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diff --git a/43841-0.txt b/43841-0.txt new file mode 100644 index 0000000..593b9f7 --- /dev/null +++ b/43841-0.txt @@ -0,0 +1,2292 @@ +*** START OF THE PROJECT GUTENBERG EBOOK 43841 *** + +Transcriber's Notes + +Changes to the text (corrections to typographical errors) are listed at +the end of the book. + +On page 45, in the reference "Beccheri's Physica Subterranea, Lipsiæ, +1738 (with supplement), 8vo., 1681-80;", no satisfactory explanation of +"1681-80" has been found. Note that the publication date of Physica +Subterranea is 1669. + +In Figure 2 on page 82, the following denote the conventional symbols +for planetary bodies: [Sun], [Moon], [Mercury], [Venus], [Mars], +[Jupiter], [Saturn], [Uranus]. + +On pages 83 & 84 in the explanation of Plate III, a single quote is used +to denote the decimal point: this convention has been retained. + +In this Plain Text version of the e-book, the Latin-1 character set +only is used. Italic typeface is denoted by surrounding _underscores_; +small caps typeface is denoted by ALL CAPS; superscript symbols are +preceded by caret (^). + +[Asterism] denotes three stars (asterisks). + +[oe] represents the oe-ligature. + + * * * * * + +[Illustration: + + EDWARD SOMERSET, + SIXTH EARL AND SECOND + MARQUIS OF WORCESTER. + +From a Bust by Mr. James Loft, Sculptor, exhibited at the Royal Academy, +1867; and now in the Sculpture Gallery of the Crystal Palace, Sydenham. + +] + + + + + SCIENTIFIC STUDIES: + + OR + + PRACTICAL, IN CONTRAST WITH CHIMERICAL PURSUITS; + + EXEMPLIFIED IN + TWO POPULAR LECTURES. + + + I. + + THE LIFE OF EDWARD SOMERSET, + SECOND + MARQUIS OF WORCESTER, + INVENTOR OF THE STEAM ENGINE. + + + II. + + CHIMERAS OF SCIENCE: + ASTROLOGY, ALCHEMY, SQUARING THE CIRCLE, + PERPETUUM MOBILE, ETC. + + With Illustrative Diagrams. + + BY + + HENRY DIRCKS, C. E., LL.D., + F.C.S., M.R.S.L., F.R.S.R., &c. &c. + + AUTHOR OF "THE LIFE OF THE MARQUIS OF WORCESTER;" + "WORCESTERIANA;" &c. + + + LONDON: + E. & F. N. SPON, 48, CHARING CROSS, S.W. + 1879. + + + + +INTRODUCTION. + + +It forms a necessary part of popular lectures that they should possess +breadth with brevity, and interest without too great profundity. It is +possible to see a large extent of country from a lofty tower without +being cognizant of every blade of grass, the perfume of blossoms, or the +notes of the sweetest songsters of the groves. In like manner the +popular lecturer has to present only so much to the eye of the mind as +will give the prominent features of his theme, omitting those details +over which the scholar, or the true lover of his subject, dwells with +the affection of a fond parent over a darling child. + +We must look with astonishment at a man of noble birth, who in a period +of civil commotion, with a monarch for his friend, and a court at his +command, secluded himself during his youth in a stately ancient tower, +engaged in abstruse studies and wonderful mechanical operations; and +who, late in life, amidst the terrors of civil war was found turning his +inventive faculties, like another Archimedes, to the construction of +means of defence, and terrible weapons of offence. But it is only those +who become immersed in studies, whether of theology, philosophy, or +kindred mental pursuits, who can appreciate the growing appetite for +what appears to unlettered men as the driest of all dry occupations. The +mere pleasure-seeker knows not how much is lost, and how little is +gained by sharing the most brilliant gaieties of fashionable life. + +Look at the ancient astrologers, whose pursuits were once as pure and +noble as those of modern astronomers. Amidst wild theories, +superstitious beliefs, empirical systems, and pagan divination, a +rupture became inevitable: one side adopted stellary divination or +Astrology, the other Astronomy, or the simple and true study of the +stars. + +Whatever a man's intellectual pursuits may be, he has the advantage over +the mere man of fashion of being engaged in employments which the +longest life cannot exhaust. + +But intellectual pursuits partake either of the negative or the +positive; they are useful or useless, and when useless they fritter away +and render nugatory the talent that might have been better employed. + +The Marquis of Worcester affords an eminent example of genius of a high +order, grandly and effectively directed towards the advancement of man's +political and social position. His contemporary, Dr. John Dee, the +Astrologer, together with his friend Kelly, the Alchemist, may be +appropriately distinguished as representing a class chimerically +inclined, and hurtful to the well-being of society; while a less eminent +and less blameable section of chimerical labourers are those of whom +the worst we can say is, that they waste much valuable time, energy, and +fortune, through attaching themselves to mathematics, mechanics, and +other learned pursuits, only in search of marvellous, instead of useful +applications. + +All chimeras are built on assumptions, and so far are "castles in the +air;" in many forms they are simply ridiculous; but when they pretend to +the supernatural they are pernicious and often wicked. + +In the two lectures now presented for his perusal, the reader will find +both these topics illustrated by suitable lives and authentic evidence. + + H. D. + +_London, February, 1869._ + + + + + I. + + Lecture + ON + THE LIFE OF EDWARD SOMERSET, + SECOND + MARQUIS OF WORCESTER. + + "He was a man, take him for all in all, + We shall not look upon his like again." + + DELIVERED AT + THE LITERARY INSTITUTION, GREENWICH, + 16TH FEBRUARY, 1864. + + + + +LECTURE I. + + +The Biographer of Edward, second MARQUIS OF WORCESTER, naturally finds +some difficulty in rendering prominent the political position that +nobleman enjoyed in the 17th century; or of impressing the minds of his +hearers or readers with a just sense of the wonderful genius of the +author of the "Century of Inventions," even although the fact be +established of that remarkable man being also the true and first +inventor of a veritable steam engine. + +When we consider the eventful period in which he lived, (from 1601 to +1667,) and his personal character, together with the social, political, +and romantic incidents of his life, the career of the Marquis of +Worcester cannot fail to interest and instruct us. He was at once the +most fortunate and unfortunate of men, living in times of mingled +enlightenment, superstition, and civil discord, and finally finding +himself cast on the tender mercies of a corrupt Court; the possessor of +a high order of mechanical genius, yet proscribed politically and +theologically; most loyal, yet falling the victim of puritanism; and +closing his life neglected by a Sovereign whose father had been the +chief ruin of his patrimony. + +Descended from the Plantagenets, Edward Somerset, second MARQUIS OF +WORCESTER, is supposed to have been born about, or soon after 1601, the +records to establish his natal year being wanting. His father, Henry +Somerset, created first Marquis of Worcester by Charles I., was married +on the 16th June, 1600, at Blackfriars; Queen Elizabeth, attending in +great state, graciously danced at the wedding ball; and the festivities +of the occasion were continued for three days. + +We obtain little information respecting the Marquis of Worcester until +about the twenty-seventh year of his age, when he married Elizabeth, +daughter of Sir William Dormer, eldest son of Lord Dormer of Weng, and +sister of Robert, Earl of Carnarvon. It is not known where he was +educated, but it was certainly neither at Oxford nor Cambridge. Mention +is made of his preceptor, Mr. Adams, at Raglan Castle, the baronial seat +of the lords of Raglan, in Monmouthshire. There is every probability, +however, that he finished his education at some foreign university. His +son and heir, Henry, born in 1629, was created by Charles II. the first +Duke of Beaufort, and from him the present Duke of Beaufort is the +eighth of that rank in lineal descent. + +It was during the first or second year of his married life that he +engaged the services of Caspar Kaltoff, whom he employed as a practical +assistant, to work out his numerous mechanical experiments, and whom he +extols as an "unparalleled workman, both for trust and skill."