surprises me that
+Bishop Wilkins has a monopoly.
+
+
+
+IMPALEMENT BY REQUEST.
+
+_Athenaeum_, August, 19, 1865. _Notice to Correspondents._
+
+"R. W.--If you will consult the opening chapter of the Budget of Paradoxes,
+you will see that the author presents only works in his own library at a
+given date; and this for a purpose explained. For ourselves we have
+carefully avoided allowing any writers to present themselves in our columns
+on the ground that the Budget has passed them over. We gather that Mr. De
+Morgan contemplates additions at a future time, perhaps in a separate and
+augmented work; if so, those who complain that others of no greater claims
+than themselves have been ridiculed may find themselves where they wish to
+be. We have done what we can for you by forwarding your letter to Mr. De
+Morgan."
+
+The author of "An Essay on the Constitution of the Earth," published in
+1844, demanded of the _Athenaeum_, as an _act of fairness_, that a letter
+from him should be published, proving that he had as much right to be
+"impaled" as Capt. Drayson. He holds, on speculative grounds, what the
+other claims to have proved by measurement, namely, that the earth is
+growing; and he believes that in time--a good long time, not _our_
+time--the earth and other planets may grow into suns, with systems of their
+own.
+
+This gentleman sent me a copy of his work, after the commencement of my
+Budget; but I have no recollection of having received it, and I cannot find
+it on the (nursery? {134} quarantine?) shelves on which I keep my
+unestablished discoveries. Had I known of this work in time, (see the
+Introduction) I should of course, have impaled it (heraldically) with the
+other work; but the two are very different. Capt. Drayson professes to
+prove his point by results of observation; and I think he does not succeed.
+The author before me only speculates; and a speculator can get any
+conclusion into his premises, if he will only build or hire them of shape
+and size to suit. It reminds me of a statement I heard years ago, that a
+score of persons, or near it, were to dine inside the skull of one of the
+aboriginal animals, dear little creatures! Whereat I wondered vastly,
+nothing doubting; facts being stubborn and not easy drove, as Mrs. Gamp
+said. But I soon learned that the skull was not a real one, but
+artificially constructed by the methods--methods which have had striking
+verifications, too--which enable zoologists to go the whole hog by help of
+a toe or a bit of tail. This took off the edge of the wonder: a hundred
+people can dine inside an inference, if you draw it large enough. The
+method might happen to fail for once: for instance, the toe-bone might have
+been abnormalized by therian or saurian malady; and the possibility of such
+failure, even when of small probability, is of great alleviation. The
+author before me is, apparently, the sole fabricator of his own premises.
+With vital force in the earth and continual creation on the part of the
+original Creator, he expands our bit of a residence as desired. But, as the
+Newtoness of Cookery observed, First catch your hare. When this is done,
+when you _have_ a growing earth, you shall dress it with all manner of
+proximate causes, and serve it up with a growing Moon for sauce, a growing
+Sun, if it please you, at the other end, and growing planets for
+side-dishes. Hoping this amount of impalement will be satisfactory, I go on
+to something else. {135}
+
+
+
+THE HAILESEAN SYSTEM OF ASTRONOMY.
+
+    _The Hailesean System of Astronomy._ By John Davey Hailes[237] (two
+    pages duodecimo, 1860).
+
+He offers to _take_ 100,000l. to 1,000l. that he shows the sun to be less
+than seven millions of miles from the earth. The earth in the center,
+revolving eastward, the sun revolving westward, so that they "meet at half
+the circle distance in the 24 hours." The diameter of the circle being
+9839458303, the circumference is 30911569920.
+
+The following written challenge was forwarded to the Council of the
+Astronomical Society: it will show the "general reader"--and help him
+towards earning his name--what sort of things come every now and then to
+our scientific bodies. I have added punctuation:
+
+                  _Challenge._
+                  1,000 to 30,000.
+ "Leverrier's[238] name stand placed first. Do the worthy Frenchman
+     justice.
+  By awarding him the medal in a trice.
+  Give Adams[239] an extra--of which neck and neck the race.
+  Now I challenge to meet them and the F.R.S.'s all,
+  For good will and _one_ thousand pounds to their _thirty_ thousand
+      withall,
+  That I produce a system, which shall measure the time,
+  When the Sun was vertical to Gibeon, afterward to Syene.
+  To meet any time in London--name your own period,
+  To be decided by a majority of twelve persons--a President, _odd_.
+  That mean, if the twelve equally divide, the President decide,
+  I should prefer the Bishop of London, over the meeting to preside.
+                                JOHN DAVY HAILES."
+  Feb. 17, 1847."
+
+Mr. Hailes still issues his flying sheets. The last I have met with
+(October 7, 1863) informs us that the latitude of {136} England is slowly
+increasing, which is the true cause of the alteration in the variation of
+the magnet.
+
+[Mr. Hailes continues his researches. Witness his new Hailesean system of
+Astronomy, displaying Joshua's miracle-time, origin of time from science,
+with Bible and Egyptian history. Rewards offered for astronomical problems.
+With magnetism, etc. etc. Astronomical challenge to all the world.
+Published at Cambridge, in 1865. The author agrees with Newton in one
+marked point. _Errores quam minimi non sunt contemnendi_,[240] says Isaac:
+meaning in figures, not in orthography. Mr. Hailes enters into the spirit,
+both positive and negative, of this dictum, by giving the distance of
+_Sidius_ from the center of the earth at 163,162,008 miles 10 feet 8 inches
+17-28ths of an inch. Of course, he is aware that the center of _figure_ of
+the earth is 17.1998 inches from the center of _gravity_. Which of the two
+is he speaking of?]
+
+
+
+    The Divine Mystery of Life. London [1861], 18mo. (pp.32).
+
+The author has added one class to zoology, which is printed in capitals, as
+derived from _zoe_, life, not from _zoon_, animal. That class is of
+_Incorporealia_, order I., _Infinitum_, of one genus without plurality,
+_Deus_: order II., _Finita_, angels good and evil. The rest is all about a
+triune system, with a diagram. The author is not aware that [Greek: zoon]
+is not _animal_, but _living being_. Aristotle had classed gods under
+[Greek: zoa], and has been called to account for it by moderns who have
+taken the word to mean _animal_.
+
+
+
+A CHANCE FOR INVENTORS.
+
+    Explication du Zodiaque de Denderah, des Pyramides, et de Genese. Par
+    le Capitaine au longcours Justin Roblin.[241] Caen, 1861. 8vo.
+
+{137}
+
+Capt. Roblin, having discovered the sites of gold and diamond mines by help
+of the zodiac of Denderah, offered half to the shareholders of a company
+which he proposed to form. One of our journals, by help of the zodiac of
+Esne, offered, at five francs a head, to tell the shareholders the exact
+amount of gold and diamonds which each would get, and to make up the amount
+predicted to those who got less. There are moods of the market in England
+in which this company could have been formed: so we must not laugh at our
+neighbors.
+
+
+
+JOHANNES VON GUMPACH.
+
+    A million's worth of property, and five hundred lives annually lost at
+    sea by the Theory of Gravitation. A letter on the true figure of the
+    earth, addressed to the Astronomer Royal, by Johannes von Gumpach.[242]
+    London, 1861, 8vo. (pp. 54).
+
+    The true figure and dimensions of the earth, in a letter addressed to
+    the Astronomer Royal. By Joh. von Gumpach. 2nd ed. entirely recast.
+    London, 1862, 8vo. (pp. 266).
+
+    Two issues of a letter published with two different title-pages, one
+    addressed to the Secretary of the Royal Society, the other to the
+    Secretary of the Royal Astronomical Society. It would seem that the
+    same letter is also issued with two other titles, addressed to the
+    British Association and the Royal Geographical Society. By Joh. von
+    Gumpach. London, 1862, 8vo.
+
+    Baby-Worlds. An essay on the nascent members of our solar household. By
+    Joh. von Gumpach. London, 1863, 8vo.
+
+The earth, it appears, instead of being flattened, is elongated at the
+poles: by ignorance of which the loss above mentioned occurs yearly. There
+is, or is to be, a substitute for attraction and an "application hitherto
+neglected, of a {138} recognized law of optics to the astronomical theory,
+showing the true orbits of the heavenly bodies to be perfectly circular,
+and their orbital motions to be perfectly uniform." all irregularities
+being, I suppose, optical delusions. Mr. Von Gumpach is a learned man; what
+else, time must show.
+
+
+
+SLANDER PARADOXES.
+
+    Perpetuum Mobile: or Search for self-motive Power. By Henry
+    Dircks.[243] London, 1861, 8vo.
+
+A useful collection on the history of the attempts at perpetual motion,
+that is, at obtaining the consequences of power without any power to
+produce them. September 7, 1863, a correspondent of the _Times_ gave an
+anecdote of George Stephenson,[244] which he obtained from Robert
+Stephenson.[245] A perpetual motionist wanted to explain his method; to
+which George replied--"Sir! I shall believe it when I see you take yourself
+up by the waistband, and carry yourself about the room." Never was the
+problem better stated.
+
+There is a paradox of which I ought to give a specimen, I mean the
+_slander-paradox_; the case of a person who takes it into his head, upon
+evidence furnished entirely by the workings of his own thoughts, that some
+other person has committed a foul act of which the world at large would no
+more suppose him guilty than they would suppose that the earth is a flat
+bordered by ice. If I were to determine on giving cases in which the
+self-deluded person imagines {139} a conspiracy against _himself_, there
+would be no end of choices. Many of the grosser cases are found at last to
+be accompanied by mental disorder, and it is difficult to avoid referring
+the whole class to something different from simple misuse of the reasoning
+power. The first instance is one which puts in a strong light the state of
+things in which we live, brought about by our glorious freedom of thought,
+speech, and writing. The Government treated it with neglect, the press with
+silent contempt, and I will answer for it many of my readers now hear of it
+for the first time, when it comes to be enrolled among circle-squarers and
+earth-stoppers, where, as the old philosopher said, it will not gravitate,
+being _in proprio loco_.[246]
+
+1862. On new year's day, 1862, when the nation was in the full tide of
+sympathy with the Queen, and regret for its own loss, a paper called the
+_Free Press_ published a number devoted to the consideration of the causes
+of the death of the Prince Consort. It is so rambling and inconsecutive
+that it takes more than one reading to understand it. It is against the
+_Times_ newspaper. First, the following insinuation:
+
+"To the legal mind, the part of [the part taken by] the _Times_ will
+present a _prima facie_ case of the gravest nature, in the evident
+fore-knowledge of the event, and the preparation to turn it to account when
+it should have occurred. The article printed on Saturday must have been
+written on Friday. That article could not have appeared had the Prince been
+intended to live."
+
+Next, it is affirmed that the _Times_ intended to convey the idea that the
+Prince had been poisoned.
+
+"Up to this point we are merely dealing with words which the _Times_
+publishes, and these can leave not a shadow of doubt that there is an
+intention to promulgate the idea that Prince Albert had been poisoned."
+
+The article then goes on with a strange olio of {140} insinuations to the
+effect that the Prince was the obstacle to Russian intrigue, and that if he
+should have been poisoned,--which the writer strongly hints may have been
+the case,--some Minister under the influence of Russia must have done it.
+Enough for this record. _Un sot trouve toujours un plus sot qui
+l'admire_:[247] who can he be in this case?
+
+
+
+THE NEPTUNE CONTROVERSY.
+
+1846. At the end of this year arose the celebrated controversy relative to
+the discovery of Neptune. Those who know it are well aware that Mr.
+Adams's[248] now undoubted right to rank with Le Verrier[249] was made sure
+at the very outset by the manner in which Mr. Airy,[250] the Astronomer
+Royal, came forward to state what had taken place between himself and Mr.
+Adams. Those who know all the story about Mr. Airy being arrested in his
+progress by the neglect of Mr. Adams to answer a letter, with all the
+imputations which might have been thrown upon himself for laxity in the
+matter, know also that Mr. Airy's conduct exhibited moral courage, honest
+feeling, and willingness to sacrifice himself, if need were, to the
+attainment of the ends of private justice, and the establishment of a
+national claim. A writer in a magazine, in a long and elaborate article,
+argued the supposition--put in every way except downright assertion, after
+the fashion of such things--that Mr. Airy had communicated Mr. Adams's
+results to M. Le Verrier, with intention that they should be used. His
+presumption as to motive is that, had Mr. Adams been recognized, "then the
+discovery must have been indisputably an _Englishman's_, and that
+Englishman not the Astronomer Royal." Mr. Adams's conclusions were
+"retouched in France, and sent {141} over the year after." The proof given
+is that it cannot be "imagined" otherwise.
+
+"Can it then be imagined that the Astronomer Royal received such results
+from Mr. Adams, supported as they were by Professor Challis's[251] valuable
+testimony as to their probable accuracy, and did not bring the French
+astronomer acquainted with them, especially as he was aware that his friend
+was engaged in matters bearing directly upon these results?"
+
+The whole argument the author styles "evidence which I consider it
+difficult to refute." He ends by calling upon certain persons, of whom I am
+one, to "see ample justice done." This is the duty of every one, according
+to his opportunities. So when the reputed author--the article being
+anonymous--was, in 1849, proposed as a Fellow of the Astronomical Society,
+I joined--if I remember right, I originated--an opposition to his election,
+until either the authorship should be denied, or a proper retraction made.
+The friends of the author neither denied the first, nor produced the
+second: and they judged it prudent to withdraw the proposal. Had I heard of
+any subsequent repentance, I would have taken some other instance, instead
+of this: should I yet hear of such a thing, I will take care to notice it
+in the continuation of this list, which I confidently expect, life and
+health permitting, to be able to make in a few years. This much may be
+said, that the author, in a lecture on the subject, given in 1849, and
+published with his name, did _not_ repeat the charge.
+
+[The libel was published in the _Mechanics' Magazine_,[252] (vol. for 1846,
+pp. 604-615): and the editor supported it as follows, (vol. for 1847, p.
+476). In answer to Mr. Sheepshanks's charitable hope that he had been
+hoaxed, {142} he says: "Mr. Sheepshanks cannot certainly have read the
+article referred to.... Severe and inculpatory it is--unjust some may deem
+it (though we ourselves are out of the number.)... A 'hoax' forsooth! May
+we be often the dupes of such hoaxes!" He then goes on to describe the
+article as directed against the Astronomer Royal's alleged neglect to give
+Mr. Adams that "encouragement and protection" which was his due, and _does
+not hint one word_ about the article containing the charge of having
+secretly and fraudulently transmitted news of Mr. Adams's researches to
+France, that an Englishman might not have the honor of the discovery. Mr.
+Sheepshanks having called this a "deliberate calumny," without a particle
+of proof or probability to support it, the editor says "what the reverend
+gentleman means by this, we are at a loss to understand." He then proceeds
+_not_ to remember. I repeat here, what I have said elsewhere, that the
+management of the journal has changed hands; but from 1846 to 1856, it had
+the collar of S.S. (scientific slander). The prayer for more such things
+was answered (See p. 349).]
+
+
+
+JAMES IVORY.[253]
+
+I have said that those who are possessed with the idea of conspiracy
+against themselves are apt to imagine both conspirators and their bad
+motives and actions. A person who should take up the idea of combination
+against himself without feeling ill-will and originating accusations would
+be indeed a paradox. But such a paradox has existed. It is very well known,
+both in and beyond the scientific world, that the late James Ivory was
+subject to the {143} impression of which I am speaking; and the diaries and
+other sources of anecdote of our day will certainly, sooner or later, make
+it a part of his biography. The consequence will be that to his memory will
+be attached the unfavorable impression which the usual conduct of such
+persons creates; unless it should happen that some one who knows the real
+state of the case puts the two sides of it properly together. Ivory was of
+that note in the scientific world which may be guessed from Laplace's
+description of him as the first geometer in Britain and one of the first in
+Europe. Being in possession of accurate knowledge of his peculiarity in
+more cases than one; and in one case under his own hand: and having been
+able to make full inquiry about him, especially from my friend the late
+Thomas Galloway[254]--who came after him at Sandhurst--one of the few
+persons with whom he was intimate:--I have decided, after full
+deliberation, to forestall the future biographies.
+
+That Ivory was haunted by the fear of which I have spoken, to the fullest
+extent, came to my own public and official knowledge, as Secretary of the
+Astronomical Society. It was the duty of Mr. Epps,[255] the Assistant
+Secretary, at the time when Francis Baily[256] first announced his
+discovery of the Flamsteed Papers, to report to me that Mr. Ivory had
+called at the Society's apartments to inquire into the contents of those
+papers, and to express his hope that Mr. Baily was not attacking living
+persons under the names of Newton and Flamsteed.[257] Mr. Galloway, to whom
+I communicated this, immediately went to Mr. Ivory, and succeeded, after
+some explanation, in setting him right. This is but one of many instances
+in which a man of thoroughly sound judgment in every other respect seemed
+to be under a complete chain of delusions about the conduct of {144} others
+to himself. But the paradox is this:--I never could learn that Ivory,
+passing his life under the impression that secret and unprovoked enemies
+were at work upon his character, ever originated a charge, imputed a bad
+motive, or allowed himself an uncourteous expression. Some letters of his,
+now in my possession, referring to a private matter, are, except in the
+main impression on which they proceed, unobjectionable in every point: they
+might have been written by a cautious friend, whose object was, if
+possible, to prevent a difference from becoming a duel without compromising
+his principal's rights or character. Knowing that in some quarters the
+knowledge of Ivory's peculiarity is more or less connected with a notion
+that the usual consequences followed, I think the preceding statement due
+to his memory.
+
+
+
+THREE CLASSES OF JOURNALS.
+
+In such a record as the present, which mixes up the grossest speculative
+absurdities with every degree of what is better, an instance of another
+kind may find an appropriate place. The faults of journalism, when merely
+exposed by other journalism pass by and are no more regarded. A distinct
+account of an undeniable meanness, recorded in a work of amusement and
+reference both, may have its use: such a thing may act as a warning. An
+editor who is going to indulge his private grudge may be prevented from
+counting upon oblivion as a matter of certainty.
+
+There are three kinds of journals, with reference to the mode of entrance
+of contributors. First, as a thing which has been, but which now hardly
+exists, there is the journal in which the editor receives a fixed sum to
+_find the matter_. In such a journal, every article which the editor can
+get a friend to give him is so much in his own pocket, which has a great
+tendency to lower the character of the articles; but I am not concerned
+with this point. Secondly, there is the journal which is supported by
+voluntary contributions of {145} matter, the editor selecting. Thirdly,
+there is the journal in which the contributor is paid by the proprietors in
+a manner with which the literary editor has nothing to do.
+
+The third class is the safe class, as its editors know: and, as a usual
+rule, they refuse unpaid contributions of the editorial cast. It is said
+that when Canning[258] declined a cheque forwarded for an article in the
+_Quarterly_, John Murray[259] sent it back with a blunt threat that if he
+did not take his money he could never be admitted again. The great
+publisher told him that if men like himself in position worked for nothing,
+all the men like himself in talent who could not afford it would not work
+for the _Quarterly_. If the above did not happen between Canning and
+Murray, it _must have happened_ between some other two. Now journals of the
+second class--and of the first, if such there be--have a fault to which
+they alone are very liable, to say nothing of the editorial function (see
+the paper at the beginning, p. 11 et seq.), being very much cramped, a sort
+of gratitude towards effective contributors leads the journal to help their
+personal likes and dislikes, and to sympathize with them. Moreover, this
+sort of journal is more accessible than others to articles conveying
+personal imputation: and when these provoke discussion, the journal is apt
+to take the part of the assailant to whom it lent itself in the first
+instance.
+
+
+
+THE MECHANICS' MAGAZINE.
+
+Among the journals which went all lengths with contributors whom they
+valued, was the _Mechanics' Magazine_[260] in the period 1846-56. I cannot
+say that matters have not mended in the last ten years: and I draw some
+{146} presumption that they have mended from my not having heard, since
+1856, of anything resembling former proceedings. And on actual inquiry,
+made since the last sentence was written, I find that the property has
+changed hands, the editor is no longer the same, and the management is of a
+different stamp. This journal is chiefly supported by voluntary articles:
+and it is the journal in which, as above noted, the ridiculous charge
+against the Astronomer Royal was made in 1849. The following instance of
+attempt at revenge is so amusing that I select it as the instance of the
+defect which I intend to illustrate; for its puerility brings out in better
+relief the points which are not so easily seen in more adult attempts.
+
+The _Mechanics' Magazine_, which by its connection with engineering, etc.,
+had always taken somewhat of a mathematical character, began, a little
+before 1846, to have more to do with abstract science. Observing this, I
+began to send short communications, which were always thankfully received,
+inserted, and well spoken of. Any one who looks for my name in that journal
+in 1846-49, will see nothing but the most respectful and even laudatory
+mention. In May 1849 occurred the affair at the Astronomical Society, and
+my share in forcing the withdrawal of the name of the alleged contributor
+to the journal. In February 1850 occurred the opportunity of payment. The
+_Companion to the Almanac_[261] had to be noticed, in which, as then usual,
+was an article signed with my name. I shall give the review of this article
+entire, as a sample of a certain style, as well as an illustration of my
+point. The reader will observe that my name is not mentioned. This would
+not have done; the readers of the Magazine would have stared to see a name
+of not infrequent occurrence in previous years all of a sudden fallen from
+the heaven of respect into the pit of contempt, like Lucifer, son of the
+morning. But before {147} giving the review, I shall observe that Mr.
+Adams, in whose _favor_ the attack on the Astronomer Royal was made, did
+not appreciate the favor; and of course did not come forward to shield his
+champion. This gave deadly offence, as appear from the following passage,
+(February 16, 1850):
+
+"It was our intention to enter into a comparison of the contents of our
+Nautical Almanack with those of its rival, the _Connaissance des Temps_;
+but we shall defer it for the present. The Nautical Almanack for 1851 will
+contain Mr. Adams's paper 'On the Perturbation of Uranus'; and when it
+comes, in due course, before the public, we are quite sure that that
+gentleman will expect that we shall again enter upon the subject with
+peculiar delight. Whilst we have a thorough loathing for mean, cowardly,
+crawlers--we have an especial pleasure in maintaining the claims of men who
+are truly grateful as well as highly talented: Mr. Adams, therefore, will
+find that he cannot be disappointed--and the occasion will afford us an
+opportunity for making the comparison to which we have adverted."
+
+This passage illustrates what I have said on the editorial function (Vol.
+I, p. 15). What precedes and follows has some criticism on the Government,
+the Astronomer Royal, etc., but reserved in allusion, oblique in sarcasm,
+and not fiercely uncourteous. The coarseness of the passage I have quoted
+shows editorial insertion, which is also shown by its blunder. The inserter
+is waiting for the Almanac of 1851 that he may review Mr. Adams's paper,
+which is to be contained in it. His own contributor, only two sentences
+before the insertion, had said, "The Nautical Almanac, we believe, is
+published three or four years in advance." In fact, the Almanac for
+1851--with Mr. Adams's paper at the end--was published at the end of 1847
+or very beginning of 1848; it had therefore been more than two years before
+the public when the passage quoted was written. And probably every person
+in the country who was fit to review Mr. Adams's {148} paper--and most of
+those who were fit to read it--knew that it had been widely circulated, in
+revise, at the end of 1846: my copy has written on it, "2d revise, December
+27, 1846, at noon," in the handwriting of the Superintendent of the
+Almanac; and I know that there was an extensive issue of these revises,
+brought out by the Le-Verrier-and-Adams discussion. I now give the review
+of myself, (February 23, 1850):
+
+"_The British Almanack and Companion._
+
+"The Companion to this Almanack, for some years after its first
+publication, annually contained scientific articles by Sir J. Lubbock[262]
+and others of a high order and great interest; we have now, however, closed
+the publication as a scientific one in remembrance of what it was, and not
+in consequence of what it is. Its list of contributors on science, has
+grown 'small by degrees and beautifully less,' until it has dwindled down
+to one--'a last rose of summer left withering alone.' The one contributor
+has contributed one paper 'On Ancient and Modern Usage in Reckoning.'
+
+"The learned critic's _chef d'oeuvre_, is considered, by competent judges,
+to be an Essay on _Old Almanacks_ printed a few years ago in this annual,
+and supposed to be written with the view of surpassing a profound memoir on
+the same subject by James O. Halliwell,[263] Esq., F.R. and A.S.S., but the
+tremendous effort which the learned writer then made to excel many titled
+competitors for honors in the antique line appears to have had a sad effect
+upon his mental powers--at any rate, his efforts have since yearly become
+duller and duller; happily, at last, we should suppose, 'the ancient {149}
+and modern usage in reckoning' indicates the lowest point to which the _vis
+inertia_ of the learned writer's peculiar genius can force him.
+
+"We will give a few extracts from the article.
+
+"The learned author says, 'Those who are accustomed to settle the meaning
+of ancient phrases by self-examination will find some _strange_ conclusions
+arrived at by us.' The writer never wrote a more correct sentence--it
+admits of no kind of dispute.
+
+"'Language and counting,' says the learned author, 'both came before the
+logical discussion of either. It is not allowable to argue that something
+is or was, because it ought to be or ought to have been. That two negatives
+make an affirmative, ought to be; if _no_ man have done _nothing_, the man
+who has done nothing does not exist, and _every_ man has done _something_.
+But in Greek, and in uneducated English, it is unquestionable that 'no man
+has done nothing' is only an emphatic way of saying that no man has done
+_anything_; and it would be absurd to reason that it could not have been
+so, because it should not.'--p. 5.
+
+"'But there _is_ another difference between old and new times, yet more
+remarkable, for we have _nothing_ of it now: whereas in things indivisible
+we count with our fathers, and should say in buying an acre of land, that
+the result has no parts, and that the purchaser, till he owns all the
+ground, owns none, the change of possession being instantaneous. This
+second difference lies in the habit of considering nothing, nought, zero,
+cipher, or whatever it may be called, to be at the beginning of the scale
+of numbers. Count four days from Monday: we should now say Tuesday,
+Wednesday, Thursday, Friday; formerly, it would have been Monday, Tuesday,
+Wednesday, Thursday. Had we asked, what at that rate is the first day from
+Monday, all would have stared at a phrase they had never heard. Those who
+were capable of extending language would have said, Why it must be Monday
+itself: the rest would have said, there can {150} be no first day from
+Monday, for the day after is Tuesday, which must be the second day: Monday,
+one; Tuesday, two,'--p. 10.
+
+"We assure our readers that the whole article is equally lucid, and its
+logic alike formal.
+
+"There are some exceedingly valuable footnotes; we give one of the most
+interesting, taken from the learned Mr. Halliwell's profound book on
+Nursery Rhymes[264]--a celebrated production, for which it is supposed the
+author was made F.R.S.
+
+ "'_One's nine_,
+  Two's some,
+  Three's a many,
+  Four's a penny,
+  Five's a little hundred.'
+
+'The last line refers to five score, the so-called hundred being more
+usually six score. The first line, looked at etymologically, is _one is not
+one_, and the change of thought by which _nine_, the decimal of _one_, aims
+to be associated with the decimal of _plurality_ is curious:'--Very.
+
+"This valuable and profound essay will very probably be transferred to the
+next edition of the learned Mr. Halliwell's rare work, of kindred worth,
+entitled 'RARA MATHEMATICA,' it will then be deservedly handed down to
+posterity as a covering for cheap trunks--a most appropriate archive for
+such a treasure."
+
+
+
+In December, 1846, the _Mechanics' Magazine_ published a libel on Airy in
+the matter of the discovery of Neptune. In May, 1849, one * * * was to have
+been brought forward for election at the Astronomical Society, and was
+opposed by me and others, on the ground that he was the probable author of
+this libel, and that he would not, perhaps could {151} not, deny it. [N.B.
+I no more doubt that he was the author then I doubt that I am the author of
+this sentence.][265]
+
+Accordingly, * * * was withdrawn, and a discussion took place, for which
+see the _Athenaeum_, No. 1126, May 26, 1849, p. 544. The _Mechanics'
+Magazine_ was very sore, but up to this day has never ventured beyond an
+attack on Airy, private whisperings against Adams--(see _ante_, p.
+147),--and the above against myself. In due time, I doubt not my name will
+appear as one of the _ames damnees_[266] of the _Mechanics' Magazine_.[267]
+
+
+
+T. S. DAVIES ON EUCLID.
+
+First, as to Mr. Halliwell. The late Thomas Stephens Davies,[268] excellent
+in geometry, and most learned in its history, was also a good hand at
+enmity, though not implacable. He and Mr. Halliwell, who had long before
+been very much one, were, at this date, very much two. I do not think T. S.
+Davies wrote this article; and I think that by giving my reasons I shall do
+service to his memory. It must have been written at the beginning of
+February; and within three days of that time T. S. Davies was making over
+to me, by his own free act, to be kept until claimed by the relatives, what
+all who knew even his writings knew that he considered as the most precious
+deposit he had ever had in his keeping--Horner's[269] papers. His letter
+announcing the transmission is dated February 2, 1850. This is a strong
+point; but there is another quite as strong. Euclid and {152} his writings
+were matters on which T. S. Davies knew neither fear nor favor: he could
+not have written lightly about a man who stood high with him as a judge of
+Euclid. Now in this very letter of Feb. 2, there is a sentence which I
+highly value, because, as aforesaid, it is on a point on which he would
+never have yielded anything, to which he had paid life-long attention, and
+on which he had the bias of having long stood alone. In fact, knowing--and
+what I shall quote confirms me,--that in the matter of Euclid his hand was
+against every man, I expected, when I sent him a copy of my 22-column
+article, "Eucleides" in Smith's _Dictionary_,[270] to have received back a
+criticism, that would have blown me out of the water: and I thought it not
+unlikely that a man so well up in the subject might have made me feel
+demolished on some points. Instead of this, I got the following: "Although
+on one or two minor points I do not quite accord with your views, yet as a
+whole and without regard to any minor points, I think you are the first who
+has succeeded in a delineation of Euclid as a geometer." All this duly
+considered, it is utterly incredible that T. S. Davies should have written
+the review in question. And yet Mr. Halliwell is treated just as T. S.
+Davies would have treated him, as to tone and spirit. The inference in my
+mind is that we have here a marked instance of the joining of hatreds which
+takes place in journals supported by voluntary contributions of matter.
+Should anything ever have revived this article--and no one ever knows what
+might have been fished up from the forgotten mass of journals--the
+treatment of Mr. Halliwell would certainly have thrown a suspicion on T. S.
+Davies, a large and regular contributor to the Magazine. It is good service
+to his memory to point out what makes it incredible that he should have
+written so unworthy an article.
+
+The fault is this. There are four extracts: the first {153} three are
+perfectly well printed. The printing of the _Mechanics' Magazine_ was very
+good. I was always exceedingly satisfied with the manner in which my
+articles appeared, without my seeing proof. Most likely these extracts were
+printed from my printed paper; if not the extractor was a good copier. I
+know this by a test which has often served me. I use the subjunctive--"if
+no man _have_ done nothing," an ordinary transcriber, narrating a quotation
+almost always lets his own habit write _has_. The fourth extract has three
+alterations, all tending to make me ridiculous. _None_ is altered, in two
+places, into _nine_, _denial_ into _decimal_, and _comes_ into _aims_; so
+that "none, the denial of one, comes to be associated with the denial of
+plurality," reads as "nine, the decimal of one, aims to be associated with
+the decimal of plurality." This is intentional; had it been a compositor's
+reading of bad handwriting, these would not have been the only mistakes; to
+say nothing of the corrector of the press. And both the compositor and
+reader would have guessed, from the first line being translated into "one
+is not one," that it must have been "one's none," not "one's nine." But it
+was not intended that the gem should be recovered from the unfathomed cave,
+and set in a Budget of Paradoxes.
+
+We have had plenty of slander-paradox. I now give a halfpennyworth of bread
+to all this sack, an instance of the paradox of benevolence, in which an
+individual runs counter to all the ideas of his time, and sees his way into
+the next century. At Amiens, at the end of the last century, an institution
+was endowed by a M. de Morgan, to whom I hope I am of kin, but I cannot
+trace it; the name is common at Amiens. It was the first of the kind I ever
+heard of. It is a Salle d'Asyle for children, who are taught and washed and
+taken care of during the hours in which their parents must be at work. The
+founder was a large wholesale grocer and colonial importer, who was made a
+Baron by Napoleon I for his commercial success and his charities. {154}
+
+
+
+JAS. SMITH AGAIN.
+
+1862. Mr. Smith replies to me, still signing himself Nauticus: I give an
+extract:
+
+"By hypothesis [what, again!] let 14 deg. 24' be the chord of an arc of
+15 deg. [but I wont, says 14 deg. 24'], and consequently equal to a side
+of a regular polygon of 24 sides inscribed in the circle. Then 4 times
+14 deg. 24' = 57 deg. 36' = the radius of the circle ..."
+
+That is, four times the chord of an arc is the chord of four times the arc:
+and the sum of four sides of a certain pentagon is equal to the fifth. This
+is the capital of the column, the crown of the arch, the apex of the
+pyramid, the watershed of the elevation. Oh! J. S.! J. S.! groans
+Geometry--_Summum J. S. summa injuria_![271] The other J. S., Joseph
+Scaliger,[272] as already mentioned, had his own way of denying that a
+straight line is always the shortest distance between two points. A
+parallel might be instituted, but not in half a column. And J. S. the
+_second_ has been so tightly handled that he may now be dismissed, with an
+inscription for his circular shield, obtained by changing _Lexica contexat_
+into _Circus quadrandus_ in an epigram of J. S. the _first_:
+
+ "Si quem dura manet sententia judicis, olim
+  Damnatum aerumnis suppliciisque caput,
+  Hunc neque fabrili lassent ergastula massa,
+  Nec rigidas vexent fossa metalla manus.
+  Circus quadrandus: nam--caetera quid moror?--omnes
+  Poenarum facies hic labor unus habet."[273]
+
+{155}
+
+I had written as far as _damnatum_ when in came the letter of Nauticus as a
+printed slip, with a request that I would consider the slip as a 'revised
+copy.' Not a word of alteration in the part I have quoted! And in the
+evening came a letter desiring that I would alter a gross error; but not
+the one above: this is revising without revision! If there were cyclometers
+enough of this stamp, they would, as cultivation progresses--and really,
+with John Stuart Mill in for Westminster, it seems on the move, even
+though, as I learn while correcting the proof, Gladstone be out from
+Oxford; for Oxford is no worse than in 1829, while Westminster is far above
+what she ever has been: election time excuses even such a parenthesis as
+this--be engaged to amuse those who can afford it with paralogism at their
+meals, after the manner of the other jokers who wore the caps and bells.
+The rich would then order their dinners with _panem et Circenses_,--up with
+the victuals and the circle-games--as the poor did in the days of old.
+
+Mr. Smith is determined that half a column shall not do. Not a day without
+something from him: letter, printed proof, pamphlet. In what is the last at
+this moment of writing he tells me that part of the title of a work of his
+will be "Professor De Morgan in the pillory without hope of escape." And
+where will he be himself? This I detected by an effort of reasoning which I
+never could have made except by following in his steps. In all matters
+connected with [pi] the letters l and g are closely related: this appears
+in the well-known formula for the time of oscillation [pi] [sqrt](l : g).
+Hence g may be written for l, but only once: do it twice, and you require
+the time to be [pi] [sqrt](l^2 : g^2). This may be reinforced by observing
+that if as a datum, or if you dislike that word, by hypothesis, the first l
+be a g, it is absurd that it should be an l. Write g for the first l, and
+we have _un fait accompli_. I shall be in pillory; and overhead, in a
+cloud, will sit Mr. James Smith on one stick laid across two others, under
+a nimbus of 3-1/8 diameters to {156} the circumference--in [pi]-glory. Oh
+for a drawing of this scene! Mr. De Morgan presents his compliments to Mr.
+James Smith, and requests the honor of an exchange of photographs.
+
+_July 26._--Another printed letter.--Mr. James Smith begs for a distinct
+answer to the following plain question: "Have I not in this communication
+brought under your notice _truths_ that were never before dreamed of in
+your geometrical and mathematical philosophy?" To which, he having taken
+the precaution to print the word _truths_ in italics, I can conscientiously
+answer, Yes, you have. And now I shall take no more notice of these
+_truths_, until I receive something which surpasses all that has yet been
+done.
+
+
+
+A FEW SMALL PARADOXERS.
+
+    The Circle secerned from the Square; and its area gauged in terms of a
+    triangle common to both. By Wm. Houlston,[274] Esq. London and Jersey,
+    1862, 4to.
+
+Mr. Houlston squares at about four poetical quotations in a page, and
+brings out [pi] = 3.14213.... His frontispiece is a variegated diagram,
+having parts designated Inigo and Outigo. All which relieves the subject,
+but does not remove the error.
+
+
+
+    Considerations respecting the figure of the Earth.... By C. F.
+    Bakewell.[275] London, 1862, 8vo.
+
+Newton and others think that in a revolving sphere the {157} loose surface
+matter will tend to the equator: Mr. Bakewell thinks it will tend to the
+poles.
+
+
+
+    On eccentric and centric force: a new theory of projection. By H. F. A.
+    Pratt, M.D.[276] London, 1862, 8vo.
+
+Dr. Pratt not only upsets Newton, but cuts away the very ground he stands
+on: for he destroys the first law of motion, and will not have the natural
+tendency of matter in motion to be rectilinear. This, as we have seen, was
+John Walsh's[277] notion. In a more recent work "On Orbital Motion,"
+London, 1863, 8vo., Dr. Pratt insists on another of Walsh's notions,
+namely, that the precession of the equinoxes is caused by the motion of the
+solar system round a distant central sun. In this last work the author
+refers to a few notes, which completely destroy the theory of gravitation
+in terms "perfectly intelligible as well to the unlearned as to the
+learned": to me they are quite unintelligible, which rather tends to
+confirm a notion I have long had, that I am neither one thing nor the
+other. There is an ambiguity of phrase which delights a writer on logic,
+always on the look-out for specimens of _homonymia_ or _aequivocatio_. The
+author, as a physician, is accustomed to "appeal from mere formulae":
+accordingly, he sets at nought the whole of the mathematics, which he does
+not understand. This equivocation between the formula of the physician and
+that of the mathematician is as good, though not so perceptible to the
+world at large, as that made by Mr. Briggs's friend in _Punch's_ picture,
+which I cut out to paste into my Logic. Mr. Briggs wrote for a couple of
+_bruisers_, meaning to prepare oats for his horses: his friend sent him the
+Whitechapel Chicken and the Bayswater Slasher, with the gloves, all ready.
+
+{158}
+
+
+
+    On matter and ether, and the secret laws of physical change. By T. R.
+    Birks, M.A.[278] Cambridge, 1862, 8vo.
+
+Bold efforts are made at molecular theories, and the one before me is ably
+aimed. When the Newton of this subject shall be seated in his place, books
+like the present will be sharply looked into, to see what amount of
+anticipation they have made.
+
+
+
+DR. THORN AND MR. BIDEN.
+
+    The history of the 'thorn tree and bush' from the earliest to the
+    present time: in which is clearly and plainly shown the descent of her
+    most gracious Majesty and her Anglo-Saxon people from the half tribe of
+    Ephraim, and possibly from the half tribe of Manasseh; and consequently
+    her right and title to possess, at the present moment, for herself and
+    for them, a share or shares of the desolate cities and places in the
+    land of their forefathers! By Theta, M.D.[279] (Private circulation.)
+    London, 1862, 8vo.
+
+This is much about _Thorn_, and its connected words, Thor, Thoth, Theta,
+etc. It is a very mysterious vagary. The author of it is the person whom I
+have described elsewhere as having for his device the round man in the
+three-cornered hole, the writer of the little heap of satirical anonymous
+letters about the Beast and 666. By accident I discovered the writer: so
+that if there be any more thorns to crackle under the pot, they need not be
+anonymous.
+
+Nor will they be anonymous. Since I wrote the above, I have received
+_onymous_ letters, as _ominous_ as the rest. The writer, William Thorn,
+M.D., is obliged to reveal {159} himself, since it is his object to prove
+that he himself is one 666. By using W for double Vau (or 12) he cooks the
+number out of his own name. But he says it is the number not of a beast but
+of a man, and adds, "Thereby hangs a tale!" which sounds like
+contradiction. He informs me that he will talk the matter over with me: but
+I shall certainly have nothing to say to a gentleman of his number; it is
+best to keep on the safe side.
+
+In one letter I am informed that not a line should I have had, but for my
+"sneer at 666," which, therefore, I am well pleased to have given. I am
+also told that my name means the "'garden of death,' that place in which
+the tree of knowledge was plucked, and so you are like your name 'dead' to
+the fact that you are an Israelite, like those in Ezekiel 37 ch." Some
+hints are given that I shall not fare well in the next world, which any one
+who reads the chapter in Ezekiel will see is quite against his comparison.
+The reader must not imagine that my prognosticator means _Morgan_ to be a
+corruption of _Mortjardin_; he proves his point by Hebrew: but any
+philologist would tell him the true derivation of the name, and how
+_Glamorgan_ came to get it. It will be of much comfort to those young men
+who have not got through to know that the tree of knowledge itself was once
+in the same case. And so good bye to 666 for the present, and the
+assumption that the enigma is to be solved by the united numeral forces of
+the letters of a word.
+
+It is worthy of note that, as soon as my Budget commenced, two guardian
+spirits started up, fellow men as to the flesh, both totally unknown to me:
+they have stuck to me from first to last. James Smith, Esq., finally
+Nauticus, watches over my character in this world, and would fain preserve
+me from ignorance, folly, and dishonesty, by inclosing me in a magic circle
+of 3-1/8 diameters in circumference. The round man in the three-cornered
+hole, finally William Thorn, M.D., takes charge of my future destiny, {160}
+and tries to bring me to the truth by unfolding a score of meanings--all
+right--of 666. He hints that I, and my wife, are servants of Satan: at
+least he desires us both to remember that we cannot serve God and Satan;
+and he can hardly mean that we are serving the first, and that he would
+have us serve the second. As becomes an interpreter of the Apocalypse, he
+uses seven different seals; but not more than one to one letter. If his
+seals be all signet-rings, he must be what Aristophanes calls a
+sphragidonychargocometical fellow. But--and many thanks to him for the
+same--though an M.D., he has not sent me a single vial. And so much for my
+tree of secular knowledge and my tree of spiritual life: I dismiss them
+with thanks from myself and thanks from my reader. The dual of the
+Pythagorean system was Isis and Diana; of the Jewish law, Moses and Aaron;
+and of the City of London, Gog and Magog; of the Paradoxiad, James Smith,
+Esq., and William Thorn, M.D.
+
+_September, 1866._ Mr. James Biden[280] has favored me with some of his
+publications. He is a rival of Dr. Thorn; a prophet by name-right and
+crest-right. He is of royal descent through the De Biduns. He is the
+_watchman_ of Ezekiel: God has told him so. He is the author of _The True
+Church_, a phrase which seems to have a book-meaning and a mission-meaning.
+He shall speak for himself:
+
+"A crest of the Bidens has significance. It is a lion rampant between
+wings--wings in Scripture denote the flight of time. Thus the beasts or
+living creatures of the Revelations have each six wings, intimating a
+condition of mankind up to and towards the close of six thousand years of
+Bible teaching. The two wings of the crest would thus intimate power
+towards the expiration of 2000 years, as time is marked in the history of
+Great Britain.
+
+{161}
+
+"In a recent publication, _The Pestilence, Why Inflicted_, are given many
+reasons why the writer thinks himself to be the appointed watchman foretold
+by Ezekiel, chapters iii. and xxxiii. Among the reasons are many prophecies
+fulfilled in him. Of these it is now needful to note two as bearing
+especially on the subject of the reign of Darius.
+
+"1.--In Daniel it is said, 'Darius the Median took the kingdom, being about
+threescore and two years old.'--Daniel v. 31.
+
+"When 'Belshazzar' the king of the Chaldeans is found wanting, Darius takes
+the kingdom. It is not given him by the popular voice; he asserts his
+right, and this is not denied. He takes it when about sixty-two years of
+age. The language of Daniel is prophetic, and Darius has in another an
+antitype. The writer was born July 18th, 1803; and the claim was asserted
+at the close of 1865, when he was about sixty-two years of age.
+
+"The claims which have been asserted demand a settled faith, and which
+could only be reached through a long course of divine teaching."
+
+When I was a little boy at school, one of my school-fellows took it into
+his head to set up a lottery of marbles: the thing took, and he made a
+stony profit. Soon, one after another, every boy had his lottery, and it
+was, "I won't put into yours unless you put into mine." This knocked up the
+scheme. It will be the same with the prophets. Dr. Thorn, Mr. Biden, Mrs.
+Cottle,[281] etc. will grow imitators, until we are all pointed out in the
+Bible: but A will not admit B's claim unless B admits his. For myself, as
+elsewhere shown, I am the first Beast in the Revelations.
+
+Every contraband prophet gets a few followers: it is a great point to make
+these sequacious people into Buridan's asses, which they will become when
+prophets are so numerous that there is no choosing.
+
+{162}
+
+
+
+SIR G. C. LEWIS.
+
+    An historical survey of the Astronomy of the Ancients. By the Rt. Hon.
+    Sir G. C. Lewis.[282] 8vo. 1862.
+
+There are few men of our day whom I admire more than the late Sir G. Lewis:
+he was honest, earnest, sagacious, learned, and industrious. He probably
+sacrificed his life to his conjunction of literature and politics: and he
+stood high as a minister of state in addition to his character as a man of
+letters. The work above named is of great value, and will be read for its
+intrinsic merit, consulted for its crowd of valuable references, quoted for
+its aid to one side of many a discussion, and opposed for its force against
+the other. Its author was also a wit and a satirist. I know of three
+classical satires of our day which are inimitable imitations: Mr.
+Malden's[283] _Pragmatized Legends_, Mr. Mansel's[284] _Phrontisterion_,
+and Sir G. Cornewall Lewis's _Inscriptio Antiqua_. In this last,
+HEYDIDDLEDIDDLETHECATANDTHEFIDDLE etc. is treated as an Oscan inscription,
+and rendered into Latin by approved methods. As few readers have seen it, I
+give the result:
+
+    "Hejus dedit libenter, dedit libenter. Deus propitius [est], deus
+    [donatori] libenter favet. Deus in viarum {163} junctura ovorum dape
+    [colitur], deus mundi. Deus in litatione voluit, benigno animo, haedum,
+    taurum intra fines [loci sacri] portandos. Deus, bis lustratus, beat
+    fossam sacrae libationis."[285]
+
+How then comes the history of astronomy among the paradoxes? Simply because
+the author, so admirably when writing about what he knew, did not know what
+he did not know, and blundered like a circle-squarer. And why should the
+faults of so good a writer be recorded in such a list as the present? For
+three reasons: First, and foremost, because if the exposure be not made by
+some one, the errors will gradually ooze out, and the work will get the
+character of inaccurate. Nothing hurts a book of which few can fathom the
+depths so much as a plain blunder or two on the surface. Secondly, because
+the reviews either passed over these errors or treated them too gently,
+rather implying their existence than exposing them. Thirdly, because they
+strongly illustrate the melancholy truth, that no one knows enough to write
+about what he does not know. The distinctness of the errors is a merit; it
+proceeds from the clear-headedness of the author. The suppression in the
+journals may be due partly to admiration of the talent and energy which
+lived two difficult lives at once, partly to respect for high position in
+public affairs, partly to some of the critics being themselves men of
+learning only, unable to detect the errors. But we know that action and
+reaction are equal and contrary. If our generation take no notice of
+defects, and allow them to go down undetected among merits, the next
+generation will discover them, will perhaps believe us incapable of
+detecting them, at least will pronounce our judgment good for nothing, and
+will form an {164} opinion in which the merits will be underrated: so it
+has been, is, and will be. The best thing that can be done for the memory
+of the author is to remove the unsound part that the remainder may thrive.
+The errors do not affect the work; they occur in passages which might very
+well have been omitted: and I consider that, in making them conspicuous, I
+am but cutting away a deleterious fungus from a noble tree.
+
+(P. 154). The periodic times of the five planets were stated by
+Eudoxus,[286] as we learn from Simplicius;[287] the following is his
+statement, to which the true times are subjoined, for the sake of
+comparison:
+
+            STATEMENT OF EUDOXUS        TRUE TIME
+  Mercury          1 year             --    87d. 23h.
+  Venus            1   "              --   224d. 16h.
+  Mars             2   "              1y.  321d. 23h.
+  Jupiter         12   "             11y.  315d. 14h.
+  Saturn          30   "             29y.  174d.  1h.
+
+Upon this determination two remarks may be made. First, the error with
+respect to Mercury and Venus is considerable; with respect to Mercury, it
+is, in round numbers, 365 instead of 88 days, more than four times too
+much. Aristotle remarks that Eudoxus distinguishes Mercury and Venus from
+the other three planets by giving them one sphere each, with the poles in
+common. The proximity of Mercury to the sun would render its course
+difficult to observe and to measure, but the cause of the large error with
+respect to Venus (130 days) is not apparent.
+
+{165}
+
+Sir G. Lewis takes Eudoxus as making the planets move round the sun; he has
+accordingly compared the _geocentric_ periods of Eudoxus with our
+_heliocentric_ periods. What greater blunder can be made by a writer on
+ancient astronomy than giving Eudoxus the Copernican system? If Mercury
+were a black spot in the middle of the sun it would of course move round
+the earth in a year, or appear to do so: let it swing a little on one side
+and the other of the sun, and the average period is still a year, with
+slight departures both ways. The same for Venus, with larger departures.
+Say that a person not much accustomed to the distinction might for once
+write down the mistake; how are we to explain its remaining in the mind in
+a permanent form, and being made a ground for such speculation as that of
+the difficulty of observing Mercury leading to a period four times what it
+ought to be, corrected in proof and published by an industrious and
+thoughtful person? Only in one way: the writer was quite out of his depth.
+This one case is conclusive; be it said with all respect for the real
+staple of the work and of the author. He knew well the difference of the
+systems, but not the effect of the difference: he is another instance of
+what I have had to illustrate by help of a very different person, that it
+is difficult to reason well upon matter which is not familiar.
+
+
+
+(P. 254). Copernicus, in fact, supposed the axis of the earth to be always
+turned towards the Sun.^{(169)} [(169). See Delambre, _Hist. Astr. Mod._,
+Vol. I, p. 96]. It was reserved to Kepler to propound the hypothesis of the
+constant parallelism of the earth's axis to itself.
+
+
+
+If there be one thing more prominent than another in the work of Copernicus
+himself, in the popular explanations of it, and in the page of
+Delambre[288] cited, it is that the _parallelism of the earth's axis_ is a
+glaring part of the {166} theory of Copernicus. What Kepler[289] did was to
+throw away, as unnecessary, the method by which Copernicus, _per fas et
+nefas_,[290] secured it. Copernicus, thinking of the earth's orbital
+revolution as those would think who were accustomed to the _solid
+orbs_--and much as the stoppers of the moon's rotation do now: why do they
+not strengthen themselves with Copernicus?--thought that the earth's axis
+would always incline the same end towards the sun, unless measures were
+taken to prevent it. He _did_ take measures: he invented a _compensating_
+conical motion of the axis to preserve the parallelism; and, which is one
+of the most remarkable points of his system, he obtained the precession of
+the equinoxes by giving the necessary trifle more than compensation. What
+stares us in the face at the beginning of the paragraph to which the author
+refers?
+
+"C'est donc pour arriver a ce parallelisme, ou pour le conserver, que
+Copernic a cru devoir recourir a ce mouvement egal et oppose qui detruit
+l'effet qu'il attribue si gratuitement au premier, de deranger le
+parallelisme."[291]
+
+Parallelism at any price, is the motto of Copernicus: you need not pay so
+dear, is the remark of Kepler.
+
+The opinions given by Sir G. Lewis about the effects of modern astronomy,
+which he does not understand and singularly undervalues, will now be seen
+to be of no authority. He fancies that--to give an instance--for the
+determination of a ship's place, the invention of chronometers has been far
+more important than any improvement in astronomical theory (p. 254). Not to
+speak of latitude,--though the omission is not without importance,--he
+ought to have known that longitude is found by the difference between what
+o'clock it is at Greenwich and at the ship's place, at {167} one absolute
+moment of time. Now if a chronometer were quite perfect--which no
+chronometer is, be it said--and would truly tell Greenwich mean time all
+over the world, it ought to have been clear that just as good a watch is
+wanted for the time at _the place of observation_, before the longitude of
+that place with respect to Greenwich can be found. There is no such watch,
+except the starry heaven itself: and that watch can only be read by
+astronomical observation, aided by the best knowledge of the heavenly
+motions.
+
+I think I have done Sir G. Lewis's very excellent book more good than all
+the reviewers put together.
+
+I will give an old instance in which literature got into confusion about
+astronomy. Theophrastus,[292] who is either the culprit or his historian,
+attributes to Meton,[293] the contriver of the lunar calendar of nineteen
+years, which lasts to this day, that his solstices were determined for him
+by a certain Phaeinus of Elis on Mount Lycabettus. Nobody else mentions
+this astronomer: though it is pretty certain that Meton himself made more
+than one appointment with him for the purpose of observing solstices; and
+we may be sure that if either were behind his time, it was Meton. For
+_Phaeinus Helius_ is the shining sun himself; and in the astronomical poet
+Aratus[294] we read about the nineteen years of the shining sun:
+
+  [Greek: Enneakaideka kukla phaeinou eelioio].[295]
+
+Some man of letters must have turned Apollo into Phaeinus of Elis; and
+there he is in the histories of astronomy to {168} this day. Salmasius[296]
+will have Aratus to have meant him, and proposes to read [Greek: eleioio]:
+he did not observe that Phaeinus is a very common adjective of Aratus, and
+that, if his conjecture were right, this Phaeinus would be the only
+non-mythical man in the poems of Aratus.
+
+[When I read Sir George Lewis's book, the points which I have criticized
+struck me as not to be wondered at, but I did not remember why at the time.
+A Chancellor of the Exchequer and a writer on ancient astronomy are birds
+of such different trees that the second did not recall the first. In 1855 I
+was one of a deputation of about twenty persons who waited on Sir G. Lewis,
+as Chancellor of the Exchequer, on the subject of a decimal coinage. The
+deputation was one of much force: Mr. Airy, with myself and others,
+represented mathematics; William Brown,[297] whose dealings with the United
+States were reckoned by yearly millions, counted duodecimally in England
+and decimally in America, was the best, but not the only, representative of
+commerce. There were bullionists, accountants, retailers, etc. Sir G. L.
+walked into the room, took his seat, and without waiting one moment, began
+to read the deputation a smart lecture on the evils of a decimal coinage;
+it would require alteration of all the tables, it would impede calculation,
+etc. etc. Of those arguments against it which weighed with many of better
+knowledge than his, he obviously knew nothing. The members of the
+deputation began to make their statements, and met with curious denials. He
+interrupted me with "Surely there is no doubt that the calculations of our
+books of arithmetic are easier {169} than those in the French books." He
+was not aware that the _universally admitted_ superiority of decimal
+_calculation_ made many of those who prefer our system for the market and
+the counter cast a longing and lingering look towards decimals. My answer
+and the smiles which he saw around, made him give a queer puzzled look,
+which seemed to say, "I may be out of my depth here!" His manner changed,
+and he listened. I saw both the slap-dash mode in which he dealt with
+subjects on which he had not thought, and the temperament which admitted
+suspicion when the means of knowledge came in his way. Having seen his two
+phases, I wonder neither at his more than usual exhibition of shallowness
+when shallow, nor at the intensity of the contrast when he had greater
+depth.]
+
+
+
+DECIMAL COINAGE.
+
+Among the paradoxers are the political paradoxers who care not how far they
+go in debate, their only object being to carry the House with them for the
+current evening. What I have said of editors I repeat of them. The
+preservation of a very marked instance, the association of political
+recklessness with cyclometrical and Apocalyptic absurdity, may have a
+tendency to warn, not indeed any hardened public-man and sinner, but some
+young minds which have yearnings towards politics, and are in formation of
+habits.
+
+In the debate on decimal coinage of July 12, 1855, Mr. Lowe,[298] then
+member for Kidderminster, an effective speaker and a smart man, exhibited
+himself in a speech on which I wrote a comment for the Decimal Association.
+I have seldom seen a more wretched attempt to distort the points of a
+public question than the whole of this speech. Looking at the intelligence
+shown by the speaker on other occasions, {170} it is clear that if charity,
+instead of believing all things, believed only all things but one, he might
+tremble for his political character; for the honesty of his intention on
+this occasion might be the incredible exception. I give a few paragraphs
+with comments:
+
+"In commenting on the humorous, but still argumentative speech of Mr. Lowe,
+the member for Kidderminster, we may observe, in general, that it consists
+of points which have been several times set forth, and several times
+answered. Mr. Lowe has seen these answers, but does not allude to them, far
+less attempt to meet them. There are, no doubt, individuals, who show in
+their public speaking the outward and visible signs of a greater degree of
+acuteness than they can summon to guide their private thinking. If Mr. Lowe
+be not one of these, if the power of his mind in the closet be at all
+comparable to the power of his tongue in the House, it may be suspected
+that his reserve with respect to what has been put forward by the very
+parties against whom he was contending, arises from one or both of two
+things--a high opinion of the arguments which he ignored--a low opinion of
+the generality of the persons whom he addressed. [Both, I doubt not].
+
+"Did they calculate in florins  In the name of common sense,
+?"                              how can it be objected to a
+                                system that people do not use
+                                it before it is introduced?
+                                Let the decimal system be
+                                completed, and calculation
+                                shall be made in florins; that
+                                is, florins shall take their
+                                proper place. If florins were
+                                introduced _now_, there must
+                                be a column for the odd
+                                shilling.
+"He was glad that some hon.     If the hon. gentleman make
+gentleman had derived benefit   this assertion of himself, it
+from the issue of florins. His  is not for us to gainsay it.
+only experience of their        It only proves that he is one
+convenience was, that when he   of that class of {171} men who
+ought to have received          are described in the old song,
+half-a-crown, he had generally  of which one couplet runs
+received a florin, and when he  thus:
+ought to have paid a florin,
+he had generally paid               I sold my cow to buy me a
+half-a-crown." (Hear, hear,     calf;
+and laughter.)                  I never make a bargain but I
+                                lose half,
+                                With a etc. etc. etc.
+
+But he cannot mean that Englishmen in general are so easily managed. And as
+to Jonathan, who is but John lengthened out a little, he would see creation
+whittled into chips before he would even split what may henceforth be
+called the Kidderminster difference. The House, not unmoved--for it
+laughed--with sly humor decided that the introduction of the florin had
+been "eminently successful and satisfactory."
+
+The truth is that Mr. Lowe here attacks nothing except the coexistence of
+the florin and half-crown. We are endeavoring to abolish the half-crown.
+Let Mr. Lowe join us; and he will, if we succeed, be relieved from the
+pressure on his pocket which must arise from having the turn of the market
+always against him.
+
+"From a florin they get to 2    Note the sophism of expressing
+2-5ths of a penny, but who      our coin in terms of the
+ever bought anything, who ever  penny, which we abandon,
+reckoned or wished to reckon    instead of the florin, which
+in such a coin as that?"        we retain. Remember that this
+(Hear, hear.)                   2 2-5ths is the hundredth part
+                                of the pound, which is called,
+                                as yet, a _cent_. Nobody buys
+                                anything at a cent, because
+                                the cent is not yet
+                                introduced. Nobody reckons in
+                                cents for the same reason.
+                                Everybody wishes to reckon in
+                                cents, who wishes to combine
+                                the advantage of decimal
+                                reckoning with the
+                                preservation of the pound as
+                                {172} the highest unit of
+                                account; amongst others, a
+                                majority of the House of
+                                Commons, the Bank of England,
+                                the majority of London
+                                bankers, the Chambers of
+                                Commerce in various places,
+                                etc. etc. etc.
+"Such a coin could never come   Does 2-1/2d. never pass from
+into general circulation        hand to hand? And is 2-1/2d.
+because it represents nothing   so precisely the modulus of
+which corresponds with any of   popular wants, that an
+the wants of the people."       alteration of 4 per cent.
+                                would make it useless? Of all
+                                the values which 2-1/2d.
+                                measures, from three pounds of
+                                potatoes down to certain
+                                arguments used in the House of
+                                Commons, there is not one for
+                                which a cent would not do just
+                                as well. Mr. Lowe has fallen
+                                into the misconception of the
+                                person who admired the
+                                dispensation of Providence by
+                                which large rivers are made to
+                                run through cities so great
+                                and towns so many. If the cent
+                                were to be introduced
+                                to-morrow, straightway the
+                                buns and cakes, the soda-water
+                                bottles, the short omnibus
+                                fares, the bunches of
+                                radishes, etc. etc. etc.,
+                                would adapt themselves to the
+                                coin.
+"If the proposed system were    The confusion of ideas here
+adopted, they would all be      exhibited is most instructive.
+compelled to live in decimals   The speaker is under the
+for ever; if a man dined at a   impression that _we_ are
+public house he would have to   introducing fractions: the
+pay for his dinner in decimal   truth is, that we only want to
+fractions. (Hear, hear.) He     abandon the _more difficult_
+objected to that, for he        fractions which we _have got_,
+thought that a man ought to be  and to introduce _easier
+able to pay for his dinner in   fractions_. Does he deny this?
+integers." (Hear, hear, and a   Let us trace his denial to its
+laugh.)                         legitimate consequences. A man
+                                ought to pay for his dinner in
+                                integers.
+
+{173}
+
+Now, if Mr. Lowe insists on it that our integer is the pound, he is bound
+to admit that the present integer is the pound, of which a shilling, etc.,
+are fractions. The next time he has a chop and a pint of stout in the city,
+the waiter should say--"A pound, sir, to you," and should add, "Please to
+remember the waiter in integers." Mr. Lowe fancies that when he pays one
+and sixpence, he pays in integers, and so he does, if his integer be a
+penny or a sixpence. Let him bring his mind to contemplate a mil as the
+integer, the lowest integer, and the seven cents five mils which he would
+pay under the new system would be payment in integers also. But, as it
+happens with some others, he looks _up_ the present system, with
+Cocker,[299] and Walkingame,[300] and always looks _down_ the proposed
+system. The word _decimal_ is obstinately associated with _fractions_, for
+which there is no need. Hence it becomes so much of a bugbear, that, to
+parody the lines of Pope, which probably suggested one of Mr. Lowe's
+phrases--
+
+ "Dinner he finds too painful an endeavor,
+  Condemned to pay in decimals for ever."
+
+"The present system, however,   A pleasant sum even for an
+had not yet been changed into   accomplished mathematician.
+decimal system. That change     What does divided by the
+might appear very easy to       decimal of a pound mean?
+accomplished mathematicians     Perhaps it means _reduced_ to
+and men of science, but it was  the decimal of a pound! Mr.
+one which it would be very      Lowe supposes, as many others
+difficult to carry out. (Hear,  do, that, after the change,
+hear). What would have to be    all calculations will be
+done? Every sum would have to   _proposed in old money_, and
+be reduced into a vulgar        then _converted into new_. He
+fraction of a pound, and then   cannot hit the {174} idea that
+divided by the decimal of a     the new coins will take the
+pound--a pleasant sum for an    place of the old. This lack of
+old applewoman to work out!"    apprehension will presently
+(Hear, hear, and laughter.)     appear further.
+"It would not be an agreeable   Let the members be assured
+task, even for some members of  that nine half-pence will be,
+that House, to reduce 4-1/2d.,  for every practical purpose,
+or nine half-pence, to mils."   18 mils. But now to the fact
+(Hear, hear.)                   asserted. Davies Gilbert[301]
+                                used to maintain that during
+                                the long period he sat in the
+                                House, he never knew more than
+                                three men in it, at one time,
+                                who had a tolerable notion of
+                                fractions. [I heard him give
+                                the names of three at the time
+                                when he spoke: they were
+                                Warburton,[302] Pollock,[303]
+                                and Hume.[304] He himself was
+                                then out of Parliament.]
+                                Joseph Hume affirmed that he
+                                had never met with more than
+                                ten members who were
+                                arithmeticians. But both these
+                                gentlemen had a high standard.
+                                Mr. Lowe has given a much more
+                                damaging opinion. He evidently
+                                means that the general run of
+                                members could not do his
+                                question. It is done as
+                                follows: Since farthings gain
+                                on mils, at the rate of a
+                                whole mil in 24 farthings (24
+                                farthings being 25 mils), it
+                                is clear that 18 farthings
+                                being three-quarters of 24
+                                farthings, will gain
+                                three-quarters of a mil; that
+                                is, 18 farthings are eighteen
+                                {175} mils and three-quarters
+                                of a mil. Any number of
+                                farthings is as many mils and
+                                as many twenty-fourths of a
+                                mil. To a certain extent, we
+                                feel able to protest against
+                                the manner in which
+                                Kidderminster has treated the
+                                other constituencies. We do
+                                not hold it impossible to give
+                                the Members of the House in
+                                general a sufficient knowledge
+                                of the meaning and
+                                consequences of the _decimal_
+                                succession of units, tens,
+                                hundreds, thousands, etc.; and
+                                we believe that there are in
+                                the House itself competent
+                                men, in number enough to teach
+                                all the rest. All that is
+                                wanted is the power of
+                                starting from the known to
+                                arrive at the unknown. Now
+                                there is one kind of decimals
+                                with which every member is
+                                acquainted--the _Chiltern
+                                Hundreds_. If public opinion
+                                would enable the competent
+                                minority to start from this in
+                                their teaching, not as a
+                                basis, but as an alternative,
+                                in three weeks the
+                                fundamentals would be
+                                acquired, and members in
+                                general would be as fit to
+                                turn 4-1/2d. into mils, as any
+                                boys on the lower forms of a
+                                commercial school.
+
+                                For a long period of years,
+                                allusion to the general
+                                ignorance of arithmetic, has
+                                been a standing mode of
+                                argument, and has always been
+                                well received: whenever one
+                                member describes others as
+                                _knownothings_, those others
+                                cry _Hear_ to the country in a
+                                transport of delight. In the
+                                meanwhile the country is
+                                gradually arriving at the
+                                conclusion that a true joke is
+                                no joke.
+"The main objection was, if     Fine words, wrongly used. The
+they went below 6d., that the   new coins are commensurable
+new scale of coins would not    with, and in a finite ratio
+be commensurate in any finite   to, the old ones. The farthing
+ratio with anything in this     is to the mil as 25 to 24. The
+new currency of mils."          speaker has something here in
+                                the bud, which we shall
+                                presently meet with in the
+                                flower; and fallacies are more
+                                easily nipped in flower than
+                                in bud. {176}
+"No less than five of our       This dreadful change of value
+present coins must be called    consists in sixpence farthing
+in, or else--which would be     going to the half-shilling
+worse--new values must be       instead of sixpence. Whether
+given to them."                 the new farthings be called
+                                mils or not is of no
+                                consequence.
+"If a poor man put a penny in   Mr. Lowe, who cannot pass a
+his pocket, it would come out   half-crown for more than a
+a coin of different value,      florin, or get in a florin at
+which he would not understand.  less than half-a-crown, has
+Suppose he owed another man a   such a high faith in the
+penny, how was he to pay him ?  sterner stuff of his fellow
+Was he to pay him in mils?      countrymen, that he believes
+Four mils would be too little,  any two of them would go to
+and five mils would be too      fisty cuffs for the 25th part
+much. The hon. gentlemen said   of a farthing. He reasons
+there would be only a mil       thus: He has often heard in
+between them. That was exactly  the streets, "I'd fight you
+it. He believed there would be  for the fiftieth part of a
+a 'mill' between them." (Much   farden:" and having (that is,
+laughter.)                      for a Member) a notion both of
+                                fractions and logic, he infers
+                                that those who would fight for
+                                the 50th of a farthing would,
+                                _a fortiori_, fight for a
+                                25th. His mistake arises from
+                                his not knowing that when a
+                                person offers to fight another
+                                for 1/200d., he really means
+                                to fight for love; and that
+                                the stake is merely a matter
+                                of form, a feigned issue, a
+                                _pro forma_ report of
+                                progress. Do the Members of
+                                the House think they have all
+                                the forms to themselves?
+"What would be the present      We should hardly believe all
+expression for four-pence?      this to be uttered in earnest,
+Why, 0.166 (a laugh); for       if we had not known {177} that
+threepence? .0125; for a        several persons who have not
+penny? .004166, and so on _ad   Mr. Lowe's humor, nevertheless
+infinitum_ (a laugh); for a     have his impressions on this
+half-penny? .002083 _ad         point. It must therefore be
+infinitum_. (A laugh). What     answered; but how is this to
+would be the present            be done seriously?
+expression for a farthing?
+Why, .0010416 _ad infinitum_.   _Dialogue between a member of
+(A laugh). And this was the     Parliament and an orange-boy,
+system which was to cause such  three days after the
+a saving in figures, and these  introduction of the complete
+were the quantities into which  decimal system. The member,
+the poor would have to reduce   going down to the House, wants
+the current coin of the realm.  oranges to sustain his voice
+(Cheers). With every respect    in a two hours' speech on
+for decimal fractions, of       moving that 100000l. be placed
+which he boasted no profound    at the disposal of Her
+knowledge, he doubted whether   Majesty, to supply the poor
+the poor were equal to mental   with ready-reckoners._
+arithmetic of this kind,
+(hear, hear) and he hoped the   _Boy._ Fine oranges! two a
+adoption of the system would    penny! two a penny! {178}
+be deferred until there were
+some proof that they would be   _Member._ Here boy, two! Now,
+able to understand it; for,     how am I to pay you?
+after all, this was the
+question of the poor, and the   _Boy._ Give you change, your
+whole weight of the change      honor.
+would fall upon them. Let the
+rich by all means have          _Member._ Ah! but how? Where's
+permission to perplex           your ready-reckoner?
+themselves by any division of
+a pound they pleased; but do    _Boy._ I sells a better sort
+not let them, by any            nor them. Mine's real Cheyny.
+experiment like this, impose
+difficulties upon the poor and  _Member._ But you see a
+compel men to carry             farthing is now .0014166666
+ready-reckoners in their        _ad infinitum_, and if we
+pocket to give them all these   multiply this by 4----
+fractional quantities." (Hear,
+hear.)                          _Boy._ Hold hard, Guv'ner; I
+                                sees what you're arter. Now
+                                what'll you stand if I puts
+                                you up to it? which Bill Smith
+                                he put me up in two minutes,
+                                cause he goes to the Ragged
+                                School.
+
+                                _Member._ You don't mean that
+                                you do without a book!
+
+                                _Boy._ Book be blowed. Come
+                                now, old un, here's summut for
+                                both on us. I got a florin,
+                                you gives me a half-a-crown
+                                for it, and I larns you the
+                                new money, gives you your
+                                oranges, and calls you a brick
+                                into the bargain.
+
+                                _Member_ (_to himself_). Never
+                                had such a chance of getting
+                                off half-a-crown for value
+                                since that ---- fellow Bowring
+                                carried his crochet.
+                                (_Aloud._) Well, boy, it's a
+                                bargain. Now!
+
+                                _Boy._ Why, look 'e here, my
+                                trump, its a farden more to
+                                the tizzy--that's what it is.
+
+                                _Member_. What's that?
+
+                                _Boy._ Why, you knows a
+                                sixpence when you sees it.
+                                (_Aside_). Blest if I think he
+                                does! Well, its six browns and
+                                a farden now. A lady buys two
+                                oranges, and forks {179} out a
+                                sixpence; well in coorse, I
+                                hands over fippence farden
+                                astead of fippence. I always
+                                gives a farden more change,
+                                and takes according.
+
+                                _Member_ (_in utter surprise,
+                                lets his oranges tumble into
+                                the gutter_). Never mind! They
+                                won't be wanted now. (_Walks
+                                off one way. Boy makes a pass
+                                of naso-digital mesmerism, and
+                                walks off the other way_).
+
+To the poor, who keep no books, the whole secret is "Sixpence farthing to
+the half shilling, twelve pence halfpenny to the shilling." The _new
+twopence halfpenny_, or cent, will be at once five to the shilling.
+
+In conclusion, we remark that three very common misconceptions run through
+the hon. Member's argument; and, combined in different proportions, give
+variety to his patterns.
+
+First, he will have it that we design to bring the uneducated into contact
+with _decimal fractions_. If it be so, it will only be as M. Jourdain was
+brought into contact with prose. In fact, _Quoi! quand je dis, Nicole,
+apportez-moi mes pantoufles, c'est de la prose?_[305] may be rendered:
+"What! do you mean that _ten to the florin is a cent a piece_ must be
+called decimal reckoning?" If we had to comfort a poor man, horror-struck
+by the threat of _decimals_, we should tell him what manner of fractions
+had been inflicted upon him hitherto; nothing less awful than
+_quarto-duodecimo-vicesimals_, we should assure him.
+
+Secondly, he assumes that the penny, such as it now is, will remain, as a
+coin of estimation, after it has ceased to be a coin of exchange; and that
+the mass of the people will continue to think of prices in old pence, and
+to calculate them in new ones, or else in new mils. No answer is required
+to this, beyond the mere statement of the nature of the assumption and
+denial.
+
+{180}
+
+Thirdly, he attributes to the uneducated community a want of perception and
+of operative power which really does not belong to them. The evidence
+offered to the Committee of the House shows that no fear is entertained on
+this point by those who come most in contact with farthing purchasers. And
+this would seem to be a rule,--that is, fear of the intelligence of the
+lower orders in the minds of those who are not in daily communication with
+them, no fear at all in the minds of those who are.
+
+A remarkable instance of this distinction happened five-and-twenty years
+ago. The Admiralty requested the Astronomical Society to report on the
+alterations which should be made in the _Nautical Almanac_, the seaman's
+guide-book over the ocean. The greatest alteration proposed was the
+description of celestial phenomena in _mean_ (or clock time), instead of
+_apparent_ (or sundial) time, till then always employed. This change would
+require that in a great many operations the seaman should let alone what he
+formerly altered by addition or subtraction, and alter by addition or
+subtraction what he formerly let alone; provided always that what he
+formerly altered by addition he should, when he altered at all, alter by
+subtraction, and _vice versa_. This was a tolerably difficult change for
+uneducated skippers, working by rules they had only learned by rote. The
+Astronomical Society appointed a Committee of forty, of whom nine were
+naval officers or merchant seamen [I was on this Committee]. Some men of
+science were much afraid of the change. They could not trust an ignorant
+skipper or mate to make those alterations in their routine, on the
+correctness of which the ship might depend. Had the Committee consisted of
+men of science only, the change might never have been ventured on. But the
+naval men laughed, and said there was nothing to fear; and on their
+authority the alteration was made. The upshot was, that, after the new
+almanacs appeared, not a word of complaint was ever heard on the matter.
+Had the House of Commons had to {181} decide this question, with Mr. Lowe
+to quote the description given by Basil Hall[306] (who, by the way, was one
+of the Committee) of an observation on which the safety of the ship
+depended, worked out by the light of a lantern in a gale of wind off a lee
+shore, this simple and useful change might at this moment have been in the
+hands of its tenth Government Commission.
+
+
+
+[_Aug. 14, 1866._ The Committee was appointed in the spring of 1830: it
+consisted of forty members. Death, of course, has been busy; there are now
+left Lord Shaftesbury,[307] Mr. Babbage,[308] Sir John Herschel,[309] Sir
+Thomas Maclear[310] (Astronomer Royal at the Cape of Good Hope), Dr.
+Robinson[311] (of Armagh), Sir James South,[312] Lord Wrottesley,[313] and
+myself].
+
+{182}
+
+
+
+THE TONAL SYSTEM.
+
+    Project of a new system of arithmetic, weight, measure, and coins,
+    proposed to be called the tonal system, with sixteen to the base. By
+    J. W. Mystrom.[314] Philadelphia, 1862, 8vo.
+
+That is to say, sixteen is to take the place of ten, and to be written 10.
+The whole language is to be changed; every man of us is to be
+sixteen-stringed Jack and every woman sixteen-stringed Jill. Our old _one_,
+_two_, _three_, up to sixteen, are to be (_Noll_ going for nothing, which
+will please those who dislike the memory of _Old Noll_) replaced by An, De,
+Ti, Go, Su, By, Ra, Me, Ni, Ko, Hu, Vy, La, Po, Fy, Ton; and then Ton-an,
+Ton-de, etc. for 17, 18, etc. The number which in the system has the symbol
+
+  28(13)5(11)7(14)0(15)
+
+(using our present compounds instead of new types) is to be pronounced
+
+  Detam-memill-lasan-suton-hubong-ramill-posanfy.
+
+The year is to have sixteen months, and here they are:
+
+  Anuary, Debrian, Timander, Gostus,
+  Suvenary, Bylian, Ratamber, Mesudius,
+  Nictoary, Kolumbian, Husamber, Vyctorius,
+  Lamboary, Polian, Fylander, Tonborius.
+
+Surely An-month, De-month, etc. would do as well. Probably the wants of
+poetry were considered. But what are we to do with our old poets? For
+example--
+
+ "It was a night of lovely June,
+  High rose in cloudless blue the moon."
+
+Let us translate--
+
+ "It was a night of lovely Nictoary,
+  High rose in cloudless blue the (what, in the name of all that is
+      absurd?)."
+
+And again, _Fylander_ thrown into our December! What is {183} to become of
+those lines of Praed, which I remember coming out when I was at
+Cambridge,--
+
+ "Oh! now's the time of all the year for flowers and fun, the Maydays;
+  To trim your whiskers, curl your hair, and sinivate the ladies."
+
+If I were asked which I preferred, this system or that of Baron
+Ferrari[315] already mentioned, proceeding by _twelves_, I should reply,
+with Candide, when he had the option given of running the gauntlet or being
+shot: Les volontes sont libres, et je ne veux ni l'un ni l'autre.[316] We
+can imagine a speculator providing such a system for Utopia as it would be
+in the mind of a Laputan: but to explain how an engineer who has surveyed
+mankind from Philadelphia to Rostof on the Don should for a moment
+entertain the idea of such a system being actually adopted, would beat a
+jury of solar-system-makers, though they were shut up from the beginning of
+Anuary to the end of Tonborius. When I see such a scheme as this imagined
+to be practicable, I admire the wisdom of Providence in providing the
+quadrature of the circle, etc., to open a harmless sphere of action to the
+possessors of the kind of ingenuity which it displays. Those who cultivate
+mathematics have a right to speak strongly on such efforts of arithmetic as
+this: for, to my knowledge, persons who have no knowledge are frequently
+disposed to imagine that their makers are true brothers of the craft, a
+little more intelligible than the rest.
+
+
+
+SOME SMALL PARADOXERS.
+
+    Vis inertiae victa,[317] or Fallacies affecting science. By James
+    Reddie.[318] London, 1862, 8vo.
+
+{184}
+
+An attack on the Newtonian mechanics; revolution by gravitation
+demonstrably impossible; much to be said for the earth being the immovable
+center. A good analysis of contents at the beginning, a thing seldom found.
+The author has followed up his attack in a paper submitted to the British
+Association, but which it appears the Association declined to consider. It
+is entitled--
+
+
+
+    _Victoria Toto Coelo_; or, Modern Astronomy recast. London, 1863, 8vo.
+
+At the end is a criticism of Sir G. Lewis's _History of Ancient Astronomy_.
+
+
+
+    On the definition and nature of the Science of Political Economy. By H.
+    Dunning Macleod,[319] Esq. Cambridge, 1862, 8vo.
+
+A paper read--but, according to the report, not understood--at the British
+Association. There is a notion that political economy is entirely
+mathematical; and its negative quantity is strongly recommended for study:
+it contains "the whole of the Funds, Credit, 32 parts out of 33 of the
+value of Land...." The mathematics are described as consisting of--first,
+number, or Arithmetic; secondly, the theory of dependent quantities,
+subdivided into dependence by cause and effect, and dependence by
+simultaneous variations; thirdly, "independent quantities or unconnected
+events, which is the theory of probabilities." I am not ashamed, having the
+British Association as a co-non-intelligent, to say I do not understand
+this: there is a paradox in it, and the author should give further
+explanation, especially of his negative quantity. Mr. Macleod has gained
+{185} praise from great names for his political economy; but this, I
+suspect, must have been for other parts of his system.
+
+
+
+    On the principles and practice of just Intonation, with a view to the
+    abolition of temperament.... By General Perronet Thompson.[320] Sixth
+    Edition. London, 1862, 8vo.
+
+Here is General Thompson again, with another paradox: but always master of
+the subject, always well up in what his predecessors have done, and always
+aiming at a useful end. He desires to abolish temperament by additional
+keys, and has constructed an enharmonic organ with forty sounds in the
+octave. If this can be introduced, I, for one, shall delight to hear it:
+but there are very great difficulties in the way, greater than stood even
+in the way of the repeal of the bread-tax.
+
+In a paper on the beats of organ-pipes and on temperament published some
+years ago, I said that equal temperament appeared to me insipid, and not so
+agreeable as the effect of the instrument when in progress towards being
+what is called out of tune, before it becomes offensively wrong. There is
+throughout that period unequal temperament, determined by accident. General
+Thompson, taking me one way, says I have launched a declaration which is
+likely to make an epoch in musical practice; a public musical critic,
+taking me another way, quizzes me for preferring music _out of tune_. I do
+not think I deserve either one remark or the other. My opponent critic, I
+suspect, takes _equally tempered_ and _in tune_ to be phrases of one
+meaning. But by equal temperament is meant equal distribution among all the
+keys of the error which an instrument _must_ have, which, with twelve
+sounds only in the octave, professes to be fit for all the keys. I am
+reminded of the equal temperament which was once applied to the postmen's
+jackets. The coats were all made for the average man: the {186} consequence
+was that all the tall men had their tails too short; all the short men had
+them too long. Some one innocently asked why the tall men did not change
+coats with the short ones.
+
+
+
+    A diagram illustrating a discovery in the relation of circles to
+    right-lined geometrical figures. London, 1863, 12mo.
+
+The circle is divided into equal sectors, which are joined head and tail:
+but a property is supposed which is not true.
+
+
+
+    An attempt to assign the square roots of negative powers; or what is
+    [sqrt] -1? By F.H. Laing.[321] London, 1863, 8vo.
+
+If I understand the author, -a and +a are the square roots of -a^2, as
+proved by multiplying them together. The author seems quite unaware of what
+has been done in the last fifty years.
+
+
+
+BYRNE'S DUAL ARITHMETIC.
+
+    Dual Arithmetic. A new art. By Oliver Byrne.[322] London, 1863, 8vo.
+
+The plan is to throw numbers into the form a(1.1)^{b} (1.01)^{c}
+(1.001)^{d}... and to operate with this form. This is an ingenious and
+elaborate speculation; and I have no doubt the author has practised his
+method until he could surprise any one else by his use of it. But I doubt
+if he will persuade others to use it. As asked of Wilkins's universal
+language, Where is the second man to come from?
+
+An effective predecessor in the same line of invention {187} was the late
+Mr. Thomas Weddle,[323] in his "New, simple, and general method of solving
+numeric equations of all orders," 4to, 1842. The Royal Society, to which
+this paper was offered, declined to print it: they ought to have printed an
+organized method, which, without subsidiary tables, showed them, in six
+quarto pages, the solution (x=8.367975431) of the equation
+
+  1379.664 x^{622} + 2686034 x 10^{432} x^{152} - 17290224 x 10^{518}
+      x^{60} + 2524156 x 10^{574} = 0.
+
+The method proceeds by successive factors of the form, a being the first
+approximation, a x 1.b x 1.0c x 1.00d.... In my copy I find a few
+corrections made by me at the time in Mr. Weddle's announcement. "It was
+read before that learned body [the R. S.] and they were pleased [but] to
+transmit their thanks to the author. The en[dis]couragement which he
+received induces [obliges] him to lay the result of his enquiries in this
+important branch of mathematics before the public [, at his own expense; he
+being an usher in a school at Newcastle]." Which is most satirical, Mr.
+Weddle or myself? The Society, in the account which it gave of this paper,
+described it as a "new and remarkably simple method" possessing "several
+important advantages." Mr. Rutherford's[324] extended value of [pi] was
+read at the very next meeting, and was printed in the _Transactions_; and
+very properly: Mr. Weddle's paper was excluded, and very very improperly.
+
+
+
+HORNER'S METHOD.
+
+I think it may be admited that the indisposition to look at and encourage
+improvements of calculation which once {188} marked the Royal Society is no
+longer in existence. But not without severe lessons. They had the luck to
+accept Horner's[325] now celebrated paper, containing the method which is
+far on the way to become universal: but they refused the paper in which
+Horner developed his views of this and other subjects: it was printed by
+T. S. Davies[326] after Horner's death. I make myself responsible for the
+statement that the Society could not reject this paper, yet felt unwilling
+to print it, and suggested that it should be withdrawn; which was done.
+
+But the severest lesson was the loss of _Barrett's Method_,[327] now the
+universal instrument of the actuary in his highest calculations. It was
+presented to the Royal Society, and refused admission into the
+_Transactions_: Francis Baily[328] printed it. The Society is now better
+informed: "_live and learn_," meaning "_must live, so better learn_," ought
+to be the especial motto of a corporation, and is generally acted on, more
+or less.
+
+Horner's method begins to be introduced at Cambridge: it was published in
+1820. I remember that when I first went to Cambridge (in 1823) I heard my
+tutor say, in conversation, there is no doubt that the true method of
+solving equations is the one which was published a few years ago in the
+_Philosophical Transactions_. I wondered it was not taught, but presumed
+that it belonged to the higher mathematics. This Horner himself had in his
+head: and in a sense it is true; for all lower branches belong to the
+higher: but he would have stared to have been told that he, Horner, {189}
+was without a European predecessor, and in the distinctive part of his
+discovery was heir-at-law to the nameless
+Brahmin--Tartar--Antenoachian--what you please--who concocted the
+extraction of the square root.
+
+It was somewhat more than twenty years after I had thus heard a Cambridge
+tutor show sense of the true place of Horner's method, that a pupil of mine
+who had passed on to Cambridge was desired by his college tutor to solve a
+certain cubic equation--one of an integer root of two figures. In a minute
+the work and answer were presented, by Horner's method. "How!" said the
+tutor, "this can't be, you know." "There is the answer, Sir!" said my
+pupil, greatly amused, for my pupils learnt, not only Horner's method, but
+the estimation it held at Cambridge. "Yes!" said the tutor, "there is the
+answer certainly; but it _stands to reason_ that a cubic equation cannot be
+solved in this space." He then sat down, went through a process about ten
+times as long, and then said with triumph: "There! that is the way to solve
+a cubic equation!"
+
+I think the tutor in this case was never matched, except by the country
+organist. A master of the instrument went into the organ-loft during
+service, and asked the organist to let him _play the congregation out_;
+consent was given. The stranger, when the time came, began a voluntary
+which made the people open their ears, and wonder who had got into the
+loft: they kept their places to enjoy the treat. When the organist saw
+this, he pushed the interloper off the stool, with "You'll never play 'em
+out this side Christmas." He then began his own drone, and the congregation
+began to move quietly away. "There," said he, "that's the way to play 'em
+out!"
+
+I have not scrupled to bear hard on my own university, on the Royal
+Society, and on other respectable existences: being very much the friend of
+all. I will now clear the Royal Society from a very small and obscure
+slander, simply because I know how. This dissertation began with {190} the
+work of Mr. Oliver Byrne, the dual arithmetician, etc. This writer
+published, in 1849, a method of calculating logarithms.[329] First, a long
+list of instances in which, as he alleges, foreign discoverers have been
+pillaged by Englishmen, or turned into Englishmen: for example,
+O'Neill,[330] so called by Mr. Byrne, the rectifier of the semi-cubical
+parabola claimed by the Saxons under the name of _Neal_: the grandfather of
+this mathematician was conspicuous enough as _Neal_; he was archbishop of
+York. This list, says the writer, might be continued without end; but he
+has mercy, and finishes with his own case, as follows:--"About twenty years
+ago, I discovered this method of directly calculating logarithms. I could
+generally find the logarithm of any number in a minute or two without the
+use of books or tables. The importance of the discovery subjected me to all
+sorts of prying. Some asserted that I committed a table of logarithms to
+memory; others attributed it to a peculiar mental property; and when
+Societies and individuals failed to extract my secret, they never failed to
+traduce the inventor and the invention. Among the learned Societies, the
+Royal Society of London played a very base part. When I have more space and
+time at my disposal, I will revert to this subject again."
+
+Such a trumpery story as this remains unnoticed at the time; but when all
+are gone, a stray copy from a stall falls into hands which, not knowing
+what to make of it, make history of it. It is a very curious distortion.
+The reader may take it on my authority, that the Royal Society played no
+part, good or bad, nor had the option of playing a part. {191} But I myself
+_pars magna fui_:[331] and when the author has "space and time" at his
+disposal, he must not take all of them; I shall want a little of both.
+
+
+
+ARE ATOMS WORLDS?
+
+    The mystery of being; or are ultimate atoms inhabited worlds? By
+    Nicholas Odgers.[332] Redruth and London, 1863, 8vo.
+
+This book, as a paradox, beats quadrature, duplication, trisection,
+philosopher's stone, perpetual motion, magic, astrology, mesmerism,
+clairvoyance, spiritualism, homoeopathy, hydropathy, kinesipathy, Essays
+and Reviews, and Bishop Colenso,[333] all put together. Of all the
+suppositions I have given as actually argued, this is the one which is
+hardest to deny, and hardest to admit. Reserving the question--as beyond
+human discussion--whether our particles of carbon, etc. are _clusters_ of
+worlds, the author produces his reasons for thinking that they are at least
+single worlds. Of course--though not mentioned--the possibility is to be
+added of the same thing being true of the particles which make up our
+particles, and so down, for ever: and, on the other hand, of our planets
+and stars as being particles in some larger universe, and so up, for ever.
+
+ "Great fleas have little fleas upon their backs to bite 'em,
+  And little fleas have lesser fleas, and so _ad infinitum._
+  And the great fleas themselves, in turn, have greater fleas to go on;
+  While these again have greater still, and greater still, and so on."[334]
+
+I have often had the notion that all the nebulae we see, including our own,
+which we call the Milky Way, may be particles of snuff in the box of a
+giant of a proportionately {192} larger universe. Of course the minim of
+time--a million of years or whatever the geologists make it[335]--which our
+little affair has lasted, is but a very small fraction of a second to the
+great creature in whose nose we shall all be in a few tens of thousands of
+millions of millions of millions of years.
+
+All this is quite possible, and the probabilities for and against are quite
+out of reach. Perhaps also all the worlds, both above and below us, are
+fac-similes of our own. If so, away goes free will for good and all;
+unless, indeed, we underpin our system with the hypothesis that all the
+fac-simile bodies of different sizes are actuated by a common soul. These
+acute supplementary notions of mine go far to get rid of the difficulty
+which some have found in the common theory that the soul inhabits the body:
+it has been stated that there is, somewhere or another, a world of souls
+which communicate with their bodies by wondrous filaments of a nature
+neither mental nor material, but of a _tertium quid_ fit to be a
+go-between; as it were a corporispiritual copper encased in a
+spiritucorporeal gutta-percha. My theory is that every soul is everywhere
+_in posse_, as the schoolmen said, but not anywhere _in actu_, except where
+it finds one of its bodies. These _a priori_ difficulties being thus
+removed, the system of particle-worlds is reduced to a dry question of
+fact, and remitted to the decision of the microscope. And a grand field may
+thus be opened, as optical science progresses! For the worlds are not
+fac-similes of ours in time: there is not a moment of _our_ past, and not a
+moment of _our_ future, but is the _present_ of one or more of the
+particles. A will write the death of Caesar, and B the building of the
+Pyramids, by actual observation of the processes with a power of a thousand
+millions; C will discover the commencement of the Millennium, and D the
+{193} termination of Ersch and Gruber's Lexicon,[336] as mere physical
+phenomena. Against this glorious future there is a sad omen: the initials
+of the forerunner of this discovery are--NO!
+
+
+
+THE SUPERNATURAL.
+
+    The History of the Supernatural in all ages and nations, and in all
+    Churches, Christian and Pagan: demonstrating a universal faith. By Wm.
+    Howitt.[337] London, 2 vols. 8vo. 1863.
+
+Mr. Howitt is a preacher of spiritualism. He cements an enormous collection
+of alleged facts with a vivid outpouring of exhortation, and an unsparing
+flow of sarcasm against the scorners of all classes. He and the Rev. J.
+Smith[338] (_ante_, 1854) are the most thoroughgoing universalists of all
+the writers I know on spiritualism. If either can insert the small end of
+the wedge, he will not let you off one fraction of the conclusion that all
+countries, in all ages, have been the theaters of one vast spiritual
+display. And I suspect that this consequence cannot be avoided, if any part
+of the system be of truly spiritual origin. Mr. Howitt treats the
+philosophers either as ignorant babies, or as conscious spirit-fearers: and
+seems much inclined to accuse the world at large of dreading, lest by the
+actual presence of the other world their Christianity should imbibe a
+spiritual element which would unfit it for the purposes of their lives.
+
+{194}
+
+
+
+FROM MATTER TO SPIRIT.
+
+    From Matter to Spirit. By C. D. With a preface by A. B.[339] London,
+    1863, 8vo.
+
+This is a work on Spiritual Manifestations. The author upholds the facts
+for spiritual phenomena: the prefator suspends his opinion as to the cause,
+though he upholds the facts. The work begins systematically with the lower
+class of phenomena, proceeds to the higher class, and offers a theory,
+suggested by the facts, of the connection of the present and future life. I
+agree in the main with A. B.; but can, of course, make none but horrescent
+reference to his treatment of the smaller philosophers. This is always the
+way with your paradoxers: they behave towards orthodoxy as the thresher
+fish behaves towards the whale. But if true, as is said, that the drubbing
+clears the great fish of parasites which he could not otherwise get rid of,
+he ought to bear no malice. This preface retorts a little of that contempt
+which the "philosophical world" has bestowed with heaped measure upon those
+who have believed their senses, and have drawn natural, even if hasty,
+inferences. There is philosophercraft as well as priestcraft, both from one
+source, both of one spirit. In English cities and towns, the minister of
+religion has been tamed: so many weapons are bared against him when he
+obtrudes his office in a dictatory manner, that, as a rule, there is no
+more quiet and modest member of society than the urban clergyman.
+Domination over religious belief is reserved for the exclusive use of those
+who admit the right: the rare exception to this mode of behavior is laughed
+at as a bigot, or shunned as a nuisance. But the overbearing minister of
+nature, who snaps you with _unphilosophical_ as the clergyman once
+frightened you with _infidel_, is still a recognized member of society,
+wants taming, and will get it. He wears the priest's cast-off {195}
+clothes, dyed to escape detection: the better sort of philosophers would
+gladly set him to square the circle.
+
+The book just named appeared about the same time as this Budget began in
+the _Athenaeum_. It was commonly attributed, the book to my wife, the
+preface to myself. Some time after, our names were actually announced by
+the publisher, who ought to know. It will be held to confirm this statement
+that I announce our having in our possession some twenty reviews of
+different lengths, and of all characters: who ever collects a number of
+reviews of a book, except the author?
+
+A great many of these reviews settle the matter _a priori_. If there had
+been spirits in the matter, they would have done this, and they would not
+have done that. Jean Meslier[340] said there could be no God over all, for,
+_if_ there had been one, He would have established a universal religion. If
+J. M. _knew_ that, J. M. was right: but if J. M. did not know that, then
+J. M. was on the "high priori road," and may be left to his course. The
+same to all who know what spirits would do and would not do.
+
+A. B. very distinctly said that he knew some of the asserted facts,
+believed others on testimony, but did not pretend to know whether they were
+caused by spirits, or had some unknown and unimagined origin. This he said
+as clearly as I could have said it myself. But a great many persons cannot
+understand such a frame of mind: their own apparatus is a kind of
+spirit-level, and their conclusion on any subject is the little bubble,
+which is always at one end or the other. Many of the reviewers declare that
+A. B. is a secret believer in the spirit-hypothesis: and one of them wishes
+that he had "endorsed his opinion more boldly." According to this reviewer,
+any one who writes "I boldly {196} say I am unable to choose," contradicts
+himself. In truth, a person who does say it has a good deal of courage, for
+each side believes that he secretly favors the other; and both look upon
+him as a coward. In spite of all this, A. B. boldly repeats that he feels
+assured of many of the facts of _spiritualism_, and that he cannot pretend
+to affirm or deny anything about their cause.
+
+The great bulk of the illogical part of the educated community--whether
+majority or minority I know not; perhaps six of one and half-a-dozen of the
+other--have not power to make a distinction, cannot be made to take a
+distinction, and of course, never attempt to shake a distinction. With them
+all such things are evasions, subterfuges, come-offs, loopholes, etc. They
+would hang a man for horse-stealing under a statute against sheep-stealing;
+and would laugh at you if you quibbled about the distinction between a
+horse and a sheep. I divide the illogical--I mean people who have not that
+amount of natural use of sound inference which is really not uncommon--into
+three classes:--First class, three varieties: the Niddy, the Noddy, and the
+Noodle. Second class, three varieties: the Niddy-Noddy, the Niddy-Noodle,
+and the Noddy-Noodle. Third class, undivided: the Niddy-Noddy-Noodle. No
+person has a right to be angry with me for more than one of these
+subdivisions.
+
+The want of distinction was illustrated to me, when a boy, about 1820, by
+the report of a trial which I shall never forget: boys read newspapers more
+keenly than men. Every now and then a bench of country magistrates rather
+astonishes the town populations, accustomed to rub their brains[341]
+against one another. Such a story as the following would, {197} in our day,
+bring down grave remarks from above: but I write of the olden (or
+Eldon[342]) time, when nothing but conviction in a court of record would
+displace a magistrate. In that day the third-class amalgamator of distinct
+things was often on the bench of quarter-sessions.
+
+An attorney was charged with having been out at night poaching. A clear
+_alibi_ was established; and perjury had certainly been committed. The
+whole gave reason to suspect that some ill-willers thought the bench
+disliked the attorney so much that any conviction was certain on any
+evidence. The bench did dislike the attorney: but not to the extent of
+thinking he could snare any partridges in the fields while he was asleep in
+bed, except the dream-partridges which are not always protected by the
+dream-laws. So the chairman said, "Mr. ----, you are discharged; but you
+should consider this one of the most fortunate days of your life." The
+attorney indignantly remonstrated, but the magistrate was right; for he
+said, "Mr. ----, you have frequently been employed to defend poachers: have
+you been careful to impress upon them the enormity of their practices?" It
+appeared in a wrangling conversation that the magistrates saw little moral
+difference between poaching and being a poacher's professional defender
+without lecturing him on his wickedness: but they admitted with reluctance,
+that there was a legal distinction; and the brain of N^3 could no further
+go. This is nearly fifty years ago; and Westernism was not quite extinct.
+If the present lords of the hills and the valleys want to shine, let them
+publish a true history of their own order. I am just old enough to remember
+some of the last of the squires and parsons who protested against teaching
+the poor to read and write. They now write books for the working classes,
+give them lectures, and the like. There is now no class, as a class, more
+highly educated, broadly educated, and deeply educated, {198} than those
+who were, in old times, best described as partridge-popping squireens. I
+have myself, when a boy, heard Old Booby speaking with pride of Young Booby
+as having too high a spirit to be confined to books: and I suspected that
+his dislike to teaching the poor arose in fact from a feeling that they
+would, if taught a little, pass his heir.
+
+A. B. recommended the spirit-theory as an hypothesis on which to ground
+inquiry; that is, as the means of suggestion for the direction of inquiry.
+Every person who knows anything of the progress of physics understands what
+is meant; but not the reviewers I speak of. Many of them consider A. B. as
+_adopting_ the spirit-hypothesis. The whole book was written, as both the
+authors point out, to suggest inquiry to those who are curious; C. D.
+firmly believing, A. B. as above. Neither C. D. nor A. B. make any other
+pretence. Both dwell upon the absence of authentications and the
+suppression of names as utterly preventive of anything like proof. And
+A. B. says that his reader "will give him credit, if not himself a goose,
+for seeing that the tender of an anonymous cheque would be of equal effect,
+whether drawn on the Bank of England or on Aldgate Pump." By this test a
+number of the reviewers are found to be geese: for they take the authors as
+offering proof, and insist, against the authors, on the very point on which
+the authors had themselves insisted beforehand.
+
+Leaving aside imperceptions of this kind, I proceed to notice a clerical
+and medical review. I have lived much in the middle ages, especially since
+the invention of printing; and from thence I have brought away a high
+respect for and grateful recollection of--the priest in everything but
+theology, and the physician in everything but medicine. The professional
+harness was unfavorable to all progress, except on a beaten road; the
+professional blinkers prevented all but the beaten road from being seen:
+the professional reins were pulled at the slightest attempt to quicken
+pace, even on the permitted path; and the {199} professional whip was
+heavily laid on at the slightest attempt to diverge. But when the
+intelligent man of either class turned his attention out of his ordinary
+work, he had, in most cases, the freshness and vigor of a boy at play, and
+like the boy, he felt his freedom all the more from the contrast of
+school-restraint.
+
+In the case of medicine, and physics generally, the learned were, in some
+essential points, more rational than many of their present impugners. They
+pass for having put _a priori_ obstacles in the way of progress: they might
+rather be reproved for too much belief in progress obtained by _a priori_
+means. They would have shouted with laughter at a dunce who--in a review I
+read, but without making a note--declared that he would not believe his
+senses except when what they showed him was capable of explanation upon
+some known principle. I have seen such stuff as this attributed to the
+schoolmen; but only by those who knew nothing about them. The following,
+which I wrote some years ago, will give a notion of a distinction worth
+remembering. It is addressed to the authorities of the College of
+Physicians.
+
+"The ignominy of the word _empiric_ dates from the ages in which scholastic
+philosophy deduced physical consequences _a priori_;--the ages in which,
+because a lion is strong, rubbing with lion's fat would have been held an
+infallible tonic. In those happy days, if a physician had given decoction
+of a certain bark, only because in numberless instances that decoction had
+been found to strengthen the patient, he would have been a miserable
+empiric. Not that the colleges would have passed over his returns because
+they were empirical: they knew better. They were as skilful in finding
+causes for facts, as facts for causes. The president and the elects of that
+day would have walked out into the forest with a rope, and would have
+pulled heartily at the tree which yielded the bark: nor would they ever
+have left it until they had pulled out a legitimate {200} reason. If the
+tree had resisted all their efforts, they would have said, 'Ah! no wonder
+now; the bark of a strong tree makes a strong man.' But if they had managed
+to serve the tree as you would like to serve homoeopathy, then it would
+have been 'We might have guessed it; all the _virtus roborativa_ has
+settled in the bark.' They admitted, as we know from Moliere, the _virtus
+dormitiva_[343] of opium, for no other reason than that opium _facit
+dormire_.[344] Had the medicine not been previously _known_, they would,
+strange as it may seem to modern pharmacopoeists, have accorded a _virtus
+dormitiva_ to the new _facit dormire_. On this point they have been
+misapprehended. They were prone to infer _facit_ from a _virtus_ imagined
+_a priori_; and they were ready in supplying _facit_ in favor of an
+orthodox _virtus_. They might have gone so far, for example, under
+pre-notional impressions, as the alliterative allopath, who, when
+maintenance of truth was busy opposing the progress of science called
+_vaccination_, declared that some of its patients coughed like cows, and
+bellowed like bulls; but they never refused to find _virtus_ when _facit_
+came upon them, no matter whence. They would rather have accepted Tenterden
+steeple than have rejected the Goodwin Sands. They would have laughed their
+modern imitators to scorn: but as they are not here, we do it for them.
+
+"The man of our day--the _a priori_ philosopher--tries the question whether
+opium can cause sleep by finding out in the recesses of his own noddle
+whether the drug can have a dormitive power: Well! but did not the
+schoolman do the same? He did; but mark the distinction. The schoolman had
+recourse to first principles, when there was no opium to try it by: our man
+settles the point in the same way _with a lump of opium before him_. The
+schoolman shifted his principles with his facts: the man of our
+drawing-rooms will fight facts with his principles, just as an old {201}
+physician would have done in actual practice, with the rod of his _Church_
+at his back.
+
+"The story about Galileo--which seems to have been either a joke made
+against him, or by him--illustrates this. _Nature abhors a vacuum_ was the
+explanation of the water rising in a pump: but they found that the water
+would not rise more than 32 feet. They asked for explanation: what does the
+satirist make the schoolmen say? That the stoppage is _not_ a fact, because
+nature abhors a vacuum? No! but that the principle should be that nature
+abhors a vacuum as far as 32 feet. And this is what would have been done.
+
+"There are still among us both priests and physicians who would have
+belonged, had they lived three or four centuries ago, to the glorious band
+of whom I have spoken, the majority of the intelligent, working well for
+mankind out of the professional pursuit. But we have a great many who have
+helped to abase their classes. Go where we may, we find specimens of the
+lower orders of the ministry of religion and the ministry of health showing
+themselves smaller than the small of other pursuits. And how is this?
+First, because each profession is entered upon a mere working smack of its
+knowledge, without any depth of education, general or professional. Not
+that this is the whole explanation, nor in itself objectionable: the great
+mass of the world must be tended, soul and body, by those who are neither
+Hookers[345] nor Harveys[346]: let such persons not venture _ultra
+crepidam_, and they are useful and respectable. But, secondly, there is a
+vast upheaving of thought from the depths of commonplace learning. I am a
+clergyman! Sir! I am a medical man! Sir! and forthwith the nature of things
+is picked to pieces, and there is a race, with the last the winner, between
+Philosophy mounted on Folly's donkey, and Folly mounted on Philosophy's
+donkey. How fortunate {202} it is for Law that her battles are fought by
+politicians in the Houses of Parliament. Not that it is better done: but
+then _politics_ bears the blame."
+
+I now come to the medical review. After a quantity of remark which has been
+already disposed of, the writer shows Greek learning, a field in which the
+old physician would have had a little knowledge. A. B., for the joke's
+sake, had left untranslated, as being too deep, a remarkably easy sentence
+of Aristotle, to the effect that what has happened was possible, for if
+impossible it would not have happened. The reviewer, in "simple
+astonishment,"--it was simple--at the pretended incapacity--I was told by
+A. B. that the joke was intended to draw out a reviewer--translates:--He
+says that this sentence is A. B.'s summing up of the evidence of
+Spiritualism. Now, being a sort of _alter ego_[347] of A. B., I do declare
+that he is not such a fool as to rest the evidence of Spiritualism--the
+_spirit explanation_--upon the occurrence of certain facts proving the
+possibility of those very facts. In truth, A. B. refuses to receive
+spiritualism, while he receives the facts: this is the gist of his whole
+preface, which simply admits spiritualism among the qualified candidates,
+and does not know what others there may be.
+
+The reviewer speaks of Aristotle as "that clear thinker and concise
+writer." I strongly suspect that his knowledge of Aristotle was limited to
+the single sentence which he had translated or got translated. Aristotle is
+concise in _phrase_, not in book, and is powerful and profound in thought:
+but no one who knows that his writing, all we have of him, is the very
+opposite of clear, will pretend to decide that he thought clearly. As his
+writing, so probably was his thought; and his books are, if not anything
+but clear, at least anything good but clear. Nobody thinks them clear
+except a person who always clears difficulties: which I have no doubt was
+the reviewer's habit; that is, if he ever took the field {203} at all. The
+gentleman who read Euclid, all except the As and Bs and the pictures of
+scratches and scrawls, is the type of a numerous class.
+
+The reviewer finds that the word _amosgepotically_, used by A. B., is
+utterly mysterious and incomprehensible. He hopes his translation of the
+bit of Greek will shield him from imputation of ignorance: and thinks the
+word may be referred to the "obscure dialect" out of which sprung
+_aneroid_, _kalos geusis sauce_, and _Anaxyridian trousers_. To lump the
+first two phrases with the third smacks of ignorance in a Greek critic; for
+[Greek: anaxuridia], _breeches_, would have turned up in the lexicon; and
+_kalos geusis_, though absurd, is not obscure. And [Greek: amosgepos],
+_somehow or other_, is as easily found as [Greek: anaxuridia]. The word
+_aneroid_, I admit, has puzzled better scholars than the critic: but never
+one who knows the unscholarlike way in which words ending in [Greek: eides]
+have been rendered. The _aneroid barometer_ does _not_ use a column of air
+in the same way as the old instrument. Now [Greek: aeroeides]--properly
+_like_ the atmosphere--is by scientific non-scholarship rendered having to
+do with the atmosphere; and [Greek: anaeroeides]--say _anaeroid_--denies
+having to do with the atmosphere; a nice thing to say of an instrument
+which is to measure the weight of the atmosphere. One more absurdity, and
+we have _aneroid_, and there you are. The critic ends with a declaration
+that nothing in the book shakes his faith in a _Quarterly_ reviewer who
+said that suspension of opinion, until further evidence arrives, is
+justifiable: a strange summing up for an article which insists upon utter
+rejection being unavoidable.[348] The expressed aim of both A. B. and C. D.
+was to excite inquiry, and get further evidence: until this is done,
+neither asks for a verdict.
+
+Oh where! and oh where! is old Medicine's learning gone! There _was_ some
+in the days of yore, when Popery {204} was on! And it's oh! for some Greek,
+just to find a word upon! The reviewer who, lexicon in hand, can neither
+make out _anaxyridical_, _amosgepotical_, _kalos geusis_, nor distinguish
+them from _aneroid_, cannot be trusted when he says he has translated a
+sentence of Aristotle. He may have done it; but, as he says of
+spiritualism, we must suspend our opinion until further evidence shall
+arrive.
+
+We now come to the theological review. I have before alluded to the faults
+of logic which are Protestant necessities: but I never said that Protestant
+argument had _nothing but_ paralogism. The writer before me attains this
+completeness: from beginning to end he is of that confusion and perversion
+which, as applied to interpretation of the New Testament, is so common as
+to pass unnoticed by sermon-hearers; but which, when applied out of church,
+is exposed with laughter in all subjects except theology. I shall take one
+instance, putting some words in italics.
+
+_A. B._                         _Theological Critic._
+
+My state of mind, which refers  ... he proceeds to argue that
+the whole _either_ to unseen    he himself is outside its
+intelligence, _or something     sacred pale because he refers
+which man has never had any     all these strange phenomena to
+conception of_, proves me to    _unseen spiritual
+be out of the pale of the       intelligence_.
+Royal Society.
+
+The possibility of a _yet unimagined_ cause is insisted on in several
+places. On this ground it is argued by A. B. that spiritualists are
+"incautious" for giving in at once to the spirit doctrine. But, it is said,
+they may be justified by the philosophers, who make the flint _axes_, as
+they call them, to be the works of men, because no one can see _what else
+they can be_. This kind of adoption, _condemned_ as a conclusion, is
+_approved_ as a provisional theory, suggestive of direction of inquiry:
+experience having shown that {205} inquiry directed by a _wrong_ theory has
+led to more good than inquiry without any theory at all. All this A. B. has
+fully set forth, in several pages. On it the reviewer remarks that "with
+infinite satisfaction he tries to justify his view of the case by urging
+that there is no other way of accounting for it; after the fashion of the
+philosophers of our own day, who conclude that certain flints found in the
+drift are the work of men, because the geologist does not see what else
+they can be." After this twist of meaning, the reviewer proceeds to say,
+and A. B. would certainly join him, "There is no need to combat any such
+mode of reasoning as this, because it would apply with equal force and
+justice to any theory whatever, however fantastic, profane, or silly." And
+so, having shown how the reviewer has hung himself, I leave him
+funipendulous.
+
+One instance more, and I have done. A reviewer, not theological, speaking
+of the common argument that things which are derided are not _therefore_ to
+be rejected, writes as follows:--"It might as well be said that they who
+laughed at Jenner[349] and vaccination were, in a certain but very
+unsatisfactory way, witnesses to the possible excellence of the system of
+St. John Long."[350] Of course it _might_: and of course it _is_ said by
+all people of common sense. In introducing the word "possible," the
+reviewer has hit the point: I suspect that this word was introduced during
+revision, to put the sentence into fighting order; hurry preventing it
+being seen that the sentence was thus made to fight on the wrong side.
+Jenner, who was laughed at, was right; therefore, it is not
+impossible--that is, it is _possible_--that a derided system may be right.
+Mark the three gradations: _in medio tutissimus ibis_.[351]
+
+{206}
+
+_Reviewer._--If a system be derided, it is no ground of suspense that
+derided systems have turned out true: if it were, you would suspend your
+opinion about St. John Long on account of Jenner.--_Ans._ You ought to do
+so, as to _possibility_; and _before examination_; not with the notion that
+J. proves St. J. _probable_; only _possible_.
+
+_Common Sense._--The past emergence of truths out of derided systems proves
+that there is a practical certainty of like occurrence to come. But,
+inasmuch as a hundred speculative fooleries are started for one truth, the
+mind is permitted to approach the examination of any one given novelty with
+a bias against it of a hundred to one: and this permission is given because
+so it will be, leave or no leave. Every one has licence not to jump over
+the moon.
+
+_Paradoxer._--Great men have been derided, and I am derided: which proves
+that my system ought to be adopted. This is a summary of all the degrees in
+which paradoxers contend for the former derision of truths now established,
+giving their systems _probability_. I annex a paragraph which D [e &c.]
+inserted in the _Athenaeum_ of October 23, 1847.
+
+"_Discoverers and Discoveries._
+
+"Aristotle once sent his servant to the cellar to fetch wine:--and the
+fellow brought him back small beer. The Stagirite (who knew the difference)
+called him a blockhead. 'Sir,' said the man, 'all I can say is, that I
+found it in the cellar.' The philosopher muttered to himself that an
+affirmative conclusion could not be proved in the second figure,--and Mrs.
+Aristotle, who was by, was not less effective in her remark, that small
+beer was not wine because it was in the same cellar. Both were right
+enough: and our philosophers might take a lesson from either--for they
+insinuate an affirmative conclusion in the second figure. Great discoverers
+have been little valued by established {207} schools,--and they are little
+valued. The results of true science are strange at first,--and so are
+their's. Many great men have opposed existing notions,--and so do they. All
+great men were obscure at first,--and they are obscure. Thinking men
+doubt,--and they doubt. Their small beer, I grant, has come out of the same
+cellar as the wine; but this is not enough. If they had let it stand awhile
+in the old wine-casks, it might have imbibed a little of the flavor."
+
+
+
+There are better reviews than I have noticed; which, though entirely
+dissenting, are unassailable on their own principles. What I have given
+represents five-sixths of the whole. But it must be confessed that the
+fraction of fairness and moderation and suspended opinion which the
+doctrine of _Spirit Manifestations_ has met with--even in the lower
+reviews--is strikingly large compared to what would have been the case
+fifty years ago. It is to be hoped that our popular and periodical
+literatures are giving us one thinker created for twenty geese
+double-feathered: if this hope be realized, we shall do! Seeing all that I
+see, I am not prepared to go the length of a friend of mine who, after
+reading a good specimen of the lower reviewing, exclaimed--Oh! if all the
+fools in the world could be rolled up into one fool, what a reviewer he
+would make!
+
+
+
+    Calendrier Universel et Perpetuel; par le Commandeur P. J. Arson.[352]
+    Publie par ses Enfans (Oeuvre posthume). Nice, 1863, 4to.
+
+I shall not give any account of this curious calendar, with all its changes
+and symbols. But there is one proposal, which, could we alter the general
+notions of time--a thing of very dubious possibility--would be convenient.
+The week is made to wax and wane, culminating on the Sunday, {208} which
+comes in the middle. Thursday, Friday, Saturday, are ascending or waxing
+days; Monday, Tuesday, Wednesday, are descending or waning days. Our six
+days, lumped together after the great distinguishing day, Sunday, are too
+many to be distinctly thought of together: a division of three preceding
+and three following the day of most note would be much more easily used.
+But all this comes too late. It may be, nevertheless, that some individuals
+may be able to adjust their affairs with advantage by referring Thursday,
+Friday, Saturday, to the following Sunday, and Monday, Tuesday, Wednesday,
+to the preceding Sunday. But M. Arson's proposal to alter the names of the
+days is no more necessary than it is practicable.
+
+
+
+CYCLOMETRY.
+
+I am not to enter anything I do not possess. The reader therefore will not
+learn from me the feats of many a man-at-arms in these subjects. He must be
+content, unless he will bestir himself for himself, not to know how Mr.
+Patrick Cody trisects the angle at Mullinavat, or Professor Recalcati
+squares the circle at Milan. But this last is to be done by subscription,
+at five francs a head: a banker is named who guarantees restitution if the
+solution be not perfectly rigorous; the banker himself, I suppose, is the
+judge. I have heard of a man of business who settled the circle in this
+way: if it can be reduced to a debtor and creditor account, it can
+certainly be done; if not, it is not worth doing. Montucla will give the
+accounts of the lawsuits which wagers on the problem have produced in
+France.
+
+Neither will I enter at length upon the success of the new squarer who
+advertises (Nov. 1863) in a country paper that, having read that the
+circular ratio was undetermined, "I thought it very strange that so many
+great scholars in all ages should have failed in finding the true ratio,
+and have been determined to try myself.... I am about to secure the {209}
+benefit of the discovery, so until then the public cannot know my new and
+true ratio." I have been informed that this trial makes the diameter to the
+circumference as 64 to 201, giving [pi] = 3.140625 exactly. The result was
+obtained by the discoverer in three weeks after he first heard of the
+existence of the difficulty. This quadrator has since published a little
+slip, and entered it at Stationers' Hall. He says he has done it by actual
+measurement; and I hear from a private source that he uses a disk of 12
+inches diameter, which he rolls upon a straight rail. Mr. James Smith did
+the same at one time; as did also his partisan at Bordeaux. We have, then,
+both 3.125 and 3.140625, by actual measurement. The second result is more
+than the first by about one part in 200. The second rolling is a very
+creditable one; it is about as much below the mark as Archimedes was above
+it. Its performer is a joiner, who evidently knows well what he is about
+when he measures; he is not wrong by 1 in 3,000.
+
+The reader will smile at the quiet self-sufficiency with which "I have been
+determined to try myself" follows the information that "so many great
+scholars in all ages" have failed. It is an admirable spirit, when
+accompanied by common sense and uncommon self-knowledge. When I was an
+undergraduate there was a little attendant in the library who gave me the
+following,--"As to cleaning this library, Sir, if I have spoken to the
+Master once about it, I have spoken fifty times: but it is of no use; he
+will not employ _littery_ men; and so I am obliged to look after it
+myself."
+
+I do not think I have mentioned the bright form of quadrature in which a
+square is made equal to a circle by making each side equal to a quarter of
+the circumference. The last squarer of this kind whom I have seen figures
+in the last number of the _Athenaeum_ for 1855: he says the thing is no
+longer a _problem_, but an _axiom_. He does not know that the area of the
+circle is greater than that of any other figure of the same circuit. This
+any one might see without {210} mathematics. How is it possible that the
+figure of greatest area should have any one length in its circuit unlike in
+form to any other part of the same length?
+
+The feeling which tempts persons to this problem is that which, in romance,
+made it impossible for a knight to pass a castle which belonged to a giant
+or an enchanter. I once gave a lecture on the subject: a gentleman who was
+introduced to it by what I said remarked, loud enough to be heard by all
+around, "Only prove to me that it is impossible, and I will set about it
+this very evening."
+
+This rinderpest of geometry cannot be cured, when once it has seated itself
+in the system: all that can be done is to apply what the learned call
+prophylactics to those who are yet sound. When once the virus gets into the
+brain, the victim goes round the flame like a moth; first one way and then
+the other, beginning where he ended, and ending where he begun: thus
+verifying the old line
+
+ "In girum imus nocte, ecce! et consumimur igni."[353]
+
+Every mathematician knows that scores of methods, differing altogether from
+each other in process, all end in this mysterious 3.14159..., which insists
+on calling itself the circumference to a unit of diameter. A reader who is
+competent to follow processes of arithmetic may be easily satisfied that
+such methods do actually exist. I will give a sketch, carried out to a few
+figures, of three: the first two I never met with in my reading; the third
+is the old method of Vieta.[354] [I find that both the first and second
+methods are contained in a theorem of Euler.]
+
+What Mr. James Smith says of these methods is worth noting. He says I have
+given three "_fancy_ proofs" of the value of [pi]: he evidently takes me to
+be offering demonstration. He proceeds thus:--
+
+"His first proof is traceable to the diameter of a circle {211} of radius
+1. His second, to the side of any inscribed equilateral triangle to a
+circle of radius 1. His third, to a radius of a circle of diameter 1. Now,
+it may be frankly admitted that we can arrive at the same result by many
+other modes of arithmetical calculation, all of which may be shown to have
+some sort of relation to a circle; but, after all, these results are mere
+exhibitions of the properties of numbers, and have no more to do with the
+ratio of diameter to circumference in a circle than the price of sugar with
+the mean height of spring tides. (_Corr._ Oct. 21, 1865)."
+
+I quote this because it is one of the few cases--other than absolute
+assumption of the conclusion--in which Mr. Smith's conclusions would be
+true if his premise were true. Had I given what follows as _proof_, it
+would have been properly remarked, that I had only exhibited properties of
+numbers. But I took care to tell my reader that I was only going to show
+him _methods_ which end in 3.14159.... The proofs that these methods
+establish the value of [pi] are for those who will read and can understand.
+
+  200000000      31415       3799
+   66666667                  2817
+   26666667                  1363
+   11428571                   661
+    5079365                   321
+    2308802                   156
+    1065601                    76
+     497281                    37
+     234014                    18
+     110849                     9
+      52785                     5
+      25245                     2
+      12118                     1
+       5834
+   --------     --------  -------
+  314153799      31415       9265
+
+{212}
+
+1. Take any diameter, double it, take 1-3d of that double, 2-5ths of the
+last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so
+on. The sum of all is the circumference of that diameter. The preceding is
+the process when the diameter is a hundred millions: the errors arising
+from rejection of fractions being lessened by proceeding on a thousand
+millions, and striking off one figure. Here 200 etc. is double of the
+diameter; 666 etc. is 1-3rd of 200 etc.; 266 etc. is 2-5ths of 666 etc.;
+114 etc. is 3-7ths of 266 etc.; 507 etc. is 4-9ths of 114 etc.; and so on.
+
+2. To the square root of 3 add its half. Take _half_ the third part of
+this; half 2-5ths of the last; half 3-7ths of the last; and so on. The sum
+is the circumference to a unit of diameter.
+
+    Square root of 3....  1.73205081
+                           .86602540
+                        ------------
+                          2.59807621
+                           .43301270
+                           .08660254
+                             1855768
+                              412393
+                               93726
+                               21629
+                                5047
+                                1188
+                                 281
+                                  67
+                                  16
+                                   4
+                                   1
+                        ------------
+                          3.14159265
+
+3. Take the square root of 1/2; the square root of half of one more than
+this; the square root of half of one more {213} than the last; and so on,
+until we come as near to unity as the number of figures chosen will permit.
+Multiply all the results together, and divide 2 by the product: the
+quotient is an approximation to the circumference when the diameter is
+unity. Taking aim at four figures, that is, working to five figures to
+secure accuracy in the fourth, we have .70712 for the square root of 1/2;
+.92390 for the square root of half one more than .70712; and so on, through
+.98080, .99520, .99880, .99970, .99992, .99998. The product of the eight
+results is .63667; divide 2 by this, and the quotient is 3.1413..., of
+which four figures are correct. Had the product been .636363... instead of
+.63667..., the famous result of Archimedes, 22-7ths, would have been
+accurately true. It is singular that no cyclometer maintains that
+Archimedes hit it exactly.
+
+A literary journal could hardly admit as much as the preceding, if it stood
+alone. But in my present undertaking it passes as the halfpennyworth of
+bread to many gallons of sack. Many more methods might be given, all ending
+in the same result, let that result mean what it may.
+
+Now since dozens of methods, to which dozens more might be added at
+pleasure, concur in giving one and the same result; and since these methods
+are declared by all who have shown knowledge of mathematics to be
+_demonstrated_: it is not asking too much of a person who has just a little
+knowledge of the first elements that he should learn more, and put his hand
+upon the error, before he intrudes his assertion of the existence of error
+upon those who have given more time and attention to it than himself, and
+who are in possession, over and above many demonstrations, of many
+consequences verifying each other, of which he can know nothing. This is
+all that is required. Let any one square the circle, and persuade his
+friends, if he and they please: let him print, and let all read who choose.
+But let him abstain from intruding himself upon those who have been
+satisfied by existing demonstration, until he is prepared {214} to lay his
+finger on the point in which existing demonstration is wrong. Let him also
+say what this mysterious 3.14159... really is, which comes in at every door
+and window, and down every chimney, calling itself the circumference to a
+unit of diameter. This most impudent and successful impostor holds false
+title-deeds in his hands, and invites examination: surely those who can
+find out the rightful owner are equally able to detect the forgery. All the
+quadrators are agreed that, be the right what it may, 3.14159... is wrong.
+It would be well if they would put their heads together, and say what this
+wrong result really means. The mathematicians of all ages have tried all
+manner of processes, with one object in view, and by methods which are
+admitted to yield demonstration in countless cases. They have all arrived
+at one result. A large number of opponents unite in declaring this result
+wrong, and all agree in two points: first, in differing among themselves;
+secondly, in declining to point out what that curious result really is
+which the mathematical methods all agree in giving.
+
+Most of the quadrators are not aware that it has been fully demonstrated
+that no two numbers whatsoever can represent the ratio of the diameter to
+the circumference with perfect accuracy. When therefore we are told that
+either 8 to 25 or 64 to 201 is the true ratio, we know that it is no such
+thing, without the necessity of examination. The point that is left open,
+as not fully demonstrated to be impossible, is the _geometrical_
+quadrature, the determination of the circumference by the straight line and
+circle, used as in Euclid. The general run of circle-squarers, hearing that
+the quadrature is not pronounced to be _demonstratively_ impossible,
+imagine that the _arithmetical_ quadrature is open to their ingenuity.
+Before attempting the arithmetical problem, they ought to acquire knowledge
+enough to read Lambert's[355] demonstration (last given in Brewster's[356]
+translation {215} of Legendre's[357] Geometry) and, if they can, to refute
+it. [It will be given in an Appendix.] Probably some have begun this way,
+and have caught a Tartar who has refused to let them go: I have never heard
+of any one who, in producing his own demonstration, has laid his finger on
+the faulty part of Lambert's investigation. This is the answer to those who
+think that the mathematicians treat the arithmetical squarers too lightly,
+and that as some person may succeed at last, all attempts should be
+examined. Those who have so thought, not knowing that there is
+demonstration on the point, will probably admit that a person who
+contradicts a theorem of which the demonstration has been acknowledged for
+a century by all who have alluded to it as read by themselves, may
+reasonably be required to point out the error before he demands attention
+to his own result.
+
+_Apopempsis of the Tutelaries._--Again and again I am told that I spend too
+much time and trouble upon my two tutelaries: but when I come to my
+summing-up I shall make it appear that I have a purpose. Some say I am too
+hard upon them: but this is quite a mistake. Both of them beat little
+Oliver himself in the art and science of asking for more; but without
+Oliver's excuse, for I had given good allowance. Both began with me, not I
+with them: and both knew what they had to expect when they applied for a
+second helping.
+
+On July 31, the Monday after the publication of my remarks on my 666
+correspondent, I found _three_ notes in separate envelopes, addressed to me
+at "7A, University College." When I saw the three new digits I was taken
+rhythmopoetic, as follows--
+
+  Here's the Doctor again with his figs, and by Heavens!
+  He was always at sixes, and now he's at sevens.
+
+To understand this fully the reader must know that the greater part of
+Apocalyptic interpretation has long been condensed, in my mind, into the
+Turkish street-cry--In the {216} name of the Prophet! figs! I make a few
+extracts. The reader will observe that Dr. Thorn grumbles at his _private_
+letters being _publicly_ ridiculed. A man was summoned for a glutolactic
+assault; he complained of the publication of his proceeding: I kicked etc.
+_in confidence_, he said.
+
+"After reading your last, which tries in every way to hold me up to public
+ridicule for daring to write you privately ['that you would be d----d,'
+omitted by accident] one would say, Why have anything to do with such a
+testy person? [Wrong word; no testy person can manage cool and consecutive
+ridicule. Quaere, what is this word? Is it anything but a corruption of the
+obsolete word _tetchy_ of the same meaning? Some think _touchy_ is our
+modern form of _tetchy_, which I greatly doubt]. My answer is, the poor man
+is lamentably ignorant; he is not only so, but 'out of the way' [quite
+true; my readers know me by this time for an out-of-the-way person. What
+other could tackle my squad of paradoxers? What other would undertake the
+job?] Can he be brought back and form one of those who in Ezekiel 37 ch.
+have the Spirit breathed into them and live.... Have I any other feeling
+towards you except that of peace and goodwill? [Not to your distinct
+knowledge; but in all those who send people to 'the other place' for
+contempt of their interpretations, there is a lurking wish which is father
+to the thought; 'you _will_ be d----d' and 'you _be_ d--d' are Siamese
+twins]. Of course your sneer at 666 brought plain words; but when men
+meddle with what they do not understand (not having the double _Vahu_) they
+must be dealt with faithfully by those who do.... [They must; which
+justifies the Budget of Paradoxes: but no occasion to send them anywhere;
+no preachee and floggee too, as the negro said]. Many will find the text
+Prov. i. 26 fully realized. [All this contains distinct assumption of a
+right 'of course' to declare accursed those who do not respect the writer's
+vagary].... If I could but get the [Hebrew: A], the Ox-head, which in Old
+Hebrew was just the Latin Digamma, F, out {217} of your name, and could
+then Thau you with the Thau of Ezekiel ix, 4, the [chi], then you would
+bear the number of a man! But this is too hard for me, although not so for
+the Lord! Jer. xxxii. 17.... And now a word: is ridicule the right thing in
+so solemn a matter as the discussion of Holy Writ? [Is food for ridicule
+the right thing? Did I discuss Holy Writ? I did not: I concussed profane
+scribble. Even the Doctor did not _discuss_; he only enunciated and
+denunciated out of the mass of inferences which a mystical head has found
+premises for in the Bible]."
+
+  M    40
+  O    70
+  R   100
+  G     6
+  N    50
+      ----
+      266
+  [Hebrew: t]=[chi] 400
+
+[That ill opinions are near relations of ill wishes, will be detected by
+those who are on the look out. The following was taken down in a Scotch
+Church by Mr. Cobden,[358] who handed it to a Roman friend of mine, for his
+delectation (in 1855): "Lord, we thank thee that thou hast brought the Pope
+into trouble; and we pray that thou wouldst be mercifully pleased to
+increase the same."]
+
+Here is a martyr who quarrels with his crown; a missionary who reviles his
+persecutor: send him to New Zealand, and he would disagree with the Maoris
+who ate him. Man of unilateral reciprocity! have you, who write to a
+stranger with hints that that stranger and his wife are children of
+perdition, the bad taste to complain of a facer in return? As James
+Smith[359]--the Attorney-wit, not the Dock-cyclometer--said, or nearly
+said,
+
+   "A pretty thing, forsooth!
+  Is he to burn, all scalding hot,
+  Me and my wife, and am I not
+    To job him out a tooth?"
+
+{218}
+
+Those who think parody vulgar will be pleased to substitute for the above a
+quotation from Butler[360]:--
+
+ "There's nothing so absurd or vain
+  Or barbarous or inhumane,
+  But if it lay the least pretence
+  To piety and godliness,
+  Or tender-hearted conscience,
+  And zeal for gospel truths profess,--
+  Does sacred instantly commence,
+  And all that dare but question it are straight
+  Pronounced th' uncircumcised and reprobate,
+  As malefactors that escape and fly
+  Into a sanctuary for defence,
+  Must not be brought to justice thence,
+  Although their crimes be ne'er so great and high.
+  And he that dares presume to do't
+  Is sentenced and delivered up
+  To Satan that engaged him to't."
+
+
+
+THE NUMBER OF THE BEAST.
+
+Of all the drolleries of controversy none is more amusing than the manner
+in which those who provoke a combat expect to lay down the laws of
+retaliation. You must not strike this way! you must not parry that way! If
+you don't take care, we shall never meddle with you again! We were not
+_prepared_ for such as this! Why did we have anything to do with such a
+testy person? M. Jourdain must needs show Nicole, his servant-maid, how
+good a thing it was to be sure of fighting without being killed, by care
+and tierce.[361] "Et cela n'est il pas beau d'etre assure de son fait quand
+on se bat contre quelqu'un? La, pousse moi un peu, pour voir. NICOLE. Eh
+bien! quoi? M. JOURDAIN. Tout beau. Hola! {219} Ho! doucement. Diantre soit
+la coquine! NICOLE. Vous me dites de pousser. M. JOURDAIN. Oui; mais tu me
+pousses en tierce, avant que de pousser en quarte, et tu n'as pas la
+patience que je pare."
+
+His colleague, my secular tutelary, who also made an anachronistic onset,
+with his repartees and his retorts, before there was anything to fire at,
+takes what I give by way of subsequent provocation with a good humor which
+would make a convert of me if he could afford .01659265 ... of a grain of
+logic. He instantly sent me his photograph for the asking, and another
+letter in proof. The Thor-hammerer does nothing but grumble, except when he
+tells a good story, which he says he had from Dr. Abernethy.[362] A Mr.
+James Dunlop was popping at the Papists with a 666-rifled gun, when Dr.
+Chalmers[363] quietly said, "Why, Dunlop, you bear it yourself," and handed
+him a paper on which the numerals in
+
+  I A C O B V S         D V N L O P V S
+  1  100    5         500 5  50     5
+
+were added up. This is almost as good as the _Filii Dei Vicarius_, the
+numerical letters of which also make 666. No more of these crazy--I first
+wrote _puerile_, but why should young cricketers be libelled?--attempts to
+extract religious use from numerical vagaries, and to make God over all a
+proposer of _salvation conundrums_: and no more of the trumpery hints about
+future destiny which is too great a compliment to call blasphemous. If the
+Doctor will cipher upon the letter in [Greek: en hoi metroi metreite
+metrethesetai humin][364] with _double Vahu_ cubic measure, he will perhaps
+learn to leave off trying to frighten me into gathering grapes from thorns.
+
+Mystical hermeneutics may be put to good use by out-of-the-way people. They
+may be made to call the attention {220} of the many to a distinction well
+known among the learned. The books of the New Testament have been for 1,500
+years divided into two classes: the _acknowledged_ ([Greek:
+homologoumena]), which it has always been paradox not to receive; and the
+_controverted_ ([Greek: antilegomena]), about which there has always been
+that difference of opinion which no scholar overlooks, however he may
+decide for himself after balance of evidence. Eusebius,[365] who first (l.