[1] There +are still to be seen on one side of the Keep--or citadel of Raglan +Castle, the remains of grooves in the wall, probably for the insertion +of large metal pipes, in some way or other connected with the waterworks +which are known to have been erected there, and which were most likely +carried out by Kaltoff, under his master's directions. + +[1] Dedication to "The Century of Inventions." + +Becoming a widower in 1635, his lordship married in 1639, his second +wife, Margaret, second daughter and co-heir of Henry O'Brien, Earl of +Thomond. + +It must have been about this period of his life that the Marquis of +Worcester made one of his most singular and perplexing mechanical +experiments, which he exhibited at the Tower before Charles I., several +of his Court, some foreign ambassadors, and the lieutenant of that +fortress. As he names Sir William Balfour (who held the latter +appointment from 1630 to 1641) we can arrive at an approximate date. The +mechanical surprise which he states he thus presented to gratify his +royal master, was no other than a gigantic wheel, 14 feet in diameter, +weighted with 40 weights of 50 lbs. each, equal to 2000 lbs., by means +of which we are left to infer that the wheel maintained a rotatory +motion, without assistance from any external aid whatever; that it was +in fact, a realization of that long sought for curiosity--perpetual +motion. As he wrote deliberately a statement of this circumstance +fifteen years later, or more, which he afterwards printed, we are left +without any grounds to suppose otherwise than that he deceived himself, +or was deceived, from interested motives, by persons in his employment. +The circumstance is scarcely worth notice except as a singular proof +that such a hallucination could exist in the mind of the same genius +that perfected the first practical steam-engine. We can only say that if +the mystery could be cleared up, although it would be of little or no +value to mathematics or mechanics, it would go far to elevate the +scientific character of the Marquis, though he was not the only +celebrity of his time infatuated with a thorough belief in the +possibility of solving the paradox. + +The Marquis of Worcester, born at the close of Queen Elizabeth's reign, +is not mentioned as appearing at the Court of James I; his courtier life +most likely commenced later, in the reign of Charles I, who was about +his own age, and with whose career, the fortunes of both the Marquis of +Worcester, and his father, family, and friends, were unhappily but too +intimately interwoven. + +It requires a visit to Raglan Castle fully to realise the grandeur, +nobleness, and strength of that romantically situated, and almost regal +stronghold. It wears all the solemnity that antiquity can bestow, it is +so gothic, so solid, and embowered, as it were, in a constant dubious +shade. Then it is so extensive in its bounds, its apartments are so +capacious, and its massy walls so lofty and so finely chiseled and +proportioned, that when we consider there is no quarry within any +reasonable distance, nor any river or stream for conveyance, the whole +structure assumes the mystery of absolute romance. Its historic +associations also rivet the attention of every beholder who is +acquainted with the part it played in determining the fate of that great +struggle between the Crown and the Parliament, which commenced in 1640, +and ended with the establishment of a Commonwealth. + +The county of Monmouth is eminently distinguished for its scenery, its +green hills and dales presenting a beautifully wooded and highly +picturesque landscape from every point of view. The village of Raglan is +a small unpretending hamlet, principally remarkable for its parish +church, which contains the chapel of the Beauforts, the resting place of +several members of the Somerset family. Peering above lofty neighbouring +trees, the Donjon, Keep, or Citadel of Raglan Castle is a conspicuous +object; itself very lofty and standing on a considerable eminence, it +commands a most delightful and extensive panoramic view of the +surrounding country in that fertile district. + +The Castle may be described as consisting of two portions, distinguished +by two courts and two fortified arched entrances. The grand entrance, +between two hexagonal towers, leads to the paved court, with the closet +tower or library to the right, a withdrawing or ball-room overhead, and +a banqueting or stately hall to the left, which last apartment attracts +much notice from its great size and remarkable state of preservation. +Externally situated is the Citadel or Tower of Gwent, surrounded with a +broad moat over which there appears to have been a drawbridge on one +side, and on the other, adjoining the castle a permanent stone bridge. + +During his youth, the Marquis of Worcester, as Lord Herbert, resided at +the Castle, and may have had his laboratory, workshop, and study +conveniently situated in the Citadel; at all events, in connection with +his early career, the ruined remains of the family mansion cannot be +visited without intense interest. His father was a noble minded, hearty, +generous man, living in princely state; an extensive and wealthy landed +proprietor, and in case of need capable of defending his Citadel against +any foe whatever. This last necessity made itself conspicuous between +the years 1640 and 1641, when the civil war broke out. After the fatal +battle of Naseby, 14th June, 1645, Charles I. three times rested at the +Castle, staying there in all twenty-seven days. The strength of that +fortress enabled it to resist the Parliamentary arms longer than any +other stronghold--its surrender following very shortly after that of +Pendennis Castle. + +When civil war was raging in this country, when King and Parliament were +in opposition, when Puritan, Protestant, and Papist sought for mastery, +when cavaliers met roundheads in mortal conflict, and every man stood in +fear of his neighbour, the Marquis of Worcester could no longer remain a +mere student of mechanism and of mathematical problems: if like +Archimedes in one sense, he was now seen, unlike him, buckling on his +armour, raising troops, and doffing the student's gown to become the +soldier. Alas! his military career forms no brilliant page in the annals +of his country's history. He was essentially neither a statesman, nor a +military man. He was bold, courageous, and energetic, but he could +neither be fierce nor ferocious on occasion. He tampered with opponents, +lost means of surprise, and was ever being tricked by the cunning and +chicanery of adversaries not over-scrupulous in their promises or +proceedings. His very goodness of heart, urbanity and uprightness were +the sources of his utter ruin. Himself incapable of deceit, he was +perpetually being made the victim of it: those who appeared his assured +friends, and had every reason to be so, proving in any emergency +shallow, empty, and worthless. Flattered by Charles I. he became +instrumental in assisting that Prince from his parent's private +fortune; and when that was exhausted, the King sapped the property of +the son, repaying both with titles, promises, and valueless bonds. He +created the Marquis of Worcester Earl of Glamorgan, during his father's +life-time; and, inducing him to raise Irish troops to fight against +English subjects, he completed the Earl's ruin; for, that untoward +enterprise failing, and being followed by the fall of Raglan Castle, and +the victories of the Cromwellian army, the Marquis of Worcester had to +quit his native land to seek refuge, with many other political refugees, +at the Court of France. His wife, who had been residing at Raglan +Castle, obtained leave from the Parliament in 1646 to flee to Paris, +where the Marquis also arrived in 1648. + +The Marquis was proscribed both as a Papist and a rebel. Throughout his +political career the religion of his father and himself had made many +weak-minded men their enemies; but that his loyalty should be considered +rebellion was nothing more than might be expected from the dominant +party of those troubled times: although undoubtedly the result of that +great moral earthquake benefited our nation. + +His only son, Henry, sat in the Cromwellian Parliament, and this fact +may, in part, explain the circumstance that most probably induced the +Marquis of Worcester to visit London in 1652; for he must have been +well-advised before committing such an apparently rash act. He was +immediately incarcerated in the Tower, from which he was released in two +years and a quarter, no doubt on his parole, as in 1655 a warrant was +signed by Cromwell to pay the Marquis of Worcester the sum of _three +pounds per week_ for his maintenance. + +He was utterly beggared; what was he to do? It seems to have occurred to +him to turn his mechanical ingenuity to account, the Pretender's +monetary consideration being insufficient for the purpose intended. This +high-minded nobleman in the same year wrote his remarkable "Century of +Inventions," although it was not printed until eight years afterwards. +The title-page declared its production to have been "at the instance of +a powerful friend," who was, as we have reason to think, no other than +Colonel Christopher Coppley, or Copley, who had served in the +Parliamentary army of the North, under the command of General Fairfax; +for agreements were drawn up between them to secure a participation in +any benefits arising from introducing the steam engine, or +water-commanding engine, as it was then called. + +It is not to the historic page, but to the calm unobtrusive volumes of +scientific record, that we must turn to be enlightened with respect to +the mental and mechanical achievements of the Marquis of Worcester; and +we must at the same time not overlook the fact, that many branches of +science were, in his day, but just emerging from that thraldom of +empiricism, which had for centuries clouded every department of +philosophical research. + +The Marquis of Worcester was so essentially a scientific, and not a +literary man, that Horace Walpole acted most inconsistently in classing +him among his _Royal and Noble Authors_. That brilliant cynic, however, +had a purpose to serve, and although he found in the Marquis a vein of +pursuit of which he was totally ignorant, he presumed to criticise the +"Century," and to question its author's veracity; a charge which, if +established, even in a minor degree, would serve a political purpose, by +proving the Marquis to be unreliable in other respects, and thus +weakening his authority in religion and politics. But the dilettante +Walpole, a connoisseur in paintings and works of _vertu_, was, in +matters of science, more ignorant of the Marquis of Worcester's worth, +than was the equally satirical Voltaire of Shakspeare's genius. Hume, +the historian, attracted by the sparkling wit of Walpole, adopted +without examination, his plausible criticism, unconscious of its +superficiality and absolute untruthfulness in every respect. + +We would here notice the probable cause of the Marquis's indefatigable +study of, and attention to, practical mechanics. As in the time of +Charles II., so also during the reign of his father, there is reason to +believe that some distinguished public officer was appointed to +superintend Government works connected with the army and navy, and that +they were situated at Vauxhall. It was probably a department similar to +that held in 1661, by Sir Samuel Morland, designated Master of +Mechanics. Otherwise how are we to account for the Marquis of +Worcester's devoting his time, his energies, and his very fortune to +inventions affecting mechanical appliances generally, and particularly +to those connected with naval and military affairs, and hydraulic +engines? + +One of his inventions (No. 56) he exhibited to Charles I. at the Tower, +and of another (No. 64) being an improvement in fire-arms, he observes +it was "tried and approved before the King (Charles I.), and an hundred +Lords and Commons." Then his great invention, the "Water-commanding +Engine," was set up at Vauxhall in 1663, where it was certainly at work +in 1667, or probably three years later. All these circumstances wear the +aspect of royal patronage, of public employment, and of the possession +of influence suitable to the holder of a dignified position. + +This view of the high and honourable public official position held by +the Marquis is also borne out by the petition of William Lambert, about +1664, to be found in the State Paper Office. It was addressed to +Charles II. and sets forth:--"That your petitioner was founder to his +late Majesty of blessed memory, in Vauxhall, under the Marquis of +Worcester, for gun and water-work, or any other thing founded in brass." +Nothing surely can be more certain than that the Marquis's was a public +situation, and his "Century" affords ample evidence of his aptitude in +_that_ respect for the post which he filled; nor can we better account +for his numerous improvements in fire-arms, cannon, sailing vessels, +fortifications, and embankments. + +His "Century of Inventions" is the mere syllabus or outline of a +proposed larger work, for he concludes with the statement of +his--"meaning to leave to posterity a book, wherein under each of these +heads the means to put in execution and visible trial all and every of +these inventions, with the shape and form of all things belonging to +them, shall be printed by brassplates,"--the usual substitute at that +time for copperplates. It is most unfortunate that he did not live to +complete his projected publication. But in common candour let it not be +forgotten that, the promise thus placed before us was published in 1663, +not long before the devastating plague, which almost depopulated the +metropolis in 1665, and the terrible conflagration of 1666, which laid +waste the city of London; and that it was in the midst of the +accumulated calamities thus inflicted on society, that his health +appears to have suddenly given way; aged, harassed, disappointed, and +dismayed, he was prematurely called to his long rest on the 3rd of +April, 1667; but whether he died at Vauxhall, at the family town +mansion, Worcester House, in the Strand, or at some other place is +unknown; so little was he understood or esteemed for his intellectual +capacity at the period of the Restoration. As though it were not a +sufficient infliction to be ruined, dishonoured, oppressed, and +neglected while living, it would almost appear that events conspired to +lessen, if possible, the lustre of his memory by the dark shades of +apocryphal history; which ascribed the invention of the steam-engine to +the pretended fact of the Marquis while in imprisonment, having seen a +pot lid blown off by the expanding steam; made out against him a false +case of political forgery; and, worse than all, scandalously forged a +letter in Paris to make it appear that in 1641 the Marquis borrowed his +idea of the steam engine from Salomon De Caus, during a visit to the +Bicêtre, at Paris. The fact that this same De Caus died at Paris, and +was buried in the Church of La Trinité, in February, 1626;[2] shows how +requisite it is for rogues to remember historical dates. + +[2] See _Worcesteriana_, 8vo. 1866, page 257. + +On the 3rd of June, in 1663, the Parliament passed an Act securing to +the Marquis of Worcester the full benefit and profit of his +"Water-commanding Engine," for the term of ninety-nine years. And in the +same year he printed his memorable "Century," in the Dedication of which +he alludes to the above Act, as one by which he feels "sufficiently +rewarded." + +The "Century" is little more than a Catalogue Raisonné, although each +matter of invention is as fully and intelligibly stated as was required +in the Patent office specifications of the period. To give some idea of +its contents, we shall enumerate only the first twenty-five. 1. Seals +abundantly significant; 2. private and particular to each owner; 3. a +one line cipher; 4. reduced to a point; 5. varied significantly to all +the 24 letters; 6. a mute and perfect discourse by colours; 7. to hold +the same by night; 8. to level cannon by night; 9. a ship-destroying +engine; 10. how to be fastened from aloof and under water; 11. how to +prevent both; 12. an unsinkable ship; 13. false destroying decks; 14. +multiplied strength in little room; 15. a boat driving against wind and +tide; 16. a sea-sailing fort; 17. a pleasant floating garden; 18. an +hour-glass fountain; 19. a coach-saving engine; 20. a balance waterwork; +21. a bucket fountain; 22. an ebbing and flowing river; 23. an ebbing +and flowing castle clock; 24. a strength increasing spring; and 25. a +double drawing engine for weight. + +We find in the "Century" that three of the articles refer to improved +seals and watches; two to games; two to arithmetic and perspective; six +to automata, or self-acting mechanical contrivances; no less than +twenty-three to ciphers, correspondence, and signals: in short, secret +writing and telegraphs; ten to useful appliances in domestic affairs; +nine are wholly mechanical; upwards of thirty-two were intended for use +in naval and military affairs; and thirteen, including his +Water-commanding Engine, were connected with hydraulics. It is singular +that he professes "to have _tried and perfected_ all these," words of +great import in all matters of novel invention. + +That age was fond of patronizing what we should now-a-days be disposed +to call "nic-nacs." Ingenious automata, curious toys and works of art, +small fountains, singing birds, and similar curiosities attracted the +serious attention of the virtuosi of the 17th century; so that we need +not feel surprised that the Marquis set up a speaking Brazen Head; or +that it should be of gigantic proportions, for he was always regardless +of cost in such matters, and was never small where he could be great in +developing his resources of ingenious contrivance. Wherever it was +possible, he was magnificent--fortifications, embankments, ships rowing +against wind and tide, great floating baths, and gardens, large cannon, +in short, he was princely in his expenditure of his private fortune on +whatever he undertook to perform, whether in war or in peace. It was +thus he spent, lent, and lost for his King and country £918,000. He +particularly notices that he laid out on buildings and experiments at +Vauxhall, the sum of £59,000. But these items are far from representing +his actual expenditure, although they indicate the scale of his +operations; and taken at their value two centuries back such sums +manifest marvellous munificence. + +We have no certain key to any of his inventions, if we except two +specimens of his cipher writing. One exists in the British Museum,[3] +and there is a deciphered letter in the Bodleian Library, Oxford.[4] + +[3] See engraving and account of it in _The Life, Times, and Scientific +Labours of the Marquis of Worcester_, 8vo. p. 398. 1865. + +[4] Ibid, page 180. + +His noblest invention, that which must for ever embalm his memory in the +breasts not alone of Englishmen, but of all classes throughout the +civilized world, was in operation at Vauxhall from 1663 to 1667, during +his life time, and appears to have been working as late as 1670. It was +ordered by the Act granted him, "that a model thereof be delivered to +the Lord Treasurer or Commissioners for the Treasury for the time being, +at or before the 29th of September, 1663; and to be put into the +Exchequer, and kept there." And in the 98th article of the "Century," +alluding to this same engine he says--"I call this a _semi_-omnipotent +engine, and do intend that a model thereof be buried with me." Yet, +strange to say, neither the one model nor the other, although zealously +searched for, has come to light: and so little attention did this +invention, notwithstanding its surprising utility, excite in the 17th +century, that all the account we have of it, besides that by the +inventor himself, is the briefest possible notice given by two foreign +travellers, Sorbière in 1663-4, and Cosmo the third, Grand Duke of +Tuscany, in 1669. It is satisfactorily ascertained, however, that +upwards of seventeen persons, all living in 1663, were more or less +acquainted with the Marquis's mechanical operations at Vauxhall, and +must have seen the great water-engine at work, if only as a novelty, and +a matter of curiosity. + +Returning to the "Century of Inventions," we find it to be a journal of +the fruits of its noble author's study of mechanical philosophy for +nearly forty years, so that in it we may almost trace the youth and age +of his mental capacity. Viewed through a modern medium we might feel +disposed to discredit the genius of a man who could contrive so many +curious alphabets for secret writing as those he mentions, but such +systems were extensively practised in political and private +correspondence during the Civil war period to baffle the curiosity of +political opponents. What may be called mechanical tricks