+3, c. 25) recorded the distinction--which was much insisted on by the early
+Protestants--states the books which are questioned as doubtful, but which
+yet are approved and acknowledged by _many_--or _the many_, it is not easy
+to say which he means--to be the Epistles of James and Jude, the second of
+Peter and the second and third of John. In other places he speaks
+doubtingly of the Epistle to the Hebrews. The Apocalypse he does not even
+admit into this class, for he proceeds as follows--I use the second edition
+of the English folio translation (1709), to avert suspicion of bias from
+myself:--
+
+"Among the _spurious_ [[Greek: nothoi]] let there be ranked both the work
+entitled the _Acts of Paul_, and the book called _Pastor_, and the
+_Revelation of Peter_: and moreover, that which is called the _Epistle of
+Barnabas_, and that named the _Doctrines of the Apostles_: and moreover, as
+I said, the _Revelation of John_ (if you think good), which some, as I have
+said, do reject, but others allow of, and admit among those books which are
+received as unquestionable and undoubted."
+
+Eusebius, though he will not admit the Apocalypse even into the
+_controverted_ list, but gives permission to call it _spurious_, yet
+qualifies his permission in a manner which almost annihilates the
+distinctive force of [Greek: nothos], and gives the book a claim to rank
+(if you think good, again) in the controverted list. And this is the
+impression received by {221} the mind of Lardner, who gives Eusebius fully
+and fairly, but when he sums up, considers his author as admitting the
+Apocalypse into the second list. A stick may easily be found to beat the
+father of ecclesiastical history. There are whole faggots in writers as
+opposite as Baronius and Gibbon, who are perhaps his two most celebrated
+sons. But we can hardly imagine him totally misrepresenting the state of
+opinion of those for whom and among whom he wrote. The usual plan, that of
+making an author take the views of his readers, is more easy in his case
+than in that of any other writer: for, as the riddle says, he is
+You-see-by-us; and to this reading of his name he has often been subjected.
+Dr. Nathaniel Lardner,[366] who, though heterodox in doctrine, tries hard
+to be orthodox as to the Canon, is "sometimes apt to think" that the list
+should be collected and divided as in Eusebius. He would have no one of the
+controverted books to be allowed, by itself, to establish any doctrine.
+Even without going so far, a due use of early opinion and long continued
+discussion would perhaps prevent rational people from being induced by
+those who have the _double Vahu_ to place the Apocalypse _above_ the
+Gospels, which all the Bivahuites do in effect, and some are said to have
+done in express words. But my especial purpose is to point out that an easy
+way of getting rid of 665 out of 666 of the mystics is to require them to
+establish the Apocalypse before they begin. See if they even know so much
+as that there is a crowd of testimonies for and against, running through
+the first four centuries, which makes this book the most difficult of the
+whole Canon. Try this method, and you will escape beautiful, as the French
+say. Dean Alford,[367] in Vol. IV, p. 8, of his New Testament, gives an
+elaborate handling of this question. He concludes by saying that he cannot
+{222} venture to refuse his consent to the tradition that the Apostle is
+the author. This modified adherence, or non-nonadherence, pretty well
+represents the feeling of orthodox Protestants, when learning and common
+sense come together.
+
+I have often, in former days, had the attempt made to place the Apocalypse
+on my neck as containing prophecies yet unfulfilled. The preceding method
+prevents success; and so does the following. It may almost be taken for
+granted that theological system-fighters do not read the New Testament:
+they hunt it for detached texts; they listen to it in church in that state
+of quiescent nonentity which is called reverent attention: but they never
+read it. When it is brought forward, you must pretend to find it necessary
+to turn to the book itself: you must read "The revelation ... to show unto
+his servants _things which must shortly come to pass_.... Blessed is he
+that readeth ... _for the time is at hand_." You must then ask your mystic
+whether things deferred for 1800 years were shortly to come to pass, etc.?
+You must tell him that the Greek [Greek: en tachei], rendered "shortly," is
+as strong a phrase as the language has to signify _soon_. The interpreter
+will probably look as if he had never read this opening: the chances are
+that he takes up the book to see whether you have been committing a fraud.
+He will then give you some exquisite evasion: I have heard it pleaded that
+the above was a _mere preamble_. This word _mere_ is all-sufficient: it
+turns anything into nothing. Perhaps he will say that the argument is that
+of the Papists: if so, tell him that there is no Christian sect but bears
+true witness against some one or more absurdities in other sects.
+
+An anonyme suggests that [Greek: en tachei] may not be "soon," it may be
+"quickly, without reference to time when:" he continues thus, "May not time
+be 'at hand' when it is ready to come, no matter how long delayed?" I now
+understand what *** and *** meant when they borrowed my books and promised
+to return them quickly, it was "without {223} reference to time when." As
+to time at _hand_--provided you make a long _arm_--I admire the quirk, but
+cannot receive it: the word is [Greek: engus], which is a word of
+_closeness_ in time, in place, in reckoning, in kindred, etc.
+
+Another gentleman is not surprised that Apocalyptic reading leads to a
+doubt of the "canonicity" of the book: it ought not to rest on church
+testimony, but on visible miracle. He offers me, or any reader of the
+_Athenaeum_, the "sight of a miracle to that effect, and within forty-eight
+hours' journey (fare paid)." I seldom travel, and my first thought was
+whether my carpet-bag would be found without a regular hunt: but, on
+reading further, I found that it was only a concordance that would be
+wanted. Forty hours' collection and numerical calculation of Greek nouns
+would make it--should I happen to agree with the writer--many hundred
+millions to one that Revelation xiii is superhuman. There is but one verse
+(the fifth) which the writer does not see verified. I looked at this verse,
+and was much startled. The Budget began in October 1863: should it last
+until March 1867--it is now August 1866--it is clear that I am the first
+Beast, and my paradoxers are the saints whom I persecute.
+
+[The Budget _did_ terminate in March 1867: I hope the gentleman will be
+satisfied with the resulting interpretation.]
+
+The same opponent is surprised that I should suppose a thing which "comes
+to pass" must be completed, and cannot contain what is to happen 1800 years
+after. All who have any knowledge of English idiom know that a thing
+_comes_ to pass when it happens, and _came_ to pass afterwards. But as the
+original is Greek, we must look at the Greek: it is [Greek: dei genesthai]
+for "must come to pass," and we know that [Greek: egeneto] is what is
+usually translated "came to pass." No word of more finished completion
+exists in Greek.
+
+And now for a last round of biter-bit with the Thor-hammerer, of whom, as
+in the other case, I shall take no {224} more notice until he can contrive
+to surpass himself, which I doubt his being able to do. He informs me that
+by changing A into [Hebrew: t] in my name he can make a 666 of _me_;
+adding, "This is too hard for me, although not so for the Lord!" Sheer
+nonsense! He could just as easily have directed to "Prof. De Morg[Hebrew:
+t]n" as have assigned me apartment 7A in University College. It would have
+been seen for whom it was intended: and if not, it would still have reached
+me, for my colleagues have for many a year handed all out-of-the-way things
+over to me. There is no 7A: but 7 is the Museum of Materia Medica. I took
+the only hint which the address gave: I inquired for hellebore, but they
+told me it was not now recognized, that the old notion of its value was
+quite obsolete, and that they had nothing which was considered a specific
+in senary or septenary cases. The great platitude is the reference of such
+a difficulty as writing [Hebrew: t] for A to the Almighty! Not childish,
+but fatuous: real childishness is delightful. I knew an infant to whom,
+before he could speak plain, his parents had attempted to give notions of
+the Divine attributes: a wise plan, many think. His father had dandled him
+up-side-down, ending with, There now! Papa could not dance on his head! The
+mannikin made a solemn face, and said, _But Dod tood_! I think the Doctor
+has rather mistaken the way of becoming as a little child, intended in
+Matt. xviii. 3: let us hope the will may be taken for the deed.
+
+Two poets have given images of transition from infancy to manhood:
+Dryden,--for the Hind is Dryden himself on all fours! and Wordsworth, in
+his own character of broad-nailed, featherless biped:
+
+ "The priest continues what the nurse began,
+  And thus the child imposes on the man."
+   "The child's the father of the man,
+    And I could wish my days to be
+    Bound each to each by natural piety."
+
+{225}
+
+In Wordsworth's aspiration it is meant that sense and piety should grow
+together: in Dryden's description a combination of Mysticism And Bigotry
+(can this be the _double Vahu_?), personified as "the priest,"--who always
+catches it on this score, though the same spirit is found in all
+associations,--succeeds the boguey-teaching of the nurse. Never was the
+contrast of smile and scowl, of light and darkness, better seen than in the
+two pictures. But an acrostic distinction may be drawn. When mysticism
+predominates over bigotry, we have the grotesque picturesque, and the
+natural order of words gives us _Mab_, an appropriate suggestion. But when
+bigotry has the upper hand, we see _Bam_, which is just as appropriate; for
+bigotry nearly always deals with facts and logic so as to require the
+application of at least one of the minor words by which dishonesty is
+signified. I think that M is the Doctor's initial, and that Queen Mab
+tickles him in his sleep with the sharp end of a 6.
+
+(_Monday, August 21._) Three weeks having elapsed without notice from me of
+the Doctor, I receive a reminder of his existence, in which I find that as
+I am the Daniel who judges the Magi of Babylon, it is to be pointed out
+that Daniel "bore a certain number, that of a man (beloved), Daniel, ch.
+10. v. 11, and which you certainly do not." Then, "by Greek power,"
+Belteshazzar is made = 666. Here is another awkward imitation of the way of
+a baby child. When you have sported with the tiny creature until it runs
+away offended, by the time you have got into conversation again you will
+find the game is to be renewed: a little head peeps out from a hiding-place
+with "I don't love you." The proper rejoinder is, "Very well! then I'll
+have pussy." But in the case before me there is a rule of three sums to do;
+as baby : Pussy Dr. :: 666 : the answer required. I will work it out, if I
+can.
+
+The squaring of the circle and the discovery of the Beast are the two
+goals--and goals also--of many unbalanced intellects, and of a few
+instances of the better kind. {226} I might have said more of 666, but I am
+not deep in its bibliography. A work has come into my hands which contains
+a large number of noted cases: to some of my readers it will be a treat to
+see the collection; and the sight will perhaps be of some use to those who
+have read controversy on the few celebrated cases which are of general
+notoriety. It is written by a learned decipherer, a man who really knew the
+history of the subject, the Rev. David Thom,[368] of Bold Street Chapel,
+Liverpool, who died, I am told, a few years ago.
+
+Anybody who reads his book will be inclined to parody a criticism which was
+once made on Paley's[369] Evidences--"Well! if there be anything in
+Christianity, this man is no fool." And, if he should chance to remember
+it, he will be strongly reminded of a sentence in my opening chapter,--"The
+manner in which a paradoxer will show himself, as to sense or nonsense,
+will not depend upon what he maintains, but upon whether he has or has not
+made a sufficient knowledge of what has been done by others, _especially as
+to the mode of doing it_, a preliminary to inventing knowledge for
+himself." And this is reinforced by the fact that Mr. Thom, though a
+scholar, was not conspicuous for learning, except in this his great
+pursuit. He was a paradoxer on other points. He reconciled Calvinism and
+eternal reprobation with Universalism and final salvation; showing these
+two doctrines to be all one.
+
+This gentleman must not be confounded with the Rev. John Hamilton Thom[370]
+(no relation), at or near the same {227} time and until recently, of
+Renshaw Street Chapel, Liverpool who was one of the minority in the
+Liverpool controversy when, nearly thirty years ago, _three_ heretical
+Unitarian schooners exchanged shotted sermons with _thirteen_ Orthodox
+ships of the line, and put up their challengers' dander--an American
+corruption of _d--d anger_--to such an extent, by quiet and respectful
+argument, that those opponents actually addressed a printed intercession to
+the Almighty for the Unitarian triad, as for "Jews, Turks, Infidels, and
+Heretics." So much for the distinction, which both gentlemen would thank me
+for making very clear: I take it quite for granted that a guesser at 666
+would feel horrified at being taken for a Unitarian, and that a Unitarian
+would feel queerified at being taken for a guesser at 666. Mr. David Thom's
+book is _The Number and Names of the Apocalyptic Beasts_, Part I, 1848,
+8vo.: I think the second part was never published. I give the Greek and
+Latin solutions, omitting the Hebrew: as usual, all the Greek letters are
+numeral, but only M D C L X V I of the Latin. I do not give either the
+decipherers or their reasons: I have not room for this; nor would I, if I
+could, bias my reader for one rather than another.
+
+D. F. Julianus Caesar Atheus (or Aug.[371]); Diocles Augustus; Ludovicus;
+Silvester Secundus; Linus Secundus; {228} Vicarius Filii Dei; Doctor et Rex
+Latinus; Paulo V. Vice-Deo; Vicarius Generalis Dei in Terris; Ipse
+Catholicae Ecclesiae Visibile Caput; Dux Cleri; Una, Vera, Catholica,
+Infallibilis Ecclesia; Auctoritas politica ecclesiasticaque Papalis (Latina
+will also do); Lutherus Ductor Gregis; Calvinus tristis fidei interpres;
+Dic Lux ; Ludvvic; Will. Laud; [Greek: Lateinos];[372] [Greek: he latine
+basileia]; [Greek: ekklesia italika]; [Greek: euanthas]; [Greek: teitan];
+[Greek: arnoume]; [Greek: lampetis]; [Greek: ho niketes]; [Greek: kakos
+hodegos]; [Greek: alethes blaberos]; [Greek: palai baskanos]; [Greek: amnos
+adikos]; [Greek: antemos]; [Greek: genserikos]; [Greek: euinas]; [Greek:
+Benediktos]; [Greek: Bonibazios g. papa x. e. e. e. a.], meaning Boniface
+III. Pope 68th, bishop of bishops the first! [Greek: oulpios]; [Greek: dios
+eimi he heras]; [Greek: he missa he papike]; [Greek: loutherana]; [Greek:
+saxoneios]; [Greek: Bezza antitheos] (Beza); [Greek: he alazoneia biou];
+[Greek: Maometis]; [Greek: Maometes b.]; [Greek: theos eimi epi gaies];
+[Greek: iapetos]; [Greek: papeiskos]; [Greek: dioklasianos]; [Greek:
+cheina]; [Greek: braski]; [Greek: Ion Paune]; [Greek: koupoks]; (cowpox,
+[Greek: s] being the _vau_; certainly the {229} vaccinated have the mark of
+the Beast); [Greek: Bonneparte]; [Greek: N. Boneparte]; [Greek: euporia];
+[Greek: paradosis]; [Greek: to megatherion].
+
+All sects fasten this number on their opponents. It is found in _Martin
+Lauter_, affirmed to be the true way of writing the name, by carrying
+numbers through the Roman Alphabet. Some Jews, according to Mr. Thorn,
+found it in [Hebrew: JSHW NTSRJ] _Jesus of Nazareth_. I find on inquiry
+that this satire was actually put forth by some medieval rabbis, but that
+it is not idiomatic: it represents quite fairly "Jesus Nazarene," but the
+Hebrew wants an article quite as much as the English wants "the."
+
+Mr. David Thom's own solution hits hard at all sides: he finds a 666 for
+both beasts; [Greek: he phren] (the mind) for the first, and [Greek:
+ekklesiai sarkikai] (fleshly churches) for the second. A solution which
+embodies all mental philosophy in one beast and all dogmatic theology in
+the other, is very tempting: for in these are the two great supports of
+Antichrist. It will not, however, mislead me, who have known the true
+explanation a long time. The three sixes indicate that any two of the three
+subdivisions, Roman, Greek, and Protestant, are, in corruption of
+Christianity, six of one and half a dozen of the other: the distinctions of
+units, tens, hundreds, are nothing but the old way (1 Samuel xviii. 7, and
+Concordance at _ten_, _hundred_, _thousand_) of symbolizing differences of
+number in the subdivisions.
+
+It may be good to know that, even in speculations on 666, there are
+different degrees of unreason. All the diviners, when they get a colleague
+or an opponent, at once proceed to reckon him up: but some do it in play
+and some in earnest. Mr. David Thom found a young gentleman of the name St.
+Claire busy at the Beast number: he forthwith added the letters in [Greek:
+st klaire] and found 666: this was good fun. But my spiritual tutelary,
+when he found that he could not make a beast of me, except by changing
+[Hebrew: A] into [Hebrew: T], solemnly referred the difficulty to the
+Almighty: this was poor earnest. {230}
+
+I am glad I did not notice, in time to insert it in the _Athenaeum_, a very
+remarkable paradoxer brought forward by Mr. Thom, his friend Mr.
+Wapshare[373]: it is a little too strong for the general public. In the
+_Athenaeum_ they would have seen and read it: but this book will be avoided
+by the weaker brethren. It is as follows:
+
+"God, the Elohim, was six days in creating all things, and having made MAN
+he entered into his rest. He is no more seen as a Creator, as Elohim, but
+as Jehovah, the _Lord_ of the Sabbath, and the Spirit of life in MAN, which
+Spirit worketh _sin in the flesh_; for the Spirit of Love, in all flesh, is
+Lust, or the spirit of a beast, So Rom. vii. And which Spirit is
+_crucified_ in the flesh. He then, as Jehovah--as the power of the Law,
+_in_ and _over_ all flesh, John viii. 44--increases that which he has made
+as the Elohim, and his power shall last for 6 days, or 6 periods of time,
+computed at a millennium of years; and at the end of which six days, he who
+is the Spirit of all flesh shall manifest himself as the Holy Spirit of
+Almighty Love, and of all truth; and so shall the Church have her Sabbath
+of Rest--all contention being at an end. This is, as well as I may now
+express it, my solution of the mystery in Hebrew, and in Greek, and also in
+Latin, IHS. For he that was lifted up _is_ King of the Jews, and is the
+Lord of all Life, working in us, both to will and to do; as is manifest in
+the Jews--they slaying him that his blood might be _good_ for the healing
+of the nations, of all people and tongues. As the Father of all _natural_
+flesh, he is the Spirit of Lust, as in all _beasts_; as the Father, or King
+of the Jews, he is the Devil, as he himself witnesseth in John viii.,
+already referred to. As lifted up, he is transformed into the Spirit of
+Love, a light to the Gentiles, and the glory of his people Israel.... For
+there is but ONE God, ONE Lord, ONE Spirit, ONE body, etc. and he who was
+Satan, the Spirit of life in that body, is, in {231} Christ crucified, seen
+in the Spirit that is in all, and through all and over all, God blessed for
+ever."
+
+All this seems well meant, and Mr. Thom prints it as convinced of its
+piety, and "pronounces no opinion." Mystics of all sorts! see what you may
+come to, or what may come to you! I have inserted the above for your good.
+
+There is nothing in this world so steady as some of the paradoxers. They
+are like the spiders who go on spinning after they have web enough to catch
+all the flies in the neighborhood, if the flies would but come. They are
+like the wild bees who go on making honey which they never can eat, proving
+_sic vos non vobis_ to be a physical necessity of their own contriving. But
+nobody robs their hives: no, unlike the bees, they go about offering their
+ware to any who will take it as a gift. I had just written the last
+sentence (Oct. 30, 1866, 8.45 A.M.) when in comes the second note received
+this morning from Dr. Thorn: at 1.30 P.M. came in a third. These arise out
+of the above account of the Rev. D. Thom, published Oct. 27: three notes
+had arrived before.
+
+For curiosity I give one day's allowance, supposing these to be all: more
+may arrive before night.
+
+29th Oct. 1866.
+
+"Dear Sir,--
+
+In re [swastika].[374]
+
+"So that 'Zaphnath Paaneah' may be after all the revealer of the 'Northern
+Tau' [Greek: Phaneroo]--To make manifest, shew, or explain; and this may
+satisfy the House of Joseph in Amos 5^c. While Belteshazzar = 666 may be
+also satisfactory to the House of David, and so we may have Zech. 10^c.
+6^v. in operation when Ezekiel 37^c. 16^v. has been realised;--but there,
+what is the use of writing, it is all Coptic {232} to a man who has not
+[swastika], The Thau of the North, the double Vahu [Hebrew: W\qamats\W].
+Look at Jeremiah 3^c. 8^v. and then to Psalm 83 for 'hidden ones' [Hebrew:
+TS\sheva\PW\dagesh\N\segol\Y Y\sheva\HW\qamats\H]--The Zephoni Jehovah, and
+say whether they have any connection with the Zephon _Thau_. The Hammer of
+Thor of Jeremiah 23^c. 29^v. as I gave you in No. 3 of my present edition.
+
+Yours truly
+
+LE CHEVALIER AU CIN."
+
+_By Greek Power._
+
+  C =  20
+  H =   8
+  E =   5
+  V =   6
+  A =   1
+  L =  30
+  I =  10
+  E =   5
+  R = 100
+
+  A =   1
+  U = 400
+
+  C =  20
+  I =  10
+  N =  50
+     ----
+      666
+
+There will be thousands of Morgans who will be among the wise and prudent
+of Hosea 14^c. 9^v. when the Seventh Angel sounds, let me number _that One_
+by Greek, Rev. 17^c. 1^v: {233}
+
+    S = 200
+    E  =   5
+  x V  =   6
+    E  =   5
+    N  =  50
+    T  = 300
+    H  =   8
+
+    A =   1
+    N  =  50
+  x G  =   6
+    E  =   5
+    L  =  30
+       ----
+        666
+
+    V and G = 12 ought to be equal to one Gammadion or ^3[swastika]3 x 4 =
+    12, what say you?
+
+London, October 29, 1866.
+
+"Dear Sir,--
+
+In re [swastika] versus [maltese cross].
+
+However pretentious the X or [maltese cross] may be, and it is peculiarly
+so just now in this land; after all it is only made of two Roman V's--and
+so is only = [ one inverted](10)--and therefore is not the perfect number
+12 of Revel^n, but is the mark of the goddess _Decima_!
+
+Yours truly
+
+WM. THORN."
+
+Had the _one_ who sent forth a pastoral (Romish) the other day, remained
+amongst the faithful expectants, see how he would have numbered, whereas he
+sold himself for the privilege of signing
+
+[maltese cross] HENRY E. MANNING.[375]
+
+{234}
+
+_By English Key._
+
+  H =   8
+  E =   5
+  N =  40
+  R =  80
+  Y = 140
+
+  E =   5
+  D =   4
+  W = 120
+  A =   1
+  R =  80
+  D =   4
+
+  M =  30
+  A =   1
+  N =  40
+  N =  40
+  I =   9
+  N =  40
+  G =   7
+  [swastika] = 12
+      ----
+       666
+
+    Can you now understand the difference between [swastika] and [maltese
+    cross] or X? Look to my challenge.
+
+Cutting from newspaper:--
+
+ITALY.
+
+Rome (_via_ Marseilles), October
+
+Mr. Gladstone has paid a visit to the Pope.
+
+_By Greek Power._
+
+  G =   6
+  L =  30
+  A =   1
+  D =   4
+  S = 200
+  T = 300
+  O =  70
+  N =  50
+  E =   5
+     ----
+      666
+
+And what then [swastika]?
+
+{235}
+
+In other letters _John Stuart Mill_ is 666 if the _a_ be left out;
+_Chasuble_ is perfect. _John Brighte_[376] is a _fait accompli_; and I am
+asked whether intellect can account for the final e. Very easily: this
+Beast is not the M. P., but another person who spells his name differently.
+But if John Sturt Mill and John Brighte choose so to write themselves, they
+may.
+
+A curious collection; a mystical phantasmagoria! There are those who will
+try to find meaning: there are those who will try to find purpose.
+
+ "And some they said--What are you at?
+  And some--What are you arter?"
+
+My account of Mr. Thom and his 666 appeared on October 27: and on the 29th
+I received from the editor a copy of Mr. Thom's sermons published in 1863
+(he died Feb. 27, 1862) with best wishes for my health and happiness. The
+editor does not name himself in the book; but he signed his name in my
+copy: and may my circumference never be more than 3-1/8 of my diameter if
+the signature, name and writing both, were not that of my [circle square]
+ing friend Mr. James Smith! And so I have come in contact with him on 666
+as well as on [pi]! I should have nothing left to live for, had I not
+happened to hear that he has a perpetual motion on hand. I returned thanks
+and kind regards: and Miss Miggs's words--"Here's forgivenesses of
+injuries! here's amicablenesses!"--rang in my ears. But I was made slightly
+uncomfortable: how could the war go on after this armistice? Could I ever
+make it understood that the truce only extended to the double Vahu and
+things thereunto relating? It was once held by seafaring men that there was
+no peace with Spaniards beyond the line: I was determined that there must
+be no concord with J. S. inside the circle; that this must be a special
+exception, like Father Huddleston {236} and old Grouse in the gun-room. I
+was not long in anxiety; twenty-four hours after the book of sermons there
+came a copy of the threatened exposure--_The British Association in
+Jeopardy, and Professor De Morgan in the Pillory without hope of escape_.
+By James Smith, Esq. London and Liverpool, 8vo., 1866 (pp. 94). This
+exposure consists of reprints from the _Athenaeum_ and _Correspondent_: of
+things new there is but one. In a short preface Mr. J. S. particularly
+recommends to "_read to the end_." At the end is an appendix of two pages,
+in type as large as the work; a very prominent peroration. It is an article
+from the _Athenaeum_, left out of its place. In the last sentence Mr. J.
+Smith, who had asked whether his character as an honest Geometer and
+Mathematician was not at stake, is warned against the _fallacia plurium
+interrogationum_.[377] He is told that there is not a more honest
+what's-his-name in the world: but that as to the counter which he calls his
+character as a mathematician, he is assured that it has been staked years
+ago, and lost. And thus truth has the last word. There is no occasion to
+say much about reprints. One of them is a letter [that given above] of
+August 25, 1865, written by Mr. J. S. to the _Correspondent_. It is one of
+his quadratures; and the joke is that I am made to be the writer: it
+appears as what Mr. J. S. hopes I shall have the sense to write in the
+_Athenaeum_ and forestall him. When I saw myself thus quoted--yes! quoted!
+double commas, first person--I felt as I suppose did Wm. Wilberforce[378]
+when he set eyes on the affectionate benediction of the potato which
+waggish comrades had imposed on a raw Irish reporter as part of his speech.
+I felt as Martin[379] of {237} Galway--kind friend of the poor dumb
+creatures!--when he was told that the newspapers had put him in Italics. "I
+appeal to you, Mr. Speaker! I appeal to the House! Did I speak in Italics?
+Do I ever speak in Italics?" I appeal to editor and readers, whether I ever
+squared the circle until a week or two ago, when I gave my charitable mode
+of reconciling the discrepant cyclometers.
+
+The absurdity of the imitation of symbolic reasoning is so lusciously rich,
+that I shall insert it when I make up my final book. Somebody mastered
+Spanish merely to read Don Quixote: it would be worth while to learn a
+little algebra merely to enjoy this a b-istical attack on the windmills.
+The principle is, Prove something in as roundabout a way as possible,
+mention the circle once or twice irrelevantly in the course of your proof,
+and then make an act of Q. E. D. in words at length. The following is
+hardly caricature:--
+
+To prove that 2 and 2 make 5. Let a = 2, b = 5: let c = 658, the number of
+the House: let d = 666, the number of the Beast. Then of necessity d = a +
+b + c + 1; so that 1 is a harmonious and logical quantification of the
+number of which we are to take care. Now, b, the middle of our digital
+system, is, by mathematical and geometrical combination, a mean between 5 +
+1 and 2 + 2. Let 1 be removed to be taken care of, a thing no real
+mathematician can refuse without serious injury to his mathematical and
+geometrical reputation. It follows of necessity that 2 + 2 = 5, _quod erat
+demonstrumhorrendum_. If Simpkin & Marshall have not, after my notice, to
+account for a gross of copies more than would have gone off without me, the
+world is not worthy of its James Smith!
+
+The only fault of the above is, that there is more {238} connection than in
+the process of Faber Cyclometricus: so much, in fact, that the blunders are
+visible. The utter irrelevance of premises to conclusion cannot be
+exhibited with the requisite obscurity by any one who is able to follow
+reasoning: it is high art displayed in a certain toning down of the _aegri
+somnia_, which brings them to a certain look of reproach to reasoning which
+I can only burlesque. Mr. J. S. produces something which resembles argument
+much as a chimpanzee in dolor, because balked of his dinner, resembles a
+thinking man at his studies. My humble attempt at imitation of him is more
+like a monkey hanging by his tail from a tree and trying to crack a
+cocoa-nut by his chatter.
+
+I could forgive Mr. J. S. anything, properly headed. I would allow him to
+prove--_for himself_--that the Quadrature of the Circle is the child of a
+private marriage between the Bull Unigenitus and the Pragmatic Sanction,
+claiming tithe of onions for repeal of the Mortmain Act, before the Bishops
+in Committee under the kitchen table: his mode of imitating reason would do
+this with ease. But when he puts his imitation into my mouth, to make me
+what _he_ calls a "real mathematician," my soul rises in epigram against
+him. I say with the doll's dressmaker--such a job makes me feel like a
+puppet's tailor myself--"He ought to have a little pepper? just a few
+grains? I think the young man's tricks and manners make a claim upon his
+friends for a little pepper?" De Faure[380] and Joseph Scaliger[381] come
+into my head: my reader may look back for them.
+
+ "Three circlesquarers to the manner born,
+  Switzerland, France, and England did adorn,
+  De Faure in equations did surpass,
+  Joseph at contradictions was an ass.
+  Groaned Folly, I'm used up! What shall I do
+  To make James Smith? Grinned Momus, _Join the two_!"
+
+{239}
+
+As to my _locus poenitentiae_,[382] the reader who is fit to enjoy the
+letter I have already alluded to will see that I have a soft and easy
+position; that the thing is really a _pillowry_; and that I am, like
+Perrette's pot of milk,
+
+ "Bien pose sur un coussinet."[383]
+
+Joanna Southcott[384] never had a follower who believed in her with more
+humble piety than Mr. James Smith believes in himself. After all that has
+happened to him, he asks me with high confidence to "favor the writer with
+a proof" that I still continue of opinion that "the best of the argument is
+in my jokes, and the best of the joke is in his arguments." I will not so
+favor him. At the very outset I told him in plain English that he has the
+whiphand of all the reasoners in the world, and in plain French that _il a
+perdu le droit d'etre frappe de l'evidence_[385]; I might have said
+_pendu_.[386] To which I now add, in plain Latin, _Sapienti pauca, indocto
+nihil_.[387] The law of Chancery says that he who will have equity must do
+equity: the law of reasoning says that he who will have proof must see
+proof.
+
+The introduction of things quite irrelevant, by way of reproach, is an
+argument in universal request: and it often happens that the argument so
+produced really tells against the producer. So common is it that we forget
+how boyish it is; but we are strikingly reminded when it actually comes
+from a boy. In a certain police court, certain small boys were arraigned
+for conspiring to hoot an obnoxious individual on his way from one of their
+school exhibitions. This proceeding was necessary, because there seemed to
+be a permanent conspiracy to annoy the gentleman; and the {240} masters did
+not feel able to interfere in what took place outside the school. So the
+boys were arraigned; and their friends, as silly in their way as
+themselves, allowed one of them to make the defence, instead of employing
+counsel; and did not even give them any useful hints. The defence was as
+follows; and any one who does not see how richly it sets off the defences
+of bigger boys in bigger matters has much to learn. The innocent conviction
+that there was answer in the latter part is delightful. Of course fine and
+recognizance followed.
+
+A---- said the boys had received great provocation from B----. He was
+constantly threatening them with a horsewhip which he carried in his hand
+[the boy did not say what had passed to induce him to take such a weapon],
+and he had repeatedly insulted the master, which the boys could not stand.
+B---- had in his own drawing-room told him (A----) that he had drawn his
+sword against the master and thrown away the scabbard. B---- knew well that
+if he came to the college he would catch it, and then he went off through a
+side door--which was no sign of pluck; and then he brought Mrs. B---- with
+him, thinking that her presence would protect him.
+
+My readers may expect a word on Mr. Thom's sermons, after my account of his
+queer doings about 666. He is evidently an honest and devout man, much
+wanting in discrimination. He has a sermon about private _judgment_, in
+which he halts between the logical and legal meanings of the word. He
+loathes those who apply their private judgment to the word of God: here he
+means those who decide what it _ought to be_. He seems in other places
+aware that the theological phrase means taking right to determine what it
+_is_. He uses his own private judgment very freely, and is strong in the
+conclusion that others ought not to use theirs except as he tells them how;
+he leaves all the rest of mankind free to think with him. In this he is not
+original: his fame must rest on his senary tripod. {241}
+
+
+
+JAMES SMITH ONCE MORE.
+
+Mr. James Smith's procedures are not caricature of reasoning; they are
+caricature of blundering. The old way of proving that 2 = 1 is solemn
+earnest compared with his demonstrations. As follows:[388]
+
+  Let x = 1
+  Then x^2 = x
+  And x^2 - 1 = x - 1
+  Divide both sides by x - 1; then x + 1 = 1; but x = 1, whence 2 = 1.
+
+When a man is regularly snubbed, bullied, blown up, walked into, and put
+down, there is usually some reaction in his favor, a kind of deostracism,
+which cannot bear to hear him always called the blunderer. I hope it will
+be so in this case. There is nothing I more desire than to see _sects_ of
+paradoxers. There are fully five thousand adults in England who ought to be
+the followers of some one false quadrature. And I have most hope of 3-1/8,
+because I think Mr. James Smith better fitted to be the leader of an
+organized infatuation than any one I know of. He wants no pity, and will
+get none. He has energy, means, good humor, strong conviction, character,
+and popularity in his own circle. And, most indispensable point of all, he
+sticks at nothing;
+
+ "In coelum jusseris, ibit."[389]
+
+When my instructor found I did not print an acceptance of what I have
+quoted, he addressed me as follows (_Corr._, Sept 23):--
+
+"In this life, however, we must do our duty, and, when {242} necessary, use
+the rod, not in a spirit of revenge, but for the benefit of the culprit and
+the good of society. Now, Sir, the opportunity has been thrown in your way
+of slipping out of the pillory without risk of serious injury; but, like an
+obstinate urchin, you have chosen to quarrel with your opportunity and
+remain there, and thus you compel me to deal with you as schoolmasters used
+to do with stupid boys in bygone days--that is to say, you force me to the
+use of the critic's rod, compel me to put you where little Jack Horner sat,
+and, as a warning to other naughty boys, to ornament you with a dunce's
+cap. The task I set you was a very simple one, as I shall make manifest at
+the proper time."
+
+In one or more places, as well as this, Mr. Smith shows that he does not
+know the legend of little Jack Horner, whom he imagines to be put in the
+corner as a bad boy. This is curious; for there had been many allusions to
+the story in the journal he was writing in, and the Christmas pie had
+become altered into the Seaforth [pi].
+
+Mr. Smith is satisfied at last that--what between argument and punishment
+he has convinced me. He says (_Corr._, Jan. 27, 1866): "I tell him without
+hesitation that he knows the true ratio of diameter to circumference as
+well as I do, and if he be wise he will admit it." I should hope I do, and
+better; but there is no occasion to admit what everybody knows.
+
+I have often wished that we could have a slight glimpse of the reception
+which was given to some of the old cyclometers: but we have nothing, except
+the grave disapprobation of historians. I am resolved to give the New
+Zealander a chance of knowing a little more than this about one of them at
+least; and, by the fortunate entrance into life of the _Correspondent_, I
+am able to do it. I omit sober mathematical answers, of which there were
+several. The following letter is grave earnest:
+
+"Sir,--I have watched Mr. James Smith's writings on this subject from the
+first, and I did hope that, as the more {243} he departs from truth the
+more easy it must be to refute him, [this by no means always true] some of
+your correspondents would by this time have done so. I own that I am unable
+to detect the fallacy of his argument; and I am quite certain that '[Pi]'
+is wrong, in No. 23, where he declares that Mr. Smith is 'ignorant of the
+very elements of mathematical truth.' I have observed an immense amount of
+geometrical reasoning on his part, and I cannot see that it is either fair
+or honest to deny this, which may be regarded as the 'elements' of
+mathematical truth. Would it not be better for '[Pi]' to answer Mr. Smith,
+to refute his arguments, to point out their fallacies, and to save learners
+from error, than to plunge into gross insult and unmanly abuse? Would it
+not be well, also, that Professor De Morgan should favour us with a little
+reasoning?
+
+"I have hitherto seen no attempt to overthrow Mr. Smith's arguments; I
+trust that this will not continue, since the subject is one of immense
+importance to science in general, especially to nautical science, and all
+that thereto belongs.
+
+Yours, etc.,
+
+A CAPTAIN, R.N."
+
+On looking at this homoeopathic treatment of the 3-1/8
+quadrature--remember, homoeopathic, _similia similibus_,[390] not
+infinitesimal--and at the imputation thrown upon it, I asked myself, what
+_is_ vulgarity? No two agree, except in this, that every one sees vulgarity
+in what is directed against himself. Mark the world, and see if anything be
+so common as the description of the other side's remarks as "vulgar attempt
+at wit." "I suppose you think that very witty:" the answer is "No my
+friend! your remark shows that you feel it as wit, so that the purpose is
+answered; I keep my razor for something else than cutting blocks;" I am
+inclined to think that "out of place" is a necessary attribute of true
+vulgarity. And further, it is to be noticed that nothing is {244}
+unproducible--_salvo pudore_[391]--which has classical authority, modern or
+ancient, in its favor. "He is a vulgar fellow; I asked him what he was
+upon, and what do you think he answered, My legs!"--"Well, and has he not
+justification? what do you find in Terence? _Quid agitur? Statur._"[392] I
+do not even blench from my principle where I find that it brings what is
+called "taking a sight" within permissible forms of expression: Rabelais
+not only establishes its antiquity, but makes it English. Our old
+translation[393] has it thus (book 2. ch. 19):
+
+"Then made the Englishman this sign. His left hand, all open, he lifted up
+into the air, then instantly shut into his fist the four fingers thereof;
+and his thumb extended at length he placed upon the tip of his nose.
+Presently after he lifted up his right hand all open and abased and bent it
+downwards, putting the thumb thereof in the very place where the little
+finger of the left hand did close in the fist, and the four right hand
+fingers he softly moved in the air. Then contrarily he did with the right
+hand what he had done with the left, and with the left what he had done
+with the right."
+
+An impressive sight! The making of a fist of the left hand is a great
+addition of power, and should be followed in modern practice. The gentle
+sullation of the front fingers, with the clenched fist behind them, says as
+plainly as possible, Put _suaviter in modo_ in the van, but don't forget to
+have _fortiter in re_[394] in the rear.
+
+{245}
+
+My Budget was announced (March 23, 1867) for completion on the 30th. Mr.
+James Smith wrote five letters, one before the completion, four after it;
+the five contained 68 pages of quarto letter paper. Mr. J. S. had picked up
+a clerical correspondent, with whom he was in the heat of battle.
+
+"_March 27._--Dear Sir. Very truly yours. Duty; for my own sake; just time
+left to retrieve my errors; sends copy of letter to clergyman; new proof
+never before thought of; merest tyro would laugh if I were to stifle it,
+whether by rhodomontade or silent contempt; keep your temper. I shall be
+convinced; and if world be right in supposing me incapable of a foul act, I
+shall proclaim glorious discovery in the _Athenaeum_.
+
+"_April 15._--Sir,... My dear Sir, Your sincere tutelary. Copy of another
+letter to clergyman; discovery tested by logarithms; reasons such as none
+but a knave or a sinner can resist. Let me advise you to take counsel
+before it is too late! Keep your temper. Let not your _pride_ get the
+better of your discretion! Screw up your courage, my good friend, and
+_resolve_ to show the world that you are an _honest_ man....
+
+"_April 20._--Sir ... Your very sincere and favorite tutelary. I have long
+played the _cur_, snapping and snarling...; suddenly lost my power, and
+became _half-starved_ dog without _spirit_ to bark; try if air cannot
+restore me; calls himself the _thistle_ in allusion to my other tutelary,
+the _thorn_; Would I prefer his next work to be, 'A whip for the
+Mathematical Cur, Prof. De M.' In some previous letter which I have
+mislaid, he told me his next would be 'a muzzle for the Mathematical Bull
+dog, Prof. De M.'
+
+"_April 23._--Sir. Very sincerely yours. More letters to clergyman; you may
+as well knock your head against a stone wall to improve your intellect as
+attempt to controvert my proofs. [I thought so too; and tried neither].
+{246}
+
+"_May 6._--My dear Sir. Very sincerely yours. All to myself, and nothing to
+note.
+
+"_July 2._--No more in this interval. All that precedes is a desperate
+attempt to induce me to continue my descriptions: notoriety at any price."
+
+I dare say the matter is finished: the record of so marked an instance of
+self-delusion will be useful.
+
+I append to the foregoing a letter from Dr. Whewell[395] to Mr. James
+Smith. The Master of Trinity was conspicuous as a rough customer, an
+intellectual bully, an overbearing disputant: the character was as well
+established as that of Sam Johnson. But there was a marked difference. It
+was said of Johnson that if his pistol missed fire, he would knock you down
+with the butt end of it: but Whewell, in like case, always acknowledged the
+miss, and loaded again or not, as the case might be. He reminded me of
+Dennis Brulgruddery, who says to Dan, Pacify me with a good reason, and
+you'll find me a dutiful master. I knew him from the time when he was my
+teacher at Cambridge, more than forty years. As a teacher, he was anything
+but dictatorial, and he was perfectly accessible to proposal of objections.
+He came in contact with me in his slashing way twice in our after joint
+lives, and on both occasions he acknowledged himself overcome, by that
+change of manner, and apologetic mode of continuance, which I had seen him
+employ towards others under like circumstances.
+
+I had expressed my wish to have a _thermometer of probability_, with
+impossibility at one end, as 2 and 2 make 5, and necessity at the other, as
+2 and 2 make 4, and a graduated rise of examples between them. Down came a
+blow: "What! put necessary and contingent propositions together! It's
+absurd!" I pointed out that the two kinds of necessity are but such
+extremes of probability as 0 and [infinity] are of number, and illustrated
+by an urn with 1 white and _n_ black {247} balls, _n_ increasing without
+limit. It was frankly seen, and the point yielded; a large company was
+present.
+
+Again, in a large party, after dinner, and politics being the subject, I
+was proceeding, in discussion with Mr. Whewell, with "I think"...--"Ugh!
+_you_ think!" was the answer. I repeated my phrase, and gave as a reason
+the words which Lord Grey[396] had used in the House of Lords the night
+before (the celebrated advice to the Bishops to set their houses in order).
+He had not heard of this, and his manner changed in an instant: he was the
+rational discutient all the rest of the evening, having previously been
+nothing but a disputant with all the distinctions strongly marked.
+
+I have said that Whewell was gentle with his pupils; it was the same with
+all who wanted teaching: it was only on an armed enemy that he drew his
+weapon. The letter which he wrote to Mr. J. Smith is an instance: and as it
+applies with perfect fidelity to the efforts of unreasoning above
+described, I give it here. Mr. James Smith is skilfully exposed, and felt
+it; as is proved by "putting the writer in the stocks."
+
+"The Lodge, Cambridge, September 14th, 1862.
+
+"Sir,--I have received your explanation of your proposition that the
+circumference of the circle is to its diameter as 25 to 8. I am afraid I
+shall disappoint you by saying that I see no force in your proof: and I
+should hope that you will see that there is no force in it if you consider
+this: In the whole course of the proof, though the word cycle occurs, there
+is no property of the circle employed. You may do this: you may put the
+word _hexagon_ or _dodecagon_, or any other word describing a polygon in
+the place of _Circle_ in your proof, and the proof would be just as good as
+before. Does not this satisfy you that you cannot have proved a property of
+that special figure--a circle? {248}
+
+"Or you may do this: calculate the side of a polygon of 24 sides inscribed
+in a circle. I think you are a Mathematician enough to do this. You will
+find that if the radius of the circle be one, the side of this polygon is
+.264 etc. Now, the arc which this side subtends is according to your
+proposition 3.125/12 = .2604, and therefore the chord is greater than its
+arc, which you will allow is impossible.
+
+"I shall be glad if these arguments satisfy you, and
+
+"I am, Sir, your obedient Servant,
+
+"W. WHEWELL."
+
+
+
+AN M.P.'S ARITHMETIC.
+
+In the debate of May, 1866, on Electoral Qualifications, a question arose
+about arithmetical capability. Mr. Gladstone asked how many members of the
+House could divide 1330l. 7s. 6d. by 2l. 13s. 8d. Six hundred and
+fifty-eight, answered one member; the thing cannot be done, answered
+another. There is an old paradox to which this relates: it arises out of
+the ignorance of the distinction between abstract and concrete arithmetic.
+_Magnitude_ may be divided by _magnitude_; and the answer is number: how
+often does 12d. contain 4d.; answer three times. _Magnitude_ may be divided
+by _number_, and the answer is _magnitude_: 12d. is divided in four equal
+parts, what is each part? Answer three _pence_. The honorable objector,
+whose name I suppress, trusting that he has mended his ways, gave the
+following utterance:
+
+"With regard to the division sum, it was quite possible to divide by a sum,
+but not by money. How could any one divide money by 2l. 16s. 8d.?
+(Laughter.) The question might be asked, 'How many times 2s. will go into
+1l.?' but that was not dividing by money; it was simply dividing 20 by 2.
+He might be asked, 'How many times will 6s. 8d. go into a pound?' but it
+was only required to divide 240 by 80. If the right hon. gentleman were to
+ask the hon. {249} member for Brighton (Professor Fawcett),[397] or any
+other authority, he would receive the same answer--viz., that it was
+possible to divide by a sum, but not by money. (Hear.)"
+
+I shall leave all comment for the second edition, if I publish one.[398] I
+shall be sure to have something to laugh at. Anything said from a
+respectable quarter, or supposed to be said, is sure to find defenders. Sam
+Johnson, a sound arithmetician, comparing himself, and what he alone had
+done in three years, with forty French Academicians and their forty years,
+said it proved that an Englishman is to a Frenchman as 40 x 40 to 3, or as
+1600 to 3. Boswell, who was no great hand at arithmetic, made him say that
+an Englishman is to a Frenchman as 3 to 1600. When I pointed this out, the
+supposed Johnson was defended through thick and thin in _Notes and
+Queries_.
+
+I am now curious to see whether the following will find a palliator. It is
+from "Tristram Shandy," book V. chapter 3. There are two curious idioms,
+"for for" and "half in half"; but these have nothing to do with my point:
+
+"A blessing which tied up my father's tongue, and a misfortune which set it
+loose with a good grace, were pretty equal: sometimes, indeed, the
+misfortune was the better of the two; for, for instance, where the pleasure
+of harangue was as _ten_, and the pain of the misfortune but as _five_, my
+father gained half in half; and consequently was as well again off as if it
+had never befallen him."
+
+This is a jolly confusion of ideas; and wants nothing but a defender to
+make it perfect. A person who invests five {250} with a return of ten, and
+one who loses five with one hand and gains ten with the other, both leave
+off five richer than they began, no doubt. The first gains "half in half,"
+more properly "half _on_ half," that is, of the return, 10, the second 5 is
+gain upon the first 5 invested. "Half _in_ half" is a queer way of saying
+cent. per cent. If the 5l. invested be all the man had in the world, he
+comes out, after the gain, twice as well off as he began, with reference to
+his whole fortune. But it is very odd to say that balance of 5l. gain is
+_twice_ as good as if nothing had befallen, either loss or gain. A
+mathematician thinks 5 an infinite number of times as great as 0. The whole
+confusion is not so apparent when money is in question: for money is money
+whether gained or lost. But though pleasure and pain stand to one another
+in the same algebraical relation as money gained and lost, yet there is
+more than algebra can take account of in the difference.
+
+Next, Ri. Milward[399] (Richard, no doubt, but it cannot be proved) who
+published Selden's[400] Table Talk, which he had collected while serving as
+amanuensis, makes Selden say, "A subsidy was counted the fifth part of a
+man's estate; and so fifty subsidies is five and forty times more than a
+man is worth." For _times_ read _subsidies_, which seems part of the
+confusion, and there remains the making all the subsidies equal to the
+first, though the whole of which they are to be the fifths is perpetually
+diminished.
+
+Thirdly, there is the confusion of the great misomath {251} of our own day,
+who discovered two quantities which he avers to be identically the same,
+but the greater the one the less the other. He had a truth in his mind,
+which his notions of quantity were inadequate to clothe in language. This
+erroneous phraseology has not found a defender; and I am almost inclined to
+say, with Falstaff, The poor abuses of the time want countenance.
+
+
+
+ERRONEOUS ARITHMETICAL NOTIONS.
+
+"Shallow numerists," as Cocker[401] is made to call them, have long been at
+work upon the question how to _multiply_ money by money. It is, I have
+observed, a very common way of amusing the tedium of a sea voyage: I have
+had more than one bet referred to me. Because an oblong of five inches by
+four inches contains 5 x 4 or 20 _square_ inches, people say that five
+inches multiplied by four inches _is_ twenty _square_ inches: and, thinking
+that they have multiplied length by length, they stare when they are told
+that money cannot be multiplied by money. One of my betters made it an
+argument for the thing being impossible, that there is no _square money_:
+what could I do but suggest that postage-stamps should be made legal
+tender. Multiplication must be _repetition_: the repeating process must be
+indicated by _number_ of times. I once had difficulty in persuading another
+of my betters that if you repeat five shillings as often as there are hairs
+in a horse's tail, you do not _multiply five shillings by a
+horsetail_.[402]
+
+I am very sorry to say that these wrong notions have found support--I think
+they do so no longer--in the University of Cambridge. In 1856 or 1857, an
+examiner was displaced by a vote of the Senate. The pretext was that he was
+too severe an examiner: but it was well known that {252} great
+dissatisfaction had been expressed, far and wide through the Colleges, at
+an absurd question which he had given. He actually proposed such a fraction
+as
+
+   6s. 3d.
+  --------.
+  17s. 4d.
+
+As common sense gained a hearing very soon, there is no occasion to say
+more. In 1858, it was proposed at a college examination, to divide 22557
+days, 20 hours, 20 minutes, 48 seconds, by 57 minutes, 12 seconds, and also
+to explain the fraction
+
+  32l. 18s. 8d.
+  -------------.
+  62l. 12s. 9d.
+
+All paradoxy, in matters of demonstration, arises out of muddle about first
+principles. Who can say how much of it is to be laid at the door of the
+University of Cambridge, for not taking care of the elements of
+arithmetical thought?
+
+
+
+ON LITERARY BARGAINS.
+
+The phenomena of the two ends of society, when brought together, give
+interesting comparisons: I mean the early beginnings of thought and
+literature, and our own high and finished state, as we think it. There is
+one very remarkable point. In the early day, the letter was matter of the
+closest adherence, and implied meanings were not admitted.
+
+The blessing of Isaac meant for Esau, went to false Jacob, in spite of the
+imposition; and the writer of Genesis seems to intend to give the notion
+that Isaac had no power to pronounce it null and void. And "Jacob's policy,
+whereby he became rich"--as the chapter-heading puts it--in speckled and
+spotted stock, is not considered as a violation of the agreement, which
+contemplated natural proportions. In {253} the story of Lycurgus the
+lawgiver is held to have behaved fairly when he bound the Spartans to obey
+his laws until he returned--intimating a short absence--he intending never
+to return. And Vishnoo, when he asked the usurper for three steps of
+territory as a dwarf, and then enlarged himself until he could bring heaven
+and earth under the bargain, was thought clever, certainly, but quite fair.
+
+There is nothing of this kind recognized in our day: so far good. But there
+is a bad contrary: the age is apt, in interpretation, to upset the letter
+in favor of the view--very often the after thought--of one side only. The
+case of John Palmer,[403] the improver of the mail coach system, is
+smothered. He was to have an office and a salary, and 2-1/2 per cent for
+life on the increased _revenue_ of the Post-Office. His rights turned out
+so large, that Government would not pay them. For misconduct, real or
+pretended, they turned him out of his _office_: but his bargain as to the
+percentage had nothing to do with his future conduct; it was payment for
+his _plan_. I know nothing, except from the debates of 1808 in the two
+Houses: if any one can redeem the credit of the nation, the field is open.
+When I was young, the old stagers spoke of this transaction sparingly, and
+dismissed it speedily.
+
+The government did not choose to remember what private persons must
+remember, and are made to remember, if needful. When Dr. Lardner[404] made
+his bargain with the {254} publishers for the _Cabinet Cyclopaedia_ he
+proposed that he, as editor, should have a certain sum for every hundred
+sold above a certain number: the publishers, who did not think there was
+any chance of reaching the turning sale of this stipulation, readily
+consented. But it turned out that Dr. Lardner saw further than they: the
+returns under this stipulation gave him a very handsome addition to his
+other receipts. The publishers stared; but they paid. They had no idea of
+standing out that the amount was too much for an editor; they knew that,
+though the editor had a percentage, they had all the rest; and they would
+not have felt aggrieved if he had received ten times as much. But
+governments, which cannot be brought to book before a sworn jury, are ruled
+only by public opinion. John Palmer's day was also the day of Thomas Fyshe
+Palmer,[405] and the governments, in their prosecutions for sedition, knew
+that these would have a reflex action upon the minds of all who wrote about
+public affairs.
+
+
+
+DECLARATION OF BELIEF
+
+1864-65.--It often happens that persons combine to maintain and enforce an
+opinion; but it is, in our state of society, a paradox to unite for the
+sole purpose of blaming the opposite side. To invite educated men to do
+this, and above all, men of learning or science, is the next paradoxical
+thing of all. But this was done by a small combination in 1864. They got
+together and drew up a _declaration_, to be signed by "students of the
+natural sciences," who were to express their "sincere regret that
+researches into {255} scientific truth are perverted by some in our own
+times into occasion for casting doubt upon the truth and authenticity of
+the Holy Scriptures." In words of ambiguous sophistry, they proceeded to
+request, in effect, that people would be pleased to adopt the views of
+churches as to the _complete_ inspiration of all the canonical books. The
+great question whether the Word of God is _in_ the Bible, or whether the
+Word of God is _all_ the Bible, was quietly taken for granted in favor of
+the second view; to the end that men of science might be induced to blame
+those who took the first view. The first public attention was drawn to the
+subject by Sir John Herschel,[406] who in refusing to sign the writ sent to
+him, administered a rebuke in the _Athenaeum_, which would have opened most
+eyes to see that the case was hopeless. The words of a man whose _suaviter
+in modo_ makes his _fortiter in re_[407] cut blocks with a razor are worth
+preserving:
+
+"I consider the act of calling upon me publicly to avow or disavow, to
+approve or disapprove, in writing, any religious doctrine or statement,
+however carefully or cautiously drawn up (in other words, to append my name
+to a religious manifesto) to be an infringement of that social forbearance
+which guards the freedom of religious opinion in this country with especial
+sanctity.... I consider this movement simply mischievous, having a direct
+tendency (by putting forward a new Shibboleth, a new verbal test of
+religious partisanship) to add a fresh element of discord to the already
+too discordant relations of the Christian world.... But no nicety of
+wording, no artifice of human language, will suffice to discriminate the
+hundredth part of the shades of meaning in which the most world-wide
+differences of thought on such subjects may be involved; or prevent the
+most gentle worded and apparently justifiable expression of regret, so
+embodied, from grating on the {256} feelings of thousands of estimable and
+well-intentioned men with all the harshness of controversial hostility."
+
+Other doses were administered by Sir J. Bowring,[408] Sir W. Rowan
+Hamilton,[409] and myself. The signed declaration was promised for
+Christmas, 1864: but nothing presentable was then ready; and it was near
+Midsummer, 1865, before it was published. Persons often incautiously put
+their names without seeing the _character_ of a document, because they
+coincide in its _opinions_. In this way, probably, fifteen respectable
+names were procured before printing; and these, when committed, were hawked
+as part of an application to "solicit the favor" of other signatures. It is
+likely enough no one of the fifteen saw that the declaration was, not
+_maintenance_ of their own opinion, but _regret_ (a civil word for _blame_)
+that others should _think differently_.
+
+When the list appeared, there were no fewer than 716 names! But analysis
+showed that this roll was not a specimen of the mature science of the
+country. The collection was very miscellaneous: 38 were designated as
+"students of the College of Chemistry," meaning young men who attended
+lectures in that college. But as all the Royal Society had been applied to,
+a test results as follows. Of Fellows of the Royal Society, 600 in number,
+62 gave their signatures; of writers in the _Philosophical Transactions_,
+166 in number, 19 gave their signatures. Roughly speaking, then, only one
+out of ten could be got to express disapprobation of the free comparison of
+the results of science with the statements of the canonical books. And I am
+satisfied that many of these thought they were signing only a declaration
+of difference of opinion, not of blame for that difference. The number of
+persons is not small who, when it comes to signing printed documents, would
+put their names to a declaration that the coffee-pot ought to be taken
+down-stairs, meaning that the teapot ought to be brought {257} up-stairs.
+And many of them would defend it. Some would say that the two things are
+not contradictory; which, with a snort or two of contempt, would be very
+effective. Others would, in the candid and quiet tone, point out that it is
+all one, because coffee is usually taken before tea, and it keeps the table
+clear to send away the coffee-pot before the teapot is brought up.
+
+The original signatures were decently interred in the Bodleian Library: and
+the advocates of scattering indefinite blame for indefinite sins of opinion
+among indefinite persons are, I understand, divided in opinion about the
+time at which the next attempt shall be made upon men of scientific
+studies: some are for the Greek Calends, and others for the Roman
+Olympiads. But, with their usual love of indefiniteness, they have
+determined that the choice shall be argued upon the basis that which comes
+first cannot be settled, and is of no consequence.
+
+I give the declaration entire, as a curiosity: and parallel with it I give
+a substitute which was proposed in the _Athenaeum_, as worthy to be signed
+both by students of theology, and by students of science, especially in
+past time. When a new attempt is made, it will be worth while to look at
+both:
+
+_Declaration._                  _Proposed Substitute._
+
+We, the undersigned Students    We, the undersigned Students
+of the Natural Sciences,        of Theology and of Nature,
+desire to express our sincere   desire to express our sincere
+regret, that researches into    regret, that common notions of
+scientific truth are perverted  religious truth are perverted
+by some in our own times into   by some in our own times into
+occasion for casting doubt      occasion for casting reproach
+upon the Truth and              upon the advocates of
+Authenticity of the Holy        demonstrated or highly
+Scriptures.                     probable scientific theories.
+
+                                {258}
+We conceive that it is          We conceive that it is
+impossible for the Word of      impossible for the Word of
+God, as written in the book of  God, as correctly read in the
+nature, and God's Word written  Book of Nature, and the Word
+in Holy Scripture, to           of God, as truly interpreted
+contradict one another,         out of the Holy Scripture, to
+however much they may appear    contradict one another,
+to differ.                      however much they may appear
+                                to differ.
+We are not forgetful that       We are not forgetful that
+Physical Science is not         neither theological
+complete, but is only in a      interpretation nor physical
+condition of progress, and      knowledge is yet complete, but
+that at present our finite      that both are in a condition
+reason enables us only to see   of progress; and that at
+as through a glass darkly,      present our finite reason
+                                enables us only to see both
+                                one and the other as through a
+                                glass darkly [the writers of
+                                the original declaration have
+                                distinctively applied to
+                                physical science the phrase by
+                                which St. Paul denotes the
+                                imperfections of theological
+                                vision, which they tacitly
+                                assume to be quite perfect],
+and we confidently believe,     and we confidently believe,
+that a time will come when the  that a time will come when the
+two records will be seen to     two records will be seen to
+agree in every particular. We   agree in every particular. We
+cannot but deplore that         cannot but deplore that
+Natural Science should be       Religion should be looked upon
+looked upon with suspicion by   with suspicion by some and
+many who do not make a study    Science by others, of the
+of it, merely on account of     students of either who do not
+the unadvised manner in which   make a study of the {259}
+some are placing it in          other, merely on account of
+opposition to Holy Writ.        the unadvised manner in which
+                                some are placing Religion in
+                                opposition to Science, and
+                                some are placing Science in
+                                opposition to Religion.
+We believe that it is the duty  We believe that it is the duty
+of every Scientific Student to  of every theological student
+investigate nature simply for   to investigate the Scripture,
+the purpose of elucidating      and of every scientific
+truth,                          student to investigate Nature,
+                                simply for the purpose of
+                                elucidating truth.
+and that if he finds that some  And if either should find that
+of his results appear to be in  some of his results appear to
+contradiction to the Written    be in contradiction, whether
+Word, or rather to his own      to Scripture or to Nature, or
+_interpretations_ of it, which  rather to his own
+may be erroneous, he should     _interpretation_ of one or the
+not presumptuously affirm that  other, which may be erroneous,
+his own conclusions must be     he should not affirm as with
+right, and the statements of    certainty that his own
+Scripture wrong;                conclusion must be right, and
+                                the other interpretation
+                                wrong:
+rather, leave the two side by   but should leave the two side
+side till it shall please God   by side for further inquiry
+to allow us to see the manner   into both, until it shall
+in which they may be            please God to allow us to
+reconciled;                     arrive at the manner in which
+                                they may be reconciled.
+and, instead of insisting upon  In the mean while, instead of
+the seeming differences         insisting, and least of all
+between Science and the         with acrimony or injurious
+Scriptures, it would be as      {260} statements about others,
+well to rest in faith upon the  upon the seeming differences
+points in which they agree.     between Science and the
+                                Scriptures, it would be a
+                                thousand times better to rest
+                                in faith as to our future
+                                state, in hope as to our
+                                coming knowledge, and in
+                                charity as to our present
+                                differences.
+
+The distinctness of the fallacies is creditable to the composers, and shows
+that scientific habits tend to clearness, even to sophistry. Nowhere does
+it so plainly stand out that the _Written Word_ means the sense in which
+the accuser takes it, while the sense of the other side is _their
+interpretation_. The infallible church on one side, arrayed against
+heretical pravity on the other, is seen in all subjects in which men
+differ. At school there were various games in which one or another
+advantage was the right of those who first called for it. In adult argument
+the same thing is often attempted: we often hear--I cried _Church_ first!
+
+I end with the answer which I myself gave to the application: its revival
+may possibly save me from a repetition of the like. If there be anything I
+hate more than another it is the proposal to place any persons, especially
+those who allow freedom to me, under any abridgment of their liberty to
+think, to infer, and to publish. If they break the law, take the law; but
+do not make the law: [Greek: agoraioi agontai enkaleitosan allelois.][410]
+I would rather be asked to take shares in an argyrosteretic company (with
+limited liability) for breaking into houses by night on fork and spoon
+errands. I should put aside this proposal with _nothing but laughter_. It
+was a joke against Sam Rogers[411] that his appearance was very like that
+of a corpse. The _John Bull_ {261} newspaper--suppose we now say Theodore
+Hook[412]--averred that when he hailed a coach one night in St. Paul's
+Churchyard, the jarvey said, "Ho! ho! my man; I'm not going to be taken in
+that way: go back to your grave!" This is the answer I shall make for the
+future to any relics of a former time who shall want to call me off the
+stand for their own purposes. What obligation have I to admit that they
+belong to our world?
+
+
+
+"SCRIPTURE AND SCIENCE.
+
+"_The Writ De Haeretico Commiserando._[413]
+
+Nov. 14, 1864.
+
+"This document was sent to me four days ago. It 'solicits the favor'--I
+thought at first it was a grocer's supplication for tea and sugar
+patronage--of my signature to expression of 'sincere regret' that some
+persons unnamed--general warrants are illegal--differ from what I am
+supposed--by persons whom it does not concern--to hold about Scripture and
+Science in their real or alleged discrepancies.
+
+"No such favor from me: for three reasons. First, I agree with Sir. J.
+Herschel that the solicitation is an intrusion to be publicly repelled.
+Secondly, I do _not_ regret that others should differ from me, think what I
+may: those others are as good as I, and as well able to think, and as much
+entitled to their conclusions. Thirdly, even if I did regret, I should be
+ashamed to put my name to bad chemistry made to do duty for good reasoning.
+The declaration is an awkward attempt to saturate sophism with truism; but
+the sophism is left largely in excess.
+
+{262}
+
+"I owe the inquisitors a grudge for taking down my conceit of myself. For
+two months I have crowed in my own mind over my friend Sir J. Herschel,
+fancying that the promoters instinctively knew better than to bring their
+fallacies before a writer on logic. Ah! my dear Sir John! thought I, if you
+had shown yourself to be well up in _Barbara Celarent_,[414] and had ever
+and anon astonished the natives with the distinction between _simpliciter_
+and _secundum quid_, no autograph-hunters would have baited a trap with
+_non sequitur_[415] to catch your signature. What can I say now? I hide my
+diminished head, diminished by the horns which I have been compelled to
+draw in.
+
+"Those who make personal solicitation for support to an opinion about
+religion are bound to know their men. The king had a right to Brother
+Neale's money, because Brother Neale offered it. Had he put his hand into
+purse after purse by way of finding out all who were of Brother Neale's
+mind, he would have been justly met by a rap on the knuckles whenever he
+missed his mark.
+
+"The kind of test before me is the utmost our time will allow of that
+inquisition into opinion which has been the curse of Christianity ever
+since the State took Providence under its protection. The writ _de haeretico
+commiserando_ is little more than the smell of the empty cask: and those
+who issue it may represent the old woman with her
+
+ "O suavis anima, quale in te dicam bonum
+  Antehac fuisse; tales cum sint reliquiae."[416]
+
+It is no excuse that the illegitimate bantling is a very little one. Its
+parents may think themselves hardly treated when they are called lineal
+successors of Tony Fire-the-faggot: {263} but, degenerate though they be,
+such is their ancestry. Let every allowance be made for them: but their
+unholy fire must be trodden out; so long as a spark is left, nothing but
+fuel is wanted to make a blaze. If this cannot be done, let the flame be
+confined to theology, though even there it burns with diminished vigor: and
+let charity, candor, sense, and ridicule, be ready to play upon it whenever
+there is any chance of its extending to literature and science.
+
+"What would be the consequence if this test-signing absurdity were to grow?
+Deep would call unto deep; counter-declaration would answer declaration,
+each stronger than the one before. The moves would go on like the dispute
+of two German students, of whom each is bound to a sharper retort on a
+graduated scale, until at last comes _dummer Junge_![417]--and then they
+must fight. There is a gentleman in the upper fifteen of the signers of the
+writ--the hawking of whose names appears to me very bad taste--whom I met
+in cordial cooperation for many a year at a scientific board. All I knew
+about his religion was that he, as a clergyman, must in some sense or other
+receive the 39 Articles:--all that he could know about mine was that I was
+some kind of heretic, or so reputed. If we had come to signing opposite
+manifestoes, turn-about, we might have found ourselves in the lowest depths
+of party discussion at our very council-table. I trust the list of
+subscribers to the declaration, when it comes to be published, will show
+that the bulk of those who have really added to our knowledge have seen the
+thing in its true light.