were also much +in vogue, such as singing and flying birds, artificial figures and +horses, and curiously contrived watches, cabinets, locks, and keys. +Unless we bear in mind the taste of the age, we shall read with surprise +such an announcement as the following, in the 88th article in the +"Century":-- + +"How to make a brazen or stone head, in the midst of a great field or +garden, so artificial and natural, that though a man speak never so +softly and even whispers into the ear thereof, it will presently open +its mouth, and resolve the question in French, Latin, Welsh, Irish, or +English, in good terms uttering it out of his mouth, and then shut it +until the next question be asked." + +No doubt the Marquis had in mind the history of the renowned Brazen Head +attributed to Friar Bacon. The authors of the works on mechanical +subjects published down to the 17th century, did not disdain to describe +the way to manufacture automatic men, animals, and birds, with suitable +joints, springs, weights, and bellows; and therefore, the Marquis did +really no more than express the character of the times, without lowering +his own superior intelligence. He was seeking the patronage of royalty, +parliament, and the public, and if he offered occasionally such trifles +as commanded the attention of the multitude, he never in the whole +course of his chequered life lost sight of his more important +occupations, the conceptions of a mind far in advance of that dismal and +dark period. At the same time, that his age neglected to uphold applied +science, and pertinaciously opposed whatever appeared to savour of +innovation on time-honoured manufactures and trades, we cannot overlook +the anomalous fact that it gave birth to Shakspeare, Bacon, and Milton; +Sir Thomas Brown, Wallis, Hook, Newton, and Boyle, together with a +brilliant constellation of luminaries who adorned every department of +our general literature. Science alone stagnated, and the construction of +public works was chiefly conducted by foreign aid. The establishment of +the Royal Society in 1660, however, gave promise of that improvement +which has steadily gone on year by year to the present day. + +We have thus before us a broad outline of the Marquis of Worcester's +birth, education, studies, and scientific pursuits. His tastes and +employments were not suited to a successful political or military +career, at a time when the rupture between the Crown and the Parliament +rendered it necessary for every man to take the side either of the +Cavaliers or the Roundheads. Both father and son displayed unbounded +loyalty, although professing the Roman Catholic faith. Had they, like +many other noble families, adopted the policy of taking opposite +courses, the family might eventually have retained estates which were +forfeited when the King was deposed, and were principally enjoyed by +Cromwell. Raglan Castle was demolished, all that could be carried away +was sold, the strong tower or citadel was partially blown up, its ditch +left dry, and all that could be most readily spoiled was mutilated, even +to the marble and alabaster monuments in Raglan Church, raised to the +memory of ancestors of the family. Such ruthless destruction and pillage +has failed, however, to obliterate the towers, walls, arches, chambers, +and numerous vaults of that once princely residence. + +From the year 1601 to 1641, (forty years of his life) was a period to +which he refers as his "Golden Age" in the dedication of his "Century." +While that from 1641 to 1647-8, (when he fled from Ireland to France,) +was the most exciting, exhausting, and disastrous of his whole +existence, and closed with utter ruin to himself and his family. He had +then living his second wife, Henry, his son and heir, and two daughters. +The family town mansion, Worcester House in the Strand, partly used as a +State Paper Office, was eventually granted to the Marchioness of +Worcester for her residence. The wearisomeness and distress attendant +on his residence as a refugee in France during four years, was +embittered by above two years imprisonment in the Tower, the result of +his venturing to revisit London while proscribed by the Parliament as +"an enemy and traitor to the Commonwealth," all such being threatened +that they shall "die without mercy, whenever they shall be found within +the limits of this nation." Burton, in his interesting Diary of Oliver +Cromwell's Parliament, says in reference to the case of the Marquis on +this occasion:--"It was urged he was an old man, had lain long in +prison, and the small-pox then raging under the same roof where he lay; +and he had not, as was said, done any actions of hostility, but only as +a soldier; and in that capacity had always shown civilities to the +English prisoners and Protestants. It was therefore ordered that he +should be bailed out of prison." He was probably then about fifty-three +years of age, but so harassed and so worn down by fatigue that he might +well appear to be a prematurely "old man." He was not, however, too old +to write his "Century" in 1655, and to re-write and publish it in 1663; +to apply for and obtain an Act of Parliament for his great invention of +a steam water-raising engine; and to get a working engine set up at +Vauxhall, and project a public company for obtaining funds sufficient to +extend its utility to the supply of towns, and canals, and for draining +mines and marsh lands. + +The Marquis of Worcester was sincerely impressed with the capabilities +and great value of his invention; and it affords a striking proof of his +high estimation and correct knowledge of the magnitude of his discovery, +that he should have bowed himself before his Maker in humble adoration, +acknowledging in a solemnly sublime strain his sense of obligation to +the Supreme Source of all intelligence, for permitting him to become +instrumental in the development of so great a mystery of nature. It is +so short and significant that no apology can be required for quoting it +entire: + + "_The Lord Marquis of Worcester's ejaculatory and extemporary + thanksgiving prayer when first with his corporal eyes, he did see + finished a perfect trial of his Water-commanding Engine, delightful + and useful to whomsoever hath in recommendation either knowledge, + profit, or pleasure._ + + "Oh! infinitely omnipotent God whose mercies are fathomless, and + whose knowledge is immense and inexhaustible, next to my creation + and redemption I render Thee most humble thanks even from the very + bottom of my heart and bowels, for thy vouchsafing me (the meanest + in understanding), an insight in so great a secret of nature + beneficial to all mankind, as this my Water-commanding Engine. + Suffer me not to be puffed up, O Lord, by the knowing of it, and + many more rare and unheard of, yea unparalleled inventions, + trials, and experiments, but humble my haughty heart, by the true + knowledge of my own ignorant, weak, and unworthy nature, prone to + all evil. O most merciful Father, my Creator, most compassionating + Son, my Redeemer, and Holiest of Spirits, the Sanctifier, three + Divine persons and one God! grant me a further concurring grace + with fortitude to take hold of thy goodness, to the end that + whatever I do, unanimously and courageously to serve my king and + country, to disabuse, rectify, and convert my undeserved, yet + wilfully incredulous enemies, to reimburse thankfully my creditors, + to remunerate my benefactors, to re-enhearten my distressed family, + and with complacence to gratify my suffering and confiding friends + may, void of vanity or self-ends, only be directed to thy honour + and glory everlastingly. Amen." + +Judging of the Marquis of Worcester's personal appearance from two +family portraits, one when he was probably about twenty-five years of +age, by Vandyck; the other when between forty and fifty years old, by +Hanneman; he must have been rather of a delicate frame, and in stature +somewhat under the average height; his face oval, with sharp bright +eyes, and wearing a cheerful benignant aspect. His dress was, of course, +the costume of the period of Charles the Second's reign, but its +character has not been observed in either of the portraits just named, +one of which represented him in armour, and the other, as was not then +unusual with artists, attired as a Roman general. We infer that he +laboured under a defect in his speech, from his remarking in a memorial +addressed to the King that he penned it--"To ease your Majesty of a +trouble incident to the prolixity of speech, and a _natural defect of +utterance_ which I accuse myself of." It might be interesting to +speculate how his sense of deficiency in physical strength, in eloquence +of speech, and volubility of language might have contributed to the +fostering of that disposition for intense application to scientific +studies which became to him like a second nature. + +During the first two years of the Restoration, the Marquis was in pretty +regular attendance on his Parliamentary duties. In 1661, he was obliged +to seek protection so that proceedings might not be taken against him by +his creditors; and about the same time his forfeited estates were +restored to him, but so encumbered and impoverished as to yield him a +very insufficient income, if any. It was in the midst of such +distractions as these that this talented inventor and noble benefactor +to his species had to maintain his social position; and, at the same +time, endeavour to convince the bigoted age in which he may be said +rather to have existed than to have flourished, that he was master of a +power of such magnitude for the abridging of human labour, as the mind +of man had never before conceived. + +It may be freely conceded that, _stupendous_ as he himself pronounced +the parent