+
+"The promoters--I say nothing about the subscribers--of the movement will,
+I trust, not feel aggrieved at the course I have taken or the remarks I
+have made. Walter Scott says that before we judge Napoleon by the
+temptation to which he yielded, we ought to remember how much he may have
+resisted: I invite them to apply this rule to myself; they can have no idea
+of the feeling with which I {264} contemplate all attempts to repress
+freedom of inquiry, nor of the loathing with which I recoil from the
+proposal to be art and part. They have asked me to give a public opinion
+upon a certain point. It is true that they have had the kindness to tender
+both the opinion they wish me to form, and the shape in which they would
+have it appear: I will let them draw me out, but I will not let them take
+me in. If they will put an asterisk to my name, and this letter to the
+asterisk, they are welcome to my signature. As I do not expect them to
+relish this proposal, I will not solicit the favor of its adoption. But
+they have given a right to think, for they have asked me to think; to
+publish, for they have asked me to allow them to publish; to blame them,
+for they have asked me to blame their betters. Should they venture to find
+fault because my direction of disapproval, publicly given, is half a
+revolution different from theirs, they will be known as having presented a
+loaded document at the head of a traveler in the highway of discussion,
+with--Your signature or your silence!"
+
+
+
+THE FLY-LEAF PARADOX.
+
+The paradox being the proposition of something which runs counter to what
+would generally be thought likely, may present itself in many ways. There
+is a _fly-leaf paradox_, which puzzled me for many years, until I found a
+probable solution. I frequently saw, in the blank leaves of old books,
+learned books, Bibles of a time when a Bible was very costly, etc., the
+name of an owner who, by the handwriting and spelling, must have been an
+illiterate person or a child, followed by the date of the book itself.
+Accordingly, this uneducated person or young child seemed to be the first
+owner, which in many cases was not credible. Looking one day at a
+Barker's[418] Bible of 1599, I saw an {265} inscription in a child's
+writing, which certainly belonged to a much later date. It was "Martha
+Taylor, her book, giuen me by Granny Scott to keep for her sake." With this
+the usual verses, followed by 1599, the date of the book. But it so chanced
+that the blank page opposite the title, on which the above was written, was
+a verso of the last leaf of a prayer book, which had been bound before the
+Bible; and on the recto of this leaf was a colophon, with the date 1632. It
+struck me immediately that uneducated persons and children, having seen
+dates written under names, and not being quite up in chronology, did
+frequently finish off with the date of the book, which stared them in the
+face.
+
+Always write in your books. You may be a silly person--for though your
+reading my book is rather a contrary presumption, yet it is not
+conclusive--and your observations may be silly or irrelevant, but you
+cannot tell what use they may be of long after you are gone where
+Budgeteers cease from troubling.
+
+I picked up the following book, printed by J. Franklin[419] at Boston,
+during the period in which his younger brother Benjamin was his apprentice.
+And as Benjamin was apprenticed very early, and is recorded as having
+learned the mechanical art very rapidly, there is some presumption that
+part of it may be his work, though he was but thirteen at the time. As this
+set of editions of Hodder[420] (by {266} Mose[421]) is not mentioned, to my
+knowledge, I give the title in full:
+
+    "Hodder's Arithmetick: or that necessary art made most easy: Being
+    explained in a way familiar to the capacity of any that desire to learn
+    it in a little time. By James Hodder, Writing-master. The Five and
+    twentieth edition, revised, augmented, and above a thousand faults
+    amended, by Henry Mose, late servant and successor to the author.
+    Boston: printed by J. Franklin, for S. Phillips, N. Buttolph, B.
+    Elliot, D. Henchman, G. Phillips, J. Elliot, and E. Negus, booksellers
+    in Boston, and sold at their shops. 1719."
+
+The book is a very small octavo, the type and execution are creditable, the
+woodcut at the beginning is clumsy. It is a perfect copy, page for page, of
+the English editions of Mose's Hodder, of which the one called seventeenth
+is of London, 1690. There is not a syllable to show that the edition above
+described might not be of Boston in England. Presumptions, but not very
+strong ones, might be derived from the name of _Franklin_, and from the
+large number of booksellers who combined in the undertaking. It chanced,
+however, that a former owner had made the following note in my copy:
+
+    "Wednessday, July y^e 14, 1796, att ten in y^e forenoon we sail^d from
+    Boston, came too twice, once in King Rode, and once in y^e Narrows.
+    Sail^d by y^e lighthouse in y^e even^g."
+
+{267}
+
+No ordinary map would decide these points: so I had to apply to my friend
+Sir Francis Beaufort,[422] and the charts at the Admiralty decided
+immediately for Massachusetts.
+
+
+
+PARADOXES OF ORTHOGRAPHY AND COMPUTATION.
+
+The French are able paradoxers in their spelling of foreign names. The Abbe
+Sabatier de Castres,[423] in 1772, gives an account of an imaginary
+dialogue between Swif, Adisson, Otwai, and Bolingbrocke. I had hoped that
+this was a thing of former days, like the literal roasting of heretics; but
+the charity which hopeth all things must hope for disappointments. Looking
+at a recent work on the history of the popes, I found referred to, in the
+matter of Urban VIII[424] and Galileo, references to the works of two
+Englishmen, the Rev. Win Worewel and the Rev. Raden Powen. [Wm. Whewell and
+Baden Powell].[425]
+
+I must not forget the "moderate computation" paradox. This is the way by
+which large figures are usually obtained. Anything surprisingly great is
+got by the "lowest computation," anything as surprisingly small by the
+"utmost computation"; and these are the two great subdivisions of "moderate
+computation." In this way we learn that 70,000 persons were executed in one
+reign, and 150,000 persons {268} burned for witchcraft in one century.
+Sometimes this computation is very close. By a card before me it appears
+that all the Christians, including those dispersed in heathen countries,
+those of Great Britain and Ireland excepted, are 198,728,000 people, and
+pay their clergy 8,852,000l. But 6,400,000 people pay the clergy of the
+Anglo-Irish Establishment 8,896,000l.; and 14,600,000 of other
+denominations pay 1,024,000l. When I read moderate computations, I always
+think of Voltaire and the "memoires du fameux eveque de Chiapa, par
+lesquels il parait qu'il avait egorge, ou brule, ou noye dix millions
+d'infideles en Amerique pour les convertir. Je crus que cet eveque
+exaggerait; mais quand on reduisait ces sacrifices a cinq millions de
+victimes, cela serait encore admirable."[426]
+
+
+
+CENTRIFUGAL FORCE.
+
+My Budget has been arranged by authors. This is the only plan, for much of
+the remark is personal: the peculiarities of the paradoxer are a large part
+of the interest of the paradox. As to subject-matter, there are points
+which stand strongly out; the quadrature of the circle, for instance. But
+there are others which cannot be drawn out so as to be conspicuous in a
+review of writers: as one instance, I may take the _centrifugal force_.
+
+When I was about nine years old I was taken to hear a course of lectures,
+given by an itinerant lecturer in a country town, to get as much as I could
+of the second half of a good, sound, philosophical omniscience. The first
+half (and sometimes more) comes by nature. To this end I smelt chemicals,
+learned that they were different kinds of _gin_, saw young wags try to kiss
+the girls under the excuse of what was called _laughing gas_--which I was
+sure {269} was not to blame for more than five per cent of the requisite
+assurance--and so forth. This was all well so far as it went; but there was
+also the excessive notion of creative power exhibited in the millions of
+miles of the solar system, of which power I wondered they did not give a
+still grander idea by expressing the distances in inches. But even this was
+nothing to the ingenious contrivance of the centrifugal force. "You have
+heard what I have said of the wonderful centripetal force, by which Divine
+Wisdom has retained the planets in their orbits round the Sun. But, ladies
+and gentlemen, it must be clear to you that if there were no other force in
+action, this centripetal force would draw our earth and the other planets
+into the Sun, and universal ruin would ensue. To prevent such a
+catastrophe, the same wisdom has implanted a centrifugal force of the same
+amount, and directly opposite," etc. I had never heard of Alfonso X of
+Castile,[427] but I ventured to think that if Divine Wisdom had just let
+the planets alone it would come to the same thing, with equal and opposite
+troubles saved. The paradoxers deal largely in speculation conducted upon
+the above explanation. They provide external agents for what they call the
+centrifugal force. Some make the sun's rays keep the planets off, without a
+thought about what would become of our poor eyes if the _push_ of the light
+which falls on the earth were a counterpoise to all its gravitation. The
+true explanation cannot be given here, for want of room.
+
+
+
+CAMBRIDGE POETS.
+
+Sometimes a person who has a point to carry will assert a singular fact or
+prediction for the sake of his point; and {270} this paradox has almost
+obtained the sole use of the name. Persons who have reputation to care for
+should beware how they adopt this plan, which now and then eventuates a
+spanker, as the American editor said. Lord Byron, in "English Bards, etc."
+(1809), ridiculing Cambridge poetry, wrote as follows:
+
+ "But where fair Isis rolls her purer wave,
+  The partial muse delighted loves to lave;
+  On her green banks a greener wreath she wove,
+  To crown the bards that haunt her classic grove;
+  Where Richards[428] wakes a genuine poet's fires,
+  And modern Britons glory in their sires."[429]
+
+There is some account of the Rev. Geo. Richards, Fellow of Oriel and Vicar
+of Bampton, (M.A. in 1791) in the _Living Authors_ by Watkins[430] and
+Shoberl[431] (1816). In Rivers's _Living Authors_, of 1798, which is best
+fitted for citation, as being published before Lord Byron wrote, he is
+spoken of in high terms. The _Aboriginal Britons_ was an Oxford (special)
+prize poem, of 1791. Charles Lamb mentions Richards as his school-fellow at
+Christ's Hospital, "author of the _Aboriginal Britons_, the most spirited
+of the Oxford Prize Poems: a pale, studious Grecian."
+
+As I never heard of Richards as a poet,[432] I conclude that his fame is
+defunct, except in what may prove to be a very ambiguous kind of
+immortality, conferred by Lord Byron. The awkwardness of a case which time
+has broken down {271} is increased by the eulogist himself adding so
+powerful a name to the list of Cambridge poets, that his college has placed
+his statue in the library, more conspicuously than that of Newton in the
+chapel; and this although the greatness of poetic fame had some serious
+drawbacks in the moral character of some of his writings. And it will be
+found on inquiry that Byron, to get his instance against Cambridge, had to
+go back eighteen years, passing over seven intermediate productions, of
+which he had either never heard, or which he would not cite as waking a
+genuine poet's fires.
+
+The conclusion seems to be that the _Aboriginal Britons_ is a remarkable
+youthful production, not equalled by subsequent efforts.
+
+To enhance the position in which the satirist placed himself, two things
+should be remembered. First, the glowing and justifiable terms in which
+Byron had spoken,--a hundred and odd lines before he found it convenient to
+say no Cambridge poet could compare with Richards,--of a Cambridge poet who
+died only three years before Byron wrote, and produced greatly admired
+works while actually studying in the University. The fame of Kirke
+White[433] still lives; and future literary critics may perhaps compare his
+writings and those of Richards, simply by reason of the curious relation in
+which they are here placed alongside of each other. And it is much to
+Byron's credit that, in speaking of the deceased Cambridge poet, he forgot
+his own argument and its exigencies, and proved himself only a paradoxer
+_pro re nata_.
+
+Secondly, Byron was very unfortunate in another passage of the same poem:
+
+{272}
+
+ "What varied wonders tempt us as they pass!
+  The cow-pox, tractors, galvanism, and gas.
+  In turns appear, to make the vulgar stare,
+  Till the swoln bubble bursts--and all is air!"
+
+Three of the bubbles have burst to mighty ends. The metallic tractors are
+disused; but the force which, if anything, they put in action, is at this
+day, under the name of mesmerism, used, prohibited, respected, scorned,
+assailed, defended, asserted, denied, declared utterly obscure, and
+universally known. It was hard lines to select for candidates for oblivion
+not one of whom got in. I shall myself, I am assured, be some day cited for
+laughing at the great discovery of ----: the blank is left for my reader to
+fill up in his own way; but I think I shall not be so unlucky in four
+different ways.
+
+
+
+FALSIFIED PREDICTION.
+
+The narration before the fact, as prophecy has been called, sometimes quite
+as true as the narration after the fact, is very ridiculous when it is
+wrong. Why, the pre-narrator could not know; the post-narrator might have
+known. A good collection of unlucky predictions might be made: I hardly
+know one so fit to go with Byron's as that of the Rev. Daniel Rivers,
+already quoted, about Johnson's biographers. Peter Pindar[434] may be
+excused, as personal satire was his object, for addressing Boswell and Mrs.
+Piozzi[435] as follows:
+
+ "Instead of adding splendor to his name,
+  Your books are downright gibbets to his fame;
+  You never with posterity can thrive,
+ 'Tis by the Rambler's death alone you live."
+
+But Rivers, in prose narrative, was not so excusable. He says:
+
+{273}
+
+"As admirers of the learning and moral excellence of their hero, we glow at
+almost every page with indignation that his weaknesses and his failings
+should be disclosed to public view.... Johnson, after the luster he had
+reflected on the name of Thrale ... was to have his memory tortured and
+abused by her detested itch for scribbling. More injury, we will venture to
+affirm, has been done to the fame of Johnson by this Lady and her late
+biographical helpmate, than his most avowed enemies have been able to
+effect: and if his character becomes unpopular with some of his successors,
+it is to those gossiping friends he is indebted for the favor."
+
+Poor dear old Sam! the best known dead man alive! clever, good-hearted,
+logical, ugly bear! Where would he have been if it had not been for Boswell
+and Thrale, and their imitators? What would biography have been if Boswell
+had not shown how to write a life?
+
+Rivers is to be commended for not throwing a single Stone at Mrs. Thrale's
+second marriage. This poor lady begins to receive a little justice. The
+literary world seems to have found out that a blue-stocking dame who keeps
+open house for a set among them has a right, if it so please her, to marry
+again without taking measures to carry on the cake-shop. I was before my
+age in this respect: as a boy-reader of Boswell, and a few other things
+that fell in my way, I came to a clearness that the conduct of society
+towards Mrs. Piozzi was _blackguard_. She wanted nothing but what was in
+that day a woman's only efficient protection, a male relation with a brace
+of pistols, and a competent notion of using them.
+
+
+
+BYRON AND WORDSWORTH.
+
+Byron's mistake about Hallam in the Pindar story may be worth placing among
+absurdities. For elucidation, suppose that some poet were now to speak--
+{274}
+
+ "Of man's first disobedience, and the fruit
+  Eve gave to Adam in his birthday suit--"
+
+and some critic were to call it nonsense, would that critic be laughing at
+Milton? Payne Knight,[436] in his _Taste_, translated part of Gray's _Bard_
+into Greek. Some of his lines are
+
+  [Greek: therma d' ho tengon dakrua stonachais]
+  [Greek: oulon melos phoberai]
+  [Greek: eeide phonai.]
+
+Literally thus:
+
+ "Wetting warm tears with groans,
+  Continuous chant with fearful
+  Voice he sang."
+
+On which Hallam remarks: "The twelfth line [our first] is nonsense." And so
+it is, a poet can no more wet his tears with his groans than wet his ale
+with his whistle. Now this first line is from Pindar, but is only part of
+the sense; in full it is:
+
+  [Greek: therma de tengon dakrua stonachais]
+      [Greek: horthion phonase.]
+
+Pindar's [Greek: tengon] must be Englished by _shedding_, and he stands
+alone in this use. He says, "shedding warm tears, he cried out loud, with
+groans." Byron speaks of
+
+ "Classic Hallam, much renowned for Greek:"
+
+and represents him as criticising _the Greek_ of all Payne's lines, and not
+discovering that "the lines" were Pindar's {275} until after publication.
+Byron was too much of a scholar to make this blunder himself: he either
+accepted the facts from report, or else took satirical licence. And why
+not? If you want to laugh at a person, and he will not give occasion, whose
+fault is it that you are obliged to make it? Hallam did criticise some of
+Payne Knight's Greek; but with the caution of his character, he remarked
+that possibly some of these queer phrases might be "critic-traps" justified
+by some one use of some one author. I remember well having a Latin essay to
+write at Cambridge, in which I took care to insert a few monstrous and
+unusual idioms from Cicero: a person with a Nizolius,[437] and without
+scruples may get scores of them. So when my tutor raised his voice against
+these oddities, I was up to him, for I came down upon him with Cicero,
+chapter and verse, and got round him. And so my own solecisms, many of
+them, passed unchallenged.
+
+Byron had more good in his nature than he was fond of letting out: whether
+he was a soured misanthrope, or whether his _vein_ lay that way in poetry,
+and he felt it necessary to fit his demeanor to it, are matters far beyond
+me. Mr. Crabb Robinson[438] told me the following story more than once. He
+was at Charles Lamb's chambers in the Temple when Wordsworth came in, with
+the new _Edinburgh Review_ in his hand, and fume on his countenance. "These
+reviewers," said he, "put me out of patience! Here is a young man--they say
+he is a lord--who has written a volume of poetry; and these fellows, just
+because he is a lord, set upon him, laugh at him, and sneer at his writing.
+The young man will do something, if he goes on as he has begun. But these
+reviewers seem to think {276} that nobody may write poetry, unless he lives
+in a garret." Crabb Robinson told this long after to Lady Byron, who said,
+"Ah! if Byron had known that, he would never have attacked Wordsworth. He
+went one day to meet Wordsworth at dinner; when he came home I said, 'Well,
+how did the young poet get on with the old one?' 'Why, to tell you the
+truth,' said he, 'I had but one feeling from the beginning of the visit to
+the end, and that was--_reverence_!'" Lady Byron told my wife that her
+husband had a very great respect for Wordsworth. I suppose he would have
+said--as the Archangel said to his Satan--"Our difference is po[li =
+e]tical."
+
+I suspect that Fielding would, if all were known, be ranked among the
+unlucky railers at supposed paradox. In his _Miscellanies_ (1742, 8vo) he
+wrote a satire on the Chrysippus or Guinea, an animal which multiplies
+itself by division, like the polypus. This he supposes to have been drawn
+up by Petrus Gualterus, meaning the famous usurer, Peter Walter. He calls
+it a paper "proper to be read before the R----l Society": and next year,
+1743, a quarto reprint was made to resemble a paper in the _Philosophical
+Transactions_. So far as I can make out, one object is ridicule of what the
+zoologists said about the polypus: a reprint in the form of the
+_Transactions_ was certainly satire on the Society, not on Peter Walter and
+his knack of multiplying guineas.
+
+Old poets have recognized the quadrature of the circle as a well-known
+difficulty. Dante compares himself, when bewildered, to a geometer who
+cannot find the principle on which the circle is to be measured:
+
+ "Quale e 'l geometra che tutto s' affige
+  Per misurar lo cerchio, e non ritruova,
+  Pensando qual principio ond' egli indige."[439]
+
+{277} And Quarles[440] speaks as follows of the _summum bonum_:
+
+ "Or is't a tart idea, to procure
+  An edge, and keep the practic soul in ure,
+  Like that dear chymic dust, or puzzling quadrature?"
+
+The poetic notion of the quadrature must not be forgotten. Aristophanes, in
+the _Birds_, introduces a geometer who announces his intention to _make a
+square circle_. Pope, in the _Dunciad_, delivers himself as follows, with a
+Greek pronunciation rather strange in a translator of Homer. Probably Pope
+recognized, as a general rule, the very common practice of throwing back
+the accent in defiance of quantity, seen in o'rator, au'ditor, se'nator,
+ca'tenary, etc.
+
+ "Mad _Mathesis_ alone was unconfined,
+  Too mad for mere material chains to bind,--
+  Now to pure space lifts her ecstatic stare,
+  Now, running round the circle, finds it square."
+
+The author's note explains that this "regards the wild and fruitless
+attempts of squaring the circle." The poetic idea seems to be that the
+geometers try to make a square circle. Disraeli quotes it as "finds _its_
+square," but the originals do not support this reading.
+
+
+
+DE BECOURT.
+
+I have come in the way of a work, entitled _The Grave of Human
+Philosophies_ (1827), translated from the French of R. de Becourt[441] by
+A. Dalmas. It supports, but I suspect not very accurately, the views of the
+old Hindu books. {278} That the sun is only 450 miles from us, and only 40
+miles in diameter, may be passed over; my affair is with the state of mind
+into which persons of M. Becourt's temperament are brought by a fancy. He
+fully grants, as certain, four millions of years as the duration of the
+Hindu race, and 1956 as that of the universe. It must be admitted he is not
+wholly wrong in saying that our errors about the universe proceed from our
+ignorance of its origin, antiquity, organization, laws, and final
+destination. Living in an age of light, he "avails himself of that
+opportunity" to remove this veil of darkness, etc. The system of the
+Brahmins is the only true one: he adds that it has never before been
+attempted, as it could not be obtained except by him. The author requests
+us first, to lay aside prejudice; next, to read all he says in the order in
+which he says it: we may then pronounce judgment upon a work which begins
+by taking the Brahmins for granted. All the paradoxers make the same
+requests. They do not see that compliance would bring thousands of systems
+before the world every year: we have scores as it is. How is a poor candid
+inquirer to choose. Fortunately, the mind has its grand jury as well as its
+little one: and it will not put a book upon its trial without a _prima
+facie_ case in its favor. And with most of those who really search for
+themselves, that case is never made out without evidence of knowledge,
+standing out clear and strong, in the book to be examined.
+
+
+
+BEQUEST OF A QUADRATURE.
+
+There is much private history which will never come to light, _caret quia
+vate sacro_,[442] because no Budgeteer comes across it. Many years ago a
+man of business, whose life was passed in banking, amused his leisure with
+quadrature, was successful of course, and bequeathed the result in a sealed
+book, which the legatee was enjoined not to sell {279} under a thousand
+pounds. The true ratio was 3.1416: I have the anecdote from the legatee's
+executor, who opened the book. That a banker should square the circle is
+very credible: but how could a City man come by the notion that a thousand
+pounds could be got for it? A friend of mine, one of the twins of my
+zodiac, will spend a thousand pounds, if he have not done it already, in
+black and white cyclometry: but I will answer for it that he, a man of
+sound business notions, never entertained the idea of [pi] recouping him,
+as they now say. I speak of individual success: of course if a company were
+formed, especially if it were of unlimited lie-ability, the shares would be
+taken. No offence; there is nothing but what a pun will either sanctify,
+justify, or nullify:
+
+ "It comes o'er the soul like the sweet South
+  That breathes upon a bank of _vile hits_."
+
+The shares would be at a premium of 3-1/8 on the day after issue. If they
+presented me with the number of shares I deserve, for suggestion and
+advertisement, I should stand up for the Archpriest of St. Vitus[443] and
+3-1/5, with a view to a little more gold on the bridge.
+
+I now insert a couple of reviews, one about Cyclopaedias, one about
+epistolary collections. Should any reader wish for explanation of this
+insertion, I ask him to reflect a moment, and imagine me set to justify all
+the additions now before him! In truth these reviews are the repositories
+of many odds and ends: they were not made to the books; the materials were
+in my notes, and the books came as to a ready-made clothes shop, and found
+what would fit them. Many remember Curll's[444] bequest of some very good
+titles {280} which only wanted treatises written to them. Well! here were
+some tolerable reviews--as times go--which only wanted books fitted to
+them. Accordingly, some tags were made to join on the books; and then as
+the reader sees.
+
+I should find it hard to explain why the insertion is made in this place
+rather than another. But again, suppose I were put to make such an
+explanation throughout the volume. The improver who laid out grounds and
+always studied what he called _unexpectedness_, was asked what name he gave
+it for those who walked over his grounds a second time. He was silenced;
+but I have an answer: It is that which is given by the very procedure of
+taking up my book a second time.
+
+
+
+REVIEW OF CYCLOPAEDIAS.
+
+    October 19, 1861. _The English Cyclopaedia._ Conducted by Charles
+    Knight.[445] 22 vols.: viz., _Geography_, 4 vols.; _Biography_, 6
+    vols.; _Natural History_, 4 vols.; _Arts and Sciences_, 8 vols.
+    (Bradbury & Evans.)
+
+    _The Encyclopaedia Britannica: a Dictionary of Arts, Sciences, and
+    General Literature._ Eighth Edition. 21 vols. and Index. (Black.)
+
+The two editions above described are completed at the same time: and they
+stand at the head of the two great branches into which pantological
+undertakings are divided, as at once the largest and the best of their
+classes.
+
+When the works are brought together, the first thing that strikes the eye
+is the syllable of difference in the names. The word _Cyclopaedia_ is a bit
+of modern purism. Though [Greek: enkuklopaideia][446] is not absolutely
+Greek of Greece, we learn from both Pliny[447] and Quintilian[448] that the
+circle {281} of the sciences was so called by the Greeks, and
+Vitruvius[449] has thence naturalized _encyclium_ in Latin. Nevertheless we
+admit that the initial _en_ would have euphonized but badly with the word
+_Penny_: and the _English Cyclopaedia_ is the augmented, revised, and
+distributed edition of the _Penny Cyclopaedia_. It has indeed been said that
+Cyclopaedia should mean the education _of_ a circle, just as Cyropaedia is
+the education _of_ Cyrus. But this is easily upset by Aristotle's word
+[Greek: kuklophoria],[450] motion _in_ a circle, and by many other cases,
+for which see the lexicon.
+
+The earliest printed Encyclopaedia of this kind was perhaps the famous
+"myrrour of the worlde," which Caxton[451] translated from the French and
+printed in 1480. The original Latin is of the thirteenth century, or
+earlier. This is a collection of very short treatises. In or shortly after
+1496 appeared the _Margarita Philosophica_ of Gregory Reisch,[452] the same
+we must suppose, who was confessor to the Emperor Maximilian.[453] This is
+again a collection of treatises, of much more pretension: and the
+estimation formed of it is proved by the number of editions it went
+through. In 1531 appeared the little collection of _works_ of
+Ringelberg,[454] which is truly called an Encyclopaedia by {282} Morhof,
+though the thumbs and fingers of the two hands will meet over the length of
+its one volume. There are more small collections; but we pass on to the
+first work to which the name of _Encyclopaedia_ is given. This is a
+ponderous _Scientiarum Omnium Encyclopaedia_ of Alsted,[455] in four folio
+volumes, commonly bound in two: published in 1629 and again in 1649; the
+true parent of all the Encyclopaedias, or collections of treatises, or works
+in which that character predominates. The first great _dictionary_ may
+perhaps be taken to be Hofman's _Lexicon Universale_[456] (1677); but
+Chambers's[457] (so called) _Dictionary_ (1728) has a better claim. And we
+support our proposed nomenclature by observing that Alsted accidentally
+called his work _En_cyclopaedia, and Chambers simply Cyclopaedia.
+
+We shall make one little extract from the _myrrour_, and one from
+Ringelberg. Caxton's author makes a singular remark for his time; and one
+well worthy of attention. The grammar rules of a language, he says, must
+have been invented by foreigners: "And whan any suche tonge was perfytely
+had and usyd amonge any people, than other people not used to the same
+tonge caused rulys to be made wherby they myght lerne the same tonge ...
+and suche rulys be called the gramer of that tonge." Ringelberg says that
+if the right nostril bleed, the little finger of the right hand should be
+crooked, and squeezed with great force; and the same for the left.
+
+{283}
+
+We pass on to _the_ Encyclopedie,[458] commenced in 1751; the work which
+has, in many minds, connected the word _encyclopaedist_ with that of
+_infidel_. Readers of our day are surprised when they look into this work,
+and wonder what has become of all the irreligion. The truth is, that the
+work--though denounced _ab ovo_[459] on account of the character of its
+supporters--was neither adapted, nor intended, to excite any particular
+remark on the subject: no work of which D'Alembert[460] was co-editor would
+have been started on any such plan. For, first, he was a real _sceptic_:
+that is, doubtful, with a mind not made up. Next, he valued his quiet more
+than anything; and would as soon have gone to sleep over an hornet's nest
+as have contemplated a systematic attack upon either religion or
+government. As to Diderot[461]--of whose varied career of thought it is
+difficult to fix the character of any one moment, but who is very
+frequently taken among us for a pure atheist--we will quote one sentence
+from the article "_Encyclopedie_," which he wrote himself:--"Dans le moral,
+il n'y a que Dieu qui doit servir de modele a 1'homme; dans les art, que la
+nature."[462]
+
+A great many readers in our country have but a very hazy idea of the
+difference between the political Encyclopaedia, as we may call it, and the
+_Encyclopedie Methodique_,[463] which we always take to be meant--whether
+rightly or not we cannot tell--when we hear of the "great French
+Encyclopaedia." This work, which takes much from its {284} predecessor,
+professing to correct it, was begun in 1792, and finished in 1832. There
+are 166 volumes of text, and 6439 plates, which are sometimes incorporated
+with the text, sometimes make about 40 more volumes. This is still the
+monster production of the kind; though probably the German Cyclopaedia of
+Ersch and Gruber,[464] which was begun in 1818, and is still in progress,
+will beat it in size. The great French work is a collection of
+dictionaries; it consists of Cyclopaedias of all the separate branches of
+knowledge. It is not a work, but a collection of works, one or another
+department is to be bought from time to time; but we never heard of a
+complete set for sale in one lot. As ships grow longer and longer, the
+question arises what limit there is to the length. One answer is, that it
+will never do to try such a length that the stern will be rotten before the
+prow is finished. This wholesome rule has not been attended to in the
+matter before us; the earlier parts of the great French work were
+antiquated before the whole were completed: something of the kind will
+happen to that of Ersch and Gruber.
+
+The production of a great dictionary of either of the kinds is far from an
+easy task. There is one way of managing the _En_cyclopaedia which has been
+largely resorted to; indeed, we may say that no such work has been free
+from it. This plan is to throw all the attention upon the great treatises,
+and to resort to paste and scissors, or some process of equally easy
+character, for the smaller articles. However it may be done, it has been
+the rule that the Encyclopaedia of treatises should have its supplemental
+Dictionary of a very incomplete character. It is true that the treatises
+are intended to do a good deal; and that the Index, if it be good, knits
+the treatises and the dictionary into one whole of reference. Still there
+are two stools, and between them a great deal will fall to the ground. The
+dictionary portion of the _Britannica_ is not to be compared with its {285}
+treatises; the part called Miscellaneous and Lexicographical in the
+_Metropolitana_[465] is a great failure. The defect is incompleteness. The
+biographical portion, for example, of the Britannica is very defective: of
+many names of note in literature and science, which become known to the
+reader from the treatises, there is no account whatever in the dictionary.
+So that the reader who has learnt the results of a life in astronomy, for
+example, must go to some other work to know when that life began and ended.
+This defect has run through all the editions; it is in the casting of the
+work. The reader must learn to take the results at their true value, which
+is not small. He must accustom himself to regard the Britannica as a
+splendid body of treatises on all that can be called heads of knowledge,
+both greater and smaller; with help from the accompanying dictionary, but
+not of the most complete character. Practically, we believe, this defect
+cannot be avoided: two plans of essentially different structure cannot be
+associated on the condition of each or either being allowed to abbreviate
+the other.
+
+The defect of all others which it is most difficult to avoid is inequality
+of performance. Take any dictionary you please, of any kind which requires
+the association of a number of contributors, and this defect must result.
+We do not merely mean that some will do their work better than others; this
+of course: we mean that there will be structural differences of execution,
+affecting the relative extent of the different parts of the whole, as well
+as every other point by which a work can be judged. A wise editor will not
+attempt any strong measures of correction: he will remember that if some
+portions be below the rest, which is a disadvantage, it follows that some
+portions must be above the rest, which is an advantage. The only practical
+level, if {286} level there must be, is that of mediocrity, if not of
+absolute worthlessness: any attempt to secure equality of strength will
+result in equality of weakness. Efficient development may be cut down into
+meager brevity, and in this way only can apparent equality of plan be
+secured throughout. It is far preferable to count upon differences of
+execution, and to proceed upon the acknowledged expectation that the
+prominent merits of the work will be settled by the accidental character of
+the contributors; it being held impossible that any editorial efforts can
+secure a uniform standard of goodness. Wherever the greatest power is
+found, it should be suffered to produce its natural effect. There are,
+indeed, critics who think that the merit of a book, like the strength of a
+chain, is that of its weakest part: but there are others who know that the
+parallel does not hold, and who will remember that the union of many
+writers must show exaggeration of the inequalities which almost always
+exist in the production of one person. The true plan is to foster all the
+good that can be got, and to give development in the directions in which
+most resources are found: a Cyclopaedia, like a plant, should grow towards
+the light.
+
+The _Penny Cyclopaedia_ had its share of this kind of defect or excellence,
+according to the way in which the measure is taken. The circumstance is not
+so much noticed as might be expected, and this because many a person is in
+the habit of using such a dictionary chiefly with relation to one subject,
+his own; and more still want it for the pure dictionary purpose, which does
+not go much beyond the meaning of the word. But the person of full and
+varied reference feels the differences; and criticism makes capital of
+them. The Useful Knowledge Society was always odious to the organs of
+religious bigotry; and one of them, adverting to the fact that geography
+was treated with great ability, and most unusual fullness, in the _Penny
+Cyclopaedia_, announced it by making it the sole merit of {287} the work
+that, with sufficient addition, it would make a tolerably good gazetteer.
+
+Some of our readers may still have hanging about them the feelings derived
+from this old repugnance of a class to all that did not associate direct
+doctrinal teaching of religion with every attempt to communicate knowledge.
+I will take one more instance, by way of pointing out the extent to which
+stupidity can go. If there be an astronomical fact of the telescopic
+character which, next after Saturn's ring and Jupiter's satellites, was
+known to all the world, it was the existence of multitudes of double stars,
+treble stars, etc. A respectable quarterly of the theological cast, which
+in mercy we refrain from naming, was ignorant of this common
+knowledge,--imagined that the mention of such systems was a blunder of one
+of the writers in the _Penny Cyclopaedia_, and lashed the presumed ignorance
+of the statement in the following words, delivered in April, 1837:
+
+    "We have forgotten the name of that Sidrophel who lately discovered
+    that the fixed stars were not single stars, but appear in the heavens
+    like soles at Billingsgate, in pairs; while a second astronomer, under
+    the influence of that competition in trade which the political
+    economists tell us is so advantageous to the public, professes to show
+    us, through his superior telescope, that the apparently single stars
+    are really three. Before such wondrous mandarins of science, how
+    continually must _homunculi_ like ourselves keep in the background,
+    lest we come between the wind and their nobility."
+
+Certainly these little men ought to have kept in the background; but they
+did not: and the growing reputation of the work which they assailed has
+chronicled them in literary history; grubs in amber.
+
+This important matter of inequality, which has led us so far, is one to
+which the _Encyclopaedia_ is as subject as the _Cyclopaedia_; but it is not
+so easily recognized as a fault. {288} We receive the first book as mainly
+a collection of treatises: we know their authors, and we treat them as
+individuals. We see, for instance, the names of two leading writers on
+Optics, Brewster[466] and Herschel.[467] It would not at all surprise us if
+either of these writers should be found criticising the other by name, even
+though the very view opposed should be contained in the same _Encyclopaedia_
+with the criticism. And in like manner, we should hold it no wonder if we
+found some third writer not comparable to either of those we have named. It
+is not so in the _Cyclopaedia_: here we do not know the author, except by
+inference from a list of which we never think while consulting the work. We
+do not dissent from this or that author: we blame the book.
+
+The _Encyclopaedia Britannica_ is an old friend. Though it holds a proud
+place in our present literature, yet the time was when it stood by itself,
+more complete and more clear than anything which was to be found elsewhere.
+There must be studious men alive in plenty who remember when they were
+studious boys, what a literary luxury it was to pass a few days in the
+house of a friend who had a copy of this work. The present edition is a
+worthy successor of those which went before. The last three editions,
+terminating in 1824, 1842, and 1861, seem to show that a lunar cycle cannot
+pass without an amended and augmented edition. Detailed criticism is out of
+the question; but we may notice the effective continuance of the plan of
+giving general historical dissertations on the progress of knowledge. Of
+some of these dissertations we have had to take separate notice; and all
+will be referred to in our ordinary treatment of current literature.[468]
+
+The literary excellence of these two extensive undertakings is of the same
+high character. To many this will {289} need justification: they will not
+easily concede to the cheap and recent work a right to stand on the same
+shelf with the old and tried magazine, newly replenished with the best of
+everything. Those who are cognizant by use of the kind of material which
+fills the _Penny Cyclopaedia_ will need no further evidence: to others we
+shall quote a very remarkable and certainly very complete testimony. The
+_Cyclopaedia of the Physical Sciences_, published by Dr. Nichol[469] in 1857
+(noticed by us, April 4), is one of the most original of our special
+dictionaries. The following is an extract from the editor's preface:
+
+    "When I assented to Mr. Griffin's proposal that I should edit such a
+    Cyclopaedia, I had it in my mind that I might make the _scissors_
+    eminently effective. Alas! on narrowly examining our best Cyclopaedias,
+    I found that the scissors had become blunted through too frequent and
+    vigorous use. One great exception exists: viz., the _Penny Cyclopaedia_
+    of Charles Knight.[470] The cheapest and the least pretending, it is
+    really the most philosophical of our _scientific_ dictionaries. It is
+    not made up of a series of treatises, some good and many indifferent,
+    but is a thorough _Dictionary_, well proportioned and generally written
+    by the best men of the time. The more closely it is examined, the more
+    deeply will our obligation be felt to the intelligence and
+    conscientiousness of its projector and editor."
+
+After Dr. Nichol's candid and amusing announcement of his scissorial
+purpose, it is but fair to state that nothing of the kind was ultimately
+carried into effect, even upon the work in which he found so much to
+praise. I quote this testimony because it is of a peculiar kind.
+
+{290}
+
+The success of the _Penny Magazine_ led Mr. Charles Knight in 1832 to
+propose to the Useful Knowledge Society a Cyclopaedia in weekly penny
+numbers. These two works stamp the name of the projector on the literature
+of our day in very legible characters. Eight volumes of 480 pages each were
+contemplated; and Mr. Long[471] and Mr. Knight were to take the joint
+management. The plan embraced a popular account of Art and Science, with
+very brief biographical and geographical information. The early numbers of
+the work had some of the _Penny Magazine_ character: no one can look at the
+pictures of the Abbot and Abbess in their robes without seeing this. By the
+time the second volume was completed, it was clearly seen that the plan was
+working out its own extension: a great development of design was submitted
+to, and Mr. Long became sole editor. Contributors could not be found to
+make articles of the requisite power in the assigned space. One of them
+told us that when he heard of the eight volumes, happening to want a shelf
+to be near at hand for containing the work as it went on, he ordered it to
+be made to hold twenty-five volumes easily. But the inexorable logic of
+facts beat him after all: for the complete work contained twenty-six
+volumes and two thick volumes of Supplement.
+
+The penny issue was brought to an end by the state of the law, which
+required, in 1833, that the first and last page of everything sold
+separately should contain the name and address of the printer. The penny
+numbers contained this imprint on the fold of the outer leaf: and _qui
+tam_[472] informations were laid against the agents in various towns. {291}
+It became necessary to call in the stock; and the penny issue was
+abandoned. Monthly parts were substituted, which varied in bulk, as the
+demands of the plan became more urgent, and in price from one sixpence to
+three. The second volume of Supplement appeared in 1846, and during the
+fourteen years of issue no one monthly part was ever behind its time. This
+result is mainly due to the peculiar qualities of Mr. Long, who unites the
+talents of the scholar and the editor in a degree which is altogether
+unusual. If any one should imagine that a mixed mass of contributors is a
+punctual piece of machinery, let him take to editing upon that hypothesis,
+and he shall see what he shall see and learn what he shall learn.
+
+The _English_ contains about ten per cent more matter than the _Penny
+Cyclopaedia_ and its supplements; including the third supplementary volume
+of 1848, which we now mention for the first time. The literary work of the
+two editions cost within 500l. and 50,000l.: that of the two editions of
+the _Britannica_ cost 41,000l. But then it is to be remembered that the
+_Britannica_ had matter to begin upon, which had been paid for in the
+former editions. Roughly speaking, it is probable that the authorship of a
+page of the same size would have cost nearly the same in one as in the
+other.
+
+The longest articles in the _Penny Cyclopaedia_ were "Rome" in 98 columns
+and "Yorkshire" in 86 columns. The only article which can be called a
+treatise is the Astronomer Royal's "Gravitation," founded on the method of
+Newton in the eleventh section, but carried to a much greater extent. In
+the _English Cyclopaedia_, the longest article of geography is "Asia," in 45
+columns. In natural history the antelopes demand 36 columns. In biography,
+"Wellington" uses up 42 columns, and his great military opponent 41
+columns. In the division of Arts and Sciences, which includes much of a
+social and commercial character, the length of articles often depends upon
+the state of the {292} times with regard to the subject. Our readers would
+not hit the longest article of this department in twenty guesses: it is
+"Deaf and Dumb" in 60 columns. As other specimens, we may cite Astronomy,
+19; Banking, 36; Blind, 24; British Museum, 35; Cotton, 27; Drama, 26;
+Gravitation, 50; Libraries, 50; Painting, 34; Railways, 18; Sculpture, 36;
+Steam, etc., 37; Table, 40; Telegraph, 30; Welsh language and literature,
+39; Wool, 21. These are the long articles of special subdivisions: the
+words under which the _En_cyclopaedia gives treatises are not so prominent.
+As in Algebra, 10; Chemistry, 12; Geometry, 8; Logic, 14; Mathematics, 5;
+Music, 9. But the difference between the collection of treatises and the
+dictionary may be illustrated thus: though "Mathematics" have only five
+columns, "Mathematics, recent terminology of," has eight: and this article
+we believe to be by Mr. Cayley,[473] who certainly ought to know his
+subject, being himself a large manufacturer of the new terms which he
+explains. Again, though "Music" _in genere_, as the schoolmen said, has
+only nine columns, "Temperament and Tuning," has eight, and "Chord" alone
+has two. And so on.
+
+In a dictionary of this kind it is difficult to make a total clearance of
+_personality_: by which we mean that exhibition of peculiar opinion which
+is offensive to taste when it is shifted from the individual on the
+corporate book. The treatise of the known author may, as we have said,
+carry that author's controversies on its own shoulders: and even his
+crotchets, if we may use such a word. But {293} the dictionary should not
+put itself into antagonism with general feeling, nor even with the feelings
+of classes. We refer particularly to the ordinary and editorial teaching of
+the article. If, indeed, the writer, being at issue with mankind, should
+confess the difference, and give abstract of his full grounds, the case is
+altered: the editor then, as it were, admits a correspondent to a statement
+of his own individual views. The dictionary portion of the Britannica is
+quite clear of any lapses on this point, so far as we know: the treatises
+and dissertations rest upon their authors. The Penny Cyclopaedia was all but
+clear: and great need was there that it should have been so. The Useful
+Knowledge Society, starting on the principle of perfect neutrality in
+politics and religion, was obliged to keep strict watch against the
+entrance of all attempt even to look over the hedge. There were two--we
+believe only two--instances of what we have called personality. The first
+was in the article "Bunyan." It is worth while to extract all that is
+said--in an article of thirty lines--about a writer who is all but
+universally held to be the greatest master of allegory that ever wrote:
+
+    "His works were collected in two volumes, folio, 1736-7: among them
+    'The Pilgrim's Progress' has attained the greatest notoriety. If a
+    judgment is to be formed of the merits of a book by the number of times
+    it has been reprinted, and the many languages into which it has been
+    translated, no production in English literature is superior to this
+    coarse allegory. On a composition which has been extolled by Dr.
+    Johnson, and which in our own times has received a very high critical
+    opinion in its favor [probably Southey], it is hazardous to venture a
+    disapproval, and we, perhaps, speak the opinion of a small minority
+    when we confess that to us it appears to be mean, jejune and
+    wearisome."
+
+--If the unfortunate critic who thus individualized himself had been a
+sedulous reader of Bunyan, his power over {294} English would not have been
+so _jejune_ as to have needed that fearful word. This little bit of
+criticism excited much amusement at the time of its publication: but it was
+so thoroughly exceptional and individual that it was seldom or never
+charged on the book. The second instance occurred in the article
+"Socinians." It had been arranged that the head-words of Christian sects
+should be intrusted to members of the sects themselves, on the
+understanding that the articles should simply set forth the accounts which
+the sects themselves give of their own doctrines. Thus the article on the
+Roman Church was written by Dr. Wiseman.[474] But the Unitarians were not
+allowed to come within the rule: as in other quarters, they were treated as
+the gypsies of Christianity. Under the head "Socinians"--a name repudiated
+by themselves--an opponent was allowed not merely to state their alleged
+doctrines in his own way, but to apply strong terms, such as "audacious
+unfairness," to some of their doings. The protests which were made against
+this invasion of the understanding produced, in due time, the article
+"Unitarians," written by one of that persuasion. We need not say that these
+errors have been amended in the English Cyclopaedia: and our chief purpose
+in mentioning them is to remark, that this is all we can find on the points
+in question against twenty-eight large volumes produced by an editor whose
+task was monthly, and whose issue was never delayed a single hour. How much
+was arrested before publication none but himself can say. We have not
+alluded to one or two remonstrances on questions of absolute fact, which
+are beside the present purpose.
+
+Both kinds of encyclopaedic works have been fashioned upon predecessors,
+from the very earliest which had a predecessor to be founded upon; and the
+undertakings before us will be themselves the ancestors of a line of
+successors. Those who write in such collections should be {295} careful
+what they say, for no one can tell how long a mis-statement may live. On
+this point we will give the history of a pair of epithets. When the
+historian De Thou[475] died, and left the splendid library which was
+catalogued by Bouillaud[476] and the brothers Dupuis[477] (Bullialdus and
+Puteanus), there was a manuscript of De Thou's friend Vieta,[478] the
+_Harmonicon Coeleste_, of which it is on record, under Bouillaud's hand,
+that he himself lent it to Cosmo de' Medici,[479] to which must be added
+that M. Libri[480] found it in the Magliabecchi Library at Florence in our
+own day. Bouillaud, it seems, entirely forgot what he had done. Something,
+probably, that Peter Dupuis said to Bouillaud, while they were at work on
+the catalogue, remained on his memory, and was published by him in 1645,
+long after; to the effect that Dupuis lent the manuscript to Mersenne,[481]
+from whom it was procured by some intending plagiarist, who would not give
+it back. This was repeated by Sherburne,[482] in 1675, who speaks of the
+work, which "being communicated to Mersennus was, by some perfidious
+acquaintance of that honest-minded person, surreptitiously taken from him,
+and irrecoverably lost or suppressed, to the unspeakable detriment of the
+lettered world." Now let the {296} reader look through the dictionaries of
+the last century and the present, scientific or general, at the article,
+"Vieta," and he will be amused with the constant recurrence of
+"honest-minded" Mersenne, and his "surreptitious" acquaintance. We cannot
+have seen less than thirty copies of these epithets.
+
+
+
+REVIEW OF MACCLESFIELD LETTERS.
+
+    October 18, 1862. _Correspondence of Scientific Men of the Seventeenth
+    Century, in the Collection of the Earl of Macclesfield._[483] 2 vols.
+    (Oxford, University Press.)
+
+Though the title-page of this collection bears the date 1841, it is only
+just completed by the publication of its Table of Contents and Index.
+Without these, a work of the kind is useless for consultation, and cannot
+make its way. The reason of the delay will appear: its effect is well known
+to us. We have found inquirers into the history of science singularly
+ignorant of things which this collection might have taught them.
+
+In the same year, 1841, the Historical Society of Science, which had but a
+brief existence, published a collection of letters, eighty-three in number,
+edited by Mr. Halliwell,[484] of English men of science, which dovetails
+with the one before us, and is for the most part of a prior date. The two
+should be bound up together. The smaller collection runs from 1562 to 1682;
+the larger, from 1606 to past 1700. We shall speak of the two as the Museum
+collection and the Macclesfield collection. And near them should be placed,
+in every scientific library, the valuable collection published, by Mr.
+Edleston,[485] for Trinity College, in 1850.
+
+{297}
+
+The history of these letters runs back to famous John Collins, the
+attorney-general of the mathematics, as he has been called, who wrote to
+everybody, heard from everybody, and sent copies of everybody's letter to
+everybody else. He was in England what Mersenne[486] was in France: as
+early as 1671, E. Bernard[487] addresses him as "the very Mersennus and
+intelligence of this age." John Collins[488] was never more than accountant
+to the Excise Office, to which he was promoted from teaching writing and
+ciphering, at the Restoration: he died in 1682. We have had a man of the
+same office in our own day, the late Prof. Schumacher,[489] who made the
+little Danish Observatory of Altona the junction of all the lines by which
+astronomical information was conveyed from one country to another. When the
+collision took place between Denmark and the Duchies, the English
+Government, moved by the Astronomical Society, instructed its diplomatic
+agents to represent strongly to the Danish Government, when occasion should
+arise, the great importance of the Observatory of Altona to the
+astronomical communications of the whole world. But Schumacher had his own
+celebrated journal, the _Astronomische Nachrichten_, by which to work out
+part of his plan; private correspondence was his supplementary assistant.
+Collins had only correspondence to rely on. Nothing is better known than
+that it was Collins's collection which furnished the materials put forward
+by the Committee of the Royal Society in 1712, as a defence of Newton
+against the partisans of Leibnitz. The noted _Commercium Epistolicum_ is
+but the abbreviation of a title which runs on with "D. Johannis Collins et
+aliorum ..."
+
+The whole of this collection passed into the hands of {298} William
+Jones,[490] the father of the Indian Judge of the same name, who died in
+1749. Jones was originally a teacher, but was presented with a valuable
+sinecure by the interest of George, second Earl of Macclesfield, the mover
+of the bill for the change of style in Britain, who died President of the
+Royal Society. This change of style may perhaps be traced to the union of
+energies which were brought into concert by the accident of a common
+teacher: Lord Macclesfield and Lord Chesterfield,[491] the mover and the
+seconder, and Daval,[492] who drew the bill, were pupils of De Moivre.[493]
+Jones, who was a respectable mathematician though not an inventor,
+collected the largest mathematical library of his day, and became possessor
+of the papers of Collins, which contained those of Oughtred[494] and
+others. Some of these papers passed into the custody of the Royal Society:
+but the bulk was either bequeathed to, or purchased by, Lord Macclesfield;
+and thus they found their way to Shirburn Castle, where they still remain.
+
+A little before 1836, this collection attracted the attention of a
+searching inquirer into points of mathematical history, the late Professor
+Rigaud,[495] who died in 1839. He examined the whole collection of letters,
+obtained Lord Macclesfield's consent to their publication, and induced the
+Oxford Press to bear the expense. It must be particularly remembered that
+there still remains at Shirburn Castle a {299} valuable mass of
+non-epistolary manuscripts. So far as we can see, the best chance of a
+further examination and publication lies in public encouragement of the
+collection now before us: the Oxford Press might be induced to extend its
+operations if it were found that the results were really of interest to the
+literary and scientific world. Rigaud died before the work was completed,
+and the publication was actually made by one of his sons, S. Jordan
+Rigaud,[496] who died Bishop of Antigua. But this publication was little
+noticed, for the reasons given. The completion now published consists of a
+sufficient table of contents, of the briefest kind, by Professor De Morgan,
+and an excellent index by the Rev. John Rigaud.[497] The work is now fairly
+started on its career.
+
+If we were charged to write a volume with the title "Small things in their
+connection with great," we could not do better than choose the small part
+of this collection of letters as our basis. The names, as well as the
+contents, are both great and small: the great names, those which are known
+to every mathematician who has any infusion of the history of his pursuit,
+are Briggs,[498] Oughtred, Charles Cavendish,[499] Gascoigne,[500] Seth
+Ward,[501] Wallis,[502] {300} Hu[y]gens,[503] Collins,[504] William
+Petty,[505] Hooke,[506] Boyle,[507] Pell,[508] Oldenburg,[509]
+Brancker,[510] Slusius,[511] Bertit,[512] Bernard,[513] Borelli,[514]
+Mouton,[515] Pardies,[516] Fermat,[517] Towneley,[518] Auzout,[519] {301}
+D. Gregory,[520] Halley,[521] Machin,[522] Montmort,[523] Cotes,[524]
+Jones,[525] Saunderson,[526] Reyneau,[527] Brook Taylor,[528]
+Maupertuis,[529] Bouguer,[530] La Condamine,[531] Folkes,[532]
+Macclesfield,[533] {302} Baker,[534] Barrow,[535] Flamsteed,[536] Lord
+Brounker,[537] J. Gregory,[538] Newton[539] and Keill.[540] To these the
+Museum collection adds the names of Thomas Digges,[541] Dee,[542] Tycho
+Brahe,[543] Harriot,[544] Lydyat,[545] Briggs,[546] Warner,[547] Tarporley,
+Pell,[548] Lilly,[549] Oldenburg,[550] Collins,[551] Morland.[552]
+
+{303}
+
+The first who appears on the scene is the celebrated Oughtred, who is
+related to have died of joy at the Restoration: but it should be added, by
+way of excuse, that he was eighty-six years old. He is an animal of extinct
+race, an Eton mathematician. Few Eton men, even of the minority which knows
+what a sliding rule is, are aware that the inventor was of their own school
+and college: but they may be excused, for Dr. Hutton,[553] so far as his
+Dictionary bears witness, seems not to have known it any more than they. A
+glance at one of his letters reminds us of a letter from the Astronomer
+Royal on the discovery of Neptune, which we printed March 20, 1847. Mr.
+Airy[554] there contends, and proves it both by Leverrier[555] and by
+Adams,[556] that the limited publication of a private letter is more
+efficient than the more general publication of a printed memoir. The same
+may be true of a dead letter, as opposed to a dead book. Our eye was caught
+by a letter of Oughtred (1629), containing systematic use of contractions
+for the words _sine_, _cosine_, etc., prefixed to the symbol of the angle.
+This is so very important a step, simple as it is, that Euler[557] is
+justly held to have greatly advanced trigonometry by its introduction.
+Nobody that we know of has noticed that Oughtred was master of the
+improvement, and willing to have taught it, if people would have learnt.
+After looking at his dead letter, we naturally turned to his dead book on
+trigonometry, and there we found the abbreviations _s_, _sco_, _t_, _tco_,
+_se_, _seco_, regularly established as part of the system of the work. But
+not one of those who have investigated the contending claims of Euler and
+Thomas {304} Simpson[558] has chanced to know of Oughtred's
+"Trigonometrie": and the present revival is due to his letter, not to his
+book.
+
+A casual reader, turning over the pages, would imagine that almost all the
+letters had been printed, either in the General Dictionary, or in
+Birch,[559] etc.: so often does the supplementary remark begin with "this
+letter has been printed in ----." For ourselves we thought, until we
+counted, that a large majority of the letters had been given, either in
+whole or in part. But the positive strikes the mind more forcibly than the
+negative: we find that all of which any portion has been in type makes up
+very little more than a quarter; the cases in which the whole letter is
+given being a minority of this quarter. The person who has been best
+ransacked is Flamsteed: of 36 letters from him, 34 had been previously
+given in whole or in part. Of 59 letters to and from Newton, only 17 have
+been culled.
+
+The letters have been modernized in spelling, and, to some extent, in
+algebraical notation; it also seems that conjectural methods of introducing
+interpolations into the text have been necessary. For all this we are
+sorry: the scientific value of the collection is little altered, but its
+literary value is somewhat lowered. But it could not be helped: the
+printers could not work from the originals, and Professor Rigaud had to
+copy everything himself. A fac-simile must have been the work of more time
+than he had to give: had he attempted it, his death would have cut short
+the whole undertaking, instead of allowing him to prepare everything but a
+preface, and to superintend the printing of one of the volumes. We may also
+add, that we believe we have notices of _all_ the letters in the
+Macclesfield collection. We judge this because several which are too
+trivial to print are numbered and described; and those would certainly not
+have been noticed if _any_ omissions had {305} been made. And we know that
+every letter was removed from Shirburn Castle to Oxford.
+
+Two persons emerge from oblivion in this series of letters. The first is
+Michael Dary,[560] an obscure mathematician, who was in correspondence with
+Newton and other stars. He was a gauger at Bristol, by the interest of
+Collins; afterwards a candidate for the mathematical school at Christ's
+Hospital, with a certificate from Newton: he was then a gunner in the
+Tower, and is lastly described by Wallis as "Mr. Dary, the tobacco-cutter,
+a knowing man in algebra." In 1674, Dary writes to Newton at Cambridge, as
+follows:--"Although I sent you three papers yesterday, I cannot refrain
+from sending you this. I have had fresh thoughts this morning." Two months
+afterwards poor Newton writes to Collins, "Mr. Dary is very solicitous
+about mathematics": but in spite of the persecution, he subscribes himself
+to Dary "your loving friend." Dary's _problem_ is that of finding the rate
+of interest of an annuity of which the value and term are given. Dary's
+_theorem_, which he seems to have invented specially for the solution of
+his problem, though it is of wide range, can be exhibited to mathematical
+readers even in our columns. In modern language, it is that the limit of
+[phi]^{_n_}_x_, when _n_ increases without limit, is a solution of [phi]_x_
+= _x_. We have mentioned the I. Newton to whom Dary looked up; we add a
+word about the one on whom he looked down. Dr. John Newton,[561] a sedulous
+publisher of logarithms, tables of interest, etc., who began his career
+before Isaac Newton, sometimes puzzles those who do not know him, when
+described as I. Newton. The scientific world was of opinion that all that
+was valuable in one of his works was taken from Dary's private
+communications.
+
+{306}
+
+The second character above alluded to is one who carried mathematical
+researches a far greater length than Newton himself: the assistance which
+he rendered in this respect, even to Newton, has never been acknowledged in
+modern times: though the work before us shows that his contemporaries were
+fully aware of it, and never thought of concealing it. In his theory of
+gravitation, in which, so far as he went, we have every reason to believe
+he was prior to Newton, he did not extend his calculations to the distance
+of the moon; his views in this matter were purely terrestrial, and led him
+to charge according to weight. He was John Stiles, the London and Cambridge
+carrier: his name is a household word in the Macclesfield Letters, and is
+even enshrined in the depths of Birch's quartos. Dary informs Newton--let
+us do his memory this justice--that he had paid John Stiles for the
+carriage. At the time when the railroad to Cambridge was opened, a
+correspondent recommended the directors, in our columns, to call an engine
+by the name of John Stiles, and never to let that name go off the road. We
+do not know whether the advice was followed: if not, we repeat it.
+
+Little points of life and manners come out occasionally. Baker, the author
+of a work on algebra much esteemed at the time, wrote to Collins that their
+circumstances are alike, "having a just and equal number of chargeable
+olive-branches, and being in the same predicament and blessed condemnation
+with you, not more preaching than unpaid, and preaching the art of
+contentment to others, am forced to practise it." But the last sentence of
+his letter runs as follows: "I have sent by the bearer ... twenty
+shillings, as a token to you; desiring you to accept of it, as a small
+taste from Yours, Thos. Baker." In our day, men of a station to pay parish
+taxes do not offer their friends hard money to buy liquor. But
+Flamsteed[562] writes to Collins as follows: "Last week he sent us down the
+counterpart, which {307} my father has scaled, and I return up to you by
+the carrier, with 5l. to be paid to Mr. Leneve for the writing, I have
+added 2s. 6d. over, which will pay the expenses and serve to drink, with
+him." This would seem as odd to us as it would have seemed thirty years ago
+that half-a-crown should pay carriage for a deed from Derby to London, and
+leave margin for a bottle of wine: in our day, the Post-office and the
+French treaty would just manage it between them. But Flamsteed does not
+limit his friend to one bottle; he adds, "If you expend more than the
+half-crown, I will make it good after Whitsuntide." Collins does not
+remember exactly where he had met James Gregory, and mentions two equally
+likely places thus: "Sir, it was once my good hap to meet with you in an
+alehouse or in Sion College." There is a little proof how universally the
+dinner-hour was twelve o'clock. Astronomers well know the method of finding
+time by equal altitudes of the sun before and after noon: Huyghens calls it
+"le moyen de deux egales hauteurs du soleil devant et apres _diner_."[563]
+
+There is one mention of "Mr. Cocker,[564] our famous English graver and
+writer, now a schoolmaster at Northampton." This is the true Cocker: his
+genuine works are specimens of writing, such as engraved copy-books,
+including some on arithmetic, with copper-plate questions and space for the
+working; also a book of forms for law-stationers, with specimens of legal
+handwriting. It is recorded somewhere that Cocker and another, whose name
+we forget, competed with the Italians in the beauty of their flourishes.
+This was his real fame: and in these matters he was great. The eighth
+edition of his book of law forms (1675), published shortly after Cocker's
+death, has a preface signed "J. H." This was John Hawkins, who became
+possessed of Cocker's papers--at least he said so--and {308} subsequently
+forged the famous Arithmetic,[565] a second work on Decimal Arithmetic, and
+an English dictionary, all attributed to Cocker. The proofs of this are set
+out in De Morgan's _Arithmetical Books_. Among many other corroborative
+circumstances, the clumsy forger, after declaring that Cocker to his dying
+day resisted strong solicitation to publish his Arithmetic, makes him write
+in the preface _Ille ego qui quondam_[566] of this kind: "I have been
+instrumental to the benefit of many, by virtue of those useful arts,
+writing and engraving; and do _now_, with the same _wonted alacrity_, cast
+this my arithmetical mite into the public treasury." The book itself is not
+comparable in merit to at least half-a-dozen others. How then comes Cocker
+to be the impersonation of Arithmetic? Unless some one can show proof,
+which we have never found, that he was so before 1756, the matter is to be
+accounted for thus.
+
+Arthur Murphy,[567] the dramatist, was by taste a man of letters, and ended
+by being the translator of Tacitus; though many do not know that the two
+are one. His friends had tried to make him a man of business; and no doubt
+he had been well plied with commercial arithmetic. His first dramatic
+performance, the farce of "The Apprentice," produced in 1756, is about an
+idle young man who must needs turn actor. Two of the best known books of
+the day in arithmetic were those of Cocker and Wingate.[568] Murphy chooses
+_Wingate_ to be the name of an old merchant who {309} delights in vulgar
+fractions, and _Cocker_ to be his arithmetical catchword--"You read
+Shakespeare! get Cocker's Arithmetic! you may buy it for a shilling on any
+stall; best book that ever was wrote!" and so on. The farce became very
+popular, and, as we believe, was the means of elevating Cocker to his
+present pedestal, where Wingate would have been, if his name had had the
+droller sound of the two to English ears.
+
+A notoriety of an older day turns up, Major-General Lambert.[569] The
+common story is that he was banished to Guernsey, where he passed thirty
+years in confinement, rearing and painting flowers. But Baker, in 1678,
+represents him as a prisoner at Plymouth, sending equations for solution as
+a challenge: probably his place of confinement was varied, and his
+occupation also.
+
+[General Lambert was removed to Plymouth, probably about 1668. His daughter
+captured the son of the Governor of Guernsey, who therefore probably was
+reckoned an unsafe custodier thenceforward; though he assured the king that
+he had turned the young couple out of doors, and had never given them a
+penny. Great importance was attached to Lambert's safe detention: probably
+the remaining republicans looked upon him as to be their next Cromwell, if
+such a thing were to be. There were standing orders to shoot him at once on
+the first appearance of any enemy before the island. See _Notes and
+Queries_, 3d S. iv. 89.]
+
+Collins informs James Gregory that "some of the Royal Academy wrote over to
+Mr. Oldenburg, who was desired to impart the same to the Council of the
+Royal Society, that the French King was willing to allow pensions to one or
+two learned Englishmen, but they never made any answer {310} to such a
+proposal." This was written in 1671, and the thing probably happened
+several years before. Mr. De Morgan communicated the account of the
+proposal to Lord Macaulay, who replied that he did not think that any
+Englishman _received_ a literary pension from Louis; but that there is a
+curious letter, about 1664, from the French Ambassador, in which he says
+that he has, by his master's orders, been making inquiries as to the state
+of learning in England, and that he is sorry to find that the best writer
+is _the infamous Miltonus_. On two such independent testimonies it may be
+held proved that the French King had attempted to buy a little adherence
+from English literature and science; and the silent contempt of the Royal
+Society is an honorable fact in their history.
+
+Another little bit of politics is as follows. Oughtred is informed that
+"Mr. Foster,[570] our Lecturer on Astronomy at Gresham College, is put out
+because he will not kneel down at the communion-table. A Scotsman [Mungo
+Murray], one that is _verbi bis minister_,[571] is now lecturer in Mr.
+Foster's place." Ward in his work on the Gresham Professors,[572]
+suppresses the reason, and the suppression lowers the character of his
+book. Foster was expelled in 1636, and re-elected on a vacancy in 1641,
+when Puritanism had gained strength.
+
+The correspondence of Newton would require deeper sifting than could be
+given in such an article as the present. The first of the letters (1669) is
+curious, as presenting the {311} appearance of forms belonging to the great
+calculus which, in this paragraph, we ought to call that of fluxions. We
+find, of the date February 18, 1669-70, what we believe is the earliest
+manifestation of that morbid part of Newton's temperament which has been so
+variously represented. He had solved a problem--being that which we have
+called Dary's--on which he writes as follows: "The solution of the annuity
+problem, if it will be of any use, you have my leave to insert into the
+_Philosophical Transactions_, so it be without my name to it. For I see not
+what there is desirable in public esteem, were I able to acquire and
+maintain it. It would perhaps increase my acquaintance, the thing which I
+chiefly study to decline."
+
+Three letters touch upon "the experiment of glass rubbed to cause various
+motions in bits of paper underneath": they are supplements to the account
+given by Newton to the Royal Society, and printed by Birch. It was Newton,
+so far as appears, who added _glass_ to the substances known to be
+electric. Soon afterwards we come to a little bit of the history of the
+appointment to the Mint. It has appeared from the researches of late years
+that Newton was long an aspirant for public employment: the only coolness
+which is known to have taken place between him and Charles Montague[573]
+[Halifax] arose out of his imagining that his friend was not in earnest
+about getting him into the public service. March 14, 1696, Newton writes
+thus to Halley: "And if the rumour of preferment for me in the Mint should
+hereafter, upon the death of Mr. Hoar [the comptroller], or any other
+occasion, be revived, I pray that you would {312} endeavour to obviate it
+by acquainting your friends that I neither _put in_ for _any_ place in the
+Mint, nor would meddle with _Mr. Hoar's place_, were it offered to me."
+This means that Mr. Hoar's place had been suggested, which Newton seems to
+have declined. Five days afterwards, Montague writes to Newton that he is
+to have the _Wardenship_. It is fair to Newton to say that in all
+probability this was not--or only in a smaller degree--a question of
+personal dignity, or of salary. It must by this time have been clear to him
+that the minister, though long bound to make him an object of patronage,
+was actually seeking him for the Mint, because he wanted both Newton's name
+and his talents for business--which he knew to be great--in the weighty and
+dangerous operation of restoring the coinage. It may have been, and
+probably was, the case that Newton had a tolerably accurate notion of what
+he would have to do, and of what degree of power would be necessary to
+enable him to do it in his own way.
+
+We have said that the non-epistolary manuscripts are still unexamined.
+There is a chance that one of them may answer a question of two centuries'
+standing, which is worth answering, because it has been so often asked.
+About 1640, Warner,[574] afterwards assisted by Pell,[575] commenced a
+table of _antilogarithms_, of the kind which Dodson[576] afterwards
+constructed anew and published. In the Museum collection there is inquiry
+after inquiry from Charles Cavendish,[577] first, as to when the
+_Analogics_, as he called them, would be finished; next, when they would be
+printed. Pell answers, in 1644, that Warner left his papers to a kinsman,
+who had become bankrupt, and proceeds thus:
+
+"I am not a little afraid that all Mr. Warner's papers, {313} and no small
+share of my labours therein, are seazed upon, and most unmathematically
+divided between the sequestrators and creditors, who (not being able to
+ballance the account where there appeare so many numbers, and much troubled
+at the sight of so many crosses and circles in the superstitious Algebra
+and that black art of Geometry) will, no doubt, determine once in their
+lives to become figure-casters, and so vote them all to be throwen into the
+fire, if some good body doe not reprieve them for pye-bottoms, for which
+purposes you know analogicall numbers are incomparably apt, if they be
+accurately calculated."
+
+Pell afterwards told Wallis[578] that the papers had fallen into the hands
+of Dr. Busby,[579] and Collins[580] writes that they were left in the hands
+of Dr. Thorndike,[581] a prebendary of Westminster; whence Rigaud[582]
+seems to say that Thorndike had left them to Dr. Busby. Birch[583] says
+that he procured for the Royal Society four boxes from Busby's trustees,
+containing papers of Warner and Pell: but there is no other tradition of
+such things in the Society. But in the Birch manuscripts at the British
+Museum, there turns up, as printed in what we call the Museum collection, a
+list of Warner's papers, with _Collins's_ receipt to Dr. Thorndike at the
+bottom, and engagement to restore them on demand. The date is December 14,
+1667; Wallis's statement being in 1693. It is possible that Busby may be a
+mistake altogether: he was very unlikely to have had charge of any
+mathematical papers: there may have been a confusion between the Prebendary
+of Westminster and the Head Master of Westminster School. If so, in all
+probability Thorndike handed {314} the cumbrous lot over to the notorious
+collector of mathematical papers, blessing himself that he got rid of them
+in a manner which would insure their return if he were called upon by the
+owners to restore them. It is much against this hypothesis that Dodson, who
+certainly recalculated, can say nothing more about Warner than a repetition
+of Wallis's story: though, had Collins kept the papers, they would probably
+have been in Jones's possession at the very time when Dodson, who was a
+friend of Jones and a user of his library, was engaged on his own
+computations. But even books, and still more manuscripts, are often
+singularly overlooked; and it remains not very improbable that Warner's
+table is now at Shirburn Castle, among the unexamined manuscripts.
+
+
+
+CYCLOMETRY AND STEEL PENS.
+
+_Redit labor actus in orbem._[584] Among the matters which have come to me
+since the Budget opened, there is a pamphlet of quadrature of two pages and
+a half from Professor Recalcati,[585] already mentioned. It ends with
+"Quelque objection qu'on fasse touchant les raisonnements ci-dessus on
+tombera toujours dans l'absurde."[586] A civil engineer--so he says--has
+made the quadrature "no longer a problem, but an axiom." As follows: "Take
+the quadrant of a circle whose circumference is given, square the quadrant
+which gives the true square of the circle. Because 30 / 4 = 7.5 x 7.5 =
+56.25 = the positive square of a circle whose circumference is 30."
+Brevity, the soul of wit, is the "wings of mighty-winds" to quadrature, and
+sends it "flying all abroad." A _surbodhicary_--something like M.A. or
+LL.D., I understand--at Calcutta, published in 1863 the division of an
+{315} angle into any odd number of parts, demonstration and all in--when
+the diagram is omitted--one page, good-sized, well-leaded type, small
+duodecimo. But in the Preface he acknowledges "sheer inability" to execute
+his task. Mr. William Dean, of Todmorden, in 1863, announced 3-9/64 as
+proved both practically and geometrically: he has been already mentioned
+anonymously. Next I have the tract of Don Juan Larriva, published at Leiria
+in 1856, and dedicated to Queen Victoria. Mr. W. Peters,[587] already
+mentioned, who has for some months been circulating diagrams on a card,
+publishes (August, 1865) _The Circle Squared_. He agrees with the
+Archpriest of St. Vitus. He hints that a larger publication will depend
+partly on the support he receives, and partly on the castigation, for which
+last, of course, he looks to me. Cyclometers have their several styles of
+wit; so have anticyclometers too, for that matter. Mr. Peters will not
+allow me any extra-journal being: I am essentially a quotation from the
+_Athenaeum_; "A. De Morgan" _et praeterea nihil_.[588] If he had to pay for
+keeping me set up, he would find out his mistake, and would be glad to
+compound handsomely for a stereotype. Next comes a magnificent sheet of
+pasteboard, printed on both sides. Having glanced at it and detected
+quadrature, I began methodically at the beginning--"By Royal Command," with
+the lion and unicorn, and all that comes between. Mercy on us! thought I to
+myself: has Her Majesty referred the question to the Judicial Committee of
+the Privy Council, where all the great difficulties go now-a-days, and is
+this proclamation the result? On reading further I was relieved by finding
+that the first side is entirely an advertisement of Joseph Gillott's[589]
+steel pens, with engraving of his {316} premises, and notice of novel
+application of his unrivalled machinery. The second side begins with "the
+circle rectified" by W. E. Walker,[590] who finds [pi] =
+3.141594789624155.... This is an off-shoot from an accurate geometrical
+rectification, on which is to be presumed Mr. Gillott's new machinery is
+founded. I have no doubt that Mr. Walker's error, which is only in the
+sixth place of decimals, will not hurt the pens, unless it be by the
+slightest possible increase of the tendency to open at the points. This
+arises from Mr. Walker having rectified above proof by .000002136034362....
+
+Lastly, I, even I myself, who have long felt that I was a quadrature below
+par, have solved the problem by means which, in the present state of the
+law of libel, I dare not divulge. But the result is permitted; and it goes
+far to explain all the discordances. The ratio of the circumference to the
+diameter is not always the same! Not that it varies with the radius; the
+geometers are right enough on that point: but it varies with the time, in a
+manner depending upon the difference of the true longitudes of the Sun and
+Moon. A friend of mine--at least until he misbehaved--insisted on the mean
+right ascensions: but I served him as Abraham served his guest in
+Franklin's parable. The true formula is, A and a being the Sun's and Moon's
+longitudes,
+
+  [pi] = 3-13/80 + 3/80 cos(A - a).
+
+Mr. James Smith obtained his quadrature at full moon; the Archpriest of St.
+Vitus and some others at new moon. Until I can venture to publish the
+demonstration, I recommend the reader to do as I do, which is to adopt
+3.14159..., and to think of the matter only at the two points of the lunar
+month at which it is correct. The _Nautical Almanac_ will no doubt give
+these points in a short time: I am in correspondence with the Admiralty,
+with nothing {317} to get over except what I must call a perverse notion on
+the part of the Superintendent of the _Almanac_, who suspects one
+correction depending on the Moon's latitude; and the Astronomer Royal leans
+towards another depending on the date of the Queen's accession. I have no
+patience with these men: what can the Moon's node of the Queen's reign
+possibly have to do with the ratio in question? But this is the way with
+all the regular men of science; Newton is to them etc. etc. etc. etc.
+
+The following method of finding the circumference of a circle (taken from a
+paper by Mr. S. Drach[591] in the _Phil. Mag._, Jan. 1863, Suppl.) is as
+accurate as the use of 3.14159265. From three diameters deduct
+8-thousandths and 7-millionths of a diameter; to the result add five per
+cent. We have then not quite enough; but the shortcoming is at the rate of
+about an inch and a sixtieth of an inch in 14,000 miles.
+
+
+
+JACOB BEHMEN.
+
+Though I have met with nothing but a little tract from the school of Jacob
+Behmen[592] (or Boehme; I keep to the old English version of his name), yet
+there has been more, and of a more recent date. I am told of an
+"Introduction to Theosophy [_Theo_ private, I suppose, as in theological];
+or, the Science of the Mystery of Christ," published in 1854, mostly from
+the writings of William Law[593]: and also of a volume of 688 pages, of the
+same year, printed for private circulation, containing notes for a
+biography of William Law. The editor of the first work wishes to grow "a
+{318} generation of perfect Christians" by founding a Theosophic College,
+for which he requests the public to raise a hundred thousand pounds. There
+is a good account of Jacob Behmen in the _Penny Cyclopaedia_. The author
+mentions inaccurate accounts, one of which he quotes, as follows: "He
+derived all his mystical and rapturous doctrine from Wood's[594] _Athenae
+Oxonienses_, Vol. I, p. 610, and _Hist. et Antiq. Acad. Oxon._, Vol. II, p.
+308." On which the author remarks that Wood was born after Behmen's death.
+There must have been a few words which slipped out: what is meant is that
+Behmen "derived his doctrine from _Robert Fludd_,[595] _for whom see_
+Wood's etc. etc." Even this is absurd enough: for Behmen began to publish
+in 1610, and Fludd in 1616. Fludd was a Rosicrucian, and a mystic of a
+different type from Behmen. I have some of his works, and could produce out
+of them paradoxes enough, according to our ways of thinking, to fit out a
+host. But the Rosicrucian system was a recognized school of its day, and
+Fludd, a man of great learning, had abettors enough in all which he
+advanced, and predecessors in most of it.
+
+[A Correspondent has recently sent a short summary of the claims of Jacob
+Behmen to rank higher than I have placed him. I shall gladly insert this
+summary in the book I contemplate, as a statement of what is said of Behmen
+far less liable to suspicion of exaggeration than anything I could write. I
+shall add a few extracts from Behmen himself, in support of his right to be
+in my list.]
+
+"_Jacob Behmen._--That Prof. De Morgan classes Jacob Behmen among
+paradoxers can only be attributed to the fact of his being avowedly
+unacquainted with the writings {319} of that author. Perhaps you may think
+a few words from one who knows them well of sufficient interest to the
+learned Professor, and your readers in general, to be worthy of space in
+your columns. The metaphysical system of Behmen--the most perfect and only
+true one--still awaits a qualified commentator. Behmen's countryman,
+Dionysius Andreas Freher,[596] who spent the greater part of his life in
+this country, and whose exposition of Behmen exists only in MS., filling
+many volumes, written in English, with the exception of two, written in
+German, with numerous beautiful, highly ingenious, and elaborate
+illustrations,--copies of some of which are in the British Museum, but all
+the originals of which are in the possession of the gentleman who is the
+editor of the two works alluded to by Professor De Morgan,--this Freher was
+the first to philosophically expound Behmen's system, which was afterwards,
+with the help of these MSS., as it were, popularized by William Law; but
+both Freher and Law confined themselves chiefly to its theological aspect.
+In Behmen, however, is to be found, not only the true ground of all
+theology, but also that of all physical science. He demonstrated with a
+fullness, accuracy, completeness and certainty that leave nothing to be
+desired, the innermost ground of Deity and Nature; and, confining myself to
+the latter, I can from my own knowledge assert, that in Behmen's writings
+is to be found the true and clear demonstration of every physical fact that
+has been discovered since his day. Thus, the science of electricity, which
+was not yet in existence when he wrote, is there anticipated; and not only
+does Behmen describe all the now known phenomena of that force, but he even
+gives us the origin, generation and birth of electricity itself. Again,
+positive evidence can be adduced that Newton derived all his knowledge of
+gravitation and its {320} laws from Behmen, with whom gravitation or
+attraction is, and very properly so, as he shows us, the first of the seven
+properties of Nature. The theory defended by Mr. Grove,[597] at the
+Nottingham meeting of last year, that all the apparently distinct causes of
+moral and physical phenomena are but so many manifestations of one central
+force, and that Continuity is the law of nature, is clearly laid down, and
+its truth demonstrated, by Behmen, as well as the distinction between
+spirit and matter, and that the moral and material world is pervaded by a
+sublime unity. And though all this was not admitted in Behmen's days,
+because science was not then sufficiently advanced to understand the deep
+sense of our author, many of his passages, then unintelligible, or
+apparently absurd, read by the light of the present age, are found to
+contain the positive enunciation of principles at whose discovery and
+establishment science has only just arrived by wearisome and painful
+investigations. Every new scientific discovery goes to prove his profound
+and intuitive insight into the most secret workings of nature; and if
+scientific men, instead of sharing the prejudice arising from ignorance of
+Behmen's system, would place themselves on the vantage ground it affords,
+they would at once find themselves on an eminence whence they could behold
+all the arcana of nature. Behmen's system, in fact, shows us the _inside_
+of things, while modern physical science is content with looking at the
+_outside_. Behmen traces back every outward manifestation or development to
+its one central root,--to that one central energy which, as yet, is only
+suspected; every link in the chain of his demonstration is perfect, and
+there is not one link wanting. He carries us from the out-births of the
+circumference, along the radius to the center, {321} or point, and beyond
+that even to the zero, demonstrating the constitution of the zero, or
+nothing, with mathematical precision. C. W. H."
+
+And so Behmen is no subject for the Budget! I waited until I should chance
+to light on one of his volumes, knowing that any volume would do, and
+almost any page. My first hap was on the second volume of the edition of
+1664 (4to, published by M. Richardson) and opening near the beginning, a
+turn or two brought me to page 13, where I saw about _sulphur_ and
+_mercurius_ as follows:
+
+
+
+"Thus SUL is the soul, in an herb it is the oil, and in man also, according
+to the spirit of _this_ world in the third principle, which is continually
+generated out of the anguish of the will in the mind, and the
+Brimstone-worm is the Spirit, which hath the fire and _burneth_: PHUR is
+the sour wheel in itself which causeth that.
+
+"_Mercurius_ comprehendeth all the four forms, even as the life springeth
+up, and yet hath not its dark beginning in the Center as the PHUR hath, but
+after the flash of fire, when the sour dark form is terrified, where the
+hardness is turned into pliant sharpness, and where the second will (_viz._
+the will of nature, which is called the Anguish) ariseth, there Mercurius
+hath its original. For MER is the shivering wheel, very horrible, sharp,
+venomous, and hostile; which assimulateth it thus in the sourness in the
+flash of fire, where the sour wrathful life _ariseth_. The syllable CU is
+the pressing out, of the _Anxious_ will of the mind, from Nature: which is
+climbing up, and _willeth_ to be out aloft. RI is the comprehension of the
+flash of fire, which in MER giveth a clear sound and tune. For the flash
+maketh the tune, and it is the Salt-Spirit which _soundeth_, and its form
+(or quality) is gritty like sand, and herein arise noises, sounds and
+voices, and thus CU comprehendeth the flash, and so the pressure is as a
+_wind_ which thrusteth, and giveth a spirit to the flash, so that it liveth
+and burneth. Thus the {322} syllable US is called the burning fire, which
+with the spirit continually driveth itself forth: and the syllable CU
+presseth continually upon the flash."
+
+
+
+Shades of Tauler[598] and Paracelsus,[599] how strangely you do mix! Well
+may Hallam call Germany the native soil of Mysticism. Had Behmen been the
+least of a scholar, he would not have divided _sulph-ur_ and _merc-ur-i-us_
+as he has done: and the inflexion _us_, that boy of all work, would have
+been rejected. I think it will be held that a writer from whom hundreds of
+pages like the above could be brought together, is fit for the Budget. If
+Sampson Arnold Mackay[600] had tied his etymologies to a mystical
+Christology, instead of a mystical infidelity, he might have had a school
+of followers. The nonsense about Newton borrowing gravitation from Behmen
+passes only with those who know neither what Newton did, nor what was done
+before him.
+
+The above reminds me of a class of paradoxers whom I wonder that I forgot;
+they are without exception the greatest bores of all, because they can put
+the small end of their paradox into any literary conversation whatever. I
+mean the people who have heard the local pronunciation of celebrated names,
+and attempt not only to imitate it, but to impose on others their broken
+German or Arabic, or what not. They also learn the vernacular names of
+those who are generally spoken of in their Latin forms; at least, they
+learn a few cases, and hawk them as evidences of erudition. They are
+miserably mistaken: scholarship, as a rule, {323} always accepts the
+vernacular form of a name which has vernacular celebrity. Hallam writes
+Behmen: his index-maker, rather superfluously, gives "_Behmen_ or Boehm."
+And he retains Melanchthon,[601] the name given by Reuchlin[602] to his
+little kinsman Schwartzerd, because the world has adopted it: but he will
+none of Capnio, the name which Reuchlin fitted on to himself, because the
+world has not adopted it. He calls the old forms pedantry: but he sees that
+the rejection of well-established results of pedantry would be greater
+pedantry still. The paradoxers assume the question that it is more
+_correct_ to sound a man by lame imitation of his own countrymen than as
+usual in the country in which the sound is to be made. Against them are,
+first, the world at large; next, an overpowering majority of those who know
+something about surnames and their history. Some thirty years ago--a
+fact--there appeared at the police-office a complainant who found his own
+law. In the course of his argument, he asked, "What does Kitty
+say?"--"Who's Kitty?" said the magistrate, "your wife, or your
+nurse?"--"Sir! I mean Kitty, the celebrated lawyer."--"Oh!" said the
+magistrate, "I suspect you mean Mr. Chitty,[603] the author of the great
+work on pleading."--"I do sir! But Chitty is an Italian name, and ought to
+be pronounced _Kitty_." This man was a full-blown flower: but there is many
+a modest bud; and all ought either to blush when seen or to waste their
+pronunciation on the desert air.
+
+{324}
+
+
+
+A PLEA FOR KING CUSTOM.
+
+I stand up for King Custom, or _Usus_, as Horace called him, with whom is
+_arbitrium_ the decision, and _jus_ the right, and _norma_ the way of
+deciding, simply because he has _potestas_ the power. He may admit one and
+another principle to advise: but Custom is not a constitutional king; he
+may listen to his cabinet, but he decides for himself: and if the ministry
+should resign, he blesses his stars and does without them. We have a
+glorious liberty in England of owning neither dictionary, grammar, nor
+spelling-book: as many as choose write by either of the three, and decide
+all disputed points their own way, those following them who please.
+
+Throughout this book I have called people by the names which denote them in
+their books, or by our vernacular names. This is the intelligible way of
+proceeding. I might, for instance (Vol. I, p. 44), have spoken of Charles
+de Bovelles,[604] of Lefevre d'Etaples,[605] of Pelerin,[606] and of
+Etienne.[607] But I prefer the old plan. Those who like another plan
+better, are welcome to substitute with a pen, when they know what to write;
+when they do not, it is clear that they would not have understood me if I
+had given modern names.
+
+The principal advisers of King Custom are as follows. First, there is
+Etymology, the _chiffonnier_, or general rag-merchant, who has made such a
+fortune of late years in his own business that he begins to be considered
+highly respectable. He gives advice which is more thought of than followed,
+partly on account of the fearful extremes into which he runs. He lately
+asked some boys of sixteen, at a matriculation examination in _English_, to
+what branch of {325} the Indo-Germanic family they felt inclined to refer
+the Pushto language, and what changes in the force of the letters took
+place in passing from Greek into Moeso-Gothic. Because all syllables were
+once words, he is a little inclined to insist that they shall be so still.
+He would gladly rule English with a Saxon rod, which might be permitted
+with a certain discretion which he has never attained: and when opposed, he
+defends himself with analogies of the Aryan family until those who hear him
+long for the discovery of an Athanasyus. He will transport a word beyond
+seas--he is recorder of Rhematopolis--on circumstantial evidence which
+looks like mystery gone mad; but, strange to say, something very often
+comes to light after sentence is passed which proves the soundness of the
+conviction.
+
+The next adviser is Logic, a swearing old justice of peace, quorum, and
+rotulorum, whose excesses brought on such a fit of the gout that for many
+years he was unable to move. He is now mending, and his friends say he has
+sown his wild oats. He has some influence with the educated subjects of
+Custom, and will have more, if he can learn the line at which interference
+ought to stop: with them he has succeeded in making an affirmative of two
+negatives; but the vulgar won't never have nothing to say to him. He has
+always railed at Milton for writing that Eve was the fairest of her
+daughters; but has never satisfactorily shown what Milton ought to have
+said instead.
+
+The third adviser has more influence with the mass of the subjects of King
+Custom than the other two put together; his name is Fiddlefaddle, the
+toy-shop keeper; and the other two put him forward to do their worst work.
+In return, he often uses their names without authority. He took Etymology
+to witness that _means_ to an end must be plural: and he would have any one
+method to be a _mean_. But Etymology proved him wrong, King Custom referred
+him to his Catechism, in which is "a means whereby we receive the same,"
+and Analogy--a subordinate of {326} Etymology--asked whether he thought it
+a great _new_ to hear that he was wrong. It was either this Fiddlefaddle,
+or Lindley Murray[608] his traveler, who persuaded the Miss Slipslops, of
+the Ladies Seminary, to put "The Misses Slipslop" over the gate. Sixty
+years ago, this bagman called at all the girls' schools, and got many of
+the teachers to insist on the pupils saying "Is it not" and "Can I not" for
+"Isn't it" and "Can't I": of which it came that the poor girls were
+dreadfully laughed at by their irreverent brothers when they went home for
+the holidays. Had this bad adviser not been severely checked, he might by
+this time have proposed our saying "The Queen's of England son," declaring,
+in the name of Logic, that the prince was the Queen's son, not England's.
+
+Lastly, there is Typography the metallurgist, an executive officer who is
+always at work in secret, and whose lawless mode of advising is often done
+by carrying his notions into effect without leave given. He it is who never
+ceases suggesting that the same word is not to occur in a second place
+within sight of the first. When the Authorized Version was first printed,
+he began this trick at the passage, "Let there be light, and there was
+light;" he drew a line on the proof under the second _light_, and wrote
+"_luminosity?_" opposite. He is strongest in the punctuations and other
+signs; he has a pepper-box full of commas always by his side. He puts
+everything under marks of quotation which he has ever heard before. An
+earnest preacher, in a very moving sermon, used the phrase Alas! and alack
+a day! Typography stuck up the inverted commas because he had read the old
+Anglo-Indian toast, "A lass and a lac a day!" If any one should have the
+sense to leave out of his Greek {327} the unmeaning scratches which they
+call accents, he goes to a lexicon and puts them in. He is powerful in
+routine; but when two routines interlace or overlap, he frequently takes
+the wrong one.
+
+Subject to bad advice, and sometimes misled for a season, King Custom goes
+on his quiet way and is sure to be right at last.
+
+ "Treason does never prosper: what's the reason?
+  Why, when it prospers, none dare call it treason."
+
+Language is in constant fermentation, and all that is thrown in, so far as
+it is not fit to assimilate, is thrown off; and this without any obvious
+struggle. In the meanwhile every one who has read good authors, from
+Shakspeare downward, knows what is and what is not English; and knows,
+also, that our language is not one and indivisible. Two very different
+turns of phrase may both be equally good, and as good as can be: we may be
+relieved of the consequences of contempt of one court by _habeas corpus_
+issuing out of another.
+
+
+
+TEST OF LANGUAGE.
+
+Hallam remarks that the Authorized Version of the Bible is not in the
+language of the time of James the First: that it is not the English of
+Raleigh or of Bacon. Here arises the question whether Raleigh and Bacon are
+the true expositors of the language of their time; and whether they were
+not rather the incipient promoters of a change which was successfully
+resisted by--among other things--the Authorized Version of the Testaments.
+I am not prepared to concede that I should have given to the English which
+would have been fashioned upon that of Bacon by imitators, such as they
+usually are, the admiration which is forced from me by Bacon's English from
+Bacon's pen. On this point we have a notable parallel. Samuel Johnson {328}
+commands our admiration, at least in his matured style: but we nauseate his
+followers. It is an opinion of mine that the works of the leading writers
+of an age are seldom the proper specimens of the language of their day,
+when that language is in its state of progression. I judge of a language by
+the colloquial idiom of educated men: that is, I take this to be the best
+medium between the extreme cases of one who is ignorant of grammar and one
+who is perched upon a style. Dialogue is what I want to judge by, and plain
+dialogue: so I choose Robert Recorde[609] and his pupil in the _Castle of
+Knowledge_, written before 1556. When Dr. Robert gets into his altitudes of
+instruction, he differs from his own common phraseology as much as probably
+did Bacon when he wrote morals and philosophy. But every now and then I
+come to a little plain talk about a common thing, of which I propose to
+show a specimen. Anything can be made to look old by such changes as
+_makes_ into _maketh_, with a little old spelling. I shall invert these
+changes, using the newer form of inflexion, and the modern spelling: with
+no other variation whatever.
+
+"_Scholar._ Yet the reason of that is easy enough to be conceived, for when
+the day is at the longest the Sun must needs shine the more time, and so
+must it needs shine the less time when the day is at the shortest: this
+reason I have heard many men declare.
+
+_Master._ That may be called a crabbed reason, for it {329} goes backward
+like a crab. The day makes not the Sun to shine, but the Sun shining makes
+the day. And so the length of the day makes not the Sun to shine long,
+neither the shortness of the day causes not [_sic_] the Sun to shine the
+lesser time, but contrariwise the long shining of the Sun makes the long
+day, and the short shining of the Sun makes the lesser day: else answer me
+what makes the days long or short?
+
+_Scholar._ I have heard wise men say that Summer makes the long days, and
+Winter makes the long nights.
+
+_Master._ They might have said more wisely, that long days make summer and
+short days make winter.
+
+_Scholar._ Why, all that seems one thing to me.
+
+_Master._ Is it all one to say, God made the earth, and the earth made God?
+Covetousness overcomes all men, and all men overcome covetousness?
+
+_Scholar._ No, not so; for here the effect is turned to be the cause, and
+the agent is made the patient.
+
+_Master._ So is it to say Summer makes long days, when you should say: Long
+days make summer.
+
+_Scholar._ I perceive it now: but I was so blinded with the vulgar error,
+that if you had demanded of me further what did make the summer, I had been
+like to have answered that green leaves do make summer; and the sooner by
+remembrance of an old saying that a year should come in which the summer
+should not be known but by the green leaves.
+
+_Master._ Yet this saying does not import that green leaves do make summer,
+but that they betoken summer; so are they the sign and not the cause of
+summer."
+
+I have taken a whole page of our author, without omission, that the reader
+may see that I do not pick out sentences convenient for my purpose. I have
+done nothing but alter the third person of the verb and the spelling: but
+great is the effect thereof. We say "the Sun shining makes the day";
+Recorde, "the Sonne shynynge maketh the daye." {330} These points apart, we
+see a resemblance between our English and that of three hundred years ago,
+in the common talk of educated persons, which will allow us to affirm that
+the language of the authorized Bible must have been very close to that of
+its time. For I cannot admit that much change can have taken place in fifty
+years: and the language of the version represents both our common English
+and that of Recorde with very close approximation. Take sentences from
+Bacon and Raleigh, and it will be apparent that these writers will be held
+to differ from all three, Recorde, the version, and ourselves, by
+differences of the same character. But we speak of Recorde's conversation,
+and of our own. We conclude that it is the plain and almost colloquial
+character of the Authorized Version which distinguishes it from the English
+of Bacon and Raleigh, by approximating it to the common idiom of the time.
+If any one will cast an eye upon the letters of instruction written by
+Cecil[610] and the Bishop of London to the translators themselves, or to
+the general directions sent to them in the King's name, he will find that
+these plain business compositions differ from the English of Bacon and
+Raleigh by the same sort of differences which distinguish the version
+itself.
+
+
+
+PRONUNCIATION.
+
+The foreign word, or the word of a district, or class of people, passes
+into the general vernacular; but it is long before the specially learned
+will acknowledge the right of those with whom they come in contact to
+follow general usage. The rule is simple: so long as a word is technical or
+local, those who know its technical or local pronunciation may reasonably
+employ it. But when the word has become general, the specialist is not very
+wise if he refuse to follow {331} the mass, and perfectly foolish if he
+insist on others following him. There have been a few who demanded that
+Euler should be pronounced in the German fashion:[611] Euler has long been
+the property of the world at large; what does it matter how his own
+countrymen pronounce the letters? Shall we insist on the French pronouncing
+_Newton_ without that final _tong_ which they never fail to give him? They
+would be wise enough to laugh at us if we did. We remember that a pedant
+who was insisting on all the pronunciations being retained, was met by a
+maxim in contradiction, invented at the moment, and fathered upon
+Kaen-foo-tzee,[612] an authority which he was challenged to dispute. Whom
+did you speak of? said the bewildered man of accuracy. Learn your own
+system, was the answer, before you impose it on others; Confucius says that
+too.[613]
+
+The old English has _fote_, _fode_, _loke_, _coke_, _roke_, etc., for
+_foot_, etc. And _above_ rhymes in Chaucer to _remove_. Suspecting that the
+broader sounds are the older, we may surmise that _remove_ and _food_ have
+retained their old sounds, and that _cook_, once _coke_, would have rhymed
+to our _Luke_, the vowel being brought a little nearer, perhaps, to the _o_
+in our present _coke_, the fuel, probably so called as used by cooks. If
+this be so, the Chief Justice _Cook_[614] of our lawyers, and the _Coke_
+(pronounced like the fuel) of the greater part of the world, are equally
+wrong. The lawyer has no right whatever to fasten his pronunciation upon
+us: even leaving aside the general custom, he cannot prove himself right,
+and is probably wrong. Those who {332} know the village of Rokeby
+(pronounced Rookby) despise the world for not knowing how to name Walter
+Scott's poem: that same world never asked a question about the matter, and
+the reception of the parody of _Jokeby_, which soon appeared, was a
+sufficient indication of their notion. Those who would fasten the hodiernal
+sound upon us may be reminded that the question is, not what they call it
+now, but what it was called in Cromwell's time. Throw away general usage as
+a lawgiver, and this is the point which emerges. Probably _R[=u]ke-by_
+would be right, with a little turning of the Italian [=u] towards [=o] of
+modern English.
+
+[Some of the above is from an old review. I do not always notice such
+insertions: I take nothing but my own writings. A friend once said to me,
+"Ah! you got that out of the _Athenaeum_!" "Excuse me," said I. "the
+_Athenaeum_ got that out of me!"]
+
+
+
+APOLOGIES TO CLUVIER.
+
+It is part of my function to do justice to any cyclometers whose methods
+have been wrongly described by any orthodox sneerers (myself included). In
+this character I must notice _Dethlevus Cluverius_,[615] as the Leipzig
+Acts call him (probably Dethleu Cluvier), grandson of the celebrated
+geographer, Philip Cluvier. The grandson was a Fellow of the Royal Society,
+elected on the same day as Halley,[616] November 30, 1678: I suppose he
+lived in England. This {333} man is quizzed in the Leipzig Acts for 1686;
+and, if Montucla insinuate rightly, by Leibnitz, who is further suspected
+of wanting to embroil Cluvier with his own opponent Nieuwentiit,[617] on
+the matter of infinitesimals. So far good: I have nothing against Leibnitz,
+who though he was ironical, told us what he laughed at. But Montucla has
+behaved very unfairly: he represents Cluvier as placing the essence of his
+method in the solution of the problem _construere mundum divinae menti
+analogum_, to construct a world corresponding to the divine mind. Nothing
+to begin with: no way of proceeding. Now, it ought to have been _ex data
+linea construere_,[618] etc.: there is a given line, which is something to
+go on. Further, there is a way of proceeding: it is to find the product of
+1, 2, 3, 4, etc. for ever. Moreover, Montucla charges Cluvier with
+_unsquaring_ the parabola, which Archimedes had squared as tight as a
+glove. But he never mentions how very nearly Cluvier agrees with the Greek:
+they only differ by 1 divided by 3n^2, where n is the infinite number of
+parts of which a parabola is composed. This must have been the conceit that
+tickled Leibnitz, and made him wish that Cluvier and Nieuwentiit should
+fight it out. Cluvier, was admitted, on terms of irony, into the Leipzig
+Acts: he appeared on a more serious footing in London. It is very rare for
+one cyclometer to refute another: _les corsaires ne se battent pas_.[619]
+The only instance I recall is that of M. Cluvier, who (_Phil. Trans._,
+1686, No. 185) refuted M. Mallemont de Messange,[620] who {334} published
+at Paris in 1686. He does it in a very serious style, and shows himself a
+mathematician. And yet in the year in which, in the _Phil. Trans._, he was
+a geometer, and one who rebukes his squarer for quoting Matthew xi. 25, in
+that very year he was the visionary who, in the Leipzig Acts, professed to
+build a world resembling the divine mind by multiplying together 1, 2, 3,
+4, etc. up to infinity.
+
+
+
+THE RAINBOW PARADOX.
+
+There is a very pretty opening for a paradox which has never found its
+paradoxer in print. The philosophers teach that the rainbow is not
+material: it comes from rain-drops, but those rain-drops do not _take_
+color. They only _give_ it, as lenses and mirrors; and each one drop gives
+_all_ the colors, but throws them in different directions. Accordingly, the
+same drop which furnishes red light to one spectator will furnish violet to
+another, properly placed. Enter the paradoxer whom I have to invent. The
+philosopher has gulled you nicely. Look into the water, and you will see
+the reflected rainbow: take a looking-glass held sideways, and you see
+another reflection. How could this be, if there were nothing colored to
+reflect? The paradoxer's facts are true: and what are called the reflected
+rainbows are _other_ rainbows, caused by those _other_ drops which are
+placed so as to give the colors to the eye after reflection, at the water
+or the looking-glass. A few years ago an artist exhibited a picture with a
+rainbow and its apparent reflection: he simply copied what he had seen.
+When his picture was examined, some started the idea that there could be no
+reflection of a rainbow; they were right: they inferred that the artist had
+made a mistake; they were wrong. When it was explained, some agreed and
+some dissented. Wanted, {335} immediately, an able paradoxer: testimonials
+to be forwarded to either end of the rainbow, No. 1. No circle-squarer need
+apply, His Variegatedness having been pleased to adopt 3.14159... from Noah
+downwards.
+
+
+
+TYCHO BRAHE REVIVED.
+
+The system of Tycho Brahe,[621] with some alteration and addition, has been
+revived and contended for in our own day by a Dane, W. Zytphen,[622] who
+has published _The Motion of the Sun in the Universe_, (second edition)
+Copenhagen, 1865, 8vo, and _Le Mouvement Sideral_, 1865, 8vo. I make an
+extract.
+
+"How can one explain Copernically that the velocity of the Moon must be
+added to the velocity of the Earth on the one place in the Earth's orbit,
+to learn how far the Moon has advanced from one fixed star to another; but
+in another place in the orbit these velocities must be subtracted (the
+movements taking place in opposite directions) to attain the same result?
+In the Copernican and other systems, it is well known that the Moon,
+abstracting from the insignificant excentricity of the orbit, always in
+twenty-four hours performs an equally long distance. Why has Copernicus
+never been denominated Fundamentus or Fundator? Because he has never
+convinced anybody so thoroughly that this otherwise so natural epithet has
+occurred to the mind."
+
+Really the second question is more effective against Newton than against
+Copernicus; for it upsets gravity: the first is of great depth.
+
+{336}
+
+
+
+JAMES SMITH WILL NOT DOWN.
+
+The _Correspondent_ journal makes a little episode in the history of my
+Budget (born May, 1865, died April, 1866). It consisted entirely of letters
+written by correspondents. In August, a correspondent who signed "Fair
+Play"--and who I was afterwards told was a lady--thought it would be a good
+joke to bring in the Cyclometers. Accordingly a letter was written,
+complaining that though Mr. Sylvester's[623] demonstration of Newton's
+theorem--then attracting public attention--was duly lauded, the possibly
+greater discovery of the quadrature seemed to be blushing unseen, and
+wasting etc. It went on as follows:
+
+"Prof. De Morgan, who, from his position in the scientific world, might
+fairly afford to look favourably on less practised efforts than his own,
+seems to delight in ridiculing the discoverer. Science is, of course, a
+very respectable person when he comes out and makes himself useful in the
+world [it must have been a lady; each sex gives science to the other]: but
+when, like a monk of the Middle Ages, he shuts himself up [it must have
+been a lady; they always snub the bachelors] in his cloistered cell,
+repeating his mumpsimus from day to day, and despising the labourers on the
+outside, we begin to think of Galileo,[624] Jenner,[625] Harvey,[626] and
+other glorious trios, who have been contemned ..."
+
+The writer then called upon Mr. James Smith[627] to come {337} forward. The
+irony was not seen; and that day fortnight appeared the first of more than
+thirty letters from his pen. Mr. Smith was followed by Mr. Reddie,[628]
+Zadkiel,[629] and others, on their several subjects. To some of the letters
+I have referred; to others I shall come. The _Correspondent_ was to become
+a first-class scientific journal; the time had arrived at which truth had
+an organ: and I received formal notice that I could not stifle it by
+silence, nor convert it into falsehood by ridicule. When my reader sees my
+extracts, he will readily believe my declaration that I should have been
+the last to stifle a publication which was every week what James Mill[630]
+would call a dose of capital for my Budget. A few anti-paradoxers brought
+in common sense: but to the mass of the readers of the journal it all
+seemed to be the difference between Tweedledum and Tweedledee. Some said
+that the influx of scientific paradoxes killed the journal: but my belief
+is that they made it last longer than it otherwise would have done. Twenty
+years ago I recommended the paradoxers to combine and publish their views
+in a common journal: with a catholic editor, who had no pet theory, but a
+stern determination not to exclude anything merely for absurdity. I suspect
+it would answer very well. A strong title, or motto, would be wanted: not
+so coarse as was roared out in a Cambridge mob when I was an
+undergraduate--"No King! No Church! No House of Lords! No nothing, blast
+me!"--but something on that _principle_.
+
+At the end of 1867 I addressed the following letter to the _Athenaeum_:
+
+PSEUDOMATH, PHILOMATH, AND GRAPHOMATH.
+
+_December 31, 1867_
+
+Many thanks for the present of Mr. James Smith's letters {338} of Sept. 28
+and of Oct. 10 and 12. He asks where you will be if you read and digest his
+letters: you probably will be somewhere first. He afterwards asks what the
+WE of the _Athenaeum_ will be if, finding it impossible to controvert, it
+should refuse to print. I answer for you, that We-We of the _Athenaeum_, not
+being Wa-Wa the wild goose, so conspicuous in "Hiawatha," will leave what
+controverts itself to print itself, if it please.
+
+_Philomath_ is a good old word, easier to write and speak than
+_mathematician_. It wants the words between which I have placed it. They
+are not well formed: _pseudomathete_ and _graphomathete_ would be better:
+but they will do. I give an instance of each.
+
+The _pseudomath_ is a person who handles mathematics as the monkey handled
+the razor. The creature tried to shave himself as he had seen his master
+do; but, not having any notion of the angle at which the razor was to be
+held, he cut his own throat. He never tried a second time, poor animal! but
+the pseudomath keeps on at his work, proclaims himself clean-shaved, and
+all the rest of the world hairy. So great is the difference between moral
+and physical phenomena! Mr. James Smith is, beyond doubt, the great
+pseudomath of our time. His 3-1/8 is the least of a wonderful chain of
+discoveries. His books, like Whitbread's barrels, will one day reach from
+Simpkin & Marshall's to Kew, placed upright, or to Windsor laid
+length-ways. The Queen will run away on their near approach, as Bishop
+Hatto did from the rats: but Mr. James Smith will follow her were it to
+John o' Groats.
+
+The _philomath_, for my present purpose, must be exhibited as giving a
+lesson to presumption. The following anecdote is found in Thiebault's[631]
+_Souvenirs de vingt ans de sejours a Berlin_, published in 1804. The book
+itself got a high character for truth. In 1807 Marshal Mollendorff[632]
+{339} answered an inquiry of the Duc de Bassano,[633] by saying that it was
+the most veracious of books, written by the most honest of men. Thiebault
+does not claim personal knowledge of the anecdote, but he vouches for its
+being received as true all over the north of Europe.[634]
+
+Diderot[635] paid a visit to Russia at the invitation of Catherine the
+Second. At that time he was an atheist, or at least talked atheism: it
+would be easy to prove him either one thing or the other from his writings.
+His lively sallies on this subject much amused the Empress, and all the
+younger part of her Court. But some of the older courtiers suggested that
+it was hardly prudent to allow such unreserved exhibitions. The Empress
+thought so too, but did not like to muzzle her guest by an express
+prohibition: so a plot was contrived. The scorner was informed that an
+eminent mathematician had an algebraical proof of the existence of God,
+which he would communicate before the whole Court, if agreeable. Diderot
+gladly consented. The mathematician, who is not named, was Euler.[636] He
+came to Diderot with the gravest air, and in a tone of perfect conviction
+said, "_Monsieur!_
+
+  (a + b^n)/n = x
+
+_donc Dieu existe; repondez!_"[637] Diderot, to whom algebra was Hebrew,
+though this is expressed in a very roundabout way by Thiebault--and whom we
+may suppose to have expected some verbal argument of alleged algebraical
+closeness, was disconcerted; while peals of laughter sounded on all sides.
+Next day he asked permission to return to France, which was granted. An
+algebraist would have {340} turned the tables completely, by saying,
+"Monsieur! vous savez bien que votre raisonnement demande le developpement
+de x suivant les puissances entieres de n".[638] Goldsmith could not have
+seen the anecdote, or he might have been supposed to have drawn from it a
+hint as to the way in which the Squire demolished poor Moses.
+
+The _graphomath_ is a person who, having no mathematics, attempts to
+describe a mathematician. Novelists perform in this way: even Walter Scott
+now and then burns his fingers. His dreaming calculator, Davy Ramsay,
+swears "by the bones of the immortal Napier." Scott thought that the the
+philomaths worshiped relics: so they do, in one sense. Look into
+Hutton's[639] Dictionary for _Napier's Bones_, and you shall learn all
+about the little knick-knacks by which he did multiplication and division.
+But never a bone of his own did he contribute; he preferred elephants'
+tusks. The author of _Headlong Hall_[640] makes a grand error, which is
+quite high science: he says that Laplace proved the precession of the
+equinoxes to be a periodical inequality. He should have said the variation
+of the obliquity. But the finest instance is the following: Mr.
+Warren,[641] in his well-wrought tale of the martyr-philosopher, was
+incautious enough to invent the symbols by which his _savant_ satisfied
+himself Laplace[642] was right on a doubtful point. And this is what he put
+together--
+
+  [sqrt]-3a^2, [rectangle]y^2 / z^2 + 9 - n = 9, n x log e.
+
+Now, to Diderot and the mass of mankind this might be Laplace all over:
+and, in a forged note of Pascal, would {341} prove him quite up to
+gravitation. But I know of nothing like it, except in the lately received
+story of the American orator, who was called on for some Latin, and
+perorated thus: "Committing the destiny of the country to your hands,
+Gentlemen, I may without fear declare, in the language of the noble Roman
+poet,
+
+  E pluribus unum,
+  Multum in parvo,
+  Ultima Thule,
+  Sine qua non."[643]
+
+But the American got nearer to Horace than the martyr-philosopher to
+Laplace. For all the words are in Horace, except _Thule_, which might have
+been there. But [rectangle] is not a symbol wanted by Laplace; nor can we
+see how it could have been; in fact, it is not recognized in algebra. As to
+the junctions, etc., Laplace and Horace are about equally well imitated.
+
+Further thanks for Mr. Smith's letters to you of Oct. 15, 18, 19, 28, and
+Nov. 4, 15. The last of these letters has two curious discoveries. First,
+Mr. Smith declares that he has _seen_ the editor of the _Athenaeum_: in
+several previous letters he mentions a name. If he knew a little of
+journalism he would be aware that editors are a peculiar race, obtained by
+natural selection. They are never seen, even by their officials; only heard
+down a pipe. Secondly, "an ellipse or oval" is composed of four arcs of
+circles. Mr. Smith has got hold of the construction I was taught, when a
+boy, for a pretty four-arc oval. But my teachers knew better than to call
+it an ellipse: Mr. Smith does not; but he produces from it such
+confirmation of 3-1/8 as would convince any _honest_ editor.
+
+Surely the cyclometer is a Darwinite development of a spider, who is always
+at circles, and always begins again when his web is brushed away. He
+informs you that he {342} has been privileged to discover truths unknown to
+the scientific world. This we know; but he proceeds to show that he is
+equally fortunate in art. He goes on to say that he will make use of you to
+bring those truths to light, "just as an artist makes use of a dummy for
+the purpose of arranging his drapery." The painter's lay-figure is for
+flowing robes; the hairdresser's dummy is for curly locks. Mr. James Smith
+should read Sam Weller's pathetic story of the "four wax dummies." As to
+_his_ use of a dummy, it is quite correct. When I was at University
+College, I walked one day into a room in which my Latin colleague was
+examining. One of the questions was, "Give the lives and fates of Sp.
+Maelius,[644] and Sp. Cassius."[645] Umph! said I, surely all know that
+Spurius Maelius was whipped for adulterating flour, and that Spurius Cassius
+was hanged for passing bad money. Now, a robe arranged on a dummy would
+look just like the toga of Cassius on the gallows. Accordingly, Mr. Smith
+is right in the drapery-hanger which he has chosen: he has been detected in
+the attempt to pass bad circles. He complains bitterly that his geometry,
+instead of being read and understood by you, is handed over to me to be
+treated after my scurrilous fashion. It is clear enough that he would
+rather be handled in this way than not handled at all, or why does he go on
+writing? He must know by this time that it is a part of the institution
+that his "untruthful and absurd trash" shall be distilled into mine at the
+rate of about 3-1/8 pages of the first to one column of the second. Your
+readers will never know how much they gain by the process, until Mr. James
+Smith publishes it all in a big book, or until they get hold of what he has
+already published. I have six pounds avoirdupois of pamphlets and letters;
+and there is more than half a pound of letters {343} written to you in the
+last two months. Your compositor must feel aggrieved by the rejection of
+these clearly written documents, without erasures, and on one side only.
+Your correspondent has all the makings of a good contributor, except the
+knowledge of his subject and the sense to get it. He is, in fact, only a
+mask: of whom the fox
+
+ "O quanta species, inquit, cerebrum non habet."[646]
+
+I do not despair of Mr. Smith on any question which does not involve that
+unfortunate two-stick wicket at which he persists in bowling. He has
+published many papers; he has forwarded them to mathematicians: and he
+cannot get answers; perhaps not even readers. Does he think that he would
+get more notice if you were to print him in your journal? Who would study
+his columns? Not the mathematician, we know; and he knows. Would others?
+His balls are aimed too wide to be blocked by any one who is near the
+wicket. He has long ceased to be worth the answer which a new invader may
+get. Rowan Hamilton,[647] years ago, completely knocked him over; and he
+has never attempted to point out any error in the short and easy method by
+which that powerful investigator condescended to show that, be right who
+may, he must be wrong. There are some persons who feel inclined to think
+that Mr. Smith should be argued with: let those persons understand that he
+has been argued with, refuted, and has never attempted to stick a pen into
+the refutation. He stated that it was a remarkable paradox, easily
+explicable; and that is all. After this evasion, Mr. James Smith is below
+the necessity of being told that he is unworthy of answer. His friends
+complain that I do nothing but _chaff_ him. Absurd! I winnow him; and if
+nothing but chaff results, whose fault is that? I am usefully employed: for
+he is the type of a class which ought to be known, and which I have done
+much to make known.
+
+{344}
+
+Nothing came of this until July 1869, when I received a reprint of the
+above letter, with a comment, described as Appendix D of a work in course
+of publication on the geometry of the circle. The _Athenaeum_ journal
+received the same: but the Editor, in his private capacity, received the
+whole work, being _The Geometry of the Circle and Mathematics as applied to
+Geometry by Mathematicians, shown to be a mockery, delusion, and a snare_,
+Liverpool, 8vo, 1869. Mr. J. S. here appears in deep fight with Professor
+Whitworth,[648] and Mr. Wilson,[649] the author of the alleged amendment of
+Euclid. How these accomplished mathematicians could be inveigled into
+continued discussion is inexplicable. Mr. Whitworth began by complaining of
+Mr. Smith's attacks upon mathematicians, continued to correspond after he
+was convinced that J. S. proved an arc and its chord to be equal, and only
+retreated when J. S. charged him with believing in 3-1/8, and refusing
+acknowledgment. Mr. Wilson was introduced to J. S. by a volunteer defense
+of his geometry from the assaults of the _Athenaeum_. This the editor would
+not publish; so J. S. sent a copy to Mr. Wilson himself. Some
+correspondence ensued, but Mr. Wilson soon found out his man, and withdrew.
+
+There is a little derision of the _Athenaeum_ and a merited punishment for
+"that unscrupulous critic and contemptible mathematical twaddler, De
+Morgan."
+
+
+
+MR. REDDIE'S ASTRONOMY.
+
+At p. 183 I mentioned Mr. Reddie,[650] the author of _Vis Inertiae Victa_
+and of _Victoria toto coelo_,[651] which last is not {345} an address to
+the whole heaven, either from a Roman Goddess or a British Queen, whatever
+a scholar may suppose. Between these Mr. Reddie has published _The
+Mechanics of the Heavens_, 8vo, 1862: this I never saw until he sent it to
+me, with an invitation to notice it, he very well knowing that it would
+catch. His speculations do battle with common notions of mathematics and of
+mechanics, which, to use a feminine idiom, he blasphemes so you can't
+think! and I suspect that if you do not blaspheme them too, _you_ can't
+think. He appeals to the "truly scientific," and would be glad to have
+readers who have read what he controverts, i.e., Newton's _Principia_: I
+wish he may get them; I mean I hope he may obtain them. To none but these
+would an account of his speculations be intelligible: I accordingly
+disposed of him in a very short paragraph of description. Now many
+paradoxers desire notice, even though it be disparaging. I have letters
+from more than one--besides what have been sent to the Editor of the
+_Athenaeum_--complaining that they are not laughed at; although they deserve
+it, they tell me, as much as some whom I have inserted. Mr. Reddie informs
+me that I have not said a single word against his books, though I have
+given nearly a column to sixteen-string arithmetic, and as much to
+animalcule universes. What need to say anything to readers of Newton
+against a book from which I quoted that revolution by gravitation is
+_demonstrably_ impossible? It would be as useless as evidence against a man
+who has pleaded guilty. Mr. Reddie derisively thanks me for "small
+mercies"; he wrote me private letters; he published them, and more, in the
+_Correspondent_. He gave me, _pro viribus suis_,[652] such a dressing you
+can't think, both for my Budget non-notice, and for reviews which he
+assumed me to have written. He outlawed himself by declaring
+(_Correspondent_, Nov. 11, 1856) that I--in a review--had made a quotation
+which was "garbled, evidently on purpose {346} to make it appear that" he
+"was advocating solely a geocentric hypothesis, which is not true." In
+fact, he did his best to get larger "mercy." And he shall have it; and at a
+length which shall content him, unless his mecometer be an insatiable
+apparatus. But I fear that in other respects I shall no more satisfy him
+than the Irish drummer satisfied the poor culprit when, after several times
+changing the direction of the stroke at earnest entreaty, he was at last
+provoked to call out, "Bad cess to ye, ye spalpeen! strike where one will,
+there's no _plasing_ ye!"
+
+Mr. Reddie attaches much force to Berkeley's[653] old arguments against the
+doctrine of fluxions, and advances objections to Newton's second section,
+which he takes to be new. To me they appear "such as have been often made,"
+to copy a description given in a review: though I have no doubt Mr. Reddie
+got them out of himself. But the whole matter comes to this: Mr. Reddie
+challenged answer, especially from the British Association, and got none.
+He presumes that this is because he is right, and cannot be answered: the
+Association is willing to risk itself upon the counter-notion that he is
+wrong, and need not be answered; because so wrong that none who could
+understand an answer would be likely to want one.
+
+Mr. Reddie demands my attention to a point which had already particularly
+struck me, as giving the means of showing to _all_ readers the kind of
+confusion into which paradoxers are apt to fall, in spite of the clearest
+instruction. It is a very honest blunder, and requires notice: it may
+otherwise mislead some, who may suppose that no one able to read could be
+mistaken about so simple a matter, {347} let him be ever so wrong about
+Newton. According to his own mis-statement, in less than five months he
+made the Astronomer Royal abandon the theory of the solar motion in space.
+The announcement is made in August, 1865, as follows: the italics are not
+mine:
+
+    "The third (_Victoria ..._), although only published in September,
+    1863, has already had its triumph. _It is the book that forced the
+    Astronomer Royal of England, after publicly teaching the contrary for
+    years, to come to the conclusion, "strange as it may appear," that "the
+    whole question of solar motion in space is at the present time in doubt
+    and abeyance."_ This admission is made in the Annual Report of the
+    Council of the Royal Astronomical Society, published in the Society's
+    _Monthly Notices_ for February, 1864."
+
+It is added that solar motion is "full of self-contradiction, which "the
+astronomers" simply overlooked, but which they dare not now deny after
+being once pointed out."
+
+The following is another of his accounts of the matter, given in the
+_Correspondent_, No. 18, 1865:
+
+    "... You ought, when you came to put me in the 'Budget,' to have been
+    aware of the Report of the Council of the Royal Astronomical Society,
+    where it appears that Professor Airy,[654] with a better appreciation
+    of my demonstrations, had admitted--'strange,' say the Council, 'as it
+    may appear,'--that 'the whole question of solar motion in space [and
+    here Mr. Reddie omits some words] is now in _doubt and abeyance_.' You
+    were culpable as a public teacher of no little pretensions, if you were
+    'unaware' of this. If aware of it, you ought not to have suppressed
+    such an important testimony to my really having been 'very successful'
+    in drawing the teeth of the pegtops, though you thought them so firmly
+    fixed. And if you still suppress {348} it, in your Appendix, or when
+    you reprint your 'Budget,' you will then be guilty of a _suppressio
+    veri_, also of further injury to me, who have never injured you...."
+
+Mr. Reddie must have been very well satisfied in his own mind before he
+ventured such a challenge, with an answer from me looming in the distance.
+The following is the passage of the Report of the Council, etc., from which
+he quotes:
+
+    "And yet, strange to say, notwithstanding the near coincidence of all
+    the results of the before-mentioned independent methods of
+    investigation, the inevitable logical inference deduced by Mr. Airy is,
+    that the whole question of solar motion in space, _so far at least as
+    accounting for the proper motion of the stars is concerned_, [I have
+    put in italics the words omitted by Mr. Reddie] appears to remain at
+    this moment in doubt and abeyance."
+
+Mr. Reddie has forked me, as he thinks, on a dilemma: if unaware, culpable
+ignorance; if aware, suppressive intention. But the thing is a _trilemma_,
+and the third horn, on which I elect to be placed, is surmounted by a
+doubly-stuffed seat. First, Mr. Airy has not changed his opinion about the
+_fact_ of solar motion in space, but only suspends it as to the sufficiency
+of present means to give the amount and direction of the motion. Secondly,
+all that is alluded to in the Astronomical Report was said and printed
+before the Victoria proclamation appeared. So that the author, instead of
+drawing the tooth of the Astronomer Royal's pegtop, has burnt his own
+doll's nose.
+
+William Herschel,[655] and after him about six other astronomers, had aimed
+at determining, by the proper motions of the stars, the point of the
+heavens towards which the solar system is moving: their results were
+tolerably accordant. Mr. Airy, in 1859, proposed an improved method, and,
+applying it to stars of large proper motion, produced {349} much the same
+result as Herschel. Mr. E. Dunkin,[656] one of Mr. Airy's staff at
+Greenwich, applied Mr. Airy's method to a very large number of stars, and
+produced, again, nearly the same result as before. This paper was read to
+the Astronomical Society in _March_, 1863, was printed in abstract in the
+_Notice_ of that month, was printed in full in the volume then current, and
+was referred to in the Annual Report of the Council in _February_, 1864,
+under the name of "the Astronomer Royal's elaborate investigation, as
+exhibited by Mr. Dunkin." Both Mr. Airy and Mr. Dunkin express grave doubts
+as to the sufficiency of the data: and, regarding the coincidence of all
+the results as highly curious, feel it necessary to wait for calculations
+made on better data. The report of the Council states these doubts. Mr.
+Reddie, who only published in _September_, 1863, happened to see the Report
+of February, 1864, assumes that the doubts were then first expressed, and
+declares that his book of September had the triumph of forcing the
+Astronomer Royal to abandon the _fact_ of motion of the solar system by the
+February following. Had Mr. Reddie, when he saw that the Council were
+avowedly describing a memoir presented some time before, taken the
+precaution to find out _when_ that memoir was presented, he would perhaps
+have seen that doubts of the results obtained, expressed by one astronomer
+in March, 1863, and by another in 1859, could not have been due to his
+publication of September, 1863. And any one else would have learnt that
+neither astronomer doubts the _solar motion_, though both doubt the
+sufficiency of present means to determine its _amount_ and _direction_.
+This is implied in the omitted words, which Mr. Reddie--whose omission
+would have been dishonest if he had seen their meaning--no doubt took for
+pleonasm, superfluity, overmuchness. The rashness which pushed him headlong
+{350} into the quillet that _his_ thunderbolt had stopped the chariot of
+the Sun and knocked the Greenwich Phaeton off the box, is the same which
+betrayed him into yet grander error--which deserves the full word,
+_quidlibet_--about the _Principia_ of Newton. There has been no change of
+opinion at all. When a person undertakes a long investigation, his opinion
+is that, at a certain date, there is _prima facie_ ground for thinking a
+sound result may be obtained. Should it happen that the investigation ends
+in doubt upon the sufficiency of the grounds, the investigator is not put
+in the wrong. He knew beforehand that there was an alternative: and he
+takes the horn of the alternative indicated by his calculations. The two
+sides of this case present an instructive contrast. Eight astronomers
+produce nearly the same result, and yet the last two doubt the sufficiency
+of their means: compare them with the what's-his-name who rushes in where
+thing-em-bobs fear to tread.
+
+I was not aware, until I had written what precedes, that Mr. Airy had given
+a sufficient answer on the point. Mr. Reddie says (_Correspondent_, Jan.
+20, 1866):
+
+    "I claim to have forced Professor Airy to give up the notion of 'solar
+    motion in space' altogether, for he admits it to be 'at present in
+    doubt and abeyance.' I first made that claim in a letter addressed to
+    the Astronomer Royal himself in June, 1864, and in replying, very
+    courteously, to other portions of my letter, he did not gainsay that
+    part of it."
+
+Mr. Reddie is not ready at reading satire, or he never would have so missed
+the meaning of the courteous reply on one point, and the total silence upon
+another. Mr. Airy must be one of those peculiar persons who, when they do
+not think an assertion worth notice, let it alone, without noticing it by a
+notification of non-notice. He would never commit the bull of "Sir! I will
+not say a word on that subject." He would put it thus, "Sir! I will only
+say ten words on that subject,"--and, having thus said them, would {351}
+proceed to something else. He assumed, as a matter of form, that Mr. Reddie
+would draw the proper inference from his silence: and this because he did
+not care whether or no the assumption was correct.
+
+The _Mechanics of the Heavens_, which Mr. Reddie sends to be noticed, shall
+be noticed, so far as an extract goes:
+
+
+
+"My connection with this subject is, indeed, very simply explained. In
+endeavoring to understand the laws of physical astronomy as generally
+taught, I happened to entertain some doubt whether gravitating bodies could
+revolve, and having afterwards imbibed some vague idea that the laws of the
+universe were chemical and physical rather than mechanical, and somehow
+connected with electricity and magnetism as opposing correlative
+forces--most probably suggested to my mind, as to many others, by the
+transcendent discoveries made in electro-magnetism by Professor
+Faraday[657]--my former doubts about gravitation were revived, and I was
+led very naturally to try and discover whether a gravitating body really
+could revolve; and I became convinced it could not, before I had ever
+presumed to look into the demonstrations of the _Principia_."
+
+
+
+This is enough against the book, without a word from me: I insert it only
+to show those who know the subject what manner of writer Mr. Reddie is. It
+is clear that "presumed" is a slip of the pen; it should have been
+_condescended_.
+
+Mr. Reddie represents me as dreaming over paltry paradoxes. He is right;
+many of my paradoxes are paltry: he is wrong; I am wide awake to them. A
+single moth, beetle, or butterfly, may be a paltry thing; but when a
+cabinet is arranged by genus and species, we then begin to admire the {352}
+infinite variety of a system constructed on a wonderful sameness of leading
+characteristics. And why should paradoxes be denied that collective
+importance, paltry as many of them may individually be, which is accorded
+to moths, beetles, or butterflies? Mr. Reddie himself sees that "there is a
+method in" my "mode of dealing with paradoxes." I hope I have atoned for
+the scantiness of my former article, and put the demonstrated impossibility
+of gravitation on that level with Hubongramillposanfy arithmetic and
+inhabited atoms which the demonstrator--not quite without reason--claims
+for it.
+
+In the Introduction to a collected edition of the three works, Mr. Reddie
+describes his _Mechanism of the Heavens_, from which I have just quoted,
+as--
+
+
+
+"a public challenge offered to the British Association and the
+mathematicians at Cambridge, in August, 1862, calling upon them to point to
+a single demonstration in the _Principia_ or elsewhere, which even attempts
+to prove that Universal Gravitation is possible, or to show that a
+gravitating body could possibly revolve about a center of attraction. The
+challenge was not accepted, and never will be. No such demonstration
+exists. And the public must judge for themselves as to the character of a
+so-called "certain science," which thus shrinks from rigid examination, and
+dares not defend itself when publicly attacked: also of the character of
+its teachers, who can be content to remain dumb under such circumstances."
+
+
+
+ON PARADOXERS IN GENERAL.
+
+The above is the commonplace talk of the class, of which I proceed to speak
+without more application to this paradoxer than to that. It reminds one of
+the funny young rascals who used, in times not yet quite forgotten, to
+abuse the passengers, as long as they could keep up with the {353} stage
+coach; dropping off at last with "Why don't you get down and thrash us?
+You're afraid, you're afraid!" They will allow the public to judge for
+themselves, but with somewhat of the feeling of the worthy uncle in _Tom
+Jones_, who, though he would let young people choose for themselves, would
+_have them_ choose wisely. They try to be so awfully moral and so ghastly
+satirical that they must be answered: and they are best answered in their
+own division. We have all heard of the way in which sailors cat's-pawed the
+monkeys: they taunted the dwellers in the trees with stones, and the
+monkeys taunted them with cocoa-nuts in return. But these were silly
+dendrobats: had they belonged to the British Association they would have
+said--No! No! dear friends; it is not in the itinerary: if you want nuts,
+you must climb, as we do. The public has referred the question to Time: the
+procedure of this great king I venture to describe, from precedents, by an
+adaptation of some smart anapaestic tetrameters--your anapaest is the foot
+for satire to halt on, both in Greek and English--which I read about twenty
+years ago, and with the point of which I was much tickled. Poetasters were
+laughed at; but Mr. Slum, whom I employed--Mr. Charles Dickens obliged me
+with his address--converted the idea into that of a hit at
+mathematicasters, as easily as he turned the Warren acrostic into Jarley.
+As he observed, when I settled his little account, it is cheaper than any
+prose, though the broom was not stolen quite ready made:
+
+  _Forty stripes save one for the smaller Paradoxers._
+
+  Hark to the wisdom the sages preach
+  Who never have learnt what they try to teach.
+  We are the lights of the age, they say!
+  We are the men, and the thinkers we!
+  So we build up guess-work the livelong day,
+  In a topsy-turvy sort of way,
+  Some with and some wanting _a_ plus b.
+  Let the British Association fuss;
+  What are theirs to the feats to be wrought by us?
+  {354}
+  Shall the earth stand still? Will the round come square?
+  Must Isaac's book be the nest of a mare?
+  Ought the moon to be taught by the laws of space
+  To turn half round without right-about-face?
+  Our whimsey crotchets will manage it all;
+  Deep! Deep! posterity will them call!
+  Though the world, for the present, lets them fall
+  Down! Down! to the twopenny box of the stall!
+
+  Thus they--But the marplot Time stands by,
+  With a knowing wink in his funny old eye.
+  He grasps by the top an immense fool's cap,
+  Which he calls a philosophaster-trap:
+  And rightly enough, for while these little men
+  Croak loud as a concert of frogs in a fen,
+  He first singles out one, and then another,
+  Down goes the cap--lo! a moment's pother,
+  A spirit like that which a rushlight utters
+  As just at the last it kicks and gutters:
+  When the cruel smotherer is raised again
+  Only snuff, and but little of that, will remain.
+
+  But though _uno avulso_ thus comes every day
+  _Non deficit alter_ is also in play:
+  For the vacant parts are, one and all,
+  Soon taken by puppets just as small;
+  Who chirp, chirp, chirp, with a grasshopper's glee,
+  We're the lamps of the Universe, We! We! We!
+  But Time, whose speech is never long,--
+  He hasn't time for it--stops the song
+  And says--Lilliput lamps! leave the twopenny boxes,
+  And shine in the Budget of Paradoxes!
+
+When a paradoxer parades capital letters and diagrams which are as good as
+Newton's to all who know nothing about it, some persons wonder why science
+does not rise and triturate the whole thing. This is why: all who are fit
+to read the refutation are satisfied already, and can, if they please,
+detect the paradoxer for themselves. Those who are not fit to do this would
+not know the difference between the true answer and the new capitals and
+diagrams on which the delighted paradoxer would declare {355} that he had
+crumbled the philosophers, and not they him. Trust him for having the last
+word: and what matters it whether he crow the unanswerable sooner or later?
+There are but two courses to take. One is to wait until he has committed
+himself in something which all can understand, as Mr. Reddie has done in
+his fancy about the Astronomer Royal's change of opinion: he can then be
+put in his true place. The other is to construct a Budget of Paradoxes,
+that the world may see how the thing is always going on, and that the
+picture I have concocted by cribbing and spoiling a bit of poetry is drawn
+from life. He who wonders at there being no answer has seen one or two: he
+does not know that there are always fifty with equal claims, each of whom
+regards his being ranked with the rest as forty-nine distinct and several
+slanders upon himself, the great Mully Ully Gue. And the fifty would soon
+be five hundred if any notice were taken of them. They call mankind to
+witness that science _will not_ defend itself, though publicly attacked in
+terms which might sting a pickpocket into standing up for his character:
+science, in return, allows mankind to witness or not, at pleasure, that it
+_does not_ defend itself, and yet receives no injury from centuries of
+assault. Demonstrative reason never raises the cry of _Church in Danger_!
+and it cannot have any Dictionary of Heresies except a Budget of Paradoxes.
+Mistaken claimants are left to Time and his extinguisher, with the
+approbation of all thinking non-claimants: there is no need of a succession
+of exposures. Time gets through the job in his own workmanlike manner as
+already described.
+
+On looking back more than twenty years, I find among my cuttings the
+following passage, relating to a person who had signalized himself by an
+effort to teach comets to the conductor of the _Nautical Almanac_:
+
+
+
+"Our brethren of the literary class have not the least idea of the small
+amount of appearance of knowledge {356} which sets up the scientific
+charlatan. Their world is large, and there are many who have that moderate
+knowledge, and perception of what is knowledge, before which extreme
+ignorance is detected in its first prank. There is a public of moderate
+cultivation, for the most part sound in its judgment, always ready in its
+decisions. Accordingly, all their successful pretenders have _some
+pretension_. It is not so in science. Those who have a right to judge are
+fewer and farther between. The consequence is, that many scientific
+pretenders have _nothing but pretension_."
+
+
+
+This is nearly as applicable now as then. It is impossible to make those
+who have not studied for themselves fully aware of the truth of what I have
+quoted. The best chance is collection of cases; in fact, a Budget of
+Paradoxes. Those who have no knowledge of the subject can thus argue from
+the seen to the unseen. All can feel the impracticability of the
+Hubongramillposanfy numeration, and the absurdity of the equality of
+contour of a regular pentagon and hexagon in one and the same circle. Many
+may accordingly be satisfied, on the assurance of those who have studied,
+that there is as much of impracticability, or as much of absurdity, in
+things which are hidden under
+
+ "Sines, tangents, secants, radius, cosines
+  Subtangents, segments and all those signs;
+  Enough to prove that he who read 'em
+  Was just as mad as he who made 'em."