engine to be, it was but as the acorn compared to the +time-honoured monarch of the forest. Just as the existence of the plant +is dependent on that of the seed, so if the Water-commanding Engine, the +great Fire Water-work he constructed had never existed, we might have +been unacquainted, to this day, with the mechanical application of +steam, and should have been deprived in consequence of the manifold +blessings it bountifully bestows on mankind. + + +ADDENDUM. + +Evidence of the Marquis of Worcester's claim to the Invention of the +Steam Engine. + +1. His personal claim to have written a statement respecting it in 1655; +his MS. being afterwards lost. + +2. The Act of Parliament[5] which was granted him for the term of +ninety-nine years, and which received the royal assent on the 3rd June, +1663. + +[5] For lists of the names of members on the several Committees +appointed on the occasion of this Act being applied for, see--"The Life, +Times, &c.," 8vo. 1866, pages 254-5. + +3. His "Century of Inventions," printed from a re-written copy of his +lost notes of 1655; and which names in the Dedication, the granting of +the above Act. + +The following list[6] comprises upwards of seventeen persons all living +in 1663:-- + +[6] From "Worcesteriana," 8vo. 1866, page viii. + +4. CASPAR KALTOFF, a confidential workman, engaged by the Marquis as his +engineer in 1628, who died about 1664, and is honourably mentioned in +the "Century." + +5. MARTHA KALTOFF, wife of Caspar Kaltoff, who is named in letters +patent dated 1672, _as lately deceased_. Her family was-- + + CATHARINE, married to Claude Denis. + CASPAR KALTOFF, and his unmarried sister-- + ISABEL KALTOFF. + +6. PETER JACOBSON, a sugar refiner, who married one of Kaltoff's +daughters, had a portion of the buildings at Vauxhall, where the +Water-commanding Engine was erected, and in operation from 1663, till at +least to the year 1669, if not some years later. + +7. WILLIAM LAMBERT, another workman, a founder at Vauxhall, in the reign +of Charles I., "under the Marquis of Worcester, for gun and waterwork, +or any other thing founded in brass," in 1647, and who was living in +1664-5. + +8. CHRISTOPHER COPLEY, who had been a Colonel in the Parliamentary +service, and was probably an iron master, having been the proprietor of +four Iron Works. He assisted the Marquis at an early period and held a +pecuniary interest in his invention of a Water-commanding Engine. Indeed +it is highly probable that he was the "powerful friend" at whose +instigation the "Century" was written in 1665. + +9. The EARL OF LOTHERDALE, written to in January, 1660, had a copy of +the "Definition" of the Engine sent to him, and is promised an +ingeniously contrived box or cabinet. He was appointed as late as March, +1665, to be one of a Commission to report on the affairs of the Marquis, +and must, therefore, have been familiar with all matters relating to the +noble inventor. + +10. DR. ROBERT HOOK, the eminent mathematician, was acquainted with +Caspar Kaltoff, and early in 1667, went purposely to see the engine +working at Vauxhall, having read the "Definition." + +11. THE HONOURABLE ROBERT BOYLE received from Dr. Hook a copy of the +"Definition," sent to him with a letter on the subject. + +12. LORD BRERETON is specially mentioned by Dr. Hook, as being so +confirmed in his doubts of the excellence of the Marquis's engine, that +he had laid a wager on the subject. + +13. HENRY SOMERSET, Lord Herbert, afterwards created first Duke of +Beaufort, by Charles II., must have frequently seen the engine in +operation. He died in 1699. + +14. JAMES ROLLOCK, who wrote a poetic eulogy on the Engine about 1663, +speaks of himself as "an ancient servant," having known his lordship +forty years, dating back to 1623.[7] + +[7] He was the author of a pamphlet now very rare, and which is absurdly +enough attributed by Horace Walpole to the Marquis of Worcester. A +reprint will be found in "The Life, Times, and Scientific Labours of the +Marquis of Worcester," 8vo. 1866, page 559. It contains the following +intimation to the reader:-- + +"I think it not amiss to give further notice in his Lordship's behalf, +that he intends within a month or two, to erect an Office, and to +entrust some very responsible and honourable persons with power to treat +and conclude with such as desire at a reasonable rate, to reap the +benefit of the same Water-commanding Engine." + +So that it is manifest a public company was intended to be established +in 1663-4, to extend operations with the engine then actually raising +water at Vauxhall. + +15. SAMUEL SORBIÈRE visited the works at Vauxhall, and published +particulars of the engine he saw there in 1663. + +16. LORD JOHN SOMERSET, the Marquis's eldest brother, appears latterly +to have lived at Vauxhall, according to a warrant dated September, 1664; +and would certainly be admitted into his brother's confidence. + +17. COSMO THE THIRD, Grand Duke of Tuscany, in his Diary exactly +describes the engine he saw at Vauxhall in 1669, "considered to be of +_greater service to the public_ than the other machine near Somerset +House." + +18. WALTER TRAVERS, a Roman Catholic priest, names the engine in a +letter which he wrote to the Dowager Marchioness of Worcester, in 1670. + +19. DR. THOMAS SPRAT, F.R.S., published in 1665, a critical work on "M. +Sorbière's Voyage into England," and could not therefore be ignorant of +the Marquis's engine, as it was named by the French traveller, although +Sprat omitted to notice it specially in his own "Observations." + +20. Among his other contemporaries were Sir Samuel Morland, Dr. Wallis, +Sir Christopher Wren, Sir Isaac Newton, and many more, who, however, (so +far as is at present known,) are silent in regard to all matters +relating to the Marquis. + + + + + II. + + LECTURE + DELIVERED ON THE 5TH NOVEMBER, 1868: + BEING THE FIRST OR INAUGURAL LECTURE + OF THE + FREE LECTURES, + AT THE CRYSTAL PALACE, SYDENHAM, + ON + CHIMERAS OF SCIENCE: + ASTROLOGY, ALCHEMY, + SQUARING THE CIRCLE, + PERPETUUM MOBILE, + ETC. + + With Illustrative Diagrams. + + AND RE-DELIVERED AT THE + BIRKBECK LITERARY AND SCIENTIFIC INSTITUTION, + 17TH FEBRUARY, 1869. + + "A little knowledge is a dangerous thing, + Drink deep, or taste not the Pierian spring; + There shallow draughts intoxicate the brain, + But drinking largely sobers us again."--POPE. + + +PREFACE. + +The present Lecture, embodying a variety of subjects, under the general +title of CHIMERAS OF SCIENCE, not only reviews them in succession, but +expresses sentiments with regard to each which result from a long +acquaintance with ancient and modern scientific authors; supported by an +experimental, and, not unfrequently, by a practical acquaintance with +several branches of natural philosophy. The consequence of this intimacy +with various scientific studies, has been a thorough conviction of the +necessity of possessing a knowledge of elementary principles, before +professing a belief in new doctrines, whose only recommendation is their +novelty, extravagance, and inutility. Without absolutely pretending to +any golden road, or short path to learning, superficial but ambitious +scholars are the first to seize on first impressions, build up some +grand theory, lay down certain postulates, seek proselytes, and display +a wonderful amount of enthusiasm in creating systems which, however +beautiful in appearance, can boast of no solid foundation. Imperfectly +educated, and shallow, but not unfrequently highly imaginative, men, if +not themselves absolute charlatans, are the easily led dupes, who become +the admirers and abettors of every "new wind of doctrine." + +Every age has been sensational. Man delights in mystery, and mysticism +is a certain sign of imperfect knowledge. A classic age was not proof +against the tricks and deceitful practices of the oracles, soothsayers +and jugglers. The dark ages only served to keep alive the human desire +for sensation; and less than a century ago, poor, simple, half idiotic +women, were burnt at the stake as witches. The Mahometans had their +prophet, and so have the Mormons. Mesmer had his disciples, and so have +many modern Spiritualists. The Astrologer of the 17th century, is +presented to us in a modern dress by the seer Zadkiel. Jacob Behmen and +Emanuel Swedenborg, but represent a class that is continually dying out, +yet is as continually reproduced; the authors of pious romances, +theological enigmas, scientific spiritualisms, and spiritualized +transcendental philosophisms. Swedenborg introduces us to the +inhabitants of the moon; they are short, the size of a youth of seven +years of age; and they speak with a thunderous voice for want of an +atmosphere, and not from the mouth, but from the abdomen! But many +persons admire such wanderings of a pretended inward and prophetic +light. + +There are still living a few faithful believers in _Alchemy_, who +earnestly look forward to the coming of the day when the grand, the +glorious secret, shall be fully revealed; not, however, to the vulgar +crowd, but to the noble, true, and virtuous adept,--to him, and him +only. + +A class of _Mathematicians_ still continues to publish papers and +pamphlets on squaring, cubing, and trisecting. On this subject, the +reader might find some amusement in the critiques of Professor De +Morgan, who wrote several papers in the _Athenæum_, 1865, under the +title of _A Budget of Paradoxes_. + +_Mechanics_ are still living who firmly believe in the possibility of +realizing a mechanical perpetual motion,--to spin, pump, or drive +carriages or machinery, by means of a constantly descending weight. And, +year by year, many such schemes, find their final resting place in the +archives of the Patent Office. + +It is melancholy to reflect on the waste of mental