+
+Not that I mean to be disrespectful to mathematical terms: they are short
+and easily explained, and compete favorably with those of most other
+subjects: for instance, with
+
+ "Horse-pleas, traverses, demurrers,
+  Jeofails, imparlances, and errors,
+  Averments, bars, and protestandos,
+  And puis d'arreign continuandos."
+
+{357}
+
+From which it appears that, taking the selections made by satirists for our
+samples, there are, one with another, four letters more in a law term than
+in one of mathematics. But pleading has been simplified of late years.
+
+All paradoxers can publish; and any one who likes may read. But this is not
+enough; they find that they cannot publish, or those who can find they are
+_not_ read, and they lay their plans athwart the noses of those who, they
+think, ought to read. To recommend them to be content with publication,
+like other authors, is an affront: of this I will give the reader an
+amusing instance. My good nature, of which I keep a stock, though I do not
+use it all up in this Budget, prompts me to conceal the name.
+
+I received the following letter, accompanied by a prospectus of a work on
+metaphysics, physics, astronomy, etc. The author is evidently one whom I
+should delight to honor:
+
+"Sir,--A friend of mine has mentioned your name in terms of panigeric
+[_sic_], as being of high standing in mathematics, and of greatly original
+thought. I send you the enclosed without comment; and, assuming that the
+bent of your mind is in free inquiry, shall feel a pleasure in showing you
+my portfolio, which, as a mathematician, you will acknowledge to be deeply
+interesting, even in an educational point of view. The work is complete,
+and the system so far perfected as to place it above criticism; and, so far
+as regards astronomy, as will Ptolemy beyond rivalry [_sic_: no doubt some
+words omitted]. Believe me to be, Sir, with the profoundest respect, etc.
+The work is the result of thirty-five years' travel and observation, labor,
+expense, and self-abnegation."
+
+I replied to the effect that my time was fully occupied, and that I was
+obliged to decline discussion with many persons who have views of their
+own; that the proper way is to publish, so that those who choose may read
+when they can find leisure. I added that I should advise a precursor in the
+shape of a small pamphlet, as two octavo volumes {358} would be too much
+for most persons. This was sound advice; but it is not the first, second,
+or third time that it has proved very unpalatable. I received the following
+answer, to which I take the liberty of prefixing a bit of leonine wisdom:
+
+ "Si doceas stultum, laetum non dat tibi vultum;
+  Odit te multum; vellet te scire sepultum.[658]"
+
+"Sir,--I pray you pardon the error I unintentionally have fallen into;
+deceived by the F.R.S. [I am not F.R.S.] I took you to be a man of science
+[_omnis homo est animal, Sortes est homo, ergo Sortes est animal_][659]
+instead of the mere mathematician, or human calculating-machine. Believe
+me, Sir, you also have mistaken your mission, as I have mine. I wrote to
+you as I would to any other man well up in mathematics, with the intent to
+call your attention to a singular fact of omission by Euclid, and other
+great mathematicians: and, in selecting you, I did you an honor which, from
+what I have just now heard, was entirely out of place. I think, considering
+the nature of the work set forth in the prospectus, you are guilty of both
+folly and presumption, in assuming the character of a patron; for your own
+sense ought to have assured you that was such my object I should not have
+sought him in a De Morgan, who exists only by patronage of others. On the
+other hand, I deem it to be an unpardonable piece of presumption in
+offering your advice upon a subject the magnitude, importance, and real
+utility of which you know nothing about: by doing so you have offered me a
+direct insult. The system is a manual of Philosophy, a one inseparable
+whole of metaphysics and physic; embracing points the most interesting,
+laws the most important, {359} doctrines the most essential to advance man
+in accordance with the spirit of the times. I may not live to see it in
+print; for, at ----, life at best is uncertain: but, live or die, be
+assured Sir, it is not my intention to debase the work by seeking
+patronage, or pandering to the public taste. Your advice was the less
+needed, seeing I am an old-established ----. I remain, etc.--P.S. You will
+oblige me by returning the prospectus of my work."
+
+
+
+My reader will, I am sure, not take this transition from the "profoundest
+respect" to the loftiest insolence for an _apocraphical_ correspondence, to
+use a word I find in the Prospectus: on my honor it is genuine. He will be
+better employed in discovering whether I exist by patronizing others, or by
+being patronized by them. I make any one who can find it out a fair offer:
+I will give him my patronage if I turn out to be Bufo, on condition he
+gives me his, if I turn out to be Bavius.[660] I need hardly say that I
+considered the last letter to be one of those to which no answer is so good
+as no answer.
+
+These letters remind me in one respect of the correspondents of the
+newspapers. My other party wrote because a friend had pointed me out: but
+he would not have written if he had known what another friend told him just
+in time for the second letter. The man who sends his complaint to the
+newspaper very often says, in effect, "Don't imagine, Sir, that I read your
+columns; but a friend who sometimes does has told me ..." It is worded
+thus: "My attention {360} has been directed to an article in your paper of
+..." Many thanks to my friend's friends for not mentioning the Budget: had
+my friend's attention been directed to it I might have lost a striking
+example of the paradoxer in search of a patron. That my Friend was on this
+scent in the first letter is revealed in the second. Language was given to
+man to conceal his thoughts; but it is not every one who can do it.
+
+Among the most valuable information which my readers will get from me is
+comparison of the reactions of paradoxers, when not admitted to argument,
+or when laughed at. Of course, they are misrepresented; and at this they
+are angry, or which is the same thing, take great pains to assure the
+reader that they are not. So far natural, and so far good; anything short
+of concession of a case which must be seriously met by counter-reasons is
+sure to be misrepresentation. My friend Mr. James Smith and my friend Mr.
+Reddie are both terribly misrepresented: they resent it by some
+insinuations in which it is not easy to detect whether I am a conscious
+smotherer of truth, or only muddle-headed and ignorant. [This was written
+before I received my last communication from Mr. James Smith. He tells me
+that I am wrong in saying that his work in which I stand in the pillory is
+all reprint: I have no doubt I confounded some of it with some of the
+manuscript or slips which I had received from my much not-agreed-with
+correspondent. He adds that my mistake was intentional, and that my reason
+is obvious to the reader. This _is_ information, as the sea-serpent said
+when he read in the newspaper that he had a mane and tusks.]
+
+
+
+THE DOUBLE VAHU PROCESS.
+
+My friend Dr. Thorn[661] sees deeper into my mystery. By the way, he still
+sends an occasional touch at the old {361} subject; and he wants me
+particularly to tell my readers that the Latin numeral letters, if M be
+left out, give 666. And so they do: witness DCLXVI. A person who thinks of
+the origin of symbols will soon see that 666 is our number because we have
+five fingers on each hand: had we had but four, our mystic number would
+have been expressed by 555, and would have stood for our present 365. Had n
+been the number on each hand, the great number would have been
+
+  (n + 1) (4n^2 + 2n + 1)
+
+With no finger on each hand, the number would have been 1: with one finger
+less than none at all on each hand, it would have been 0. But what does
+this mean? Here is a question for an algebraical paradoxer! So soon as we
+have found out how many fingers the inhabitants of any one planet have on
+each hand, we have the means of knowing their number of the Beast, and
+thence all about them. Very much struck with this hint of discovery, I
+turned my attention to the means of developing it. The first point was to
+clear my vision of all the old cataracts. I propose the following
+experiment, subject of course to the consent of parties. Let Dr. Thorn
+Double-Vahu Mr. James Smith, and Thau Mr. Reddie: if either be deparadoxed
+by the treatment, I will consent to undergo it myself. Provided always that
+the temperature required be not so high as the Doctor hints at: if the
+Turkish Baths will do for this world, I am content.
+
+The three paradoxers last named and myself have a pentasyllable convention,
+under which, though we go far beyond civility, we keep within civilization.
+Though Mr. James Smith pronounced that I must be dishonest if I did not see
+his argument, which he knew I should not do [to say nothing of recent
+accusation]; though Dr. Thorn declared me a competitor for fire and
+brimstone--and my wife, too, which doubles the joke: though Mr. Reddie
+{362} was certain I had garbled him, evidently on purpose to make falsehood
+appear truth; yet all three profess respect for me as to everything but
+power to see truth, or candor to admit it. And on the other hand, though
+these were the modes of opening communication with me, and though I have no
+doubt that all three are proper persons of whom to inquire whether I should
+go up-stairs or down-stairs, etc., yet I am satisfied they are thoroughly
+respectable men, as to everything but reasoning. And I dare say our several
+professions are far more true in extent than in many which are made under
+more parliamentary form. We find excuses for each other: they make
+allowances for my being hoodwinked by Aristotle, by Newton, by the Devil;
+and I permit them to feel, for I know they cannot get on without it, that
+their reasons are such as none but a knave or a sinner can resist. But
+_they_ are content with cutting a slice each out of my character: neither
+of them is more than an uncle, a Bone-a-part; I now come to a dreadful
+nephew, Bone-the-whole.
+
+I will not give the name of the poor fellow who has fallen so far below
+both the _honestum_ and the _utile_, to say nothing of the _decorum_ or the
+_dulce_.[662] He is the fourth who has taken elaborate notice of me; and my
+advice to him would be, _Nec quarta loqui persona laboret_.[663] According
+to him, I scorn humanity, scandalize learning, and disgrace the press; it
+admits of no manner of doubt that my object is to mislead the public and
+silence truth, at the expense of the interests of science, the wealth of
+the nation, and the lives of my fellow men. The only thing left to be
+settled is, whether this is due to ignorance, natural distaste for truth,
+personal malice, a wish to curry favor with the Astronomer Royal, or mere
+toadyism. The only accusation which has truth in it is, that I have made
+myself a "public scavenger of science": the assertion, which is the {363}
+most false of all is, that the results of my broom and spade are "shot
+right in between the columns of" the _Athenaeum_. I declare I never in my
+life inserted a word between the columns of the _Athenaeum_: I feel huffed
+and miffed at the very supposition. I _have_ made myself a public
+scavenger; and why not? Is the mud never to be collected into a heap? I
+look down upon the other scavengers, of whom there have been a few--mere
+historical drudges; Montucla, Hutton, etc.--as not fit to compete with me.
+I say of them what one crossing-sweeper said of the rest: "They are well
+enough for the common thing; but put them to a bit of fancy-work, such as
+sweeping round a post, and see what a mess they make of it!" Who can touch
+me at sweeping round a paradoxer? If I complete my design of publishing a
+separate work, an old copy will be fished up from a stall two hundred years
+hence by the coming man, and will be described in an article which will end
+by his comparing our century with his own, and sighing out in the best New
+Zealand pronunciation--
+
+ "Dans ces tems-la
+  C'etait deja comme ca!"[664]
+
+
+
+ORTHODOX PARADOXERS.
+
+And pray, Sir! I have been asked by more than one--do your orthodox never
+fall into mistake, nor rise into absurdity? They not only do both, but they
+admit it of each other very freely; individually, they are convinced of
+sin, but not of any particular sin. There is not a syndoxer among them all
+but draws his line in such a way as to include among paradoxers a great
+many whom I should exclude altogether from this work. My worst specimens
+are but exaggerations of what may be found, occasionally, in the thoughts
+of sagacious investigators. At the end of the {364} glorious dream, we
+learn that there is a way to Hell from the gates of Heaven, as well as from
+the City of Destruction: and that this is true of other things besides
+Christian pilgrimage is affirmed at the end of the Budget of Paradoxes. If
+D'Alembert[665] had produced _enough_ of a quality to match his celebrated
+mistake on the chance of throwing head in two throws, he would have been in
+my list. If Newton had produced _enough_ to match his reception of the
+story that Nausicaa, Homer's Phaeacian princess, invented the celestial
+sphere, followed by his serious surmise that she got it from the
+Argonauts,--then Newton himself would have had an appearance entered for
+him, in spite of the _Principia_. In illustration, I may cite a few words
+from _Tristram Shandy_:
+
+
+
+"'A soldier,' cried my uncle Toby, interrupting the Corporal, 'is no more
+exempt from saying a foolish thing, Trim, than a man of letters.'--'But not
+so often, an' please your honor,' replied the Corporal. My uncle Toby gave
+a nod."
+
+
+
+I now proceed to die out. Some prefatory remarks will follow in time.[666]
+I shall have occasion to insist that all is not barren: I think I shall
+find, on casting up, that two out of five of my paradoxers are not to be
+utterly condemned. Among the better lot will be found all gradations of
+merit; at the same time, as was remarked on quite a different subject,
+there may be little to choose between the last of the saved and the first
+of the lost. The higher and better class is worthy of blame; the lower and
+worse class is worthy of praise. The higher men are to be reproved for not
+taking up things in which they could do some good: the lower men are to be
+commended for taking up things in which they can do no great harm. The
+circle problem is like Peter Peebles's lawsuit:
+
+{365}
+
+
+
+"'But, Sir, I should really spoil any cause thrust on me so hastily.'--'Ye
+cannot spoil it, Alan,' said my father, 'that is the very cream of the
+business, man,--... the case is come to that pass that Stair or Arniston
+could not mend it, and I don't think even you, Alan, can do it much harm.'"
+
+
+
+I am strongly reminded of the monks in the darker part of the Middle Ages.
+To a certain proportion of them, perhaps two out of five, we are indebted
+for the preservation of literature, and their contemporaries for good
+teaching and mitigation of socials evils. But the remaining three were the
+fleas and flies and thistles and briars with whom the satirist lumps them,
+about a century before the Reformation:
+
+ "Flen, flyys, and freris, populum domini male caedunt;
+  Thystlis and breris crescentia gramina laedunt.
+  Christe nolens guerras qui cuncta pace tueris,
+  Destrue per terras breris, flen, flyys, and freris.
+  Flen, flyys, and freris, foul falle hem thys fyften yeris,
+  For non that her is lovit flen, flyys ne freris."[667]
+
+I should not be quite so savage with my second class. Taken together, they
+may be made to give useful warning to those who are engaged in learning
+under better auspices: aye, even useful hints; for bad things are very
+often only good things spoiled or misused. My plan is that of a predecessor
+in the time of Edward the Second:
+
+ "Meum est propositum genti imperitae
+  Artes frugi reddere melioris vitae."[668]
+
+To this end I have spoken with freedom of books as books, of opinions as
+opinions, of ignorance as ignorance, of {366} presumption as presumption;
+and of writers as I judge may be fairly inferred from what they have
+written. Some--to whom I am therefore under great obligation--have
+permitted me to enlarge my plan by assaults to which I have alluded;
+assaults which allow a privilege of retort, of which I have often availed
+myself; assaults which give my readers a right of partnership in the
+amusement which I myself have received.
+
+For the present I cut and run: a Catiline, pursued by a chorus of Ciceros,
+with _Quousque tandem? Quamdiu nos? Nihil ne te?_[669] ending with, _In te
+conferri pestem istam jam pridem oportebat, quam tu in nos omnes jamdiu
+machinaris!_ I carry with me the reflection that I have furnished to those
+who need it such a magazine of warnings as they will not find elsewhere; _a
+signatis cavetote_:[670] and I throw back at my pursuers--_Valete, doctores
+sine doctrina; facite ut proxima congressu vos salvos corporibus et sanos
+mentibus videamus._[671] Here ends the Budget of Paradoxes.
+
+{367}
+
+       *       *       *       *       *
+
+
+APPENDIX.
+
+I think it right to give the proof that the ratio of the circumference to
+the diameter is incommensurable. This method of proof was given by
+Lambert,[672] in the _Berlin Memoirs_ for 1761, and has been also given in
+the notes to Legendre's[673] Geometry, and to the English translation of
+the same. Though not elementary algebra, it is within the reach of a
+student of ordinary books.[674]
+
+Let a continued fraction, such as
+
+  a
+  -----
+  b + c
+      -----
+      d + e
+          -
+          f + etc.,
+
+be abbreviated into a/b+ c/d+ e/f+ etc.: each fraction being understood as
+falling down to the side of the preceding sign +. In every such fraction we
+may suppose b, d, f, etc. {368} positive; a, c, e, &c. being as required:
+and all are supposed integers. If this succession be continued ad
+infinitum, and if a/b, c/d, e/f, etc. all lie between -1 and +1, exclusive,
+the limit of the fraction must be incommensurable with unity; that is,
+cannot be A/B, where A and B are integers.
+
+First, whatever this limit may be, it lies between -1 and +1. This is
+obviously the case with any fraction p/(q + [omega]), where [omega] is
+between +-1: for, p/q, being < 1, and p and q integer, cannot be brought up
+to 1, by the value of [omega]. Hence, if we take any of the fractions
+
+  a/b, a/b+ c/d, a/b+ c/d+ e/f, etc.
+
+say a/b+ c/d+ e/f+ g/h we have, g/h being between +-1, so is e/f+ g/h, so
+therefore is c/d+ e/f+ g/h; and so therefore is a/b+ c/d+ e/f+ g/h.
+
+Now, if possible, let a/b+ c/d+ etc. be A/B at the limit; A and B being
+integers. Let
+
+  P = A c/d+ e/f+ etc., Q = P e/f+ g/h+ etc., R = Q g/h + i/k + etc.
+
+P, Q, R, etc. being integer or fractional, as may be. It is easily shown
+that all must be integer: for
+
+{369}
+
+  A/B = a/b+ P/A, or, P = aB - bA
+
+  P/A = c/d+ Q/P, or, Q = cA - dP
+
+  Q/P = e/f+ R/Q, or, R = eP - fQ
+
+etc., etc. Now, since a, B, b, A, are integers, so also is P; and thence Q;
+and thence R, etc. But since A/B, P/A, Q/P, R/Q, etc. are all between -1
+and +1, it follows that the unlimited succession of integers P, Q, R, are
+each less in numerical value than the preceding. Now there can be no such
+_unlimited_ succession of _descending_ integers: consequently, it is
+impossible that a/b+ c/d+, etc. can have a commensurable limit.
+
+It easily follows that the continued fraction is incommensurable if a/b,
+c/d, etc., being at first greater than unity, become and continue less than
+unity after some one point. Say that i/k, l/m,... are all less than unity.
+Then the fraction i/k+ l/m+ ... is incommensurable, as proved: let it be
+[kappa]. Then g/(h + [kappa]) is incommensurable, say [lambda]; e/(f +
+[lambda]) is the same, say [mu]; also c/(d + [mu]), say [nu], and a/(b +
+[nu]), say [rho]. But [rho] is the fraction a/b+ c/d+ ... itself; which is
+therefore incommensurable.
+
+Let [phi]z represent
+
+      a     a^2          a^3
+  1 + - + ------- + -------------- + ....
+      z   2z(z+1)   2.3.z(z+1)(z+2)
+
+{370} Let z be positive: this series is convergent for all values of a, and
+approaches without limit to unity as z increases without limit. Change z
+into z + 1, and form [phi]z - [phi](z+1): the following equation will
+result--
+
+                        a
+  [phi]z-[phi](z+1) = ------([phi](z+2))
+                      z(z+1)
+
+         a [phi](z+1)       a [phi](z+1)    a  [phi](z+2)
+  or a = - ---------- . z + - ---------- . --- ----------
+         z   [phi]z         z   [phi]z     z+1 [phi](z+1)
+
+  a = [psi]z(z+[psi](z+1))
+
+[psi]z being (a/z)([phi](z+1)/[phi]z); of which observe that it diminishes
+without limit as z increases without limit. Accordingly, we have
+
+  [psi]z = a/z+ [psi](z+1) = a/z+ a/(z+1)+ [psi](z+2)
+                           = a/z+ a/(z+1)+ a/(z+2)+ [psi](z+3), etc.
+
+And, [psi](z + n) diminishing without limit, we have
+
+  a/z . [phi](z+1)/[phi]z = (a/z+) (a/(z+1)+) (a/(z+2)+) (a/((z+3)+ ...))
+
+Let z = 1/2; and let 4a = -x^2. Then (a/z)[phi](z+1) is -(x^2/2) ( 1 -
+x^2/(2.3) + x^4/(2.3.4.5...)) or -(x/2) sin x. Again [phi]z is 1 - x^2/2 +
+x^4/(2.3.4) or cos x: and the continued fraction is
+
+  (1/4)x^2/(1/2)+ (1/4)x^2/(3/2)+ (1/4)x^2/(5/2)+ ...
+   or -x/2 x/1+ -x^2/3+ -x^2/5+
+      ...
+
+{371} whence tan x = x/1+ -x^2/3+ -x^2/5+ -x^2/7+ ...
+
+Or, as written in the usual way,
+
+  tan x = x
+          -------
+          1 - x^2
+              -------
+              3 - x^2
+                  -------
+                  5 - x^2
+                      -------
+                      7 - ...
+
+This result may be proved in various ways: it may also be verified by
+calculation. To do this, remember that if
+
+  a_1/b_1+ a_2/b_2+ a_3/b_3+ ...  a_n/b_n = P_n/Q_n; then
+
+  P_1=a_1, P_2=b_2 P_1,     P_3=b_3 P_2+a_3 P_1, P_4=b_4 P_3+a_4 P_2, etc.
+  Q_1=b_1, Q_2=b_2 Q_1+a_2, Q_3=b_3 Q_2+a_3 Q_1, Q_4=b_4 Q_3+a_4 Q_2, etc.
+
+in the case before us we have
+
+  a_1=x, a_2=-x^2, a_3=-x^2, a_4=-x^2, a_5=-x^2, etc.
+  b_1=1, b_2=3,    b_3=5,    b_4=7,    b_5=9, etc.
+
+  P_1=x                     Q_1=1
+  P_2=3x                    Q_2=3-x^2
+  P_3=15x-x^3               Q_3=15-6x^2
+  P_4=105x-10x^3            Q_4=105-45x^2+x^4
+  P_5=945x-105x^3+x^5       Q_5=945-420x^2+15x^4
+  P_6=10395x-1260x^3+21x^5  Q_6=10395-4725x^2+210x^4-x^6
+
+We can use this algebraically, or arithmetically. If we divide P_n by Q_n,
+we shall find a series agreeing with the known series for tan x, _as far
+as_ n _terms_. That series is
+
+  x + x^3/3 + 2x^5/15 + 17x^7/315 + 62x^9/2835 + ...
+
+{372} Take P_5, and divide it by Q_5 in the common way, and the first five
+terms will be as here written. Now take _x_ = .1, which means that the
+angle is to be one tenth of the actual unit, or, in degrees 5 deg..729578.
+We find that when x = .1, P_6 = 1038.24021, Q_6 = 10347.770999; whence P_6
+divided by Q_6 gives .1003346711. Now 5 deg..729578 is 5 deg.43'46-1/2";
+and from the old tables of Rheticus[675]--no modern tables carry the
+tangents so far--the tangent of this angle is .1003347670.
+
+Now let x = (1/4)[pi]; in which case tan x = 1. If (1/4)[pi] be
+commensurable with the unit, let it be (m/n), m and n being integers:
+we know that (1/4)[pi] < 1. We have then
+
+  1=(m/n)/1- (m^2/n^2)/3- (m^2/n^2)/5- ...  = m/n- m^2/3n- m^2/5n- m^2/7n-
+      ...
+
+Now it is clear that m^2/3n, m^2/5n, m^2/7n, etc. must at last become and
+continue severally less than unity. The continued fraction is therefore
+incommensurable, and cannot be unity. Consequently [pi]^2 cannot be
+commensurable: that is, [pi] is an incommensurable quantity, and so also
+is [pi]^2.
+
+
+
+I thought I should end with a grave bit of appendix, deeply mathematical:
+but paradox follows me wherever I go. The foregoing is--in my own
+language--from Dr. (now Sir David) Brewster's[676] English edition of
+Legendre's Geometry, (Edinburgh, 1824, 8vo.) translated by some one who is
+not named. I picked up a notion, which others had at Cambridge in 1825,
+that the translator was the late Mr. Galbraith,[677] then known at
+Edinburgh as a writer and teacher.
+
+{373} But it turns out that it was by a very different person, and one
+destined to shine in quite another walk; it was a young man named Thomas
+Carlyle.[678] He prefixed, from his own pen, a thoughtful and ingenious
+essay on Proportion, as good a substitute for the fifth Book of Euclid as
+could have been given in the space; and quite enough to show that he would
+have been a distinguished teacher and thinker on first principles. But he
+left the field immediately.
+
+       *       *       *       *       *
+
+(The following is the passage referred to at Vol. II, page 54.)
+
+Michael Stifelius[679] edited, in 1554, a second edition of the Algebra
+(_Die Coss._), of Christopher Rudolff.[680] This is one of the earliest
+works in which + and - are used.
+
+Stifelius was a queer man. He has introduced into this very work of Rudolff
+his own interpretation of the number of the Beast. He determined to fix the
+character of Pope Leo: so he picked the numeral letters from LEODECIMVS,
+and by taking in X from LEO X. and striking out M as standing for
+_mysterium_, he hit the number exactly. This discovery completed his
+conversion to Luther, and his determination to throw off his monastic vows.
+Luther dealt with him as straight-forwardly as with Melanchthon about his
+astrology: he accepted the conclusions, but told him to clear his mind of
+all the premises about the Beast. Stifelius {374} did not take the advice,
+and proceeded to settle the end of the world out of the prophet Daniel: he
+fixed on October, 1533. The parishioners of some cure which he held, having
+full faith, began to spend their savings in all kinds of good eating and
+drinking; we may charitably hope this was not the way of preparing for the
+event which their pastor pointed out. They succeeded in making themselves
+as fit for Heaven as Lazarus, so far as beggary went: but when the time
+came, and the world lasted on, they wanted to kill their deceiver, and
+would have done so but for the interference of Luther. {375}
+
+       *       *       *       *       *
+
+
+INDEX.
+
+Pages denoted by numerals of this kind (_287_) refer to biographical notes,
+chiefly by the editor. Numerals like 426 refer to books discussed by De
+Morgan, or to leading topics in the text. Numerals like 126 indicate minor
+references.
+
+  Abbott, Justice, I, _181_.
+  Abernethy, J., II, _219_.
+  Aboriginal Britons, a poem, II, 270.
+  Academy of Sciences, French, I, 163.
+  Adair, J., I, _223_.
+  Adam, M., I, _65_.
+  Adams, J. C., I, _43_, 82, 385, 388; II, 131, 135, 140, 303.
+  Ady, Joseph, II, 42, _42_.
+  Agnew, H. C., I, 328.
+  Agricola, J., I, 394.
+  Agricultural Laborer's letter, II, 16.
+  Agrippa, H. C., I, _48_, 48.
+  Ainsworth, W. H., II, _132_.
+  Airy, I, _85_, 88, 152, 242; II, 85, 140, 150, 303, 347.
+  Alchemy, I, 125.
+  Alfonso X (El Sabio), II, _269_.
+  Alford, H., II, _221_.
+  Alfred, King, Ballad of, II, 22.
+  Algebra, I, 121.
+  Algebraic symbols, I, 121.
+  Almanac, I, 300; II, 147, 148, 207.
+    (_See Easter._)
+  Aloysius Lilius, I, 362.
+  Alsted, J. H., II, _282_.
+  Ameen Bey, II, 15.
+  Amicable Society, I, 347.
+  Ampere, I, 86.
+  Amphisbaena serpent, I, 31.
+  Anagrams, De Morgan, I, 138.
+  Anaxagoras, II, _59_.
+  Anghera, II, 60, _60_, 61, 279.
+  Annuities, Fallacies of, I, 157.
+  Antichrist, I, 130.
+  Antimony, I, 125.
+  Antinewtonism, I, 162.
+  Antinomians, I, 394.
+  Antiphon, II, _59_.
+  Antonie, F., I, _126_, 126.
+  Apollonius, I, 41, 107.
+  Apparitions, II, 47.
+  Arago, I, _243_, 390.
+  Aratus, II, _167_.
+  Arbuthnot, I, _133_, 134.
+  Archer, H., II, 90.
+  Archimedes,  I, 5, 11, 42, 83, 107.
+  Archytas, I, _53_.
+  Argoli, I, _104_.
+  Aristocrat, as a scientist, I, 131.
+  Aristotle, I, 5, 331.
+  Arnobius, II, _73_.
+  Arson, P. J., II, _207_.
+  Ashton, R., II, _99_.
+  Astrology, I, 118, 127, 128, 350; II, 43.
+  Astronomer's Drinking Song, I, 380.
+  Astronomical Aphorisms, I, 398.
+    Paradox, I, 394.
+    Police Report, I, 390.
+    Society. (_See Royal Astronomical Society._)
+  Astronomy, Bailly's exaggerated view of, I, 166.
+  Astunica, Didacas, I, 90.
+  Athanasian Creed, I, 371.
+  Atheists, Philosophical, I, 1.
+  Atoms, II, 191.
+  {376}
+  Attraction, I, 136, 151, 155.
+  Augustine, St., II, _23_.
+  Aurora borealis, I, 134.
+  Austen, Jane, I, 191.
+  Auzout, A., II, _300_.
+  Aviation, Early ideas of, II, 8.
+
+  Babbage, C., I, _207_, 290, 291; II, 181.
+  Bachet, de Meziriac, I, _161_.
+  Bacon, F., I, 5, _75_, 75, 76, 79, 89, 145, 331.
+  Bacon, R., I, 5, _126_, 126, 360; II, 94.
+  Baconian controversy, I, 141.
+  Baden Powell, II, _267_.
+  Bailly, J. S., I, 166, _166_, 308.
+  Baily, F., I, 308, _309_; II, 16, 143, 188.
+  Baily, R., II, 16.
+  Baker, T., II, _302_.
+  Bakewell, F. C., II, 156, _156_.
+  Banks, J., I, 28.
+  Barberini, M., II, _267_.
+  Barker, C., II, _262_.
+  Baronius, I, 33, 35; II, _62_.
+  Barreme, I, _42_.
+  Barrett, G., II, _188_.
+  Barrow, I., I, _160_; II, 302.
+  Baruel, de, I, 165.
+  Bassano, Duc de, II, 3, 339.
+  Baxter, T., I, 146.
+  Bayle, P., II, _73_.
+  Beaufort, F., II, _267_.
+  Beaugrand, I, 119, _121_.
+  Beaulieu, I, _119_, 119, 121.
+  Beaune, de, II, _59_.
+  Becourt, R., II, 277.
+  Bedford, Duke of, (6th), I, _182_.
+  Behmen, I, _168_, 254; II, 317.
+  Bellenden, W., I, _175_.
+  Bentley, I, _110_.
+  Berkeley, G., II, 346.
+  Bernard, E., II, _297_, 300.
+  Bernardus Trevisanus, I, _126_, 126.
+  Bernoullis, I, 130, _150_, _335_, 336.
+  Bertius, P., II, _300_.
+  Bese, I, _66_.
+  Bessel, I, _384_; II, 2.
+  Bethune, I, _99_, 279, 291.
+  Bettesworth, I, 19.
+  Beza. (_See Bese._)
+  Bickersteth, E. H., I, _238_.
+  Bidder, I, _86_.
+  Biden, J., II, 158, _160_.
+  Bidle, (Biddle), I, 239.
+  Biot, I, _85_.
+  Birch, T., I, _108_; II, 304, 313.
+  Birks, T. R., II, 158, _158_.
+  Bishop, G., I, _386_.
+  Bishops as Paradoxers, I, 226.
+  Boccaccio, I, 38.
+  Boethius, I, _42_, 45.
+  Boehme. (_See Behmen._)
+  Boncompagni, I, _298_.
+  Boniface, St., I, 32.
+  Bonnycastle, J., II, _16_.
+  Booker, I, 115.
+  Boole, G., I, _261_, 332; II, 75, 79.
+    --A tribute to, II, 79.
+  Borelli, G. A., II, _300_.
+  Borello, I, _69_.
+  Boreman,  I, 113.
+  Borron, Mrs., II, 7.
+  Boscovich, I, _156_, 164.
+  Bouguer, II, _301_.
+  Bouillaud, I, _87_; II, 295.
+  Bouvard, A., I, _327_.
+  Bovillus, I, _44_; II, 324.
+    --Epitome of, I, 44.
+  Bowdler, H. M., I, _194_.
+  Bowring, J., I, _352_; II, 256.
+  Boyle, R., I, 24, _125_; II, 300.
+  Bradley, I, 24.
+  Bradwardine, I, _227_, 228, 229.
+  Brahe. (_See Tycho B._)
+  Brancker, I, 107; II, _300_.
+  Brenan, J., I, 330, _330_.
+  Brewster, D., I, 39, _137_, 140; II, 214, 288, 372.
+  Briggs, I, _69_; II, 299, 302.
+  Bright, J., II, _235_.
+  Brinkley, J., I, _311_.
+  Britannicus, D., II, 8.
+  British Museum library, I, 151.
+  Brothers, R., I, _315_; II, 97.
+  Brougham, Henry, Lord, I, _191_.
+  Brouncker (Brounker), I, _132_; II, 302.
+  Brown, W., II, _168_.
+  Browne, T., I, 31.
+  Brucker, I, _61_.
+  Brunet, I, _402_.
+  Bruennow, I, _386_.
+  Bruno, I, _59_, 59.
+  Bryson, II, _59_.
+  Buergi, I, 52.
+  Buffon, I, _282_.
+  Bulstrode, II, 84.
+  Bungus, I, _55_, 55, 57.
+  Buoncompagno, U., I, _362_.
+  {377}
+  Burgon, J. W., II, _30_.
+  Buridan, I, _37_.
+    --Questiones morales, I, 37.
+  Buridan's Ass, I, 37.
+  Burke, E., I, _173_.
+  Burlesque, Frend's, I, 208.
+  Burnet, G., I, _107_.
+  Burney, Frances, I, _190_.
+  Burton, Frances B., I, 374.
+  Busby, R., II, _313_.
+  Buteo, I, _51_.
+  Butler, G., I, _199_.
+  Butler, S., II, _218_.
+  Buxton, J., I, _86_.
+  Byrgius. (_See Buergi._)
+  Byrne, O., I, _329_; II, 186, 190.
+  Byron, I, 186; II, 270, 273.
+
+  Cabbala, I, 272.
+  Calculating Boys, I, 86.
+  Calculus, I, 129.
+  Calendar. (_See Easter._)
+  Cambridge Poets, II, 269.
+  Campanus, I, 42, _43_.
+  Canning, Geo., II, _145_.
+  Carcavi, I, _106_.
+  Cardanus, II, _59_.
+  Carlile, R., I, _271_.
+  Carlyle, T., II, _373_.
+  Carnot, I, 107.
+  Caroline tables, I, 124.
+  Casaubon, I, _111_.
+  Case, J., I, _128_, 128.
+  Cassini, J., I, _172_.
+  Castel, I, _148_, 148.
+  Castiglioni, I, _139_.
+  Castlereagh, I, 185, _186_.
+  Cataldi, I, _69_, 69.
+  Catcott, A., I, _237_.
+  Causans, de, I, _298_.
+  Cavalieri, I, _106_.
+  Cavendish, C., I, _106_; II, 299, 312.
+  Cavendish, W., I, _290_.
+  Caxton, W., II, _281_.
+  Cayley, A., II, _292_.
+  Cecil, R. (1st Earl of Salisbury), II, _330_.
+  Centrifugal force, II, 268.
+  Ceulen. (_See Van Ceulen._)
+  Challis, J., I, _390_; II, 141.
+  Chalmers, I, _102_; II, 219.
+  Chambers, E., II, _282_.
+  Chambers, R., I, _344_, 344.
+  Charles IX, II, 94.
+  Charles X, II, 1.
+  Chasles, I, _39_, 229.
+  Chesterfield, Earl of (4th), II, _298_.
+  Chiffinch, W., II, _50_.
+  Ch'in Chiu-shang, II, 66.
+  Chitty, J., II, _323_.
+  Chiu-chang, Suan-shu, II, 67.
+  Christian Evidence Society, I, 270.
+  Christie, I, 27.
+  Christmann, I, 272, _272_.
+  Church question, I, 62.
+  Church, The word, II, 30.
+  Circle squarers. (_See Squaring the Circle._)
+  Circulating media of mathematics, I, 107.
+  Ciruelo. (_See Sanchez._)
+  Clairaut, I, _219_, 382.
+  Clarence, Duke of, I, 179.
+  Clarke, R., I, _255_.
+  Clavius, I, 11, _69_, 111, 112, 335, 362, 363, 372; II,
+      59.
+  Clayton., Geo., II, _98_.
+  Cluvier, D., II, 332, _332_.
+  Cobb, Mary, II, 117.
+  Cobbett, W., I, _177_, 200, 399.
+  Cobden, R., II, 217.
+  Cocker, I, _42_; II, 64, 173, 251, 307.
+  Cody, P., II, 208.
+  Coke, E., II, _331_.
+  Colburn, Z., I, _86_.
+  Colenso, I, _63_, 247; II,  191.
+  Collins, J., I, _107_; II, 297, 300,  302, 313.
+  Colvill, W. H., II, 68.
+  Cometic astrology, I, 128.
+  Comets, I, 128; II, 68, 83.
+  Cominale, C., I, _162_, 162.
+  Compton, S. J. A., II, _19_.
+  Computation, Paradoxes of, II, 251, 267.
+  Condamine, C. M. de la, II, _301_.
+  Conduitt, John, I, _397_.
+  Conduitt, Mrs., I, _136_.
+  Congregation of the Index, I, 90.
+  Converse propositions, I, 295.
+  Convocation at Oxford, I, 96.
+  Cooke, Margaret, I, _310_.
+  Cooper, A. A. (Shaftsbury), II, _181_.
+  Copernicus, I, 5, 6, _76_, 90, 121, 172, 380; II, 165, 335.
+  Copley, J. S., I, _198_.
+  Cormouls, I, 225.
+  Cosmology, I, 172.
+  {378}
+  Cotes, R., II, _301_.
+  Cottle, Mrs., II, 97, _97_, 161.
+  Craig, J., I, _129_, 129.
+  Creed, Mathematics of a, I, 329.
+  Cribb, T., I, _314_.
+  Crotus, J., I, 318.
+  Cruickshank, G., I, _186_.
+  Cube, Duplication of, I, 349.
+  Cumyns, Eliza, I, 299.
+  Cunningham, I, 172, _172_.
+  Curabelle, I, _221_.
+  Curious Calculations, II, 66.
+  Curll, E., II, _279_.
+  Cusa, I, _44_, 47, 360.
+  Custom, II, 324.
+  Cyclometry, II, 208. (_See  Squaring of the Circle._)
+  Cyclopaedias, Review of, II, 280.
+
+  D'Alembert, I, _382_; II, 283, 364.
+  Dalgarno, I, 116, _117_.
+  Dalton, J., I, _255_.
+  D'Arblay, Mme., I, _190_.
+  Darwin, E., II, _8_.
+  Darwinism, Primitive, I, 344.
+  Dary, M., II, _305_.
+  Daval, P., II, _298_.
+  Davies, T. S., II, 151, _151_, 188.
+  Day, A., I, 295, _295_.
+  De Baruel, I, 165.
+  De Beaune. (_See Beaune._)
+  De Becourt, II, 277, _277_.
+  Debenham, J., I, _393_.
+  De Causans. (_See Causans._)
+  Dechales. (_See de Challes._)
+  De Challes, I, _45_.
+  Decimal coinage, II, 80, 168, 169.
+  Decimals run riot, II, 80.
+  Dee, J., II, _302_.
+  De Faure, I, 149.
+  De la Leu, I, _297_.
+  Delambre, I, _160_, 167, 354; II, 165.
+  Democritus, II, _34_.
+  De Moivre, I, 24, _376_; II, 298.
+  De Molieres, I, _220_.
+  De Molina, I, _297_.
+  Demonville, I, 291, 293.
+  De Morgan, A., I, 191, 383; II, 194.
+    --Refusal of LL. D., I, 191.
+  De Morgan, G. C., I, 383.
+  De Morgan, Mrs., I, _196_; II, 194.
+  Denison, J., I, 348, 353.
+  Desaguliers, I, _153_, 156, 157.
+  Desargues, I, _119_, 221.
+  Descartes, I, 5, 59, 105, 132, 165, 204, 220; II, 94.
+  De Serres, II, _60_.
+  De Sluse. (_See Sluse._)
+  De Thou, I, 51, _111_, 113; II, 295.
+  De Vausenville, I, 12.
+  Devonshire, Duke of (7th), I, _290_.
+  Diamandi, I, 86.
+  Didacus Astunica, I, 90.
+  Diderot, II, _4_, 283, 339.
+  Digby, K., I, _108_.
+  Digges, T., and L., II, _302_.
+  Dionysius Exiguus, I, _360_.
+  Dircks, H., II, 138, _138_.
+  Discoverers and discoveries, II, 206.
+  Discovery, Basis of, I, 85.
+  D'Israeli, I., I, _115_, 118, 136, 188, 227.
+  Ditton, I, _133_, 133.
+  Division, Nature of, II, 248.
+  Dobson, J., I, _234_, 234.
+  Dodson, J., II, _312_.
+  Dodt, I, _52_.
+  Doggerel verse, I, 341.
+  Dolland, I, _377_.
+  Double Vahu Process, II, 360.
+  Douglas, G., I, _232_.
+  Drach, S. M., II, _317_.
+  Drayson, G. A. W., II, _132_, 132.
+  Dryden, II, _71_.
+  Dual arithmetic, II, 186.
+  Duchesne, I, _52_.
+  Dumortier, I, 313.
+  Duncan, A., I, _179_.
+  Dunkin, E., II, _349_.
+  Duodecimal scale, II, 68.
+  Duplication Problem, I, 349.
+  Dupuy, J. and P., II, _295_.
+  Dutens, L., II, _90_.
+  Dyer, G., I, _178_.
+
+  Earth, Figure of, II, 54.
+  Easter, I, 359.
+  Easter Day Paradoxes, I, 353.
+  Ebrington, Thos., I, _247_.
+  Edgeworth, Maria, I,  _191_.
+  Editorial System, I, 15.
+  Edleston, I, _140_; II, 296.
+  Edwards, J., I, _144_.
+  Edwards, T., I, _112_.
+  Eirenaeus Philalethes, I, _125_, 125, 126.
+  Eldon, Lord (1st), II, _197_.
+  Elephant story, I, 58.
+  Elizabeth, Queen, I, 128.
+  Ellenborough, Baron, I, _181_.
+  {379}
+  Ellicot, I, 24.
+  Ellis, I, _76_, 82.
+  Engel, I, 230.
+  English language, Origin of, I, 215.
+  Enriques, F., II, _367_.
+  Epps, J., I, _153_; II, 143.
+  Equation of fifth degree, I, 250, 373.
+  Erasmus, I, 110.
+  Erastus, I, _65_.
+  Erichsen, I, 163.
+  Ersch, II, _193_, 282.
+  Erskine, T., II, _127_.
+  Esperanto, Forerunner of, I, 116.
+  Euclid, I, 5, 43; II, 118, 151.
+    --Without Axioms, I, 287.
+  Eudoxus, II, _164_.
+  Euler, I, 221, _382_; II, 3, 4, 303, 331, 339.
+  Eusebius, II, _220_.
+  Eustace, J. C., II, _46_.
+  Eutocius, I, _41_; II, 60.
+  Evelyn, J., I, _108_.
+  Everett, J., I, _346_.
+  Evidence, I, 57, 58.
+
+  Faber. (_See Stapulensis._)
+  Fairfax, Mary, I, _242_.
+  Falco, I, 53.
+  Faraday, M., II, _351_.
+  Faure, de, I, 149; II, 238.
+  Fawcett, H., II, _249_.
+  Ferguson, J., II, _20_.
+  Fermat, I, 122, 221; II, _300_.
+  Ferrari, S., II, 68.
+  Fiction, New era in, I, 189.
+  Fienus, I, _74_, 74.
+  Filopanti, Q. B., II, _93_.
+  Finaeus, I, _50_, 50, 113.
+  Finleyson, J., I, 314, _314_.
+  Flamsteed, I, _87_, 309; II, 45, 143, 302, 306.
+  Fletcher, I, 378.
+  Fludd, II, _318_.
+  Fly-leaf Paradox, II, 264.
+  Folkes, M., I, _136_; II, 301.
+  Fontenelle, I, _103_.
+  Forbes, D., I, _237_.
+  Forman, W., I, 296, _296_, 306.
+  Forster, T. I. M., I, 320, _320_.
+  Foscarini, I, _90_.
+  Foster, S., II, _310_.
+  Fourier, II, _66_.
+  Fox, G., I, _397_.
+  Francis, P., II, _96_.
+  Francoeur, I, _365_.
+  Frankland, W. B., I, 230, 287.
+  Franklin, J., II, _265_.
+  Freedom of opinion, Growth of, I, 265.
+  Freher, A., II, 319.
+  French academy on circle squaring, I, 163.
+  Frend, W., I, _196_, 196, 206, 208, 252.
+  Fresnel, II, _48_.
+  Fromondus, I, _74_, 74, 99.
+  Frost, I. and J., I, 394.
+  Fry, Elizabeth, I, 224.
+  Fuller, T., I, _86_.
+  Fulton, R., I, _148_.
+
+  Gadbury, J., I, _115_, 115.
+  Galbraith, J. A., II, 372.
+  Galileo, I, 5, 6, 32, _76_, 82, 83, 96, 122, 381.
+  Galle, J. G., I, _386_; II, 7.
+  Galloway, I, _56_, 57; II, 143.
+  Gamblers, I, 280.
+  Garrick, I, 21.
+  Gascoigne, W., II, _299_.
+  Gassendi, I, _107_.
+  Gauss, I, 86, 107, 310.
+  Gemistus, G., I, _188_.
+  Gentleman's Monthly, Miscellany, I, 208.
+  Gephryander. (_See Salicetus._)
+  Gergonne, I, _336_.
+  Ghetaldi, I, _83_; II, 59.
+  Ghost paradox, II, 47.
+  Giddy (Gilbert), II, _174_.
+  Gilbert, Davies, II, 66, _174_.
+  Gilbert, William, I, 6, _68_, 68, 76.
+  Gillot, II, _315_.
+  Glazier (Glazion), II, 7.
+  Godwin, F., I, _103_.
+  Godwin, W., I, _174_.
+  Golius, I, _106_.
+  Gompertz, B., I, _378_.
+  Goulburn, I, _288_.
+  Goulden, S., II, 88.
+  Graham, I, 24.
+  Grandamicus, I, _104_, 104.
+  Granger, J., I, _156_.
+  Grant, A. R., II, 131.
+  Grant, R., I, _392_; II, 131.
+  Grassi, O., I, _262_.
+  Grassini, I, _231_.
+  Graunt, J., I, 113, _114_, 154.
+  Gravity, I, 151, 244, 348, 353.
+  {380}
+    --Newton's apple, I, 136.
+  Greek numerals, II, _77_.
+  Greene, R., I, _135_, 135.
+  Greenhill, Sir G., I, 136.
+  Greenwich observatory,  I, 87.
+  Gregg, T. D., II, 75, _75_.
+  Gregorian Calendar, I, 363.
+  Gregory, D., I, _66_; II, 301.
+  Gregory, J., I, _118_, 118, 207; II, 302.
+  Gregory O., II, _71_.
+  Gregory, Pope, I, 362.
+  Grevil, I, _202_.
+  Grey, C., (2d Earl), I, _315_; II, 247.
+  Grosart, I, _141_, 141, 145.
+  Grove, W. R., II, _320_.
+  Gruber, II, _193_, 282.
+  Gruenberger, I, _70_.
+  Grynaeus, I, _66_.
+  Guaricus, I, _43_.
+  Guillim, J., II, _28_.
+  Guldin, I, _83_.
+  Gumpach, Von, II, 137, _137_.
+  Gunning, H., I, _198_.
+  Gurney. (_See Fry, E._)
+  Guthrie, W., I, _395_.
+
+  Hailes, J. D., II, 135, _135_.
+  Hailesean system of astronomy, II, 135.
+  Hale, M., I, _123_, 123.
+  Hales, S., I, _123_.
+  Hall, B., II, _181_.
+  Hallam, I, 159.
+  Halley, I, 24, _124_, 311; II, 301, 332.
+  Halliwell-Phillips, II, _148_, 296.
+  Hamilton, W., I, _112_, 117, 331, 335, 339, 341, 342; II,
+      52, 53, 111.
+  Hamilton, W. Rowan, I, _332_; II, 104, 256, 343.
+  Hanover, King of, I, 201.
+  Hardy, C., I, _298_.
+  Hardy, T., I, _178_.
+  Harriot, T., II, _302_.
+  Harvey, I, _76_, 78; II, 201.
+  Hauff, I, _230_.
+  Haughton, S., II, 372.
+  Hauksbee, F., I, _156_.
+  Hayes, C., I, _132_, 132.
+  Heath, D. D., I, _76_.
+  Heinfetter, H., II, 94, _94_.
+  Helmont, J. B. van, I, _125_.
+  Henson, II, 8.
+  Heraclitus, II, _34_.
+  Herbart, J. F., I, 253, _253_; II, 78.
+  Herigone, II, _59_.
+  Herschel, J., I, _80_, 299, 326, 383, 386; II, 88, 95, 181,
+      255, 261, 262.
+  Herschel, W., I, _81_, 151, 192, 225, 233, 299; II, 288, 348.
+  Heywood, F., II, _49_.
+  Hicks, J. P., II, _67_.
+  Higgins, G., I, _257_, 274.
+  Hilarius, Pope, I, _359_.
+  Hill, J., I, 21, 22, 23, 24.
+  Hill, Rev. R., I, _192_.
+  Hill, Sir R., I, _165_, 232.
+  Hind, J. R., I, _384_.
+  Hippocrates, II, _59_.
+  Hoax, An interesting, I, 163.
+    --Lunar Caustic, I, 288.
+    --Moon (Herschel), I, 326; II, 131.
+  Hobbes, I, _105_, 109, 143, 144; II, 80.
+  Hobhouse, J. C., II, _126_.
+  Hodder, J., II, _265_.
+  Hodge, C. B., I, 114.
+  Hodges, W., I, 237.
+  Hoffmann, J. J., II, _282_.
+  Hoffmann, J. J. I. von, I, _230_.
+  Holloway, B., I, _237_.
+  Holmes, O. W., I, 109.
+  Holyoake, G. J., I, _399_, 399.
+  Hone, W., I, 124, 180, 184, 185.
+  Hook, T. E., II, _261_.
+  Hooke, I, _77_; II, 300.
+  Hooker, R., II, _201_.
+  Hopkins, J., II, 41.
+  Horace, I, 40.
+  Horne, G., I, _152_, 152, 154, 155, 236.
+  Horne, J., I, _178_.
+  Horner, L., I, _176_.
+  Horner, W. G., II, _66_, 151, 187.
+  Houlston, W., II, 156, _156_.
+  Howard, E., I, 131.
+  Howison, W., I, 256, _256_.
+  Howitt, W., II, 193, _193_.
+  Howley, I, 63.
+  Hulls, I, _147_, 147; II, 8.
+  Hume, J., I, _352_; II, 174.
+  Husain Rifki, II, 16.
+  Hussein Effendi, II, 15.
+  Hutchinson, J., I, 154, _154_.
+  Hutton, C., I, _153_, 161; II, 303, 340.
+  Huyghens, I, _100_, 133; II, 300.
+
+  Imaginary numbers, II, 186.
+  Impalement by request, II, 133.
+  Inaudi, I, 86.
+  Index Expurgatorius, I, 90.
+  {381}
+  Infant prodigies, I, 86.
+  Inglis, J. B., II, _52_.
+  Inglis, R. H., I, _352_.
+  Ingliz Selim Effendi, II, 15.
+  Innocent I., I, _359_.
+  Irving, E., II, _54_.
+  Ivory, J., II, 142, _142_.
+
+  Jabir ben Aflah, II, _59_.
+  Jack, R., I, 149.
+  Jacotot, J., I, 278, _278_.
+  Jameson, Mrs., II, _63_.
+  Jeffreys, G., I, _183_.
+  Jenner, E., II, _205_.
+  Jesuit contributions, I, 164.
+  Johnson, H. C., I, 350.
+  Johnson, S., I, 20, _190_, 259; II, 117.
+  Johnston, W. H., II, 67.
+  Jombert, I, _161_.
+  Jonchere, I, _146_, 146.
+  Jones, W., I, _135_; II, 298, 301.
+  Jones, Rev. W., I, _237_.
+  Jonson, B., I, 13.
+  Journals, Three classes of, II,  144.
+
+  Kantesian Jeweler,  I, 258.
+  Karsten, I, _230_.
+  Kaestner, I, _43_, 110, 112.
+  Kater, I, 11.
+  Keckermann, I, 3.
+  Keill, J., II, _302_.
+  Kepler, I, 52, _76_, 82, 381; II, 166.
+  Kerigan, T., I, _308_, 353.
+  Keroualle, De, II, 50.
+  Kersey, I, 107.
+  King, Wm., I, _246_.
+  Kircher, Adolphe, I, 229.
+  Kircher, Athanasius, I, _103_.
+  Kirkringius, T., I, 125, _125_.
+  Kittle, I, 236.
+  Klein, F., II, 367.
+  Knight, C., II, _109_, 280, 289.
+  Knight, G., I, 151, _151_.
+  Knight, R. P., II, _274_.
+  Knight, Wm., I, _97_.
+  Koenig, S., I, _150_.
+
+  Lacomme, I, 46.
+  La Condamine, II, _301_.
+  Lacroix, I, 41, 159, 207.
+  Lactantius, I, 33, _96_.
+  Lagrange, I, 221, _288_, 313, 382; II, 86.
+  Laing, F. H., II, _186_, 186.
+  Lalande, I, _159_.
+  Lamb, C., I, 178; II, 270.
+  Lambert, J. H., I, _336_; II, 214, 367.
+  Lambert, John, II, _309_.
+  Language, Test of, II, 327.
+  Lansbergius, I, _70_, 70.
+  Laplace, I, 24, _255_, 382; II, 1, 340.
+  Lardner, D., II, _253_.
+  Lardner, N., I, 14; II, _221_.
+  Laud, I, _145_.
+  Lauder, W., I, 297.
+  Laurent, P., I, _309_, 309.
+  Laurie, J., II, 4.
+  Laurie, P., II, _42_.
+  Laurus, I, 381.
+  Law, Edmund, I, _181_.
+  Law, Edward, I, _181_.
+  Law, W., I, 168, _254_; II, 317.
+  Le Coq, I, _86_.
+  Lee, R., I, _66_.
+  Lee, S., I, _131_.
+  Lee, W., I, 157.
+  Legate, I, _59_.
+  Legendre, I, _229_; II, 215, 367.
+  Legh, P., II, _68_, 83.
+  Leibnitz, I, 5, 7; II, 46.
+  Leo, St., I, _359_.
+  Leverrier, I, _43_, 82, 383, 386, 388, 390; II, 7, 135, 140,
+      303.
+  Lewis, G. C., II, 162, _162_.
+  Libri, I, _40_, 62; II, 295.
+  Lilius, Aloysius, I, 362.
+  Lilly, I, _115_; II, 302.
+  Lipen, M., I, _298_.
+  Little, J., I, 206.
+  Livingston, R., I, _148_.
+  Locke, J., I, _142_, 142, 144;
+    --and Socinianism, I, 142.
+  Locke, R., I, 146.
+  Locke, R. A., I, _326_; II, 86, 131.
+  Logan, W. E., I, _337_.
+  Logic, Formal, I, 158; II, 75.
+    --Has no paradoxes, I, 330.
+  London Mathematical Society, I, 383.
+  London, University of, I, 259; II, 71.
+  Long, G., II, _290_.
+  Long, J. St. J., II. _38_, 205.
+  Longitude problems, I, 132, 146, 249.
+  Longley, C. T., I, _325_.
+  Longomontanus, I, _105_, 105.
+  Lottery, I. 281.
+  Lovett, R., I, 165, _166_.
+  Lowe, R., II, _169_.
+  Lowndes, W. T., I. _402_.
+  Lubbock, J., I, _279_; II, 148.
+  {382}
+  Lucas, F., II, _28_.
+  Lucian, I, _102_.
+  Lunar Caustic Joke, I, 288.
+  Lunn, J. R., II, _66_.
+  Lydiat, T., II, _302_.
+  Lyndhurst, I, _198_.
+
+  Macclesfield, Earls of, I, 7; II, _296_, 301.
+  Macclesfield, Letters, II, 296.
+  MacElshender, II, 87.
+  Machin, J., II, _301_.
+  Mackey, John,  I, 349.
+  Mackey, S. A., I, _256_.
+  Maclear, T., II, _181_.
+  Macleod, H. D., II, 184, _184_.
+  Magic, I, 118.
+  Magna Charta, I, 25.
+  Magnus, I, 42.
+  Maitland, S., I, _63_, 163.
+  Malacarne, I, 119.
+  Malden, H., II, _162_.
+  Malius, II, _342_.
+  Mallemens, II, _333_.
+  Mankind gullible, I, 115.
+  Manning, H. E., (Card.), II, _233_.
+  Mansel, H. L., II, _162_.
+  Marcelis, J., I, _129_, 129.
+  Maret, II, _3_.
+  Margarita Philosophica. (_See Reisch._)
+  Marryat, Capt., II, _87_.
+  Marsh, H., I, _199_, 271.
+  Martin, B., I, _152_, 153.
+  Martin, R., II, _236_.
+  Maseres, F., I, _197_, 203.
+  Mason, M., II, _132_.
+  Mathematical Illustrations of Doctrine, II, 70;
+    --Psychology, I, 253;
+    --Society, I, 374, 376, 382;
+    --Theology, I, 149.
+  Mathematics, Condensed history of, II, 58.
+  Matter to Spirit, II, 194.
+  Maty, I, 23.
+  Maupertuis, II, _301_.
+  Maurice, F. D., II, _101_.
+  Maurolycus, I, _121_.
+  Maxwell, A., I, _102_.
+  Meadley, G. W., I, _223_.
+  Mechanics Magazine, II, 141, 145.
+  Medici, Cosmo de, II, _295_.
+  Medicine, Status of, I, 266.
+  Melanchthon, II, _323_.
+  Menestrier, I, _127_, 127.
+  Mercator, G., II, _92_.
+  Mercator's projection, I, 84.
+  Mersenne, I, _106_, 107; II, 295, 297.
+  Meslier, J., II, _195_.
+  Meteorologist, An early, I, 320.
+  Meteorology, I, 327.
+  Metius, A. and P., I, _52_, _99_, 99.
+  Meton, II, 167.
+  Metric System, Forerunner of, I, 171.
+  Meziriac, I, 161.
+  Milbanke, A. I., I, 225.
+  Mill, Jas., I, 260.
+  Miller, Joe, I, _182_.
+  Miller, S., I, 167.
+  Mills, Elizabeth, W., II, 7.
+  Milne, J., I, _286_.
+  Milner, I., I, _251_, 251.
+  Milner, J., II, _23_.
+  Milner's lamp, I, 252.
+  Milward, II, _250_.
+  Miracles _vs_. Nature, II, 6.
+  Mitchell, J., I, _242_.
+  Moliere, I, _232_.
+  Molina, A. C. de, I, _297_.
+  Mollendorff, von, II, _3_, 338.
+  Mondeux, I, 86.
+  Montague, C., II, _311_.
+  Montmort, P. R. de, II, _301_.
+  Montucla, I, 40, 45, 54, 65, 117, 120, 159, 163; II, 60.
+  Moon Hoax, I, 326; II, 131.
+  Moon, Nature of, II, 84;
+    --Rotation of, II, 4, 19, 84, 87.
+  More, Hannah, I, _189_, 192.
+  More, Henry, I, 123.
+  Moore, Dr. John, I, _190_.
+  Moore, Sir John, I, _190_.
+  Morgan, S., I, 6.
+  Morgan, T., I, 191.
+  Morgan, W., I, _223_, 224.
+  Morhof, I, _61_.
+  Morin, I, _99_, 99.
+  Morinus, J. B., I, 149.
+  Morland, S., II, _302_.
+  Mormonism, II, 69.
+  Morrison, R. J., I, _321_; II, 43.
+  Mose, H., II, _266_.
+  Mottelay, I, 68.
+  Motti, II, 60.
+  Mouton, I, _172_; II, 300.
+  Muggleton, I, 394, _395_.
+  Multiplication, Nature of, II, 251.
+  Murchison, R. I., I, _384_.
+  Murhard, I, _43_, 298.
+  {383}
+  Murphy, A., II, _308_.
+  Murphy, J. L., II, 54, _54_.
+  Murphy, P., I, _327_, 398.
+  Murphy, R., I, 349, _349_.
+  Murray, J., I, _186_; II, 145.
+  Murray, L., II, _326_.
+  Murray, Mungo, II, 310.
+  Musgrave, T., I, _324_.
+  Mydorge, I, _298_.
+  Mystrom, J. W., II, 182.
+  Mythological paradoxes, I, 256.
+
+  Names of Religious Bodies, II, 22.
+  Napier, J., I, 5, 66, _67_, 82.
+  Napoleon, Doubts as to, I, 246.
+  Nautical Almanac, I, 300; II, 147.
+  Neal, I, _98_.
+  Negative numbers, I, 196, 203.
+  Neile, W., II, _190_.
+  Neptune, Discovery of, I, 387; II, 140. (_See Adams, Leverrier._)
+  Nesse, C, I, _128_, 128.
+  Newcomb, S., I, 162.
+  Newcomen, T., I, _147_.
+  Newton, Sir Isaac, I, 5, 6, 8, 24, 39, 84, 88, 130,
+      136, 139, 144, 145, 148, 152, 154, 155, 162, 165,
+      167, 197, 225, 237, 242, 257, 282, 296, 297, 309,
+      311, 382, 394, 395, 396, 397; II, 2, 70, 184, 297, _302_,
+      305.
+  Newton, John, II, _305_.
+  Nicene Creed, I, 371.
+  Nichol, J. P., II, _289_.
+  Nicholas. (_See Cusa._)
+  Nichols, J., I, _175_.
+  Nicolas, N. H., I, _354_.
+  Nicollet, I, _326_; II, 131.
+  Nicolson, W., I, _201_.
+  Nieuwentijt, II, _333_.
+  Nizzoli, M., II, 275.
+  Non-Euclidean geometry, II, 83.
+  Northampton, Marquis of (2d), II, _19_.
+  Novum Organum Moralium, II, 74.
+  Number, Mystery of, I, 55, 56, 169.
+  Number of the Beast (666), I, 55, 130, 272, 298, 352; II, 77,
+      159, 217, 218, 361, 373.
+  Numeral system, II, 68.
+  Nursery rhymes, II, 150.
+
+  Occam, Wm. of, II, _40_.
+  Odgers, N., II, 191, _191_.
+  Oinopides of Chios, II, _59_.
+  Oldenburgh, H., II, _300_, 302.
+  Orthodox Paradoxes, II, 363.
+  Orthography, Paradoxes of, II, 267.
+  Ortwinus, I, 319.
+  Oughtred, W., II, _298_, 303.
+  Owenson, I, _191_.
+  Ozanam, I, _161_, 312.
+
+  Pagi, I, 32.
+  Paine, T., I, 173, _173_, 271.
+  Paley, W., I, _222_; II, 226.
+  Palmer, C., I, 225.
+  Palmer, H., I, _141_, 141, 145.
+  Palmer, J., II, _253_.
+  Palmer, T. F., II, _254_.
+  Palmer, W., II, _37_.
+  Palmerston, Viscount (3d), I, _290_, 352.
+  Palmezeaux, I, 167.
+  Panizzi, A., I, _151_.
+  Papist, II, 26.
+  Paracelsus, II, 322.
+  Paradox defined, I, 2, 31.
+  Paradox, religious, I, 236.
+  Paradoxers in general, II, 352.
+  Parallels, Theory of, I, 229, 344.
+  Pardies, I. G., II, _300_.
+  Park, Mungo, II, _91_, 132.
+  Parker, F., II, _94_.
+  Parker, G. (Earl of Macclesfield), II, _296_.
+  Parr, S., I, 173, _173_, 175, 176, 184.
+  Parsey, I, 293, _293_.
+  Partridge, J., I, _305_.
+  Pasbergius, I, 381.
+  Pascal, I, 39, 119, 122, _220_, _221_; II, 73.
+  Pascal's Hexagram, I, 221.
+  Passot, I, 279, _279_.
+  Passover, I, 358, 372.
+  Patriotic paradox, I, 231.
+  Paucton, I, _172_.
+  Paulian, I, 165, _165_.
+  Peacock, Geo., I, _196_, 350.
+  Peacock, T. L., I, _190_, 340.
+  Pearce, A. J., II, 43.
+  Pearne, T., I, _239_.
+  Peel, Sir R., I, 290, _352_.
+  Peel, W. Y., I, _290_.
+  Pelerin, J., II, _324_.
+  Pell, J., I, _105_, 105, 107; II, 300, 302, 312.
+  Pepys, I, _113_, 114.
+  Perigal, H., II, 19, _20_.
+  {384}
+  Perpetual motion, I, 118, 348; II, 55, 138.
+  Perspective, New theory of, I, 293.
+  Peters, W., II, 11, 315.
+  Petitioning Comet, I, 127.
+  Petrie, W. M. F., I, _328_.
+  Petty, I, _114_; II, 300.
+  Philalethes, Eirenaeus, I, _125_, 125, 126.
+  Philalethes, Eugenius, I, _255_.
+  Phillips, R., I, 242, _242_, 245.
+  Philo of Gadara, I, 40, _40_.
+  Philosopher's stone, I, 118, 125.
+  Philosophical atheists, II, 1.
+  Philosophy and Religion, II, 37.
+  Phonetic spelling, II, 81.
+  [pi], values of, I, 11, 43, 45, 46, 52, 69, 100, 110,
+      129, 135, 146, 245, 283, 284, 294, 347, 348, 349,
+      350; II, 60, 63, 105, 110, 118, 135, 156, 209, 279, 315, 316.
+  Pighius, I, _372_.
+  Pike, S., I, 236, _236_.
+  Pindar, P., II, _272_.
+  Piozzi, Mrs., I, _235_; II, 272.
+  Piscator, B., II, 25.
+  Pitman, F., II, 81, _81_.
+  Place, F., I, _199_.
+  Planets inhabitable, I, 100, 102.
+  Plato, I, 5.
+  Platt, H., I, _126_, 126.
+  Playfair, J., I, _233_.
+  Pletho, G., I, _188_.
+  Pliny, II, 280.
+  Ploucquet, I, _336_, 337.
+  Poe, E. A., II, 132.
+  Poincare, I, 136.
+  Poisson, I, _292_; II, 2.
+  Pollock, J. F., II, _174_.
+  Pons, II, _45_.
+  Pope, Wm., I, 277, _277_.
+  Porta, I, _68_, 68, 83.
+  Porteus, B., I, _193_, 203.
+  Porteus, H. F. A., II, 157, _157_.
+  Porus, I, 44.
+  Powell, Baden, II, _267_.
+  Powell, W. S., I, _222_.
+  Pratt, H. F. A., II, 157, _157_.
+  Pratt, O., II, _69_.
+  Predaval, Count de, I, _348_.
+  Prescot, B., I, 270, _270_, 278.
+  Prester John, I, 70, _71_, 152.
+  Price, R., I, _223_.
+  Probability, Discourse on, I, 279.
+  Proclus, I, 188, _188_.
+  Prodigies, Youthful, I, 219, 332.
+  Pronunciation, II, 330.
+  Protestant and Papal Christendom, II, 33.
+  Protimalethes, II, 6.
+  Ptolemy, I, 5, 33, _380_.
+  Pullicino, II, 61, _61_.
+  Pusey, I, _64_.
+  Pyramids, The, I, 328; II, 95, 136.
+  Pythagoras, II, _59_.
+
+  Quadrature problem. (_See Squaring the circle._)
+  Quarles, F., II, _277_.
+  Quintilian, II, 280.
+  Quotem, C., I, 399.
+
+  Rabelais, I, _102_.
+  Rainbow Paradox, II, 334.
+  Ramachandra, Y., I, _374_.
+  Ramchundra, I, 374.
+  Ramus, I, 5.
+  Recalcati, II, 208, 314.
+  Recorde, R., II, _328_.
+  Reddie, Jas., II, 183, _183_, 344, 360.
+  Reeve, J., I, _395_.
+  Regiomontanus, I, _48_, 360.
+  Reisch, I, _45_; II, 281.
+  Religion and Philosophy, II, 37.
+  Religious bodies, Names of, II, 22;
+    --customs, Attacks on, I, 177;
+    --Insurance, I, 345;
+    --Paradox, I, 236;
+    --Tract society, I, 192.
+  Remigius, I, _50_.
+  Reuchlin, J., II, _323_.
+  Revelations, Napier on, I, 66.
+  Revilo, (O. Byrne), I, 241, 329, _329_.
+  Reyneau, C. R., II, _301_.
+  Rheticus, I, _69_; II, 372.
+  Rhonius, II, 300.
+  Ribadeneira, P. de, II, _62_.
+  Riccioli, I, _96_.
+  Richards, G., II, _270_.
+  Rigaud, J., II, _299_.
+  Rigaud, S. J., II, _299_.
+  Rigaud, S. P., I, _140_; II, 298, 313.
+  Ringelbergh, J. S., II, _281_.
+  Ripley, G., I, _126_, 126.
+  Ritchie, W., I, 295, _295_.
+  Ritterhusius, I, _60_.
+  Rive, J.-J., I, _160_.
+  Robertson, Jas., I, _237_.
+  Roberval, I, _105_, 122.
+  {385}
+  Robinson, B., I, _148_, 148.
+  Robinson, H. C., I, _314_; II, 52, 275.
+  Robinson, R., I, _177_.
+  Robinson, T. R., II, _181_.
+  Roblin, J., II, 136.
+  Rogers, S., II, _260_.
+  Roget, P. M., I, _398_.
+  Roomen, A. van, I, _110_.
+  Ross, J. C., I, _303_.
+  Rosse, I, 26.
+  Rossi, G., I, 231, _231_.
+  Rotation of the Moon, II, 4, 19.
+  Rough, W., I, 198.
+  Rowning, J., I, _155_.
+  Royal Astronomical Society, I, 27;
+    --Forerunner of, I, 374.
+  Royal Society, I, 21, 22, 24-30, 56, 57, 136, 153, 163,
+      164, 165.
+  Rudio, I, 159; II, 367.
+  Rudolff, C., II, 373.
+  Russell, Earl (1st), I, _296_.
+  Rutherford, W., II, _109_.
+
+  Sabatier, A., II, _267_.
+  Sabellius, I, _241_.
+  Sacrobosco, I, _360_.
+  Sadler, T., I, _238_, 241.
+  Saint-Martin, I, 167, _168_, 206.
+  St.-Mesmin, M. de., I, 280.
+  St. Vincent, G. de., I, _110_, 117.
+  St. Vitus, Patron of Cyclometers, II, 60.
+  Sales, de, I, 167.
+  Salicetus, I, 64.
+  Salisbury, Earl of (1st), II, _330_.
+  Salmasius, Claudius, II, _168_.
+  Salusbury, Hester, I, _235_.
+  Sanchez, Petro, I, 229, _229_.
+  Sanders, W., I, 207.
+  Sanderson, R., I, _135_.
+  Sara, R., I, _297_.
+  Saunderson, N., I, _377_; II, 301.
+  Scaliger, I, _44_, 110, 111, 112, 113; II, 238.
+  Scevole de St. Marthe, I, 113.
+  Schooten, Van, II, _59_.
+  Schopp, I, _60_.
+  Schott, I, _64_; II, 64.
+  Schumacher, H. C., I, _107_; II, 297.
+  Schwab, I, _230_.
+  Scientific paradoxes, I, 232.
+  Scott, Michael, I, _38_.
+  Scott's Devils, I, 38.
+  Scott, W., I, 20, 27, 38, 39, 155, _191_.
+  Scripture and Science, II, 261.
+  Search, John, I, 247.
+  Selden, J., II, _250_.
+  Senarmont, II, _48_.
+  Serres, De, II, _60_.
+  Shaftesbury, Earl of, II, _181_.
+  Shakespeare, I, 13.
+  Shanks, II, _63_, 65, 109.
+  Shaw, P., I, _142_.
+  Sheepshanks, J., I, _147_.
+  Sheepshanks, R., I, _290_.
+  Shelley, I, 174.
+  Shepherd, S., I, _124_.
+  Sherburne, E., II, _295_.
+  Sheridan, R. B., I, _175_.
+  Sheridan, T., I, _175_.
+  Shoberl, F., II, _270_.
+  Shrewsbury, I, _108_.
+  Siddons, Mrs., I, 189.
+  Simms, W., I, _152_.
+  Simplicius, II, _164_.
+  Simpson, T., I, 377; II, 304.
+  Simson, R., I, _197_, 202, 233.
+  Sinclair, G., I, _207_.
+  Slander Paradoxes, II, 138.
+  Sloane, I, 24.
+  Sluse, R. de, I, _118_, 118; II, 300.
+  Smith, Adam, II, _112_.
+  Smith, Jas., I, _46_; II, 103, _103_, 154, 236, 237, 238, 241, 336,
+      360.
+  Smith, Jas., II, _217_.
+  Smith, Jas. (Shepherd), II, _55_, 193.
+  Smith, Joseph, II, _69_.
+  Smith, Richarda, I, _242_.
+  Smith, Thomas, I, 346, _346_.
+  Smith, Wm., II, _152_.
+  Smyth, C. P., I, _328_; II, 65.
+  Snell, I, _75_, 75.
+  Socinianism, I, 142, 143.
+  Socinus, I, 3, _143_.
+  Socrates Scholasticus, I, _358_.
+  Sohncke, L. A., II, _131_.
+  Somerville, Mrs., I, _242_.
+  South, J., II, _181_.
+  Southcott, Joanna, II, _58_, 97, 239.
+  Spearman, R., I, _237_.
+  Speculative thought in England, I, 374.
+  Spedding, I, _76_, 82, 142.
+  Speed, J., I, _201_.
+  Speke, I, _70_.
+  Spelling, phonetic, II, 81.
+  Spence, W., I, _231_, 231.
+  Spencer, Earl (3d), II, _9_.
+  {386}
+  Spinoza, I, 3, _37_.
+  Spiritualism, II, 47, 55, 207.
+  Spurius Cassius Viscellinus, II, _342_.
+  Spurius Maelius, II, _342_.
+  Squaring the circle, I, 8, 42, 44, 46, 47, 50, 52, 53,
+      69, 70, 75, 109, 117, 119, 129, 135, 146, 149,
+      159, 163, 164, 347, 348, 374; II, 10, 11, 60, 105, 154,
+      156, 208, 278, 314.
+  Staeckel, I, 230.
+  Stanhope, P. D., (Earl of Chesterfield), II, _298_.
+  Stapulensis, I, _44_; II, 324.
+  Star polygons, I, 229.
+  Starkie, G., I, _126_, 126.
+  Statter, D., II, 80.
+  Steamship suggested, I, 147.
+  Steel, Jas., II, 68.
+  Stenography, II, 81.
+  Stephens, I, _44_; II, 324.
+  Stephenson, G., II, _138_.
+  Stephenson, R., II, _138_.
+  Stevin, I, _83_, 313; II, 59.
+  Stewart, D., II, _53_.
+  Stewart, R., I, _186_.
+  Stifel, M., II, _373_.
+  Strafford, Earl of, I, _240_.
+  Stratford, W. S., I, _300_.
+  Street, T., I, _124_.
+  Stukely, W., I, _236_.
+  Suffield, G., II, _66_.
+  Suidas, II, _29_.
+  Sumner, C. R., I, _324_.
+  Sumner, J. B., I, _324_.
+  Sun as an electric space, II, 41.
+  Supernatural, The, II, 193.
+  Suvaroff, II, _85_.
+  Swastika, II, 231.
+  Swedenborg, E., I, _255_.
+  Swift, I, 19, 133.
+  Sylvester, J. J., II, _336_.
+  Symington, W., I, _148_.
+  Symons, II, 4, 5, 20, 84, 85.
+  Sympathetic powder, I, 108.
+  Synesius, I, 125.
+
+  Talbot, G., I, _22_, _108_.
+  Talbot's powder, I, 108.
+  Tartaglia, II, 59.
+  Tasse, I, _106_.
+  Tate, J., I, _199_.
+  Tauler, J., II, _322_.
+  Taylor, Brook, II, _301_.
+  Taylor, John, I, _352_; II, 95.
+  Taylor, Robt., I, _270_.
+  Taylor, T., I, 188, _188_.
+  Teissier, I, _113_.
+  Temple, H. J., I, 290.
+  Tenterden, Chief Justice, I, _181_.
+  Thales, II, _59_, 83.
+  Theism independent of Revelation, I, 399.
+  Thelwall, J., I, _178_.
+  Theodoretus, I, _358_.
+  Theological Paradoxes, I, 316.
+  Theology, Mathematical, I, 129, 149.
+  Theophrastus, II, _167_.
+  Thiebault, II, _3_, 338.
+  Thom, D., II, _226_, 240.
+  Thom, J. H., II, _226_.
+  Thompson, P., I, _7_.
+  Thompson, T. P., I, _252_, 287, 344; II, 83, 185.
+  Thomson, Dr., I, 21.
+  Thomson, W., I, _325_.
+  Thorn, W., II, 158, _158_, 360.
+  Thorndike, H., II, _313_.
+  Thrale, Mrs., I, _235_.
+  Thurlow, Baron, I, _222_.
+  Thyraeus, I, 50.
+  Tides, New theory of, I, 393.
+  Tombstones of mathematicians, I, 106.
+  Tonal System, II, 182.
+  Tooke, H., I, _178_.
+  Torriano, E., I, 250.
+  Towneley, II, 300.
+  Townley, C., II, _300_.
+  Trisection problem, I, 118; II, 10, 12, 13, 15.
+  Troughton, I, _152_.
+  Turnor, E., I, _137_.
+  Tycho Brahe, I, 5, _76_, 381; II, 302, 335.
+
+  Upton, W., II, 12, _12_, 15.
+  Ursus, I, _52_.
+
+  Valentine, B., I, _125_, 125.
+  Van Ceulen, I, 52, 70, 100.
+  Van de Weyer, I, _313_.
+  Van Etten, I, _161_.
+  Van Helmont, I, _125_, 125.
+  Van Roomen, I, _110_.
+  Van Schooten, II, _59_.
+  Vaughan, T., I, _255_.
+  Victorinus, I, _359_.
+  Viete, I, _51_; II, 210, 295.
+  Virgil, St., I, 32, _33_, 34, 99.
+  {387}
+  Virginia, University of, I, 233.
+  Viscellinus, II, _342_.
+  Vitruvius, II, _281_.
+  Vivian, T., I, 172, _172_.
+  Vogel, A. F., I, 373.
+  Voltaire, I, 103, 165, 166, 167, 168, 248; II, 268.
+  Von Gumpach, II, 137, _137_.
+  Von Hutten, I, 318.
+  Von Wolzogen. (_See Wolzogen._)
+  Vyse, R. W. H., I, _328_.
+
+  Walker, W. E., II, _316_.
+  Walkingame, F., II, _173_.
+  Wallich, N., II, _14_.
+  Wallis, J., I, 107, 109, 110; II, 299, 313.
+  Walpole, I, _23_, 131.
+  Walsh, John, I, 260, _260_; II, 157.
+  Wapshare, J., II, _230_.
+  Warburton, H., I, _349_.
+  Warburton, Wm., I, _55_, 112; II, 174.
+  Ward, S., II, _299_.
+  Waring, E., I, _203_, 222.
+  Warner, W., II, _302_, 312.
+  Warren, S., II, _340_.
+  Watkins, J., II, _270_.
+  Watson, Bp., I, _223_.
+  Watt, R., I, _102_, 402.
+  Watts, I., II, 18.
+  Weddle, T., II, _187_.
+  Wentworth, Thos., I, _240_.
+  Wharton, I, 115.
+  Whately, R., I, 246, _246_, 324.
+  Whately's Paradox, I, 246.
+  Whewell, I, _101_, 101, 273, 314, 380; II, 104, 246, 247.
+  Whigs, II, 22.
+  Whiston, J., I, _147_.
+  Whiston, W., I, 133, _133_, 146, 156, 311.
+  White, H. K., II, _271_.
+  White, J. B., I, 248.
+  White, R., I, 11.
+  Whitford, I, 105.
+  Whitworth, W. A., II, _344_.
+  Whizgig, On the, I, 254.
+  Wightman, I, 59.
+  Wilberforce, W., II, _236_.
+  Wilkins, J., I, 96, _100_, 116, 226.
+  Williams, J. B., I, _378_.
+  Williams, T., I, 171, _171_.
+  Wilson, Sir J., I, _221_.
+  Wilson, J. M., II, _344_.
+  Wilson, R., II, 7, _7_.
+  Wilson's Theorem, I, _222_.
+  Wingate, E., II, _308_.
+  Winter, I, 46.
+  Wirgman, T., I, 258, _258_.
+  Wiseman, N. P. S., II, _26_, 61, 294.
+  Wolcot, J. (Peter Pindar), II, _272_.
+  Wollstonecraft, I, 173, _173_.
+  Wolzogen, I, _106_.
+  Wood, A., I, _98_.
+  Wood, John, I, _233_.
+  Wood, Wm., I, 246, _246_.
+  Woodley, W., I, 307, _307_.
+  Wordsworth, II, 273.
+  Wright, E., I, 84.
+  Wright, T., I, 151, _151_, 152, 153.
+  Wright, W., II, 9.
+  Wronski, I, 249, _250_.
+  Wrottesley, J. (Baron), II, _181_.
+
+  Young, B., II, _69_.
+  Young, J. W. A., II, 367.
+  Young, T., I, 24, 30, _250_.
+  Youthful Prodigies, I, 219.
+  Yvon, I, _297_.
+
+  Zach, von, II, _45_, 196.
+  Zachary, Pope, I, 32, 34.
+  Zadkiel, I, _321_; II, 43.
+  Zetetic Astronomy, II, 88.
+  Zodiac, II, 136.
+  Zytphen, II, _335_.
+
+       *       *       *       *       *
+
+
+Notes
+
+Transcriber's note: References to Notes in Volume I are shown as in the
+printed book, with the resequenced footnote numbers in the Project
+Gutenberg Edition (EText-No. 23100) added thus {123}.
+
+[1] See Vol. I, page 255, note 6 {584}.
+
+[2] "I have no need for this hypothesis."
+
+[3] "Ah, it is a beautiful hypothesis; it explains many things."
+
+[4] "What we know is very slight; what we don't know is immense."
+
+[5] Brewster relates (_Life of Sir Isaac Newton_, Vol. II, p. 407) that, a
+short time before his death, Newton remarked: "I do not know what I may
+appear to the world, but to myself I seem to have been only like a boy
+playing on the seashore, and diverting myself in now and then finding a
+smoother pebble or a prettier shell than ordinary, whilst the great ocean
+of truth lay all undiscovered before me."
+
+[6] See Vol. I, p. 292, note 1 {632}.
+
+[7] "What is all that!"
+
+[8] "I have some good news to tell you: at the Bureau of Longitudes they
+have just received a letter from Germany announcing that M. Bessel has
+verified by observation your theoretical discoveries on the satellites of
+Jupiter."
+
+[9] "Man follows only phantoms."
+
+[10] See Vol. I, page 382, note 13 {786}.
+
+[11] Dieudonne Thiebault (1733-1807) was a Jesuit in his early life, but he
+left the order and took up the study of law. In 1765 he went to Prussia and
+became a favorite of Frederick the Great. He returned to France in 1785 and
+became head of the Lycee at Versailles.
+
+[12] _Memories of Twenty Years of Residence in Berlin._ There was a second
+French and an English edition in 1805.
+
+[13] Richard Joachim Heinrich von Mollendorff (1724-1816) began his career
+as a page of Frederick the Great (1740) and became field marshal (1793) and
+commander of the Prussian army on the Rhine (1794).
+
+[14] Hugues Bernard Maret (1763-1839) was not Duc de Bassano in 1807, this
+title not being conferred upon him until 1809. He was ambassador to England
+in 1792 and to Naples in 1793. Napoleon made him head of the cabinet and
+his special confidant. The Bourbons exiled him in 1816.
+
+[15] Denis Diderot (1713-1784), whose _Lettre sur les aveugles_ (1749)
+introduced him to the world as a philosopher, and whose work on the
+_Encyclopedie_ is so well known.
+
+[16] "Sir, (a + b^{n}) / n = x, whence God exists; answer!"
+
+[17] This was one James Laurie of Musselburgh.
+
+[18] Jelinger Cookson Symons (1809-1860) was an office-holder with a
+decided leaning towards the improvement of education and social conditions.
+He wrote _A Plea for Schools_ (1847), _The Industrial Capacities of South
+Wales_ (1855), and _Lunar Motion_ (1856), to which last work the critic
+probably refers.
+
+[19] "Protimalethes" followed this by another work along the same line the
+following year, _The Independence of the Testimony of St. Matthew and St.
+John tested and vindicated by the theory of chances_.
+
+[20] Wilson had already taken up the lance against science in his
+_Strictures on Geology and Astronomy, in reference to a supposed want of
+harmony between these sciences and some parts of Divine Revelation_,
+Glasgow, 1843. He had also ventured upon poetry in his _Pleasures of
+Piety_, Glasgow, 1837.
+
+[21] Mrs. Borron was Elizabeth Willesford Mills before her marriage. She
+made an attempt at literature in her _Sibyl's Leaves_, London (printed at
+Devonport), 1826.
+
+[22] See Vol. I, page 386, note 10 {801}.
+
+[23] See Vol. I, page 43, notes 7 {32} and 8 {33}.
+
+[24] His flying machine, designed in 1843, was one of the earliest attempts
+at aviation on any extensive scale.
+
+[25] Erasmus Darwin (1731-1802) was the grandfather of Charles Darwin. The
+work here mentioned had great influence, being translated into French,
+Portuguese, and Italian. Canning parodied it in his _Loves of the
+Triangles_.
+
+[26] See Vol. I, page 147, note 1 {312}.
+
+[27] The notes on this page were written on the day of the funeral of
+Wilbur Wright, June 1, 1912, the man who realized all of these prophecies,
+and then died a victim of municipal crime,--of typhoid fever.
+
+[28] John Charles, third Earl Spencer (1782-1845), to whose efforts the
+Reform Bill was greatly indebted for its final success.
+
+[29] This was published in London in 1851 instead of 1848.
+
+[30] This appeared in 1846.
+
+[31] This was done in _The Circle Squared_, published at Brighton in 1865.
+
+[32] It first appeared in 1847, under the title, _The Scriptural Calendar
+and Chronological Reformer, 1848. Including a review of tracts by Dr.
+Wardlaw and others on the Sabbath question. By W. H. Black._ The one above
+mentioned, for 1849, was printed in 1848, and was also by Black
+(1808-1872). He was pastor of the Seventh Day Baptists and was interested
+in archeology and in books. He catalogued the manuscripts of the Ashmolean
+Museum at Oxford.
+
+[33] William Upton, a Trinity College man, Dublin. He also wrote _Upton's
+Physioglyphics_, London, 1844; _Pars prima. Geometria vindicata;
+antiquorumque Problematum, ad hoc tempus desperatorum, Trisectionis Anguli,
+Circulique Quadraturae, Solutio, per Eucliden effecta, London_ (printed at
+Southampton), 1847; _The Uptonian Trisection_, London, 1866; and _The
+Circle Squared_, London, 1872.
+
+[34] For example, if [theta] = 90 deg. we should have 3 cos 30 deg. = 1
++ [root](4 - sin^2 90 deg.), or 3. 1/2 [root]3 = 1 + [root]3, or
+1/2 [root]3 = 1.
+
+[35] Nathaniel Wallich (1786-1854) was surgeon at the Danish settlement at
+Serampore when the East India Company took over the control in 1807. He
+entered the British medical service and was invalided to England in 1828.
+His _Plantae Asiaticae Rariores_ (3 vols., London, 1830-1832) was
+recognized as a standard. He became vice-president of the Linnean Society,
+F. R. S., and fellow of the Royal Asiatic Society.
+
+[36] But if [theta] = 90 deg. this asserts that
+
+  cos 30 deg. = (sin 270 deg. . cos 225 deg. + sin^2 90 deg.
+  . sin 225 deg.) / [root](sin^2
+      270 deg. . cos^2 225 deg. + sin^{4} 90 deg. + sin 270 deg.
+      . sin 450 deg. . sin^2 90 deg.),
+
+or that
+
+  1/2 [root]3 = (-1 . (-1 /[root]2) + 1 . (-1/[root]2) / [root]1
+      . 1/2 + 1 - 1 . 1 . 1) = 0 / [root](1/2),
+
+so that De Morgan must have made some error in copying.
+
+[37] John Bonnycastle (died in 1821) was professor of mathematics at
+Woolwich. His edition of Bossut's _History of Mathematics_ (1803), and his
+works on elementary mathematics were well known.
+
+[38] The bibliographies give Husain Rifki as the translator, a practical
+geometry as the work, and 1802 as the date.
+
+[39] See Vol. I, page 309, note 2 {670}.
+
+[40] Probably in _The Improvement of the Mind_ which Isaac Watts
+(1674-1748) published in 1741. His _Horae Lyricae_ appeared in 1706, and
+the _Hymns_, by which he is still well known, in 1707.
+
+[41] Spencer Joshua Alwyne Compton, second Marquis of Northampton
+(1790-1851), was a poet, a scientist, and a statesman. He was president of
+the Royal Society from 1838 to 1849.
+
+[42] Besides the writings here mentioned Perigal published a work on
+_Geometric Maps_ (London, 1853), and _Graphic Demonstrations of Geometric
+Problems_ (1891).
+
+[43] See Vol. II, page 5, note 18.
+
+[44] James Ferguson (1710-1776) was a portrait painter, an astronomer, and
+a popular writer and lecturer on various subjects.
+
+[45] In the old ballad of King Alfred and the Shepherd, when the latter is
+tempting the disguised king into his service, he says:
+
+ "Of whig and whey we have good store,
+  And keep good pease-straw fire."
+
+_Whig_ is then a preparation of milk. But another commonly cited derivation
+may be suspected from the word _whiggamor_ being used before _whig_, as
+applied to the political party; _whig_ may be a contraction. Perhaps both
+derivations conspired: the word _whiggamor_, said to be a word of command
+to the horses, might contract into _whig_, and the contraction might be
+welcomed for its own native meaning.--A. De M.
+
+[46] This was p. 147 in the first edition.
+
+[47] St. Augustine (354-430) was bishop of Hippo. His _Confessiones_, in
+13 books, was written in 397, and his _De Civitate Dei_ in 426.
+
+[48] "He was wont to indulge in certain Punic subtleties lest he should
+weary the reader by much speaking."
+
+[49] John Milner (1751-1826), bishop of Castabala, a well-known
+antiquarian.
+
+[50] It will be said that when the final happiness is spoken of in "sure
+and certain hope," it is _the_ Resurrection, generally; but when afterwards
+application is made to the individual, simple "hope" is all that is
+predicated which merely means "wish?" I know it: but just before the
+general declaration, it is declared that it _has_ pleased God of his great
+mercy to _take unto Himself_, the soul of our dear brother: and between the
+"hopes" hearty thanks are given that it _has_ pleased God to deliver our
+dear brother out of the miseries of this wicked world, with an additional
+prayer that the number of the elect may shortly be accomplished. All which
+means, that our dear brother is declared to be taken to God, to be in a
+place not so miserable as this world--a description which excludes the
+"wicked place"--and to be of the elect. Yes, but it will be said again! do
+you not know that when this Liturgy was framed, all who were not in the
+road to Heaven were excommunicated burial service read over them. Supposing
+the fact to have been true in old time, which is a very spicy supposition,
+how does that excuse the present practice? Have you a right _always_ to say
+what you believe _cannot always_ be true, because you think it was once
+_always_ true? Yes, but, choose whom you please, you cannot be _certain_ He
+is _not_ gone to Heaven. True, and choose which Bishop you please, you
+cannot be demonstratively _certain_, he is _not_ a concealed unbeliever:
+may I therefore say of the whole bench, _singulatim et seriatim_, that they
+_are_ unbelievers? No! No! The voice of common sense, of which common logic
+is a part, is slowly opening the eyes of the multitude to the unprincipled
+reasoning of theologians. Remember 1819. What chance had Parliamentary
+Reform when the House of Commons thanked the Manchester sabre-men? If you
+do not reform your Liturgy, it will be reformed for you, and sooner than
+you think! The dishonest interpretations, by defence of which even the
+minds of children are corrupted, and which throw their shoots into
+literature and commerce, will be sent to the place whence they came: and
+over the door of the established organization for teaching religion will be
+posted the following notice:
+
+ "Shift and Subterfuge, Shuffle and Dodge,
+  No longer here allowed to lodge!"
+
+All this ought to be written by some one who belongs to the Establishment:
+in him, it would be quite prudent and proper; in me, it is kind and
+charitable.--A. De M.
+
+[51] But few do have access to it, for the work is not at all common, and
+this Piscator is rarely mentioned.
+
+[52] This derivation has been omitted.--S. E. De M.
+
+[53] A blow for a blow. Roland and Oliver were two of the paladins of
+Charlemagne whose exploits were so alike that each was constantly receiving
+credit for what the other did. Finally they met and fought for five days on
+an island in the Rhine, but even at the end of that period it was merely a
+drawn battle.
+
+[54] "In the name of the church."
+
+[55] "From the chair," officially.
+
+[56] Nicholas Patrick Stephen Wiseman (1802-1865), whose elevation to the
+archbishopric of Westminster and the cardinalate (1850) led to the act
+prohibiting Roman Catholics from assuming episcopal titles in England, a
+law that was never enforced.
+
+[57] He was born in 1812 and was converted to Catholicism in 1839. He
+founded the _Tablet_ in London in 1840, removing its office to Dublin in
+1849. He became M. P. in 1852, and at the time of his death (1855) he was
+preparing a memorial to the Pope asking him to annul the proclamation of an
+Irish bishop prohibiting his priests from taking part in politics.
+
+[58] John Guillim (1565-1621) was the first to systematize and illustrate
+the whole science of heraldry. He published _A display of Heraldrie:
+manifesting a more easie accesse to the knowledge thereof_ in 1610.
+
+[59] "Faith."
+
+[60] "Faithful."
+
+[61] "For the faith vindicated."
+
+[62] The words are of the same root, and hence our word _fiddle_. Some
+suppose this root means a _rope_, which, as that to which you trust,
+becomes, in one divergence, confidence itself--just as a _rock_, and other
+words, come to mean reliance--and in another, a little string.--A. De M.
+
+[63] The Greek lexicographer, a Christian, living after 1000 A. D. His
+lexicon was first printed at Milan in 1499.
+
+[64] _Skindapsos._
+
+[65] This was John William Burgon (1813-1888), Gresham professor of
+theology (1867) and dean of Chichester. He was an ultra-conservative,
+opposing the revised version of the New Testament, and saying of the
+admission of women to the university examinations that it was "a thing
+inexpedient and immodest."
+
+[66] _Ekklesia_, or _ecclesia_.
+
+[67] _Ennomos ekklesia._
+
+[68] "Without doubt I shall perish forever."
+
+[69] "Every man is an animal." "Sortes is a man." "Sortes is an animal."
+
+[70] "For a special purpose."
+
+[71] Heraclitus of Ephesus, the weeping philosopher, 6th century B. C.
+
+[72] Democritus, the laughing philosopher, founder of the atomistic theory,
+5th century B. C.
+
+[73] "Ends to which."
+
+[74] "Ends from which."
+
+[75] "In just as many syllables," "With just as many letters," "In just as
+many words."
+
+[76] "I shall make a way," "I shall find a way."
+
+[77] The notion that the Evil Spirit is a functionary liable to be
+dismissed for not attending to his duty, is, so far as my reading goes,
+utterly unknown in theology. My first wrinkle on the subject was the remark
+of the Somersetshire farmer upon Palmer the poisoner-- "Well! if the Devil
+don't take he, he didn't ought to be allowed to be devil no longer."--A. De
+M.
+
+William Palmer (1824-1856) was a member of the Royal College of Surgeons
+and practised medicine at London. He was hanged in 1856 for having poisoned
+a friend and was also suspected of having poisoned his wife and brother for
+their insurance money, besides being guilty of numerous other murders. His
+trial was very much in the public attention at the time.
+
+[78] Advantages and dangers.
+
+[79] The old priory of St. Mary of Bethlehem in London, was used as an
+asylum for the insane. The name was corrupted to Bedlam.
+
+[80] Referring to the common English pronunciation of St. John, almost
+Sinjin. John St. John Long (1798-1834), an Irishman by birth, practised
+medicine in London. He claimed to have found a specific for rheumatism and
+tuberculosis, but upon the death of one of his patients in 1830 he was
+tried for manslaughter. He died of tuberculosis four years later, refusing
+to take his own treatment.
+
+[81] William of Occam (d. 1349), so called from his birthplace, Ockham, in
+Surrey. He was a Franciscan, and lectured on philosophy in the Sorbonne.
+
+[82] He signs himself "James Hopkins, schoolmaster," and this seems to have
+been his only published effort.
+
+[83] Joseph Ady (1770-1852) was a famous swindler. One of his best-known
+schemes was to send out letters informing the recipients that they would
+learn something to their advantage on payment of a certain sum. He spent
+some time in prison.
+
+[84] Sir Peter Laurie (c. 1779-1861) was worth referring to, for he was
+prominent as a magistrate and was honored because of his interest in all
+social reforms. He made a fortune as a contractor, became sheriff of London
+in 1823, and was knighted in the following year. He became Lord Mayor of
+London in 1832.
+
+[85] See Vol. I, page 321, note 2 {691}. The _Astronomy in a nutshell_
+appeared in 1860. _The Herald of Astrology_ was first published in London
+in 1831, "by Zadkiel the Seer." It was continued as _The Astrological
+Almanac_ (London, 1834), as _Zadkiel's Almanac and Herald of Astrology_
+(_ibid._, 1835, edited by R. J. Morrison, and subsequently by A. J.
+Pearce), and as _Raphael's Prophetic Almanac_ (1840-1855).
+
+[86] See Vol. I, page 172, note 3 {382}.
+
+[87] See Vol. I, page 87, note 4 {133}.
+
+[88] Franz Xaver, Freiherr von Zach (1754-1832) was director of the
+observatory at Seeberge near Gotha. He wrote the _Tabulae speciales
+aberrationis et mutationis_ (1806-7), _Novae et correctae tabulae solis_
+(1792), and _L'attraction des montagnes et ses effets sur le fil a plomb_
+(1814).
+
+[89] Jean Louis Pons (1761-1831) was connected with the observatory at
+Marseilles for thirty years (1789-1819). He later became director of the
+observatory at Marlia, near Lucca, and subsequently filled the same office
+at Florence. He was an indefatigable searcher for comets, discovering 37
+between 1801 and 1827, among them being the one that bears Encke's name.
+
+[90] This hypothesis has now become an established fact.
+
+[91] John Chetwode Eustace (c. 1762-1815) was born in Ireland. Although a
+Roman Catholic priest he lived for a time at Cambridge where he did some
+tutoring. His _Classical Tour_ appeared in 1813 and went through several
+editions.
+
+[92] "Crimes should be exposed when they are punished, but disgraceful acts
+should be hidden."
+
+[93] Henri Hureau de Senarmont (1808-1862) was professor of mineralogy at
+the _Ecole des mines_ and examiner at the _Ecole polytechnique_ at Paris.
+
+[94] Augustin Jean Fresnel (1788-1827), "Ingenieur des ponts et chaussees,"
+gave the first experimental proofs of the wave theory of light. He studied
+the questions of interference and polarization, and determined the
+approximate velocity of light.
+
+[95] "As is my custom."
+
+[96] Francis Heywood (1796-1858) made the first English translation of
+Kant's _Critick of Pure Reason_ (1838, reprinted in 1848). The _Analysis_
+came out, as here stated, in 1844.
+
+[97] Louise Renee de Keroualle, Duchess of Portsmouth and Aubigny
+(1649-1734), was a favorite of Charles II. She used her influence to keep
+him under the control of Louis XIV.
+
+[98] William Chiffinch (c. 1602-1688) was page of the king's bed-chamber
+and keeper of the private closet to Charles II. He was one of the king's
+intimates and was an unscrupulous henchman.
+
+[99] "Well devised."
+
+[100] "John Bellingham Inglis. His _Philobiblion_ "translated from the
+first edition (of Ricardus d'Aungervile, Bishop of Durham), 1473," appeared
+at London in 1832. It was republished in America (Albany, N. Y.) in 1864.
+
+[101] "What are you laughing at?"
+
+[102] See Vol. I, page 314, note 4 {681}.
+
+[103] See Vol. I, page 112, note 7 {211}.
+
+[104] Referring to Hamilton's edition of the _Collected Works of Dugald
+Stewart_, 10 volumes, Edinburgh, 1854-58. It is not commonly remembered
+that Stewart (1753-1828) taught mathematics at the University of Edinburgh
+before he took up philosophy.
+
+[105] This was Hamilton's edition of the _Works of Thomas Reid_ (2 vols.,
+Edinburgh, 1846-1863). Reid (1710-1796) included mathematics in his work in
+philosophy at Aberdeen. In 1764 he succeeded Adam Smith at Glasgow.
+
+[106] Edward Irving (1792-1834), the famous preacher. At first he assisted
+Dr. Chalmers at Glasgow, but in 1822 he went to London where he met with
+great success. A few years later he became mentally unbalanced and was
+finally expelled from his church (1832) for heresy. He was a great friend
+of Carlyle.
+
+[107] He also wrote a number of other paradoxes, including _An Essay
+towards a Science of Consciousness_ (1838), _Instinctive Natural Religion_
+(1858), _Popular Treatise on the structure, diseases, and treatment of the
+human teeth_ (1837), and _On Headache_ (1859).
+
+[108] James Smith (1801-1857), known as Shepherd Smith, was a socialist and
+a mystic, with a philosophy that was wittily described as "Oriental
+pantheism translated into Scotch." He was editor of several journals.
+
+[109] Joanna Southcott (1750-1814) was known for her rhyming prophecies in
+which she announced herself as the woman spoken of in Revelations xii. She
+had at one time as many as 100,000 disciples, and she established a sect
+that long survived her.
+
+[110] Thales, c. 640-548 B. C.
+
+[111] Pythagoras, 580-501 B. C.
+
+[112] Anaxagoras, 499-428 B. C., the last of the Ionian school, teacher of
+Euripides and Pericles. Plutarch speaks of him as having squared the
+circle.
+
+[113] Oinopides of Chios, contemporary of Anaxagoras. Proclus tells us that
+Oinopides was the first to show how to let fall a perpendicular to a line
+from an external point.
+
+[114] Bryson and Antiphon, contemporaries of Socrates, invented the
+so-called method of exhaustions, one of the forerunners of the calculus.
+
+[115] He wrote, c. 440 B. C., the first elementary textbook on mathematics
+in the Greek language. The "lunes of Hippocrates" are well known in
+geometry.
+
+[116] Jabir ben Aflah. He lived c. 1085, at Seville, and wrote on astronomy
+and spherical trigonometry. The _Gebri filii Affla Hispalensis de
+astronomia libri_ IX was published at Nuremberg in 1533.
+
+[117] Hieronymus Cardanus, or Girolamo Cardano (1501-1576), the great
+algebraist. His _Artis magnae sive de regulis Algebrae_ was published at
+Nuremberg in 1545.
+
+[118] Nicolo Tartaglia (c. 1500-1557), the great rival of Cardan.
+
+[119] See note 5 {98}, Vol. I, page 69.
+
+[120] See note 10 {124}, Vol. I., page 83.
+
+[121] See note 9 {123}, Vol. I, page 83.
+
+[122] Pierre Herigone lived in Paris the first half of the 17th century.
+His _Cours mathematique_ (6 vols., 1634-1644) had some standing but was not
+at all original.
+
+[123] Franciscus van Schooten (died in 1661) was professor of mathematics
+at Leyden. He edited Descartes's _La Geometrie_.
+
+[124] Florimond de Beaune (1601-1652) was the first Frenchman to write a
+commentary on Descartes's _La Geometrie_. He did some noteworthy work in
+the theory of curves.
+
+[125] See note 3 {23}, Vol. I, page 41.
+
+[126] Olivier de Serres (b. in 1539) was a writer on agriculture. Montucla
+speaks of him in his _Quadrature du cercle_ (page 227) as having asserted
+that the circle is twice the inscribed equilateral triangle, although, as
+De Morgan points out, this did not fairly interpret his position.
+
+[127] Anghera wrote not only the three works here mentioned, but also the
+_Problemi del piu alto interesse scientifico, geometricamente risoluti e
+dimostrati_, Naples, 1861. His quadrature was defended by Giovanni Motti in
+a work entitled _Matematica Vera. Falsita del sistema ciclometrico
+d'Archimede, quadratura del cerchio d'Anghera, ricerca algebraica dei lati
+di qualunque poligono regolare inscritto in un circolo_, Voghera, 1877. The
+_Problemi_ of 1861 contains Anghera's portrait, and states that he lived at
+Malta from 1849 to 1861. It further states that the Malta publications are
+in part reproduced in this work.
+
+[128] This was his friend Paolo Pullicino whose _Elogio_ was pronounced by
+L. Farrugia at Malta in 1890. He wrote a work _La Santa Effegie della Blata
+Vergine Maria_, published at Valetta in 1868.
+
+[129] St. Vitus, St. Modestus, and St. Crescentia were all martyred the
+same day, being torn limb from limb after lions and molten lead had proved
+of no avail. At least so the story runs.
+
+[130] The reference is to Cardinal Wiseman. See Vol. II, page 26, note 56.
+
+[131] "Worthy of esteem."
+
+[132] Pedro de Ribadeneira (Ribadeneyra, Rivadeneira), was born at Toledo
+in 1526 and died in 1611. He held high position in the Jesuit order. The
+work referred to is the _Flos Sanctorum o libro de las vidas de los
+santos_, of which there was an edition at Barcelona in 1643. His life of
+Loyola (1572) and _Historia ecclesiastica del Cisma del reino de
+Inglaterra_ were well known.
+
+[133] Caesar Baronius (1538-1607) was made a cardinal in 1595 and became
+librarian at the Vatican in 1597. The work referred to appeared at Rome in
+1589.
+
+[134] Mrs. Jameson's (1794-1860) works were very popular half a century
+ago, and still have some circulation among art lovers. The first edition of
+the work mentioned appeared in 1848.
+
+[135] The barnyard cock.
+
+[136] Shanks did nothing but computing. The title should, of course, read
+"to 607 Places of _Decimals_." He later carried the computation to 707
+decimal places. (_Proc. Roy. Society_, XXI, p. 319.) He also prepared a
+table of prime numbers up to 60,000. (_Proc. Roy. Society_, XXII, p. 200.)
+
+[137] See Vol. I, page 42, note 4 {24}.
+
+[138] See Vol. I, page 64, note 1 {78}.
+
+[139] See Vol. I, page 328, note 1 {704}.
+
+[140] George Suffield published _Synthetic Division in Arithmetic_, to
+which reference is made, in 1863.
+
+[141] John Robert Lunn wrote chiefly on Church matters, although he
+published a work on motion in 1859.
+
+[142] Jean Baptiste Joseph, Baron Fourier (1768-1830), sometime professor
+in the Military School at Paris, and later at the _Ecole polytechnique_. He
+is best known by his _Theorie analytique de la chaleur_ (Paris, 1822), in
+which the Fourier series is used. The work here referred to is the _Analyse
+des equations determinees_ (Paris, 1831).
+
+[143] William George Horner (1786-1837) acquired a name for himself in
+mathematics in a curious manner. He was not a university man nor was he a
+mathematician of any standing. He taught school near Bristol and at Bath,
+and seems to have stumbled upon his ingenious method for finding the
+approximate roots of numerical higher equations, including as a special
+case the extracting of the various roots of numbers. Davies Gilbert
+presented the method to the Royal Society in 1819, and it was reprinted in
+the _Ladies' Diary_ for 1838, and in the _Mathematician_ in 1843. The
+method was original as far as Horner was concerned, but it is practically
+identical with the one used by the Chinese algebraist Ch'in Chiu-shang, in
+his _Su-shu Chiu-chang_ of 1247. But even Ch'in Chiu-shang can hardly be
+called the discoverer of the method since it is merely the extension of a
+process for root extracting that appeared in the _Chiu-chang Suan-shu_ of
+the second century B. C.
+
+[144] He afterwards edited Loftus's _Inland Revenue Officers' Manual_
+(London, 1865). The two equations mentioned were x^3 - 2x = 5 and y^3 -
+90y^2 + 2500y - 16,000 = 0, in which y = 30 - 10x. Hence each place of y is
+the complement of the following place of x with respect to 9.
+
+[145] Probably the John Power Hicks who wrote a memoir on T. H. Key,
+London, 1893.
+
+[146] Possibly the one who wrote on the quadrature of the circle in 1881.
+
+[147] As it is. But what a pity that we have not 12 fingers, with
+duodecimal fractions instead of decimals! We should then have 0.6 for 1/2,
+0.4 for 1/3, 0.8 for 2/3, 0.3 for 1/4, 0.9 for 3/4, and 0.16 for 1/8,
+instead of 0.5, 0.333+, 0.666+, 0.25, 0.75, and 0.125 as we now have
+with our decimal system. In other words, the most frequently used
+fractions in business would be much more easily represented on the
+duodecimal scale than on the decimal scale that we now use.
+
+[148] He wrote Hints for an _Essay on Anemology and Ombrology_ (London,
+1839-40) and _The Music of the Eye_ (London, 1831).
+
+[149] Brigham Young (1801-1877) was born at Whitingham, Vermont, and
+entered the Mormon church in 1832. In 1840 he was sent as a missionary to
+England. After the death of Joseph Smith he became president of the Mormons
+(1847), leading the church to Salt Lake City (1848).
+
+[150] Joseph Smith (1805-1844) was also born in Vermont, and was four years
+the junior of Brigham Young. The _Book of Mormon_ appeared in 1827, and the
+church was founded in 1830. He was murdered in 1844.
+
+[151] Orson Pratt (1811-1881) was one of the twelve apostles of the Mormon
+Church (1835), and made several missionary journeys to England. He was
+professor of mathematics in the University of Deseret (the Mormon name for
+Utah). Besides the paper mentioned Pratt wrote the _Divine Authenticity of
+the Book of Mormon_ (1849), _Cubic and Biquadratic Equations_ (1866), and a
+_Key to the Universe_ (1866).
+
+[152] "It does not follow."
+
+[153] Dryden (1631-1700) published his _Religio Laici_ in 1682. The use of
+the word "proportion" in the sense of ratio was common before his time, but
+he uses it in the sense of having four terms; that is, that price is to
+price as offence is to offence.
+
+[154] Olinthus Gilbert Gregory (1774-1841) succeeded Hutton as professor of
+mathematics at Woolwich. He was, with De Morgan, much interested in
+founding the University of London. He wrote on astronomy (1793), mechanics
+(1806), practical mathematics (1825), and Christian evidences (1811).
+
+[155] See Vol. I, page 220, note 6 {482}. The _Pensees_ appeared
+posthumously in 1670.
+
+[156] "The right thing to do is not to wager at all." "Yes, but you ought
+to wager; you have started out; and not to wager at all that God exists is
+to wager that he does not exist."
+
+[157] He lived about 300 A.D., in Africa, and wrote _Libri septem adversus
+Gentes_. This was printed at Rome in 1542-3.
+
+[158] Pierre Bayle (1647-1706) was professor of philosophy at the
+Prostestant University at Sedan from 1675 until its dissolution in 1681. He
+then became professor at Rotterdam (1681-1693). In 1684 he began the
+publication of his journal of literary criticism _Nouvelles de la
+Republique des Lettres_. He is best known for his erudite _Dictionnaire
+historique et critique_ (1697).
+
+[159] "But Christ himself does not prove what he promises. It is true. For,
+as I have said, there cannot be any absolute proof of future events.
+Therefore since it is a condition of future events that they cannot be
+grasped or comprehended by any efforts of anticipation, is it not more
+reasonable, out of two alternatives that are uncertain and that are hanging
+in doubtful expectation, to give credence to the one that gives some hope
+rather than to the one that offers none at all? For in the former case
+there is no danger if, as is said to threaten, it becomes empty and void;
+while in the latter case the danger is greatest, that is, the loss of
+salvation, if when the time comes it is found that it was not a falsehood."
+
+[160] Gregg wrote several other paradoxes, including the following: _The
+Authentic Report of the extraordinary case of Tresham Dames Gregg ... his
+committal to Bridewell for refusing to give his recognizance_ (Dublin,
+1841), _An Appeal to Public Opinion upon a Case of Injury and Wrong ... in
+the case of a question of prerogative that arose between_ [R. Whately] _...
+Archbishop of Dublin and the author_ (London, 1861), _The Cosmology of Sir
+Isaac Newton proved to be in accordance with the Bible_ (London, 1871),
+_The Steam Locomotive as revealed in the Bible_ (London 1863) and _On the
+Sacred Law of 1866, conferring perpetual life with immunity from decay and
+disease. A cento of decisive scriptural oracles strangely discovered_
+(London and Dublin, 1875). These titles will help the reader to understand
+the man whom De Morgan so pleasantly satirizes.
+
+[161] See Vol. I, page 261, note 2 {592}.
+
+[162] "They have found it."
+
+[163] The late Greeks used the letters of their alphabet as numerals,
+adding three early alphabetic characters. The letter [chi] represented 600,
+[xi] represented 60, and [digamma] stood for 6. This gives 666, the number
+of the Beast given in the Revelation.
+
+[164] "Allowing for necessary exceptions."
+
+[165] Mr. Gregg is not alone in his efforts to use the calculus in original
+lines, as any one who has read Herbart's application of the subject to
+psychology will recall.
+
+[166] See Vol. I, page 105, note 4 {188}; page 109, note 1 {197}.
+
+[167] The full title shows the plan,--_The Decimal System as a whole, in
+its relation to time, measure, weight, capacity, and money, in unison with
+each other._ But why is this so much worse than the French plan of which we
+have only the metric system and the decimal division of the angle left?
+
+[168] One of the brothers of Sir Isaac Pitman (1813-1897), the inventor of
+modern stenography. Of these brothers, Benjamin taught the art in America,
+Jacob in Australia, and Joseph, Henry, and Frederick in England.
+
+[169] For example, _The Phonographic Lecturer_ (London, 1871 etc.), _The
+Phonographic Student_ (1867, etc.), and _The Shorthand Magazine_ (1866,
+etc.).
+
+[170] See Vol. II, page 68, note 148.
+
+[171] It involves the theory of non-Euclidean geometry, Euclid's postulate
+of parallels being used in proving this theorem.
+
+[172] Referring to the fact that none of the works of Thales is extant.
+
+[173] The author was one B. Bulstrode. Parts 4 and 5 were printed at
+Calcutta.
+
+[174] See Vol. II, page 5, note 18.
+
+[175] See Vol. I, page 85, note 2 {129}.
+
+[176] Alexander Vasilievich Suvaroff (1729-1800), a Russian general who
+fought against the Turks, in the Polish wars, and in the early Napoleonic
+campaigns. When he took Ismail in 1790 he sent this couplet to Empress
+Catherine.
+
+[177] "Newton hath determined rightly," "Newton hath not determined
+rightly."
+
+[178] See Vol. I, page 288, note 3 {621}.
+
+[179] See Vol. I, page 326, note 1 {700}.
+
+[180] "With great honor."
+
+[181] Apparently unknown to biographers. He seems to have written nothing
+else.
+
+[182] Captain Marryat (1792-1848) published _Snarley-yow, or the Dog Fiend_
+in 1837.
+
+[183] He is not known to biographers, and published nothing else under this
+name.
+
+[184] See Vol. I, page 80, note 5 {119}.
+
+[185] He published a _Family and Commercial Illustrated Almanack and Year
+Book ... for 1861_ (Bath, 1860).
+
+[186] Louis Dutens (1730-1812) was born at Tours, but went to England as a
+young man. He made the first collection of the works of Leibnitz, against
+the advice of Voltaire, who wrote to him: "Les ecrits de Leibnitz sont
+epars comme les feuilles de la Sybille, et aussi obscurs que les ecrits de
+cette vieille." The work appeared at Geneva, in six volumes, in 1769.
+
+[187] Mungo Park (1771-1806), the first European to explore the Niger
+(1795-6). His _Travels in the Interior of Africa_ appeared in 1799. He died
+in Africa.
+
+[188] Gerhard Mercator (1512-1594) the well-known map maker of Louvain. The
+"Mercator's Projection" was probably made as early as 1550, but the
+principle of its construction was first set forth by Edward Wright (London,
+1599).
+
+[189] Quirico Barilli Filopanti wrote a number of works and monographs. He
+succeeded in getting his _Cesare al Rubicone_ and _Degli_ _usi idraulici
+della Tela_ in the _Memoria letta ... all' Accademia delle Scienze in
+Bologna_ (1847, 1866). He also wrote _Dio esiste_ (1881), _Dio Liberale_
+(1880), and _Sunto della memoria sulle geuranie ossia di alcune singolari
+relazioni cosmiche della terra e del cielo_ (1862).
+
+[190] The periods of disembodiment may be interesting. They will be seen
+from the following dates: Descartes (1596-1650), William III (1650-1702);
+Roger Bacon (1214 to c. 1294), Boccaccio (1313-1375). Charles IX was born
+in 1550 and died in 1574.
+
+[191] His real name was Frederick Parker, and he wrote several works on the
+Greek language and on religion. Among these were a translation of the New
+Testament from the Vatican MS. (1864), _The Revealed History of Man_
+(1854), _An Enquiry respecting the Punctuation of Ancient Greek_ (1841),
+and _Rules for Ascertaining the sense conveyed in Ancient Greek
+Manuscripts_ (1848, the seventh edition appearing in 1862).
+
+[192] See Vol. I, page 352, second note 1 {736}.
+
+The literature on the subject of the Great Pyramid, considered from the
+standpoint of metrology, is extensive.
+
+[193] See Vol. I, page 80, note 5 {119}.
+
+[194] Sir Philip Francis (1740-1818) was a Whig politician. The evidence
+that he was the author of the _Letters of Junius_ (1769-1772) is purely
+circumstantial. He was clerk in the war office at the time of their
+publication. In 1774 he was made a member of the Supreme Council of Bengal,
+and was a vigorous opponent of Warren Hastings, the two fighting a duel in
+1780. He entered parliament in 1784 and was among the leaders in the
+agitation for parliamentary reform.
+
+[195] Mrs. Cottle published a number of letters that attracted attention at
+the time. Among these were letters to the emperor of France and king of
+Sardinia (1859) relating to the prophecies of the war between France and
+Austria; to G. C. Lavis and Her Majesty's Ministers (1859) relating to her
+claims as a prophetess; and to the "Crowned Heads" at St. James, the King
+of Prussia, and others (1860), relating to certain passages of Scripture.
+She also wrote _The Lamb's Book of Life for the New Jerusalem Church and
+Kingdom, interpreted for all nations_ (1861).
+
+[196] See Vol. I, page 315, note 2 {685}, and Vol. II, page 58, note 109.
+
+[197] A Congregational minister, who published a number of sermons, chiefly
+obituaries, between 1804 and 1851. His _Frailty of Human Life_, two sermons
+delivered on the occasion of the death of Princess Charlotte, went through
+at least three editions.
+
+[198] He was secretary of the Congregational Board and editor of the
+_Congregational Year Book_ (from 1846) and the _Congregational Manual_.
+
+[199] Frederick Denison Maurice (1805-1872) began his preaching as a
+Unitarian but entered the Established Church in 1831, being ordained in
+1834. He was professor of English and History at King's College, London,
+from 1840 to 1853. He was one of the founders of Queen's College for women,
+and was the first principal of the Working Men's College, London. The
+subject referred to by De Morgan is his expression of opinion in his
+_Theological Essays_ (1853) that future punishment is not eternal. As a
+result of this expression he lost his professorship at King's College. In
+1866 he was made Knightbridge Professor of Casuistry, Moral Theology, and
+Moral Philosophy at Cambridge.
+
+[200] See Vol. I, page 46, note 1 {42}. Besides the books mentioned in
+this list he wrote _The Ratio between Diameter and Circumference
+demonstrated by angles, and Euclid's Theorem, Proposition 32, Book I,
+proved to be fallacious_ (Liverpool, 1870). This is the theorem which
+asserts that the exterior angle of a triangle is equal to the sum of the
+two opposite interior angles, and that the sum of the interior angles
+equals two right angles. He also published his _Curiosities of Mathematics_
+in 1870, a work containing an extensive correspondence with every one who
+would pay any attention to him. De Morgan was then too feeble to show any
+interest in the final effort of the subject of some of his keenest satire.
+
+[201] See Vol. I, page 332, note 4 {709}.
+
+[202] See Vol. I, page 101, note 4 {174}.
+
+[203] "The circle-squaring disease"; literally, "the circle-measuring
+disease."
+
+[204] See Vol. II, page 63, note 136.
+
+[205] William Rutherford (c. 1798-1871), teacher of mathematics at
+Woolwich, secretary of the Royal Astronomical Society, editor of _The
+Mathematician_, and author of various textbooks. _The Extension of [pi] to
+440 places_, appeared in the _Proceedings_ of the Royal Society in 1853 (p.
+274).
+
+[206] Charles Knight (1791-1873) was associated with De Morgan for many
+years. After 1828 he superintended the publications of the Society for the
+Diffusion of Useful Knowledge, to which De Morgan contributed, and he
+edited the _Penny Cyclopedia_ (1833-1844) for which De Morgan wrote the
+articles on mathematics.
+
+[207] Sir William Hamilton. See Vol. I, page 112, note 7 {211}.
+
+[208] Adam Smith (1723-1790) was not only known for his _Wealth of Nations_
+(1776), but for his _Theory of Moral Sentiments_ (1759), published while he
+was professor of moral philosophy at Glasgow (1752-1764). He was Lord
+Rector of the university in 1787.
+
+[209] See Vol. I, page 332, note 4 {709}.
+
+[210] "Whip."
+
+[211] "Terrible lash."
+
+[212] "An accomplished fact [an accomplished fault]."
+
+[213] See _Extracts from the Diary and Letters of Mrs. Mary Cobb_, London,
+1805.
+
+[214] "Gentle in manner."
+
+[215] "Brave in action." The motto of Earl Newborough was "Suaviter in
+modo, fortiter in re."
+
+[216] "Reduction to an absurdity," a method of proof occasionally used in
+geometry and in logic.
+
+[217] "He has lost the right of being moved (struck) by evidence."
+
+[218] For _radix quadratus_. The usual root sign is supposed to be derived
+from _r_ (for radix), and at one time _q_ was commonly used for square, as
+in Viete's style of writing Aq for A^2.
+
+[219] The Garde Douloureuse was a castle in the marches of Wales and
+received its name because of its exposure to attacks by the Welsh.
+
+[220] "Out of the fight."
+
+[221] "Hidden."
+
+[222] John Cam Hobhouse (1786-1869), Baron Broughton, was committed to
+Newgate for two months in 1819 for his anonymous pamphlet, _A Trifling
+Mistake_. This was a great advertisement for him, and upon his release he
+was at once elected to parliament for Westminster. He was a strong
+supporter of all reform measures, and was Secretary for War in 1832. He was
+created Baron Broughton de Gyfford in 1851.
+
+[223] Thomas Erskine (1750-1823), the famous orator. He became Lord
+Chancellor in 1806, but sat in the House of Commons most of his life.
+
+[224] The above is explained in the MS. by a paragraph referring to some
+anagrams, in one of which, by help of the orthography suggested, a
+designation for this cyclometer was obtained from the letters of his
+name.--S. E. De M.
+
+[225] "A personal verb agrees with its subject."
+
+[226] See Vol. I, page 326, note 1 {700}.
+
+[227] See Vol. I, page 326, note 2 {701}.
+
+[228] Apparently unknown to biographers.
+
+[229] The _Bibliotheca Mathematica_ of Ludwig Adolph Sohncke (1807-1853),
+professor of mathematics at Koenigsberg and Halle, covered the period from
+1830 to 1854, being completed by W. Engelmann. It appeared in 1854.
+
+[230] See Vol. I, page 392, note 2 {805}.
+
+[231] See Vol. I, page 43, note 7 {32}.
+
+[232] See Vol. II, page 91, note 187.
+
+[233] Mason made a notable balloon trip from London to Weilburg, in the
+Duchy of Nassau, in November, 1836, covering 500 miles in 18 hours. He
+published an account of this trip in 1837, and a work entitled
+_Aeronautica_ in 1838.
+
+[234] William Harrison Ainsworth (1805-1885) the novelist.
+
+[235] On this question see Vol. I, page 326, note 2 {701}.
+
+[236] Major General Alfred Wilks Drayson, author of various works on
+geology, astronomy, military surveying, and adventure.
+
+[237] Hailes also wrote several other paradoxes on astronomy and circle
+squaring during the period 1843-1872.
+
+[238] See Vol. I, page 43, note 8 {33}.
+
+[239] See Vol. I, page 43, note 7 {32}.
+
+[240] "Very small errors are not to be condemned."
+
+[241] He seems to have written nothing else.
+
+[242] Besides the paradoxes here mentioned by De Morgan he wrote several
+other works, including the following: _Abriss der Babylonisch-Assyrischen
+Geschichte_ (Mannheim, 1854), _A Popular Inquiry into the Moon's rotation
+on her axis_ (London, 1856), _Practical Tables for the reduction of the
+Mahometan dates to the Christian kalendar_ (London, 1856), _Grundzuege einer
+neuen Weltlehre_ (Munich, 1860), and _On the historical Antiquity of the
+People of Egypt_ (London, 1863).
+
+[243] Dircks (1806-1873) was a civil engineer of prominence, and a member
+of the British Association and the Royal Society of Edinburgh. He wrote
+(1863) on "Pepper's Ghost," an ingenious optical illusion invented by him.
+There was a second edition of the _Perpetuum Mobile_ in 1870.
+
+[244] George Stephenson (1781-1848), the inventor of the first successful
+steam locomotive. His first engine was tried in 1814.
+
+[245] Robert Stephenson (1803-1859), the only son of George. Most of the
+early improvements in locomotive manufacture were due to him. He was also
+well known for his construction of great bridges.
+
+[246] "In its proper place."
+
+[247] "A fool always finds a bigger fool to admire him."
+
+[248] See Vol. I, page 43, note 7 {32}.
+
+[249] See Vol. I, page 43, note 8 {33}.
+
+[250] See Vol. I, page 85, note 2 {129}.
+
+[251] See Vol. I, page 390, note 1 {390}.
+
+[252] From 1823 to 1852 it was edited by I. C. Robertson; from 1852 to 1857
+by R. A. Brooman; and from 1857 to 1863 by Brooman and E. J. Reed.
+
+[253] Sir James Ivory (1765-1842) was, as a young man, manager of a flax
+mill in Scotland. In 1804 he was made professor of mathematics at the Royal
+Military College, then at Marlow and later at Sandhurst. He was deeply
+interested in mathematical physics, and there is a theorem on the
+attraction of ellipsoids that bears his name. He was awarded three medals
+of the Royal Society, and was knighted together with Herschel and Brewster,
+in 1831.
+
+[254] See Vol. I, page 56, note 1 {64}.
+
+[255] See Vol. I, page 153, note 5 {338}.
+
+[256] See Vol. I, page 309, note 2 {670}.
+
+[257] See Vol. I, page 87, note 4 {133}.
+
+[258] George Canning (1770-1857), the Tory statesman and friend of Scott,
+was much interested in founding the _Quarterly Review_ (1808) and was a
+contributor to its pages.
+
+[259] See Vol. I, page 186, note 14 {418}.
+
+[260] See Vol. II, page 141, note 252.
+
+[261] De Morgan had a number of excellent articles in this publication.
+
+[262] See Vol. I, page 279, note 1 {611}.
+
+[263] James Orchard Halliwell (1820-1889), afterwards Halliwell-Phillips,
+came into prominence as a writer at an early age. When he was seventeen he
+wrote a series of lives of mathematicians for the _Parthenon_. His _Rara
+Mathematica_ appeared when he was but nineteen. He was a great bibliophile
+and an enthusiastic student of Shakespeare.
+
+[264] This was written at the age of twenty-two.
+
+[265] The subject of this criticism is of long past date, and as it has
+only been introduced by the author as an instance of faulty editorship, I
+have omitted the name of the writer of the libel, and a few lines of
+further detail.--S. E. De M.
+
+[266] "Condemned souls."
+
+[267] The editor of the _Mechanics' Magazine_ died soon after the above was
+written.--S. E. De M.
+
+[268] Thomas Stephens Davies (1795-1851) was mathematical master at
+Woolwich and F. R. S. He contributed a series of "Geometrical Notes" to the
+_Mechanics' Magazine_ and edited the _Mathematician_. He also published a
+number of text-books.
+
+[269] See Vol. II, page 66, note 143.
+
+[270] The _Dictionary of Greek and Roman Biography_ (1849), edited by Sir
+William Smith (1813-1893), whose other dictionaries on classical and
+biblical matters are well known.
+
+[271] "O J. S.! This is the worst! the greatest possible injury!"
+
+[272] See Vol. I, page 44, note 9 {34} and page 110, note 5 {201}.
+
+[273]
+
+ "If there's a man whom the judge's pitiless sentence awaiteth,
+  His head condemned to penalties and tribulations,
+  Let neither penitentiaries tire him with laborer's burdens
+  Nor let his stiffened hands be harrassed by work in the mines.
+  He must square the circle! For what else do I care?--all
+  Known punishments this one task hath surely included."
+
+[274] Houlston was in the customs service. He also published _Inklings of
+Areal Autometry_, London, 1874.
+
+[275] This is Frederick C. Bakewell. He had already published _Natural
+Evidence of a Future Life_ (London, 1835), _Philosophical Conversations_
+(London, 1833, with other editions), and _Electric Science_ (London, 1853,
+with other editions).
+
+[276] Henry F. A. Pratt had already published _A Dissertation on the power
+of the intercepted pressure of the Atmosphere_ (London, 1844) and _The
+Genealogy of Creation_ (1861). Later he published a work _On Orbital
+Motion_ (1863), and _Astronomical Investigations_ (1865).
+
+[277] See Vol. I, page 260, note 1 {591}.
+
+[278] Thomas Rawson Birks (1810-1883), a theologian and controversialist,
+fellow of Trinity College, Cambridge, and (1872) professor of moral
+philosophy in that university. He wrote _Modern Rationalism_ (1853), _The
+Bible and Modern Thought_ (1861), _The First Principles of Moral Science_
+(1873), and _Modern Physical Fatalism and the Doctrine of Evolution_
+(1876), the last being an attack on Herbert Spencer's _First Principles_.
+
+[279] Pseudonym for William Thorn. In the following year (1863) he
+published a second work, _The Thorn-Tree: being a History of Thorn
+Worship_, a reply to Bishop Colenso's work entitled _The Pentateuch and the
+Book of Joshua critically examined_.
+
+[280] Besides _The Pestilence_ (1866) he published _The True Church_
+(1851), _The Church and her destinies_ (1855), _Religious reformation
+imperatively demanded_ (1864), and _The Bible plan unfolded_ (second
+edition, 1872).
+
+[281] See Vol. II, page 97, note 195.
+
+[282] Sir George Cornewall Lewis (1806-1863) also wrote an _Essay on the
+Origin and Formation of the Romance Languages_ (1835), an _Essay on the
+Government of Dependencies_ (1841), and an _Essay on Foreign Jurisdiction
+and the Extradition of Criminals_ (1859). He was Chancellor of the
+Exchequer in 1855 and Home Secretary in 1859.
+
+[283] Henry Malden (1800-1876), a classical scholar, fellow of Trinity
+College, Cambridge, and professor of Greek at University College
+(1831-1876), then (1831) the University of London. He wrote a _History of
+Rome to 390 B. C._ (1830), and _On the Origin of Universities and
+Academical Degrees_ (1835).
+
+[284] Henry Longueville Mansel (1820-1871), theologian and metaphysician,
+reader in theology at Magdalen College, Oxford (1855), and professor of
+ecclesiastical history and Dean of St. Paul's (1866). He wrote on
+metaphysics, and his Bampton Lectures (1858) were reprinted several times.
+
+[285] "Hejus gave freely, gave freely. God is propitious, God is favorable
+to him who gives freely. God is honored with a banquet of eggs at the cross
+roads, the god of the world. God, with benignant spirit, desired in
+sacrifice a goat, a bull to be carried within the precincts of the holy
+place. God, twice propitiated, blesses the pit of the sacred libation."
+
+[286] Eudoxus of Cnidus (408-355 B. C.) had much to do with the early
+scientific astronomy of the Greeks. The fifth book of Euclid is generally
+attributed to him. His astronomical works are known chiefly through the
+poetical version of Aratus mentioned in note 13, page 167.
+
+[287] Simplicius, a native of Cilicia, lived in the 6th century of our era.
+He was driven from Athens by Justinian and went to Persia (531), but he
+returned later and had some fame as a teacher.
+
+[288] See Vol. I, page 160, note 3 {348}.
+
+[289] See Vol. I, page 76, note 3 {112}.
+
+[290] "Through right and wrong."
+
+[291] "It is therefore to arrive at this parallelism, or to preserve it,
+that Copernicus feared to be obliged to have recourse to this equal and
+opposite movement which destroys the effect which he attributed so freely
+to the first, of deranging the parallelism."
+
+[292] A contemporary of Plato and a disciple of Aristotle.
+
+[293] Meton's solstice, the beginning of the Metonic cycles, has been
+placed at 432 B. C. Ptolemy states that he made the length of the year
+365-1/4 + 1/72 days.
+
+[294] Aratus lived about 270 B. C., at the court of Antigonus of Macedonia,
+and probably practiced medicine there. He was the author of two
+astronomical poems, the [Greek: Phainomena], apparently based on the lost
+work of Eudoxus, and the [Greek: Dioseeia] based on Aristotle's
+_Meteorologica_ and _De Signis Ventorum_ of Theophrastus.
+
+[295] "The nineteen (-year) cycle of the shining sun."
+
+[296] Claudius Salmasius (1588-1653), or Claude Saumaise, was a
+distinguished classicist, and professor at the University of Leyden. The
+word [Greek: eleioio] means Elian, thus making the phrase refer to the
+brilliant one of Elis.
+
+[297] Sir William Brown (1784-1864). In 1800 the family moved to Baltimore,
+and there the father, Alexander Brown, became prominent in the linen trade.
+William went to Liverpool where he acquired great wealth as a merchant and
+banker. He was made a baronet in 1863.