energy, inflicted on +society by such vanities as Astrology, Alchemy, and their kindred +empirical employments. Look at the centuries wasted, and worse than +wasted, in studying such intellectual abortions, and in writing +thousands of volumes of inanity to uphold falsehood and delude the +unwary. What the sword has done physically, the pen and the wand of the +sorcerer have done mentally, in prostrating the intellectuality of +mankind. + +It would tend to promote the progress of society at large, if education +were so far general that the acquirements of the middle and lower +classes should act on the upper classes as a stimulant to the pursuit of +those higher branches of study, which mostly fall to the lot of the +nobility and men of fortune: whose birth and ample means otherwise +relieve them from all incitements other than such as are fostered by the +necessities of public office. With title and fortune, and no ambition +to hold public employment, any education is thought to be sufficient +that serves to obtain the usual dignities, and to give that polish which +completes the accomplished gentleman. To the spread of education alone, +can we look with any reliance for the downfall, or at least the +diminishing of the hold on the human mind which Chimeras of every order +usurp in our own, in common with every other country. + +Among other works that might be consulted by the curious in such +matters, in the Libraries of the British Museum, the Patent Office, +Chetham College Manchester, &c.; may be named, on ASTROLOGY,--B. Porta's +Works, folio, 1616;--The Compost of Ptolomeus, Prince of Astronomie, +1645;--W. Ramsey's Vox Stellarum, 8vo., 1652;--The Geomancie of Maister +Christopher Cattan, 4to., 1608;--Dr. John Dee's Work on Spirits, folio, +1659;--J. Goad's Astro-Meteorologica, folio, 1686;--Godfridus's Work on +the Effects of the Planets, &c., 1649;--M. Manilius's System of the +Ancient Astronomy and Astrology, &c., 8vo., 1697;--John Merrifield's +Catastasis Mundi, 4to., 1684;--Jo. Holwells's Catastrophe Mundi, 4to., +1682;--with many others of modern date. + +On ALCHEMY,--Ashmole's Theatrum Chemicum Britannicum, 4to., 1652;--Dr. +John French's Art of Distillation;--Four Books of J. S. Weidenfeld, +4to., 1685;--A Philosophicall Epitaph, in Hierogliphicall Figures, +1673;--George Ridley's Compound of Alchemy, 1591;--Roger Bacon's Art +and Nature, (in French,) 1557; his Mirror of Alchemy, 1597; his +Philosopher's Stone, or Grand Elixir, 8vo., 1739; Theatrum Chemicum, 6 +vols., 8vo., 1659-61;--Sandivogius's New Light of Alchymie, 4to., +1650;--Opuscula quædam Chemica, 8vo., 1514;--The Works of Geber, +1678;--Hermes Trismegistus's Works, collected in Theatrum Chemicum, 4 +vols.;--Raimond Lully's De Secretis Naturæ, 1541;--Crollius's Philosophy +Reformed and Improved, in four profound Tractates, 1657;--Beguinus (J.) +Trocinium Chymicum, or Chymical Essays, 8vo., 1669;--Artis Auriferae, +Quam Chemiam Vocant (a collection of treatises), woodcuts, 2 vols. 8vo. +1593;--Balduinus's Aurum Superius et Inferius Hermeticum, plates, 1675; +Beccheri's Physica Subterranea, Lipsiæ, 1738 (with supplement), 8vo., +1681-80; with many others, ancient and modern. Interesting compendious +treatises will be found in Dr. Thomas Thomson's History of Chemistry, +("The National Library,") 2 vols., 12mo., 1830; Justus von Liebig's +Familiar Letters on Chemistry, edited by Dr. Blyth, 8vo., 1859. And-- + +On MATHEMATICAL and MECHANICAL Chimeras, many popular notices may be +found in Encyclopædias; and particularly in Dr. Hutton's Mathematical +Dictionary, 2 vols., 4to.; and the Author's "Perpetuum Mobile; or, +History of the Search for Self-Motive Power; with an Introductory +Essay," post 8vo., 1861; to which work, a second series will shortly be +added. + + +CHIMERAS OF SCIENCE. + + +INTRODUCTION. + +Although the present lecture seems to require some introductory remarks, +they must necessarily be brief--our time being limited and this +discourse rather discursive; yet it is sufficiently condensed to suit +the present occasion, and illustrates fully the truthfulness of the +axiom that--_A little learning is a dangerous thing_: from its tendency +to inspire its possessors with vanity rather than with the humility +which always accompanies profound knowledge. + +You are no doubt all, or most of you, well acquainted with the use made +of Astrology and Alchemy in the dramas of Shakspeare--"The Antiquary" of +the "Wizard of the North"--the "Strange Story" of Lord Lytton--the +"Faust" of Goëthe; and are probably familiar with the more instructive +works of Scott on Demonology, and of Brewster on Natural Magic. Now we +always find that fiction is more suitable than truth for romantic +writings; truth is circumscribed, but the fictions whether of Astrology, +Alchemy, or any other pseudo-philosophy are erratic, the delight of +poets and romance writers, being the comets and _ignes fatui_ of many +popular compositions in our light literature. + +There is no end of fabulous writings of the class we call novels and +romances, and no end of deceptions which we patronize as tricks of +legerdemain; the one gratifies our imagination and fancy, the other +takes our common sense by surprise; but all these are harmless because +only presented to us for our amusement. + +Delusion, however, assumes a startling character when romance in the +form of mystic writings, and jugglery in the form of pretended +communication with the spirit-world demand our respect and serious +attention, by claiming to have a divine origin. But hallucination of the +human intellect, as we shall see, is not confined to such remote +visionary speculations, and it is not unimportant to remark that in +mathematics, as in physics, and in other branches of investigation, +there is a singular persistency in upholding errors. + +A contemporary astrologer, assuming the pseudonym of Zadkiel, tauntingly +observes in his preface to a recent publication: "_This is the age of +inquiry_; and yet prejudice continues to press down her leaden foot upon +the neck of examination in this matter"--that is, Astrology. Now with +this reproof before us we hope to discuss the subject with becoming +propriety. + + +ASTROLOGY. + +The splendour of the sun by day, the glories of the firmament by night, +together with the sublimity of all celestial phenomena, attract alike +the attention of the most simple and the most intellectual among +mankind. The distance, the magnitude, and the grandeur of the entire +planetary system while exciting emotions of awe, reverence, and devotion +among the mass of the human race, have at the same time been studied +from the earliest period of man's history to the present time +superstitiously by one class of observers, and scientifically by +another. + +As the telescope was not invented before the 17th century, it is evident +that the study of Astronomy without that instrument must previously have +been pursued under amazing difficulties; and we might have expected that +when first used by Galileo at Venice in 1609, its introduction would +have been hailed without a dissentient voice. Such, however, was not the +fact, according to Sir David Brewster,[8] who says:-- + +"The principal Professor of Philosophy at Padua resisted Galileo's +repeated and urgent entreaties to look at the moon and planets through +his telescope; and he even laboured to convince Cosmo de Medici, the +Grand Duke of Tuscany, that the satellites of Jupiter could not possibly +exist. Sizzi, an astronomer of Florence, maintained that as there were +only _seven_ apertures in the head--_two_ eyes, _two_ ears, _two_ +nostrils, and _one_ mouth--and as there were only _seven_ metals, and +_seven_ days in the week, so there could only be _seven_ planets. He +seems (eventually), however, to have admitted the visibility of the four +satellites through the telescope; but he argues, that as they are +invisible to the naked eye, they can exercise no influence on the earth; +and being useless they do not exist." + +[8] See his "_Martyrs of Science_." + +Such being the crude state of astronomical science in the 17th century, +it must have been comparatively imperfect throughout all preceding +centuries; and open to mystical appropriation and abuse by Egyptians, +Chaldeans, Hindus, Chinese, and European and other ancient astrologers. +Among that motley group the most learned were found strangely associated +with ignorant impostors, and their activity in writing and travelling +served to spread their different systems over the entire civilized +world. It was not until late in the 17th century that Astrology could be +absolutely declared to be in its decline. In England, William Lilly, +the Sidrophel of Hudibras, and the most famous astrologer of his time, +died in 1681, leaving behind him his _Introduction to Astrology_, +together with many other works of the same character. + +Astrology is merely a philosophism, being empirical, wholly visionary, a +mere fanciful system compounded of incongruous mixtures of astronomical +with human events, of mythology with theology, and of facts with pure +fiction. It has been variously designated Judicial, Hororary, +Atmospherical, and Mundane, Astrology. It has also many off-shoots +subservient to Magic or the black art, Sorcery, Witchcraft, and other +pretended mysticisms ostentatiously styled occult philosophy. + +We may first observe that Astrology lays no claim to inspiration, but +affects a very ancient unknown origin, tracing back to a dark, +heathenish, and superstitious age, in the very infancy of traditional +knowledge, when the boldest assertions of the seer were received as the +authority of an oracle, no one daring to question their validity. +Whatever is remotely possible the Astrologer accepts as a fact; while +ignorant of much around him, he assumes with the utmost complacency an +intimate acquaintance with the sun and planets thousands upon thousands +of miles off; yea with the sun 969,272 miles in diameter, while he +himself inhabits a globe only 7,916 miles in diameter; from which the +moon is 237,000 miles distant, and the sun 400 times that distance.[9] +And these immense bodies revolving millions on millions of miles away in +immeasurable space are described by him as fashioning an infant's nose, +directing the fortunes or misfortunes of lovers, ordering the property +of traders, meting out diseases, and improving or deranging man's mental +faculties. And as if such puerile influences were not sufficiently +preposterous we are informed by the modern seer, Zadkiel, that the 12 +signs of the Zodiac not only rule the several parts of the human frame, +but also those of a ship, as _Aries_, the bows; _Taurus_, the cutwater; +_Gemini_, the rudder; _Cancer_, the bottom; _Leo_, the upper works; +_Virgo_, the hold; _Libra_, parts above the water's edge; _Scorpio_, the +seamen's berths; _Sagittarius_, the seamen; _Capricorn_, the ends of the +vessel; _Aquarius_, the Captain; _Pisces_, the oars in galleys, the +wheels in steam vessels, and the sails in others; but these latter being +above water, we are left in doubt about the ruler of the submerged screw +propeller. + +[9] This portion of the subject was illustrated by means of a Diagram +exhibiting the Diameters and Magnitudes of Planets, thus:-- + +[Illustration: + + _Miles._ +The Sun 882,000 +Jupiter 91,522 +Saturn 76,018 +Uranus 35,100 +Neptune 33,600 +Earth 7,916 +Venus 7,702 +Mars 4,398 +Mercury 3,123 + +The Moon's diameter is 2,160 miles; and its distance from the Earth is +237,000 miles.] + +To show what a modicum of learning, and how trifling an acquaintance +with matters of natural philosophy will serve the Astrologer, we will +turn to a modern treatise published in the year 1801, by Francis +Barrett, (styling himself a student of Natural and Occult Philosophy) a +quarto volume of upwards of 370 pages, entitled, "The Magus, or +Celestial Intelligencer," which affords a pretty clear insight into the +nature of the superstitions which from an ancient period even to that +date obtained credence and were popular with the multitude. + +Treating of the wonders of Natural Magic previous to entering on the +main topic of his treatise, he adduces a few of what he conceives to be +ordinary matters of fact, assuring us that:-- + +If any one shall, with an entire new knife, cut asunder a lemon, using +words expressive of hatred, contumely, or dislike, against any +individual, the absent party, though at an unlimited distance, feels a +certain inexpressible and cutting anguish of the heart, together with a +cold chilliness, and failure throughout the body;--likewise of living +animals, if a live pigeon be cut through the heart, it causes the heart +of the party intended, to be affected with a sudden failure;--likewise +fear is induced by suspending the magical image of a man by a single +thread;--also death and destruction by means similar to these; and all +these from a fatal and magical sympathy. + +The loadstone, (he observes), possesses an eminent medical faculty +against many violent and implacable disorders;--the back of the +loadstone, as it repulses iron, so also it removes gout, swellings, +rheum, &c. that is of the nature or quality of iron. Likewise the +wearing the loadstone eases and prevents the cramp, and such like +disorders and pains. + +The influences of the stars appear to be as intimately known to +Astrologers as though they had walked among, and carefully examined and +fully realized their occult properties, for example:-- + +In every work observe Mercury, for he is a messenger between the higher +gods and the infernal gods; when he goes to the good, he increases +their goodness--when to the bad, he hath influence on their wickedness. +It is an unfortunate sign or planet, when it is by the aspect of Saturn +or Mars especially, apposite or quadrant, for these are the aspects of +enmity; but a conjunction, a trine, and a sextile aspect, are of +friendship; but yet if you do already behold it through a trine, and the +planet be received, it is accounted as already conjoined. Now all +planets are afraid of the conjunction of the sun, rejoicing in the +trine, and sextile aspect thereof. + +They say of the Sun and Moon:-- + +The Sun is the lord of all elementary virtues;--it disposes even the +very spirit and mind of men. + +The Moon (says Barrett) measures the whole space of the Zodiac in the +time of 28 days, hence it is that the wise men of the Indians, and most +of the ancient astrologers have granted 28 mansions to the Moon, which, +being fixed in the eighth sphere, do enjoy divers names and properties, +from the various signs and stars which are contained in them; through +which, while the Moon wanders, it obtains many other powers and virtues; +but every one of these mansions, according to the opinion of Abraham, +contained twelve degrees, and fifty-one minutes, and almost twenty-six +seconds. In the first quarter of these mansions the 1st conduces to +discords and journies; the second to the finding of treasures, and to +the retaining of captives; the 3rd to benefit sailors, huntsmen, and +alchymists; the 4th the destruction and hindrances of buildings, +fountains, mills, gold mines, the flight of creeping things, and begets +discord; the 5th to help the return from a journey, the instruction of +scholars, and confirms edifices, gives good health and good will; the +6th to hunting and besieging towns, and revenge of princes, destroying +harvests and fruits, and hinders the operation of the physician; the 7th +to confirm gain and friendship; is profitable to lovers, and destroys +magistracies. + +In a similar manner the remaining three quarters have the characters of +their several mansions allotted to them with equal exactness, and of +course indisputable veracity also. + +We have here a fair example of the arrogant assumptions of ancient and +indeed of all astrologers, magicians, and sorcerers, men who are +incompetent to elucidate the ordinary phenomena of nature in the animal +or vegetable creation, and yet with unbounded effrontery affect to build +up an empirical system, delivered in a language of their own invention, +a pompous parade of jargon made up of the most incomprehensible +materials--which if wholly due to antiquity partakes of ancient +simplicity, credulity, deceit, and superstition; and if somewhat +polished and refined to suit the advances of literature and science, has +never been able to prove the correctness of its groundwork, or afford a +solitary instance of its possessing any meritorious quality beneficial +to mankind; while on the other hand its evil consequences have been +many, by destroying the peace and happiness of thousands, encouraging +deceit, and misapplying in its ignoble pursuit the time and labour and +property of its ardent but deluded admirers. + +In Judicial Astrology it is not thought requisite to consider more than +a certain number of the planets, after a method simplified by antient +astrologers or astronomers, which is found to be so compact and so +complete in governing the destinies of the human race that modern +intelligence has failed to enlarge the field of heavenly influences. +Varley notes that:--the antients discovered that the circle of the +Zodiac, about 16 degrees in width, and through the middle of which runs +the Ecliptic, or sun's path through the 12 signs, contains the heavenly +bodies, named planets, and the principal fixed stars, and nearly the +whole of the materials or significators, from which predictions are +obtained. + +He remarks that:--In forming a horoscope, this circle is divided into 12 +equal parts, corresponding with the spaces containing the 12 hours. +These 12 divisions are called houses; and they always remain fixed, +while the Zodiac with the 12 signs, and all the heavenly bodies +belonging to it, are considered to be moving through them all, every 24 +hours. The _lord_ of the ascendant is the planet which rules the signs +rising at birth. In drawing horoscopes it is usual to make the figure +square instead of round. (_See_ Plate 1, Fig. 1.) + +The various significations arising from the aspects of the starry +heavens at the time of birth are so exceedingly numerous, that we must +refer the curious in such matters to the works themselves, in which all +these pretended revelations are minutely recorded. + +Mankind rank astrologically as being of four temperaments. + +1. One class is said to answer to the fiery trigon, also called diurnal, +masculine, and choleric, consisting of Aries, Leo, and Sagittarius, +which contains the spirited, generous, magnanimous, and princely +natures. + +2. We have next the earthy trigon, being nocturnal, feminine, and +melancholic, consisting of Taurus, Virgo, and Capricorn, containing the +careful, sordid, and penurious qualities. + +3. Thirdly, the aërial trigon, which is diurnal, masculine, and +sanguine, consisting of Gemini, Libra, and Aquarius, contains the humane +harmonies, and courteous principles. And-- + +4. Fourthly, the watery trigon, which is nocturnal, feminine, and +phlegmatic; namely, Cancer, Scorpio, and Pisces, including the cold, +prolific, cautious and severe qualities. + +Take as a brief illustration of the manner in which Astrologers +presumptuously assign to the planets their several offices relating to +human nature the following:-- + +Those born when Aries ascends are born under the sign Aries and planet +Mars. This is the diurnal, fair, and masculine house of Mars, and +partakes also largely of the nature of the magnanimous Sun, and the +benevolent and moral Jupiter, who rule the fiery trigon, of which Aries +is the first