+
+[298] Robert Lowe (1811-1892), viscount Sherbrooke, was a fellow of
+Magdalen College, Oxford (1835). He went to Australia in 1842 and was very
+successful at the bar. He returned to England in 1850 and became leader
+writer on the _Times_. He was many years in parliament, and in 1880 was
+raised to the peerage.
+
+[299] See Vol. I, page 42, note 4 {24}.
+
+[300] Francis Walkingame (fl. about 1751-1785), whose _Tutor's Assistant_
+went through many editions from 1751-1854.
+
+[301] Davies Gilbert (1767-1839). His family name was Giddy, but he assumed
+his wife's name. He sat in parliament from 1806 to 1832. In 1819 he secured
+the establishment of the Cape of Good Hope observatory. He was Treasurer
+(1820-1827) and President (1827-1830) of the Royal Society.
+
+[302] See Vol. I, page 55, note 2 {63}.
+
+[303] Sir Jonathan Frederick Pollock (1783-1870) entered parliament in 1831
+and was knighted in 1834.
+
+[304] Joseph Hume (1777-1855) entered parliament in 1812 and for thirty
+years was leader of the Radical party.
+
+[305] "What! when I say, 'Nicole, bring me my slippers,' is that prose?"
+
+[306] Captain Basil Hall (1788-1844), a naval officer, carried on a series
+of pendulum observations in 1820-1822, while on a cruise of the west coast
+of North America. The results were published in 1823 in the _Philosophical
+Transactions_. He also wrote two popular works on travel that went through
+numerous editions.
+
+[307] Anthony Ashley Cooper (1801-1885), Earl of Shaftesbury. His name is
+connected with philanthropic work and factory legislation.
+
+[308] See Vol. I, page 207, note 12 {469}.
+
+[309] See Vol. I, page 80, note 5 {119}.
+
+[310] Sir Thomas Maclear (1794-1879), an Irishman by birth, became
+Astronomer Royal at the Cape of Good Hope in 1833. He was an indefatigable
+observer. He was knighted in 1860.
+
+[311] Thomas Romney Robinson (1792-1882), another Irish astronomer of
+prominence. He was a deputy professor at Trinity College, Dublin, but took
+charge of the Armagh observatory in 1823 and remained there until his
+death.
+
+[312] Sir James South (1785-1867) was in early life a surgeon, but gave up
+his practice in 1816 and fitted up a private observatory. He contributed to
+the science of astronomy, particularly with respect to the study of double
+stars.
+
+[313] Sir John Wrottesley (1798-1867), second Baron Wrottesley. Like Sir
+James South, he took up the study of astronomy after a professional
+career,--in his case in law. He built a private observatory in 1829 and
+made a long series of observations, publishing three star catalogues. He
+was president of the Astronomical Society from 1841 to 1843, and of the
+Royal Society from 1854 to 1857.
+
+[314] He seems to have written nothing else.
+
+[315] See Vol. II, page 68, note 147.
+
+[316] "The wills are free, and I wish neither the one nor the other."
+
+[317] "The force of inertia conquered."
+
+[318] Reddie also wrote _The Mechanics of the Heavens_, referred to later
+in this work. He must not be confused with Judge James Reddie (1773-1852),
+of Glasgow, who wrote on international law, although this is done in the
+printed edition of the British Museum catalogue, for he is mentioned by De
+Morgan somewhat later as alive in 1862.
+
+[319] Henry Dunning Macleod (1821-1902), a lawyer and writer on political
+economy, was a Scotchman by birth. He wrote on economical questions, and
+lectured on banking at Cambridge (1877) and at King's College, London
+(1878). He was a free lance in his field, and was not considered orthodox
+by the majority of economists of his time. He was an unsuccessful candidate
+for the chairs of political economy at Cambridge (1863), Edinburgh (1871),
+and Oxford (1888).
+
+[320] See Vol. I, page 252, note 2 {576}.
+
+[321] Francis Henry Laing (1816-1889) was a graduate of Queen's College,
+Cambridge, and a clergyman in the Church of England until 1846, when he
+entered the Church of Rome. He taught in various Jesuit colleges until
+1862, when his eccentricity was too marked to warrant the Church in
+allowing him to continue. He published various controversial writings
+during his later years. Of course if he had known the works of Wessel,
+Gaus, Buee, Argand, and others, he would not have made such a sorry
+exhibition of his ignorance of mathematics.
+
+[322] See Vol. I, page 329, note 1 {705}. The book went into a second
+edition in 1864.
+
+[323] Thomas Weddle (1817-1853) was, at the time of publishing this paper,
+a teacher in a private school. In 1851 he became professor of mathematics
+at Sandhurst. He contributed several papers to the _Cambridge and Dublin
+Mathematical Journal_, chiefly on geometry.
+
+[324] See Vol. II, page 109, note 205.
+
+[325] See Vol. II, page 66, note 143.
+
+[326] See Vol. II, page 151, note 268.
+
+[327] George Barrett (1752-1821) worked from 1786 to 1811 on a set of life
+insurance and annuity tables. He invented a plan known as the "columnar
+method" for the construction of such tables, and as De Morgan states, this
+was published by Francis Baily, appearing in the appendix to his work on
+annuities, in the edition of 1813. Some of his tables were used in
+Babbage's _Comparative View of the various Institutions for the Assurance
+of Lives_ (1826).
+
+[328] See Vol. I, page 309, note 2 {670}.
+
+[329] This was his _Practical short and direct Method of Calculating the
+Logarithm of any given Number, and the Number corresponding to any given
+Logarithm_ (1849).
+
+[330] This is William Neile (1637-1670), grandson of Richard Neile (not
+Neal), Archbishop of York. At the age of 19, in 1657, he gave the first
+rectification of the semicubical parabola. Although he communicated it to
+Brouncker, Wren, and others, it was not published until 1639, when it
+appeared in John Wallis's _De Cycloide_.
+
+[331] I myself "was a considerable part."
+
+[332] He also wrote _A Glance at the Universe_ ("2d thousand" in 1862), and
+_The Resurrection Body_ (1869).
+
+[333] See Vol. I, page 63, note 1 {74}.
+
+[334] As Swift gave it in his _Poetry. A Rhapsody_, it is as follows:
+
+ "So, naturalists observe, a flea
+  Has smaller fleas that on him prey;
+  And these have smaller still to bite 'em.
+  And so proceed _ad infinitum_."
+
+[335] Perhaps 1,600,000,000 years, if Boltwood's recent computations based
+on radium disintegration stand the test. This would mean, according to
+MacCurdy's estimate, 60,000,000 years since life first appeared on the
+earth.
+
+[336] De Morgan wrote better than he knew, for this work, the _Allgemeine
+Encyclopaedie der Wissenschaften und Kuenste_, begun at Leipsic in 1818, is
+still (1913) unfinished. Section I, A-G, consists of 99 parts in 56
+volumes; Section II, H-N, consists of 43 volumes and is not yet completed;
+and Section III, O-Z, consists of 25 volumes thus far, with most of the
+work still to be done. Johann Samuel Ersch (1766-1828), the founder, was
+head librarian at Halle. Johann Gottfried Gruber (1774-1851), his
+associate, was professor of philosophy at the same university.
+
+[337] William Howitt (1792-1879) was a poet, a spiritualist, and a
+miscellaneous writer. He and his wife became spiritualists about 1850. He
+wrote numerous popular works on travel, nature and history.
+
+[338] See Vol. II, page 55, note 108.
+
+[339] As will be inferred from the text, C. D. was Mrs. De Morgan, and
+A. B. was De Morgan.
+
+[340] Jean Meslier (1678-1733), cure of Estrepigny, in Champagne, was a
+skeptic, but preached only strict orthodoxy to his people. It was only in
+his manuscript, _Mon Testament_, that was published after his death, and
+that caused a great sensation in France, that his antagonism to
+Christianity became known.
+
+[341] Baron Zach relates that a friend of his, in a writing intended for
+publication, said _Un esprit doit se frotter contre un autre_. The censors
+struck it out. The Austrian police have a keen eye for consequences.--A. De
+M.
+
+"One mind must rub against another." On Baron Zach, see Vol. II, page 45,
+note 4.
+
+[342] Referring to the first Lord Eldon (1751-1838), who was Lord
+Chancellor from 1799 to 1827, with the exception of one year.
+
+[343] "Sleeping power."
+
+[344] "Causes sleep."
+
+[345] Richard Hooker (c. 1554-1600), a theologian, "the ablest living
+advocate of the Church of England as by law established."
+
+[346] See Vol. I, page 76, note 3 {112}.
+
+[347] "Other I,"--other self.
+
+[348] This "utter rejection" has been repeated (1872) by the same
+writer.--S. E. De M.
+
+[349] Edward Jenner (1749-1823) was a physician and biologist. His first
+experiments in vaccination were made in 1796, and his discovery was
+published in 1798.
+
+[350] See Vol. II, page 38, note 80.
+
+[351] "You will go most safely in the middle (way)."
+
+[352] Pierre Joseph Arson was known early in the 19th century for his
+controversy with Hoene Wronski the mathematician, whom he attacked in his
+_Document pour l'histoire des grands fourbes qui ont figure sur la terre_
+(1817-1818).
+
+[353] "We enter the course by night and are consumed by fire."
+
+[354] See Vol. I, page 51, note 3 {51}.
+
+[355] See Vol. I, page 336, note 8 {713}.
+
+[356] See Vol. I, page 137, note 8 {286}.
+
+[357] See Vol. I, page 229, note 2 {515}.
+
+[358] Richard Cobden (1804-1865), the cotton manufacturer and statesman who
+was prominent in his advocacy of the repeal of the Corn Laws.
+
+[359] James Smith (1775-1839), solicitor to the Board of Ordnance. With his
+brother Horatio he wrote numerous satires. His _Horace in London_ (1813)
+imitated the Roman poet. His works were collected and published in 1840.
+
+[360] Samuel Butler (1612-1680), the poet and satirist, author of
+_Hudibras_ (1663-1678).
+
+[361] "Is it not fine to be sure of one's action when entering in a combat
+with another? There, push me a little in order to see. NICOLE. Well! what's
+the matter? M. JOURDAIN. Slowly. Ho there! Ho! gently. Deuce take the
+rascal! NICOLE. You told me to push. M. JOURDAIN. Yes, but you pushed me
+_en tierce_, before you pushed _en quarte_, and you did not give me time to
+parry."
+
+[362] John Abernethy (1764-1831), the famous physician and surgeon.
+
+[363] See Vol. I, page 102, note 5 {175}.
+
+[364] "With what measure ye mete, it shall be measured to you again."
+
+[365] Eusebius of Caesarea (c. 260-340), leader of the moderate party at the
+Council of Nicaea, and author of a _History of the Christian Church_ in ten
+books (c. 324 A. D.).
+
+[366] Nathaniel Lardner (1684-1768), a non-conformist minister and one of
+the first to advocate the scientific study of early Christian literature.
+
+[367] Henry Alford (1810-1871) Dean of Canterbury (1857-1871) and editor of
+the Greek Testament (1849-1861).
+
+[368] The work was _The Number and Names of the Apocalyptic Beasts: with an
+explanation and application. Part I._ London, 1848, as mentioned below.
+Thom also wrote _The Assurance of Faith, or Calvinism identified with
+Universalism_ (London, 1833), and various other religious works.
+
+[369] See Vol. I, page 222, note 14 {490}.
+
+[370] John Hamilton Thom (1808-1894) was converted to Unitarianism and was
+long a minister in that church, preaching in the Renshaw Street Chapel from
+1831 to 1866. De Morgan refers to the Liverpool Unitarian controversy
+conducted by James Martineau and Henry Giles in response to a challenge by
+thirteen Anglican Clergy. In 1839 Thom contributed four lectures and a
+letter to this controversy. Among his religious works were a _Life of
+Blanco White_ (1845) and _Hymns, Chants, and Anthems_ (1854).
+
+[371] The spelling of these names is occasionally changed to meet the
+condition that the numerical value of the letters shall be 666, "the number
+of the beast" of Revelations. The names include Julius Caesar; Valerius
+Jovius Diocletianus (249-313), emperor from 287 to 305, persecutor of the
+Christians; Louis, presumably Louis XIV; Gerbert (940-1003), who reigned as
+Pope Sylvester II from 999 to 1003, known to mathematicians for his abacus
+and his interest in geometry, and accused by his opponents as being in
+league with the devil; Linus, the second Bishop of Rome, the successor of
+Peter; Camillo Borghese (1552-1621), who reigned as Pope Paul V from 1605
+to 1621, and who excommunicated all Venice in 1606 for its claim to try
+ecclesiastics before lay tribunals, thus taking a position which he was
+forced to abandon; Luther, Calvin; Laud (see Vol. I, page 145, note 7
+{307}); Genseric (c. 406-477), king of the Vandals, who sacked Rome in 455
+and persecuted the orthodox Christians in Africa; Boniface III, who was
+pope for nine months in 606; Beza (see Vol. I, page 66, note 6 {83});
+Mohammed; [Greek: braski], who was Giovanni Angelo Braschi (1717-1799), and
+who reigned as Pope Pius VI from 1775 to 1799, dying in captivity because
+he declined to resign his temporal power to Napoleon; Bonaparte; and, under
+[Greek: Ion Paune], possibly Pope John XIV, who reigned in 983 and 984
+during the absence of Boniface VII in Constantinople.
+
+[372] The Greek words and names are also occasionally misspelled so as to
+fit them to the number 666. They are [Greek: Lateinos] (Latin), [Greek: he
+latine basileia] (the Latin kingdom), [Greek: ekklesia italika] (the
+Italian Church), [Greek: euanthas] (blooming), [Greek: teitan] (Titan),
+[Greek: arnoume] (renounce), [Greek: lampetis] (the lustrous), [Greek: ho
+niketes] (conqueror), [Greek: kakos hodegos] (bad guide), [Greek: alethes
+blaberos] (truthful harmful one), [Greek: palai baskanos] (a slanderer of
+old), [Greek: amnos adikos] (unmanageable lamb), [Greek: antemos]
+(Antemos), [Greek: genserikos] (Genseric), [Greek: euinas] (with stout
+fibers), [Greek: Benediktos] (Benedict), [Greek: Bonibazios g. papa x. e.
+e. e. a.] (Boniface III, pope 68, bishop of bishops I), [Greek: oulpios]
+(baneful), [Greek: dios eimi he heras] (I, a god, am the), [Greek: he missa
+he papike] (the papal brief), [Greek: loutherana] (Lutheran), [Greek:
+saxoneios] (Saxon), [Greek: Bezza antitheos] (Beza antigod), [Greek: he
+alazoneia biou] (the illusion of life), [Greek: Maometis] (Mahomet);
+[Greek: Maometes b.] (Mahomet II), [Greek: theos eimi epi gaies] (I am lord
+over the earth), [Greek: iapetos] (Iapetos, father of Atlas), [Greek:
+papeiskos] (Papeiskos), [Greek: dioklasianos] (Diocletian), [Greek: cheina]
+(Cheina = Cain? China?), [Greek: braski] (Braschi, as explained in note
+10), [Greek: Ion Paune] (Paunian violet, but see note 10), [Greek: koupoks]
+(cowpox), [Greek: Bonneparte] (Bonneparte), [Greek: N. Boneparte] (N.
+Boneparte), [Greek: euporia] (facility), [Greek: paradosis] (surrender),
+[Greek: to megatherion] (the megathereum, the beast).
+
+[373] James Wapshare, whose _Harmony of the Word of God in Spirit and in
+Truth_ appeared in 1849.
+
+[374] The literature relating to the _Swastika_ is too extended to permit
+of any adequate summary in these notes.
+
+[375] Henry Edward Manning (1808-1892), at first an Anglican clergyman, he
+became a Roman Catholic priest in 1851, and became Cardinal in 1875. He
+succeeded Cardinal Wiseman as Archbishop of Westminster in 1865. He wrote a
+number of religious works.
+
+[376] John Bright (1811-1889), Quaker, cotton manufacturer, and statesman.
+He worked with Cobden for free trade, peace, and reform of the electorate.
+
+[377] "The fallacy of many questions."
+
+[378] William Wilberforce (1759-1833), best known for his long fight for
+the abolition of the slave trade.
+
+[379] Richard Martin (1754-1834), high sheriff of County Galway and owner
+of a large estate in Connemara. Curiously enough, he was known both for his
+readiness in duelling and for his love for animals. He was known as
+"Humanity Martin," and in 1822 secured the passage of an act "to prevent
+the cruel and improper treatment of cattle." He was one of the founders
+(1824) of the Royal Society for the Prevention of Cruelty to Animals. He is
+usually considered the original of Godfrey O'Malley in Lever's novel,
+_Charles O'Malley_.
+
+[380] See Vol. I, page 149, note 1 {323}, also text on same page.
+
+[381] See Vol. I, page 44, note 9 {34}, also text, Vol. I, page 110.
+
+[382] "Penitential seat."
+
+[383] "Well placed upon the cushion."
+
+[384] See Vol. II, page 58, note 109.
+
+[385] "He has lost the right of being influenced by evidence."
+
+[386] "Hung up."
+
+[387] "A few things to the wise, nothing to the unlettered."
+
+[388] The fallacy results from dividing both members of an equation by 0, x
+- 1 being the same as 1 - 1, and calling the quotients finite.
+
+[389] "If you order him to the sky he will go."
+
+[390] _Similia similibus curanter_, "Like cures like," the homeopathic
+motto.
+
+[391] "Without harm to the proprieties."
+
+[392] "What are you doing? I am standing here."
+
+[393] Lors feist l'Anglois tel signe. La main gausche toute ouverte il leva
+hault en l'aer, puis ferma au poing les quatres doigtz d'icelle et le
+poulce estendu assit sus la pinne du nez. Soubdain apres leva la dextre
+toute ouverte, et toute ouverte la baissa, joignant la poulce au lieu que
+fermait le petit doigt de la gausche, et les quatre doigtz d'icelle mouvoit
+lentement en l'aer. Puis au rebours feit de la dextre ce qu'il avoit faict
+de la gausche, et de la gausche ce que avoit faict de la dextre.--A. De M.
+
+[394] _Suaviter in modo, fortiter in re_, "Gentle in manners, firm in
+action."
+
+[395] See Vol. I, page 101, note 4 {174}.
+
+[396] See Vol. I, page 315, note 3 {686}.
+
+[397] Henry Fawcett (1833-1884) became totally blind in 1858, but in spite
+of this handicap he became professor of political economy at Cambridge and
+sat in parliament for a number of years. He championed the cause of reform
+and in particular he was prominent in the protection of the native
+interests of India. The establishing of the parcels post (1882) took place
+while he was postmaster general (1880-1884).
+
+[398] Of course the whole thing depends upon what definition of division is
+taken. We can multiply 2 ft. by 3 ft. if we define multiplication so as to
+allow it, or 2 ft. by 3 lb, getting foot-pounds, as is done in physics.
+
+[399] Richard Milward (1609-1680), for so the name is usually given, was
+rector of Great Braxted (Essex) and canon of Windsor. He was long the
+amanuensis of John Selden, and the _Table Talk_ was published nine years
+after Milward's death, from notes that he left. Some doubt has been cast
+upon the authenticity of the work owing to many of the opinions that it
+ascribes to Selden.
+
+[400] John Selden (1584-1654) was a jurist, legal antiquary, and Oriental
+scholar. He sat in the Long Parliament, and while an advocate of reform he
+was not an extremist. He was sent to the Tower for his support of the
+resolution against "tonnage and poundage," in 1629. His _History of Tythes_
+(1618) was suppressed at the demand of the bishops. His _De Diis Syriis_
+(1617) is still esteemed a classic on Semitic mythology.
+
+[401] See Vol. I, page 42, note 4 {24}.
+
+[402] See Vol. II, page 249, note 398.
+
+[403] John Palmer (1742-1818) was a theatrical manager. In 1782 he set
+forth a plan for forwarding the mails by stage coaches instead of by
+postmen. Pitt adopted the plan in 1784. Palmer was made comptroller-general
+of the post office in 1786 and was dismissed six years later for
+arbitrarily suspending a deputy. He had been verbally promised 2-1/2% on
+the increased revenue, but Pitt gave him only a pension of L3000. In 1813
+he was awarded L50,000 in addition to his pension.
+
+[404] Dionysius Lardner (1793-1859), professor of natural philosophy in
+London University (now University College). His _Cabinet Cyclopaedia_
+(1829-1849) contained 133 volumes. De Morgan wrote on probabilities, and
+Lardner on various branches of mathematics, and there were many other
+well-known contributors. Lardner is said to have made $200,000 on a lecture
+tour in America.
+
+[405] Thomas Fysche Palmer (1747-1802) joined the Unitarians in 1783, and
+in 1785 took a charge in Dundee. He was arrested for sedition because of an
+address that it was falsely alleged that he gave before a society known as
+the "Friends of Liberty." As a matter of fact the address was given by an
+uneducated weaver, and Palmer was merely asked to revise it, declining to
+do even this. Nevertheless he was sentenced to Botany Bay (1794) for seven
+years. The trial aroused great indignation.
+
+[406] See Vol. I, page 80, note 5 {119}.
+
+[407] See Vol. II, page 244, note 394.
+
+[408] See Vol. I, page 352, note 1 {731}.
+
+[409] See Vol. I, page 332, note 4 {709}.
+
+[410] "The lawyers are brought into court; let them accuse each other."
+
+[411] Samuel Rogers (1763-1855), the poet and art connoisseur. He declined
+the laureateship on the death of Wordsworth (1850). Byron, his pretended
+friend, wrote a lampoon (1818) ridiculing his cadaverous appearance.
+
+[412] Theodore Edward Hook (1788-1841), the well-known wit. He is satirized
+as Mr. Wagg in _Vanity Fair_. The _John Bull_ was founded in 1820 and Hook
+was made editor.
+
+[413] "On pitying the heretic."
+
+[414] A term of medieval logic. Barbara: All M is P, all S is M, hence all
+S is P. Celarent: No M is P, all S is M, hence no S is P.
+
+[415] "Simply," "According to which," "It does not follow."
+
+[416]
+
+ "O sweet soul, what good shall I declare
+  That heretofore was thine, since such are thy remains!"
+
+[417] "Stupid fellow!"
+
+[418] Christopher Barker (c. 1529-1599), also called Barkar, was the
+Queen's printer. He began to publish books in 1569, but did no actual
+printing until 1576. In 1575 the Geneva Bible was first printed in England,
+the work being done for Barker. He published 38 partial or complete
+editions of the Bible from 1575 to 1588, and 34 were published by his
+deputies (1588-1599).
+
+[419] James Franklin (1697-1735) was born in Boston, Mass., and was sent to
+London to learn the printer's trade. He returned in 1717 and started a
+printing house. Benjamin, his brother, was apprenticed to him but ran away
+(1723). James published the _New England Courant_ (1721-1727), and Benjamin
+is said to have begun his literary career by writing for it.
+
+[420] James Hodder was a writing master in Tokenhouse Yard, Lothbury, in
+1661, and later kept a boarding school in Bromley-by-Bow. His famous
+arithmetic appeared at London in 1661 and went through many editions. It
+was the basis of Cocker's work. (See Vol. I, page 42, note 4 {24}.) It was
+long thought to have been the first arithmetic published in America, and it
+was the first English one. There was, however, an arithmetic published much
+earlier than this, in Mexico, the _Sumario compendioso ... con algunas
+reglas tocantes al Aritmetica_, by "Juan Diaz Freyle," in 1556.
+
+[421] Henry Mose, Hodder's successor, kept a school in Sherborne Lane,
+London.
+
+[422] Rear Admiral Sir Francis Beaufort (1774-1857), F.R.S., was
+hydrographer to the Navy from 1829 to 1855. He prepared an atlas that was
+printed by the Society for the Diffusion of Useful Knowledge.
+
+[423] Antoine Sabatier (1742-1817), born at Castres, was known as the Abbe
+but was really nothing more than a "clerc tonsure." He lived at Court and
+was pensioned to write against the philosophers of the Voltaire group. He
+posed as the defender of morality, a commodity of which he seems to have
+possessed not the slightest trace.
+
+[424] Maffeo Barberini was pope, as Urban VIII, from 1623 to 1644. It was
+during his ambitious reign that Galileo was summoned to Rome to make his
+recantation (1633), the exact nature of which is still a matter of dispute.
+
+[425] This Baden Powell (1796-1860) was the Savilian professor of geometry
+(1827-1860) at Oxford.
+
+[426] "Memoirs of the famous bishop of Chiapa, by which it appears that he
+had butchered or burned or drowned ten million infidels in America in order
+to convert them. I believe that this bishop exaggerated; but if we should
+reduce these sacrifices to five million victims, this would still be
+admirable."
+
+[427] Alfonso X (1221-1284), known as El Sabio (the Wise), was interested
+in astronomy and caused the Alphonsine Tables to be prepared. These table
+were used by astronomers for a long time. It is said that when the
+Ptolemaic system of the universe was explained to him he remarked that if
+he had been present at the Creation he could have shown how to arrange
+things in a much simpler fashion.
+
+[428] George Richards (c. 1767-1837), fellow of Oriel (1790-1796), Bampton
+lecturer (1800), Vicar of St. Martin's-in-the-Fields, Westminster (1824),
+and a poet of no mean ability.
+
+[429] The "Aboriginal Britons," an excellent poem, by Richards. (Note by
+Byron.)--A. De M.
+
+[430] John Watkins (d. after 1831), a teacher and miscellaneous writer.
+
+[431] Frederic Shoberl (1775-1853), a miscellaneous writer.
+
+[432] He wrote, besides the _Aboriginal Britons_, _Songs of the Aboriginal
+Bards_ (1792), _Modern France: a Poem_ (1793), _Odin, a drama_ (1804),
+_Emma, a drama on the model of the Greek theatre_ (1804), _Poems_ (2
+volumes, 1804), and a _Monody on the Death of Lord Nelson_ (1806).
+
+[433] Henry Kirke White (1785-1806), published his first volume of poems at
+the age of 18. Southey and William Wilberforce became interested in him and
+procured for him a sizarship at St. John's College, Cambridge. He at once
+showed great brilliancy, but he died of tuberculosis at the age of 21.
+
+[434] John Wolcot, known as Peter Pindar (1738-1819), was a London
+physician. He wrote numerous satirical poems. His _Bozzy and Piozzi, or the
+British Biographers_, appeared in 1786, and reached the 9th edition in
+1788.
+
+[435] See Vol. I, page 235, note 8 {532}.
+
+[436] Richard Payne Knight (1750-1824) was a collector of bronzes, gems,
+and coins, many of his pieces being now in the British Museum. He sat in
+parliament for twenty-six years (1780-1806), but took no active part in
+legislation. He opposed the acquisition of the Elgin Marbles, holding them
+to be of little importance. His _Analytical Inquiry into the Principles of
+Taste_ appeared in 1808.
+
+[437] Mario Nizzoli (1498-1566), a well-known student of Cicero, was for a
+time professor at the University of Parma. His _Observationes in M. Tullium
+Ciceronem_ appeared at Pratalboino in 1535. It was revised by his nephew
+under the title _Thesaurus Ciceronianus_ (Venice, 1570).
+
+[438] See Vol. I, page 314, note 4 {681}.
+
+[439]
+
+ "Like the geometer, who bends all his powers
+  To measure the circle, and does not succeed,
+  Thinking what principle he needs."
+
+[440] Francis Quarles (1592-1644), a religious poet. He wrote paraphrases
+of the Bible and numerous elegies. In the early days of the revolutionary
+struggle he sided with the Royalists. One of his most popular works was the
+_Emblems_ (1635), with illustrations by William Marshall.
+
+[441] Regnault de Becourt wrote _La Creation du monde, ou Systeme
+d'organisation primitive suivi de l'interpretation des principaux
+phenomenes et accidents que se sont operes dans la nature depuis l'origine
+de univers jusqu'a nos jours_ (1816). This may be the work translated by
+Dalmas.
+
+[442] "Because it lacks a holy prophet."
+
+[443] Anghera. See Vol. II, page 60, note 127.
+
+[444] Edmund Curll (1675-1747), a well-known bookseller, publisher, and
+pamphleteer. He was for a time at "The Peacock without Temple Bar," and
+later at "The Dial and Bible against St. Dunstan's Church." He was fined
+repeatedly for publishing immoral works, and once stood in the pillory for
+it. He is ridiculed in the _Dunciad_ for having been tossed in a blanket by
+the boys of Westminster School because of an oration that displeased them.
+
+[445] See Vol. II, page 109, note 206.
+
+[446] Encyclopaedia.
+
+[447] Author of the _Historia Naturalis_ (77 A.D.)
+
+[448] Author of the _De Institutione Oratorio Libri_ XII (c. 91 A.D.)
+
+[449] His _De Architectures Libri_ X was not merely a work on architecture
+and building, but on the education of the architect.
+
+[450] Cyclophoria.
+
+[451] William Caxton (c. 1422-c.1492), sometime Governor of the Company of
+Merchant Adventurers in Bruges (between 1449 and 1470). He learned the art
+of printing either at Bruges or Cologne, and between 1471 and 1477 set up a
+press at Westminster. Tradition says that the first book printed in England
+was his _Game and Playe of Chesse_ (1474). The _Myrrour of the Worlde and
+th'ymage of the same_ appeared in 1480. It contains a brief statement on
+arithmetic, the first mathematics to appear in print in England.
+
+[452] See Vol. I, page 45, note 6 {40}. De Morgan is wrong as to the date
+of the _Margarita Philosophica_. The first edition appeared at Freiburg in
+1503.
+
+[453] Reisch was confessor to Maximilian I (1459-1519), King of the Romans
+(1486) and Emperor (1493-1519).
+
+[454] Joachim Sterck Ringelbergh (c. 1499-c. 1536), teacher of philosophy
+and mathematics in various cities of France and Germany. His _Institutionum
+astronomicarum libri III_ appeared at Basel in 1528, his _Cosmographia_ at
+Paris in 1529, and his _Opera_ at Leyden in 1531.
+
+[455] Johannes Heinrich Alsted (1588-1638) was professor of philosophy and
+theology at his birthplace, Herborn, in Nassau, and later at Weissenberg.
+He published several works, including the _Elementale mathematicum_ (1611),
+_Systema physicae harmonicae_ (1612), _Methodus admirandorum
+mathematicorum_ (1613), _Encyclopaedia septem tomis distincta_ (1630), and
+the work mentioned above.
+
+[456] Johann Jakob Hoffmann (1635-1706), professor of Greek and history at
+his birthplace, Basel. He also wrote the _Epitome metrica historiae
+universalis civilis et sacrae ab orbe condito_ (1686).
+
+[457] Ephraim Chambers (c. 1680-1740), a crotchety, penurious, but
+kind-hearted freethinker. His _Cyclopaedia, or an Universal Dictionary_ was
+translated into French and is said to have suggested the great
+_Encyclopedie_.
+
+[458] _Encyclopedie, ou Dictionnaire raisonne des sciences, des arts et des
+metiers, par un societe de gens de lettres. Mis en ordre et publie par M.
+Diderot, et quant a la partie mathematique, par M. d'Alembert._ Paris,
+1751-1780, 35 volumes.
+
+[459] "From the egg" (state).
+
+[460] See Vol. I, page 382, note 12 {785}.
+
+[461] See Vol. II, page 4, note 15.
+
+[462] "In morals nothing should serve man as a model but God; in the arts,
+nothing but nature."
+
+[463] _Encyclopedie Methodique, ou par ordre de matieres._ Paris,
+1782-1832, 166-1/2 volumes.
+
+[464] See Vol. II, page 193, note 336.
+
+[465] _Encyclopaedia Metropolitana; or, Universal Dictionary of Knowledge._
+London, 1845, 29 volumes. A second edition came out in 1848-1858 in 40
+volumes.
+
+[466] See Vol. I, page 137, note 8 {286}.
+
+[467] See Vol. I, page 80, note 5 {119}.
+
+[468] De Morgan should be alive to satirize some of the statements on the
+history of mathematics in the eleventh edition.
+
+[469] John Pringle Nichol (1804-1859), Regius professor of astronomy at
+Glasgow and a popular lecturer on the subject. He lectured in the United
+States in 1848-1849. His _Views of the Architecture of the Heavens_ (1838)
+was a very popular work, and his _Planetary System_ (1848, 1850) contains
+the first suggestion for the study of sun spots by the aid of photography.
+
+[470] See Vol. II, page 109, note 206.
+
+[471] George Long (1800-1879), a native of Poulton, in Lancashire, was
+called to the University of Virginia when he was only twenty-four years old
+as professor of ancient languages. He returned to England in 1828 to become
+professor of Greek at London University. From 1833 to 1849 he edited the
+twenty-nine volumes of the _Penny Cyclopaedia_. He was an authority on Roman
+law.
+
+[472] A legal phrase, "Qui tam pro domina regina, quam pro se ipso
+sequitur,"--"Who sues as much on the Queen's account as on his own."
+
+[473] Arthur Cayley (1821-1895) was a fellow of Trinity College, Cambridge
+(1842-1846) and was afterwards a lawyer (1849-1863). During his fourteen
+years at the bar he published some two hundred mathematical papers. In 1863
+he became professor of mathematics at Cambridge, and so remained until his
+death. His collected papers, nine hundred in number, were published by the
+Cambridge Press in 13 volumes (1889-1898). He contributed extensively to
+the theory of invariants and covariants. De Morgan's reference to his
+coining of new names is justified, although his contemporary, Professor
+Sylvester, so far surpassed him in this respect as to have been dubbed "the
+mathematical Adam."
+
+[474] See Vol. II, page 26, note 56.
+
+[475] See Vol. I, page 111, note 3 {207}.
+
+[476] See Vol. I, page 87, note 6 {135}.
+
+[477] Pierre Dupuy (1582-1651) was a friend and relative of De Thou. With
+the collaboration of his brother and Nicolas Rigault he published the 1620
+and 1626 editions of De Thou's History. He also wrote on law and history.
+His younger brother, Jacques (died in 1656), edited his works. The two had
+a valuable collection of books and manuscripts which they bequeathed to the
+Royal Library at Paris.
+
+[478] See Vol. I, page 51, note 3 {51}.
+
+[479] It was Cosmo de' Medici (1590-1621) who was the patron of Galileo.
+
+[480] See Vol. I, page 40, note 4 {20}.
+
+[481] See Vol. I, page 106, note 4 {188}.
+
+[482] Sir Edward Sherburne (1618-1702), a scholar of considerable
+reputation. The reference by De Morgan is to _The Sphere of Marcus
+Manilius_, in the appendix to which is a _Catalogue of Astronomers, ancient
+and modern_.
+
+[483] George Parker, second Earl of Macclesfield (1697-1764). He erected an
+observatory at Shirburn Castle, Oxfordshire, in 1739, and fitted it out
+with the best equipment then available. He was President of the Royal
+Society in 1752.
+
+[484] See Vol. II, page 148, note 263.
+
+[485] See Vol. I, page 140, note 7 {296}.
+
+[486] See Vol. I, page 106, note 4 {188}.
+
+[487] Edward Bernard (1638-1696), although Savilian professor of astronomy
+at Oxford, was chiefly interested in archeology.
+
+[488] See Vol. I, page 107, note 1 {190}.
+
+[489] See Vol. I, page 107, note 1 {190}.
+
+[490] See Vol. I, page 135, note 3 {281}.
+
+[491] Philip Dormer Stanhope, fourth Earl of Chesterfield (1694-1773), well
+known for the letters written to his son which were published posthumously
+(1774).
+
+[492] Peter Daval (died in 1763), Vice-President of the Royal Society, and
+an astronomer of some ability.
+
+[493] See Vol. I, page 376, note 1 {766}.
+
+[494] William Oughtred (c. 1573-1660), a fellow of King's College,
+Cambridge, and afterwards vicar of Aldbury, Surrey, wrote the best-known
+arithmetic and trigonometry of his time. His _Arithmeticae in Numero &
+Speciebus Institutio ... quasi Clavis Mathematicae est_ (1631) went through
+many editions and appeared in English as _The Key to the Mathematicks new
+forged and filed_ in 1647.
+
+[495] See Vol. I, page 140, note 5 {294}.
+
+[496] Stephen Jordan Rigaud (1816-1859) was senior assistant master of
+Westminster School (1846) and head master of Queen Elizabeth's School at
+Ipswich (1850). He was made Bishop of Antigua in 1858 and died of yellow
+fever the following year.
+
+[497] He also wrote a memoir of his father, privately printed at Oxford in
+1883.
+
+[498] See Vol. I, page 69, note 3 {96}.
+
+[499] See Vol. I, page 106, note 4 {188}.
+
+[500] William Gascoigne was born at Middleton before 1612 and was killed in
+the battle of Marston Moor in 1644. He was an astronomer and invented the
+micrometer with movable threads (before 1639).
+
+[501] Seth Ward (1617-1689) was deprived of his fellowship at Cambridge for
+refusing to sign the covenant. He became professor of astronomy at Oxford
+(1649), Bishop of Exeter (1662), Bishop of Salisbury (1667), and Chancellor
+of the Garter (1671). He is best known for his solution of Kepler's problem
+to approximate a planet's orbit, which appeared in his _Astronomia
+geometrica_ in 1656.
+
+[502] See Vol. I, page 110, note 2 {198}.
+
+[503] See Vol. I, page 100, note 2 {172}.
+
+[504] See Vol. I, page 107, note 1 {190}.
+
+[505] See Vol. I page 114, note 6 {220}.
+
+[506] See Vol. I, page 77, note 4 {118}.
+
+[507] See Vol. I, page 125, note 3 {253}.
+
+[508] See Vol. I, page 105, note 2 {186}.
+
+[509] Heinrich Oldenburgh (1626-1678) was consul in England for the City
+of Bremen, his birthplace, and afterwards became a private teacher in
+London. He became secretary of the Royal Society and contributed on
+physics and astronomy to the _Philosophical Transactions_.
+
+[510] Thomas Brancker, or Branker (1636-1676) wrote the _Doctrinae
+sphaericae adumbratio et usus globorum artificialium_ (1662) and
+translated the algebra of Rhonius with the help of Pell. The latter work
+appeared under the title of _An Introduction to Algebra_ (1668), and
+is noteworthy as having brought before English mathematicians the
+symbol / for division. The symbol never had any standing on the
+Continent for this purpose, but thereafter became so popular in England
+that it is still used in all the English-speaking world.
+
+[511] See Vol. I, page 118, note 1 {230}.
+
+[512] Pierre Bertius (1565-1629) was a native of Flanders and was educated
+at London and Leyden. He became a professor at Leyden, and later held the
+chair of mathematics at the College de France. He wrote chiefly on
+geography.
+
+[513] See Vol. II, page 297, note 487.
+
+[514] Giovanni Alphonso Borelli (1608-1679) was professor of mathematics at
+Messina (1646-1656) and at Pisa (1656-1657), after which he taught in Rome
+at the Convent of St. Panteleon. He wrote several works on geometry,
+astronomy, and physics.
+
+[515] See Vol. I, page 172, note 2 {381}.
+
+[516] Ignace Gaston Pardies (c. 1636-1673), a Jesuit, professor of ancient
+languages and later of mathematics and physics at the College of Pau, and
+afterwards professor of rhetoric at the College Louis-le-Grand at Paris. He
+wrote on geometry, astronomy and physics.
+
+[517] Pierre Fermat was born in 1608 (or possibly in 1595) near Toulouse,
+and died in 1665. Although connected with the parliament of Toulouse, his
+significant work was in mathematics. He was one of the world's geniuses in
+the theory of numbers, and was one of the founders of the theory of
+probabilities and of analytic geometry. After his death his son published
+his edition of Diophantus (1670) and his _Varia opera mathematica_ (1679).
+
+[518] This may be Christopher Townley (1603-1674) the antiquary, or his
+nephew, Richard, who improved the micrometer already invented by Gascoigne.
+
+[519] Adrien Auzout a native of Rouen, who died at Rome in 1691. He
+invented a screw micrometer with movable threads (1666) and made many
+improvements in astronomical instruments.
+
+[520] See Vol. I, page 66, note 9 {86}.
+
+[521] See Vol. I, page 124, note 7 {248}.
+
+[522] John Machin (d. 1751) was professor of astronomy at Gresham College
+(1713-1751) and secretary of the Royal Society. He translated Newton's
+_Principia_ into English. His computation of [pi] to 100 places is given in
+William Jones's _Synopsis palmariorum matheseos_ (1706).
+
+[523] Pierre Remond de Montmort (1678-1719) was canon of Notre Dame until
+his marriage. He was a gentleman of leisure and devoted himself to the
+study of mathematics, especially of probabilities.
+
+[524] Roger Cotes (1682-1716), first Plumian professor of astronomy and
+physics at Cambridge, and editor of the second edition of Newton's
+_Principia_. His posthumous _Harmonia Mensurarum_ (1722) contains "Cotes's
+Theorem" on the binomial equation. Newton said of him, "If Mr. Cotes had
+lived we had known something."
+
+[525] See Vol. I, page 135, note 3 {281}.
+
+[526] See Vol. I, page 377, note 4 {769}.
+
+[527] Charles Rene Reyneau (1656-1728) was professor of mathematics at
+Angers. His _Analyse demontree, ou Maniere de resoudre les problemes de
+mathematiques_ (1708) was a successful attempt to popularize the theories
+of men like Descartes, Newton, Leibnitz, and the Bernoullis.
+
+[528] Brook Taylor (1685-1731), secretary of the Royal Society, and student
+of mathematics and physics. His _Methodus incrementorum directa et inversa_
+(1715) was the first treatise on the calculus of finite differences. It
+contained the well-known theorem that bears his name.
+
+[529] Pierre Louis Moreau de Maupertuis (1698-1759) was sent with Clairaut
+(1735) to measure an arc of a meridian in Lapland. He was head of the
+physics department in the Berlin Academy from 1745 until 1753. He wrote
+_Sur la figure de la terre_ (1738) and on geography and astronomy.
+
+[530] Pierre Bouguer (1698-1758) was professor of hydrography at Paris, and
+was one of those sent by the Academy of Sciences to measure an arc of a
+meridian in Peru (1735). The object of this and the work of Maupertuis was
+to determine the shape of the earth and see if Newton's theory was
+supported.
+
+[531] Charles Marie de la Condamine (1701-1774) was a member of the Paris
+Academy of Sciences and was sent with Bouguer to Peru, for the purpose
+mentioned in the preceding note. He wrote on the figure of the earth, but
+was not a scientist of high rank.
+
+[532] See Vol. I, page 136, note 5 {283}.
+
+[533] See Vol. II, page 296, note 483.
+
+[534] Thomas Baker (c. 1625-1689) gave a geometric solution of the
+biquadratic in his _Geometrical Key, or Gate of Equations unlocked_ (1684).
+
+[535] See Vol. I, page 160, note 5 {350}.
+
+[536] See Vol. I, page 87, note 4 {133}.
+
+[537] See Vol. I, page 132, note 2 {272}.
+
+[538] See Vol. I, page 118, second note 1 {231}.
+
+[539] The name of Newton is so well known that no note seems necessary. He
+was born at Woolsthorpe, Lincolnshire, in 1642, and died at Kensington in
+1727.
+
+[540] John Keill (1671-1721), professor of astronomy at Oxford from 1710,
+is said to have been the first to teach the Newtonian physics by direct
+experiment, the apparatus being invented by him for the purpose. He wrote
+on astronomy and physics. His _Epistola de legibus virium centripetarum_,
+in the Philosophical Transactions for 1708, accused Leibnitz of having
+obtained his ideas of the calculus from Newton, thus starting the priority
+controversy.
+
+[541] Thomas Digges (d. in 1595) wrote _An Arithmeticall Militare Treatise,
+named Stratioticos_ (1579), and completed _A geometrical practise, named
+Pantometria_ (1571) that had been begun by his father, Leonard Digges.
+
+[542] John Dee (1527-1608), the most famous astrologer of his day, and
+something of a mathematician, wrote a preface to Billingsley's translation
+of Euclid into English (1570).
+
+[543] See Vol. I, page 76, note 3 {112}.
+
+[544] Thomas Harriot (1560-1621) was tutor in mathematics to Sir Walter
+Raleigh, who sent him to survey Virginia (1585). He was one of the best
+English algebraists of his time, but his _Artis Analyticae Praxis ad
+Aequationes Algebraicas resolvendas_ (1631) did not appear until ten years
+after his death.
+
+[545] Thomas Lydiat (1572-1626), rector of Alkerton, devoted his life
+chiefly to the study of chronology, writing upon the subject and taking
+issue with Scaliger (1601).
+
+[546] See Vol. I, page 69, note 3 {96}.
+
+[547] Walter Warner edited Harriot's _Artis Analyticae Praxis_ (1631).
+Tarporley is not known in mathematics.
+
+[548] See Vol. I, page 105, note 2 {186}.
+
+[549] See Vol. I, page 115, note 3 {224}.
+
+[550] See Vol. II, page 300, note 509.
+
+[551] See Vol. I, page 107, note 1 {190}.
+
+[552] Sir Samuel Morland (1625-1695) was a diplomat and inventor. For some
+years he was assistant to John Pell, then ambassador to Switzerland. He
+wrote on arithmetical instruments invented by him (1673), on hydrostatics
+(1697) and on church history (1658).
+
+[553] See Vol. I, page 153, note 4 {337}.
+
+[554] See Vol. I, page 85, note 2 {129}.
+
+[555] See Vol. I, page 43, note 8 {33}.
+
+[556] See Vol. I, page 43, note 7 {32}.
+
+[557] See Vol. I, page 382, note 13 {786}. The history of the subject may
+be followed in Braunmuehl's _Geschichte der Trigonometrie_.
+
+[558] See Vol. I, page 377, note 3 {768}.
+
+[559] See Vol. I, page 108, note 2 {192}.
+
+[560] Michael Dary wrote _Dary's Miscellanies_ (1669), _Gauging epitomised_
+(1669), and _The general Doctrine of Equation_ (1664).
+
+[561] John Newton (1622-1678), canon of Hereford (1673), educational
+reformer, and writer on elementary mathematics and astronomy.
+
+[562] See Vol. I, page 87, note 4 {133}.
+
+[563] "The average of the two equal altitudes of the sun before and after
+dinner."
+
+[564] See Vol. I, page 42, note 4 {24}.
+
+[565] London, 1678. It went though many editions.
+
+[566] "This I who once ..."
+
+[567] Arthur Murphy (1727-1805) worked in a banking house until 1754. He
+then went on the stage and met with some success at Covent Garden. His
+first comedy, _The Apprentice_ (1756) was so successful that he left the
+stage and took to play writing. His translation of Tacitus appeared in
+1793, in four volumes.
+
+[568] Edmund Wingate (1596-1656) went to Paris in 1624 as tutor to Princess
+Henrietta Maria and remained there several years. He wrote _L'usage de la
+regle de proportion_ (Paris, 1624, with an English translation in 1626),
+_Arithmetique Logarithmetique_ (Paris, 1626, with an English translation in
+1635), and _Of Natural and Artificial Arithmetick_ (London, 1630, revised
+in 1650-1652), part I of which was one of the most popular textbooks ever
+produced in England.
+
+[569] John Lambert (1619-1694) was Major-General during the Revolution and
+helped to draw up the request for Cromwell to assume the protectorate. He
+was imprisoned in the Tower by the Rump Parliament. He was confined in
+Guernsey until the clandestine marriage of his daughter Mary to Charles
+Hatton, son of the governor, after which he was removed (1667) to St.
+Nicholas in Plymouth Sound.
+
+[570] Samuel Foster (d. in 1652) was made professor of astronomy at Gresham
+College in March, 1636, but resigned in November of that year, being
+succeeded by Mungo Murray. Murray vacated his chair by marriage in 1641 and
+Foster succeeded him. He wrote on dialling and made a number of
+improvements in geometric instruments.
+
+[571] "Twice of the word a minister," that is, twice a minister of the
+Gospel.
+
+[572] This is _The Lives of the Professors of Gresham College to which is
+prefixed the Life of the Founder, Sir Thomas Gresham_, London, 1740. It was
+written by John Ward (c. 1679-1758), professor of rhetoric (1720) at
+Gresham College and vice-president (1752) of the Royal Society.
+
+[573] Charles Montagu (1661-1715), first Earl of Halifax, was Lord of the
+Treasury in 1692, and was created Baron Halifax in 1700 and Viscount
+Sunbury and Earl of Halifax in 1714. He introduced the bill establishing
+the Bank of England, the bill becoming a law in 1694. He had troubles of
+his own, without considering Newton, for he was impeached in 1701, and was
+the subject of a damaging resolution of censure as auditor of the exchequer
+in 1703. Although nothing came of either of these attacks, he was out of
+office during much of Queen Anne's reign.
+
+[574] See Vol. II, page 302, note 547.
+
+[575] See Vol. I, page 105, note 2 {186}.
+
+[576] James Dodson (d. 1757) was master of the Royal Mathematical School,
+Christ's Hospital. He was De Morgan's great-grandfather. The
+_Anti-Logarithmic Canon_ was published in 1742.
+
+[577] See Vol. I, page 106, note 4 {188}.
+
+[578] See Vol. I, page 110, note 2 {198}.
+
+[579] Richard Busby, (1606-1695), master of Westminster School (1640) had
+among his pupils Dryden and Locke.
+
+[580] See Vol. I, page 107, note 1 {190}.
+
+[581] Herbert Thorndike (1598-1672), fellow of Trinity College, Cambridge
+(1620-1646), and Prebend of Westminster (1661), was a well-known
+theological writer of the time.
+
+[582] See Vol. I, page 140, note 5 {294}.
+
+[583] See Vol. I, page 108, note 2 {192}.
+
+[584] "Labor performed returns in a circle."
+
+[585] See Vol. II, page 208.
+
+[586] "Whatever objections one may make to the above arguments, one always
+falls into an absurdity."
+
+[587] See Vol. II. page 11, note 29. _The Circle Squared; and the solution
+of the problem adapted to explain the difference between square and
+superficial measurement_ appeared at Brighton in 1865.
+
+[588] "And beyond that nothing."
+
+[589] Gillott (1759-1873) was the pioneer maker of steel pens by machinery,
+reducing the price from 1s. each to 4d. a gross. He was a great collector
+of paintings and old violins.
+
+[590] William Edward Walker wrote five works on circle squaring (1853,
+1854, 1857, 1862, 1864), mostly and perhaps all published at Birmingham.
+
+[591] Solomon M. Drach wrote _An easy Rule for formulizing all Epicyclical
+Curves_ (London, 1849), _On the Circle area and Heptagon-chord_ (London,
+1864), _An easy general Rule for filling up all Magic Squares_ (London,
+1873), and _Hebrew Almanack-Signs_ (London, 1877), besides numerous
+articles in journals.
+
+[592] See Vol. I, page 168, note 3 {371}.
+
+[593] See Vol. I, page 254, note 2 {580}.
+
+[594] See Vol. I, page 98, note 6 {163}.
+
+[595] Robert Fludd or Flud (1574-1637) was a physician with a large London
+practice. He denied the diurnal rotation of the earth, and was attacked by
+Kepler and Mersenne, and accused of magic by Gassendi. His _Apologia
+Compendiania, Fraternitatem de Rosea Cruce suspicionis ... maculis
+aspersam, veritatis quasi Fluctibus abluens_ (Leyden, 1616) is one of a
+large number of works of the mystic type.
+
+[596] Consult _To the Christianity of the Age. Notes ... comprising an
+elucidation of the scope and contents of the writings ... of Dionysius
+Andreas Freher_ (1854).
+
+[597] Sir William Robert Grove (1811-1896), although called to the bar
+(1835) and to the bench (1853), is best known for his work as a physicist.
+He was professor of experimental philosophy (1840-1847) at the London
+Institution, and invented a battery (1839) known by his name. His
+_Correlation of Physical Forces_ (1846) went through six editions and was
+translated into French.
+
+[598] Johann Tauler (c. 1300-1361), a Dominican monk of Strassburg, a
+mystic, closely in touch with the Gottesfreunde of Basel. His _Sermons_
+first appeared in print at Leipsic in 1498.
+
+[599] Paracelsus (c. 1490-1541). His real name was Theophrastes Bombast von
+Hohenheim, and he took the name by which he is generally known because he
+held himself superior to Celsus. He was a famous physician and pharmacist,
+but was also a mystic and neo-Platonist. He lectured in German on medicine
+at Basel, but lost his position through the opposition of the orthodox
+physicians and apothecaries.
+
+[600] See Vol. I, page 256, note 2 {588}.
+
+[601] Philip Schwarzerd (1497-1560) was professor of Greek at Wittenberg.
+He helped Luther with his translation of the Bible.
+
+[602] Johann Reuchlin (1455-1522), the first great German humanist, was
+very influential in establishing the study of Greek and Hebrew in Germany.
+His lectures were mostly delivered privately in Heidelberg and Stuttgart.
+Unlike Melanchthon, he remained in the Catholic Church.
+
+[603] Joseph Chitty (1776-1841) published his _Precedents of Pleading_ in
+1808 and his _Reports of Cases on Practice and Pleading_ in 1820-23 (2
+volumes).
+
+[604] See Vol. I, page 44, note 1 {35}.
+
+[605] See Vol. I, page 44, note 4 {38}.
+
+[606] Jean Pelerin, also known as Viator, who wrote on perspective. His
+work appeared in 1505, with editions in 1509 and 1521.
+
+[607] Henry Stephens. See Vol. I, page 44, note 3 {37}.
+
+[608] The well-known grammarian (1745-1826). He was born at Swatara, in
+Pennsylvania, and practised law in New York until 1784, after which he
+resided in England. His grammar (1795) went through 50 editions, and the
+abridgment (1818) through 120 editions. Murray's friend Dalton, the
+chemist, said that "of all the contrivances invented by human ingenuity for
+puzzling the brains of the young, Lindley Murray's grammar was the worst."
+
+[609] Robert Recorde (c. 1510-1558) read and probably taught mathematics
+and medicine at Cambridge up to 1545. After that he taught mathematics at
+Oxford and practised medicine in London. His _Grounde of Artes_, published
+about 1540, was the first arithmetic published in English that had any
+influence. It went through many editions. The _Castle of Knowledge_
+appeared in 1551. It was a textbook on astronomy and the first to set forth
+the Copernican theory in England. Like Recorde's other works it was written
+on the catechism plan. His _Whetstone of Witte ... containying thextraction
+of Rootes: The Cosike practise, with the rule of Equation: and the woorkes
+of Surde Nombres_ appeared in 1557, and it is in this work that the modern
+sign of equality first appears in print. The word "Cosike" is an adjective
+that was used for a long time in Germany as equivalent to algebraic, being
+derived from the Italian _cosa_, which stood for the unknown quantity.
+
+[610] Robert Cecil (c. 1563-1612), first Earl of Salisbury, Secretary of
+State under Elizabeth (1596-1603) and under James I (1603-1612).
+
+[611] In America the German pronunciation is at present universal among
+mathematicians, as in the case of most other German names. This is due, no
+doubt, to the great influence that Germany has had on American education in
+the last fifty years.
+
+[612] The latest transliteration is substantially K'ung-fu-tz[vu].
+
+[613] The tendency seems to be, however, to adopt the forms used of
+individuals or places as rapidly as the mass of people comes to be prepared
+for it. Thus the spelling Leipzig, instead of Leipsic, is coming to be very
+common in America.
+
+[614] Sir Edward Coke (1552-1634), the celebrated jurist.
+
+[615] Dethlef Cluvier or Cluever (d. 1708 at Hamburg) was a nephew, not a
+grandson, of Philippe Cluvier, or Philipp Cluever (1580-c. 1623). Dethlef
+traveled in France and Italy and then taught mathematics in London. He
+wrote on astronomy and philosophy and also published in the _Acta
+Eruditorum_ (1686) his _Schediasma geometricum de nova infinitorum
+scientia_. _Quadratura circuli infinitis modis demonstrata_, and his
+_Monitum ad geometras_ (1687). Philippe was geographer of the Academy of
+Leyden. His _Introductionis in universam geographiam tam veterem quam novam
+libri sex_ appeared at Leyden in 1624, about the time of his death.
+
+[616] See Vol. I, page 124, note 7 {248}.
+
+[617] Bernard Nieuwentijt (1654-1718), a physician and burgomaster at
+Purmerend. His _Considerationes circa Analyseos ad quantitates infinite
+parvas applicatae Principia et Calculi Differentialis usum_ (Amsterdam,
+1694) was attacked by Leibnitz. He replied in his _Considerationes secundae_
+(1694), and also wrote the _Analysis Infinitorum, seu Curvilineorum
+Proprietates ex Polygonorum Natura deductae_ (1695). His most famous work
+was on the existence of God, _Het Regt Gebruik der Werelt Beschouwingen_
+(1718).
+
+[618] "From a given line to construct" etc.
+
+[619] "Pirates do not fight one another."
+
+[620] Claude Mallemens (Mallement) de Messanges (1653-1723) was professor
+of philosophy at the College du Plessis, in Paris, for 34 years. The work
+to which De Morgan refers is probably the _Fameux Probleme de la quadrature
+du cercle, resolu geometriquement par le cercle et a ligne droite_ that
+appeared in 1683.
+
+[621] On Tycho Brahe see Vol. I, page 76, note 3 {112}.
+
+[622] Wilhelm Frederik von Zytphen also published the _Tidens Stroem_, a
+chronological table, in 1840. The work to which De Morgan refers, the
+_Solens Bevaegelse i Verdensrummet_, appeared first in 1861. De Morgan seems
+to have missed his _Nogl Ord om Cirkelens Quadratur_ which appeared in
+1865, at Copenhagen.
+
+[623] James Joseph Sylvester (1814-1897), professor of natural philosophy
+at University College, London (1837-1841), professor of mathematics at the
+University of Virginia (1841-1845), actuary in London (1845-1855),
+professor of mathematics at Woolwich (1877-1884) and at Johns Hopkins
+University, Baltimore (1877-1884), and Savilian professor of geometry at
+Oxford (1884-1894).
+
+[624] See Vol. I, page 76, note 3 {112}.
+
+[625] See Vol. II, page 205, note 349.
+
+[626] See Vol. I, page 76, note 3 {112}.
+
+[627] See Vol. I, page 46, note 1 {42}.
+
+[628] See Vol. II, page 183, note 318.
+
+[629] See Vol. I, page 321, note 2 {691}.
+
+[630] James Mill, born 1773, died 1836.
+
+[631] See Vol. II, page 3, note 11.
+
+[632] See Vol. II, page 3, note 13.
+
+[633] See Vol. II, page 3, note 14.
+
+[634] This anecdote is printed at page 4 (Vol. II); but as it is used in
+illustration here, and is given more in detail, I have not omitted
+it.--S.E. De M.
+
+[635] See Vol. II, page 4, note 15.
+
+[636] See Vol. I, page 382, note 13 {786}.
+
+[637] "Monsieur, (a + b^{n})/n = x, whence God exists; answer that!"
+
+[638] "Monsieur, you know very well that your argument requires the
+development of x according to integral powers of n."
+
+[639] See Vol. I, page 153, note 4 {337}.
+
+[640] Thomas Love Peacock (1785-1866) an English novelist and poet.
+
+[641] Perhaps Dr. Samuel Warren (1807-1877), the author of _Ten Thousand a
+Year_ (serially in Blackwood's in 1839; London, 1841).
+
+[642] See Vol. I, page 255, note 6 {584}.
+
+[643] "From many, one; much in little; Ultima Thule (the most remote
+region); without which not."
+
+[644] Spurius Maelius (fl. 440 B. C.), who distributed corn freely among the
+poor in the famine of 440 B. C. and was assassinated by the patricians.
+
+[645] Spurius Cassius Viscellinus, Roman consul in 502, 493, and 486 B. C.
+Put to death in 485.
+
+[646] "O what a fine bearing, he said, that has no brain."
+
+[647] Sir William Rowan Hamilton. See Vol. I, page 332, note 4 {709}.
+
+[648] William Allen Whitworth, the author of the well-known _Choice and
+Chance_ (Cambridge, 1867), and other works.
+
+[649] James Maurice Wilson, whose _Elementary Geometry_ appeared in 1868
+and went through several editions.
+
+[650] See Vol. II, page 183, note 315.
+
+[651] "Force of inertia conquered," and "Victory in the whole heavens."
+
+[652] "With all his might."
+
+[653] George Berkeley (1685-1753), Bishop of Cloyne, the idealistic
+philosopher and author of the _Principles of Human Knowledge_ (1710), _The
+Analyst, or a Discourse addressed to an Infidel Mathematician_ (1734), and
+_A Defense of Freethinking in Mathematics_ (1735). He asserted that space
+involves the idea of movement without the sensation of resistance. Space
+sensation less than the "minima sensibilia" is, therefore, impossible. From
+this he argues that infinitesimals are impossible concepts.
+
+[654] See Vol. I, page 85, note 2 {129}.
+
+[655] See Vol. I, page 81, note 6 {120}.
+
+[656] Edwin Dunkin revised Lardner's _Handbook of Astronomy_ (1869) and
+Milner's _The Heavens and the Earth_ (1873) and wrote _The Midnight Sky_
+(1869).
+
+[657] Michael Faraday (1791-1867) the celebrated physicist and chemist. He
+was an assistant to Sir Humphrey Davy (1813) and became professor of
+chemistry at the Royal Institution, London, in 1827.
+
+[658] "If you teach a fool he shows no joyous countenance; he cordially
+hates you; he wishes you buried."
+
+[659] "Every man is an animal, Sortes is a man, therefore Sortes is an
+animal."
+
+[660]
+
+ "May some choice patron bless each grey goose quill;
+  May every Bavius have his Bufo still."--POPE, _Prologue to the Satires._
+
+Bavius has become proverbial as a bad poet from the lines in Vergil's
+_Eclogues_ (III, 90):
+
+ "Qui Bavium non odit, amet tua carmina, Maevi,
+  Atque idem jungat vulpes, et mulgeat hircos."
+
+"He who does not hate Bavius shall love thy verses, O Maevius; and the same
+shall yoke foxes and shall milk he-goats."
+
+Bavius and Maevius were the worst of Latin poets, condemned by Horace as
+well as Vergil.
+
+[661] See Vol. II, page 158, note 279.
+
+[662] "Honest," "useful," "handsome," "sweet."
+
+[663] "Let not the fourth man attempt to speak."
+
+[664]
+
+ "In those old times,--ah
+ 'Twas just like this, ah!"
+
+[665] See Vol. I, page 382, note 12 {785}.
+
+[666] These remarks were never written.--S. E. De M.
+
+[667]
+
+ "Fleas, flies, and friars, are masters who sadly the people abuse,
+  And thistles and briars are sure growing grains to abuse.
+  O Christ, who hatest strife and slayst all things in peace,
+  Destroy where'er are rife, briars, friars, flies and fleas.
+  Fleas, flies, and friars foul fall them these fifteen years
+  For none that there is loveth fleas, flies, nor freres."
+
+[668] "It is my plan to restore to an unskilled race the worthy arts of a
+better life."
+
+[669] The first sentences of the first oration of Cicero against Catiline:
+"Quo usque tandem abutere, Catilina, patientia nostra?" (How long, O
+Catiline, will you abuse our patience?) "Quamdiu etiam furor iste tuus nos
+eludet?" (How long will this your madness baffle us?) "Nihilne te nocturnum
+praesidium Palati, ... nihil horum ora voltusque moverunt?" (Does the night
+watch of the Palatium, ... do the faces and expressions of all these men
+fail to move you?) "In te conferri ..." (This plague should have been
+inflicted upon you long ago, which you have plotted against us so long.)
+
+[670] "Beware of the things that are marked."
+
+[671] "Farewell, ye teachers without learning! See to it that at our next
+meeting we may find you strong in body and sound in mind."
+
+[672] See Vol. I, page 336, note 8 {713}.
+
+[673] See Vol. I, page 229, note 2 {515}.
+
+[674] This proof, although capable of improvement, is left as in the
+original. Those who may be interested in the mathematics of the question,
+may consult F. Enriques, _Fragen der Elementargeometrie_ (German by
+Fleischer), Leipsic, 1907, Part II, p. 267; F. Rudio, _Archimedes_,
+_Huygens_, _Lambert_, _Legendre_. _Vier Abhandlungen ueber die
+Kreismessung_, Leipsic, 1892; F. Klein, _Famous Problems of Elementary
+Geometry_ (English by Beman and Smith), Boston, 1895; J. W. A. Young,
+_Monographs on Modern Mathematics_, New York, 1911, Chap. IX (by the editor
+of the present edition of De Morgan.)
+
+[675] See Vol. I, page 69, note 2 {95}.
+
+[676] See Vol. I, page 137, note 8 {286}.
+
+[677] Joseph Allen Galbraith who, with Samuel Haughton, wrote the Galbraith
+and Haughton's _Scientific Manuals_. (Euclid, 1856; Algebra, 1860;
+Trigonometry, 1854; Optics, 1854, and others.)
+
+[678] This note on Carlyle (1795-1881) is interesting. The translation of
+Legendre appeared in the same year (1824) as his translation of Goethe's
+_Wilhelm Meister_.
+
+[679] Michael Stifel (1487-1567), also known as Stiefel, Styfel, and
+Stifelius, was an Augustine monk but became a convert to Lutheranism. He
+was professor of mathematics at Jena (1559-1567). His edition of the _Coss_
+appeared at Koenigsberg in 1553, the first edition having been published in
+1525. The + and - signs first appeared in print in Widman's arithmetic of
+1489, but for purposes of algebra this book was one of the first to make
+them known.
+
+[680] Christoff Rudolff was born about 1500 and died between 1540 and 1552.
+_Die Coss_ appeared in 1525 and his arithmetic in 1526.
+
+       *       *       *       *       *
+
+
+Corrections made to printed original.
+
+Page 9, "long-fostered prejudice": 'perjudice' in original.
+
+Page 73, "Pensees, ch. 7": 'Pansees' in original.
+
+Page 127, "and pulled out a plum": 'und' in original.
+
+Page 147, "did not come forward": 'forword' in original.
+
+Page 172, "come into general circulation": 'circulalation' in original.
+
+Ibid., "the more difficult fractions which we have got": 'he have got' in
+original.
+
+Page 192, "it has been stated": 'started' in original.
+
+Page 216, "the obsolete word tetch of the same meaning": 'meaing' in
+original.
+
+Page 228, "[Greek: dioklasianos]": 'dioklalasianos' in original.
+
+Page 233. After `Henry E. Manning' were printed two paragraphs `Shilling
+versus Franc.' and `Teutonic Long Hundred 120 versus 100 or the Decimal
+question.' These appear to have been set in error, there is no applicable
+context.
+
+Page 316, "in a manner depending upon the difference": 'maner' in original.
+
+Page 322, "neither what Newton did, nor what was done before him.": 'not'
+(for 'nor') in original.
+
+Page 344, "Victoria toto coelo": 'tolo' in original.
+
+Page 368, "cannot be brought up to 1": 'up to +-' in original.
+
+Page 371, "Q_2=b_2 Q_1+a_2": 'Q_2=b_2 Q_1-a_2' in original.
+
+Note 50, "all who were not in the road to Heaven were excommunicated":
+'excomunicated' in original.
+
+Note 372, "[Greek: he alazoneia biou]": 'alaxoneia' in original.
+
+Ibid., "Iapetos": 'Ispetos' in original.
+
+Ibid., "Papeiskos": 'Paspeisoks' in original.
+
+Ibid., "[Greek: dioklasianos]": 'dioklalasianos' in original.
+
+
+
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