sign. + +As affecting physiognomy we are assured that: + +The Scorpio noses are more aquiline than those of Aries, and are more +frequently conspicuous for a sort of bracket shape beneath, which +prevents the under part of the nose from forming a right angle with the +upper lip; while the under lip, both being usually small, recedes in a +greater degree, as if drawn tightly against the teeth; so that the +mouth appears in the act of pronouncing the word SEVERE. + +When we meet in volume after volume with page after page of such +composition as this, when we reflect on the sublimity of the heavens and +the paltriness of such combinations as are here given of the planets +with mundane affairs, we ask the reasons for arriving at such judgments. +To be told that it is so because it is so; or because it was an ancient +belief, and is to be found in the writings of Ptolemy, Nostradamus, Dr. +John Dee, William Lilly, or Zadkiel; or because it has often proved as +true in its predictions as the telling fortunes by means of a pack of +cards, is no evidence whatever; yet the Astrologer boasts of his very +paralogisms. + +Zadkiel, in prefacing a work by Lilly, says:--If a proposition of _any +nature_ be made to any individual, about the result of which he is +anxious, and, therefore, uncertain whether to accede to it or not, let +him but note the hour and minute when it was _first_ made, and erect a +figure of the heavens, (_See_ Plate 1, Fig. 1,)--and his doubts will be +instantly resolved. He may thus, in five minutes, learn infallibly +whether the affair will succeed or not; and, consequently, whether it is +prudent to adopt the offer made or not. + +Such is the belief of this sound, intelligent man, as we fully believe +him to be in other respects. But we say it is not given to man to assign +special influences to the stars, to select one portion and discard all +the rest, or to be more intimately acquainted with the starry heavens +above him, than with the stony earth he inhabits, and with his fellow +creatures around him. + +The works claiming to expound this pretended Occult Philosophy prescribe +such childish processes that one naturally wonders how in the midst of +so much impudent imposture Astrology and its kindred pursuits ever found +or retained any honest partizans. + +Take, for example, the use of fumigations, such as of frankincense, &c. +to Saturn; of cloves, &c. to Jupiter; of odoriferous woods to Mars; of +all gums to the Sun; of roses, violets, &c. to Venus; of cinnamon, &c. +to Mercury; of the leaves of vegetables to the Moon; of all or any of +which there must be a good perfume, odoriferous, and precious, in good +matters; but in evil ones quite the contrary. + +The Zodiac is also favourably affected by proper suffumigations. + +Astrologers in their Demonology profess to be able to ascertain the +characters and seals of spirits,[10] and according to the Cabalists, +tables are given of many of these in their books, in the so-called +Theban Alphabet; in characters of Celestial Writing; in that called +Mallachim; or in the writing called Passing the River. + +[10] See the Table, Plate I. Fig. 2, for distinguished names of their +angels, spirits, or demons. + +They affect to have suitable bonds by which spirits can be bound, +invoked, or cast out. + +Of Necromancy they pretend to two kinds, one of which is raising the +body of a deceased person, which it is said cannot be done without +blood;--the other sciomancy, which is the production of a mere shade or +shadow. + +The exorcisms and conjurations of Magicians are so audaciously profane +and blasphemous as to be unworthy of even a passing notice. + + +ALCHEMY. + +We shall now proceed to consider Alchemy, another but very different +chimerical pursuit, which was early cultivated in the East, and is +generally ascribed to Hermes Trismegistus, although its more +enthusiastic admirers pretend to trace a knowledge of it to Adam. From +the earliest periods of history man was acquainted with gold, silver, +and other metals, with bitumen, sulphur, sea salt, sal-ammoniac, gums, +and resins, together with other varieties of substances and liquids +common to modern chemistry. For the compounding and heating of certain +of these materials a multiplicity of means were adopted requiring +furnaces, crucibles, and distillatory apparatus. The first workers in +these experimental operations formed a body of investigators into the +nature and properties of all manner of substances, whether animal, +vegetable or mineral, the members of which were distinguished as adepts, +alchemists, and later in their career as common chemists. The most +esteemed branch of the art however was Alchemy, a pseudo-science which +ultimately took three forms. First, the Hermetic Art for the discovery +of the Philosopher's stone; and the Alkahest, or universal +solvent;--Second, a Medical Alchemy;--and Third, a Theological Alchemy +pretending to conceal divine mysteries under an allegorical form, +treating of the spiritual while apparently describing alchemical +discoveries. + +Our principal business, however, is with the so-called Hermetic +Philosophy, treating of vaunted methods of transmuting the base metals +into gold. It is doubtful whether this particular delusion of the +adepts can be referred to a date earlier than the 8th century, but even +then we cannot refrain from surprise at the fallibility of the human +intellect, which could be swayed by a belief in the pretended _lapis +philosophorum_ for upwards of ten centuries. It was believed to be so +secret and rare that its possession was never ascribed at any time to +more than two or three favourite adepts, who transmitted it to some +single favoured individual after his taking the sacrament, and going +through certain prescribed religious ceremonies, preparatory to being +entrusted with a verbal recipe for the composition of a peculiar +smelling red powder, of which it was affirmed that when projected on +heated mercury or any solid metal, it would at once change it into pure +gold. Ashmole gravely assures us that Dr. John Dee and his associate +Kelly, having in some way procured this precious substance, Kelly--to +use Ashmole's own words--"made projection with one small grain thereof, +in proportion no bigger than the least grain of sand, upon one ounce and +a quarter of common mercury, and it produced almost an ounce of pure +gold." With equal simplicity and earnestness, Ashmole asserts that this +same Kelly was often seen to make these extraordinary transmutations,-- +"and in particular (he adds) upon a piece of metal cut out of a +warming-pan, and without touching or handling it, or melting the metal, +only warming it in the fire, the elixir being put thereon, it was +transmuted into pure silver. The warming-pan and this piece of it, was +sent to Queen Elizabeth by her Ambassador who then lay at Prague, that +by fitting the piece into the place whence it was cut, it might exactly +appear to be once part of the warming-pan." + +Among the adepts there were no doubt a select few who employed +themselves in their prolonged labours in all sincerity, and who were not +unfrequently repaid with remarkable, and unexpected results. Brass, +being the result of copper combined with zinc, would appear a singular +transformation. Many stones, or more properly, ores, would yield sulphur +and metals; sulphur would be found apparently to dissolve iron; and +certain salts, when distilled, would yield corrosive acids. Alchemy thus +presented to the ancient adepts many of the ordinary wonders of modern +chemistry; in short, the latest adept of the present century is no other +than an unlettered chemist. It was peculiar to the Alchemists to treat +all their operations as secrets; which, when recorded, were described +partly by symbols and partly in a novel nomenclature, invented to +conceal their mysteries from vulgar gaze or imitation. Thus, to prepare +the philosopher's stone, we have merely to--"Take of moisture, an ounce +and a half; of meridional redness, that is the soul of the sun, a fourth +part, that is, half an ounce; of yellow seyr, likewise half an ounce; +and of auripigmentum, a half ounce; making in all three ounces. Know +that the vine of wise men is extracted in threes, and its wine at last +is completed in thirty." To the incredulous in these matters, Ashmole +offers the admonition that, he knows "_Incredulity is given to the world +as a punishment!_" However, when the Alkahest, or pretended Universal +Solvent, was alluded to by the modern chemist Kunckel, he could not +refrain from incredulously enquiring--"If it dissolves all substances, +in what vessel can it be contained?" + +Alchemical writings are very numerous, it might be impossible to procure +a complete bibliographical list of them, but they may be estimated at +from 3000 to 4000 works, and an astonishing number of manuscripts. Their +authors indulge in such terms as the Ph[oe]nix, to indicate the +quintessence of Fire; Realgar, for the fume of minerals; Guma, also Luna +Compacta, for quicksilver; Hadid, for iron; Aurum potabile, for liquor +of gold; Anathron, for saltpetre; Malek, for salt; Terra fidelis, for +silver; Tinkar, for borax; and in a similar strain for all matters and +operations; so that Dr. Johnson was justified in deriving the word +Gibberish from the mysterious jargon employed by Geber, a celebrated +Alchemist; who has, nevertheless, been appropriately styled the Pliny of +the 8th century. + +Weidenfeld, in an Alchemical Treatise, published in 1685, addressing +students, says:-- + +"Under heaven is not such an art, more promoting the honour of God, more +conducing to mankind, and more narrowly searching into the most profound +secrets of nature, than is our true and more than laudable Chymy." + +And at the conclusion of his address he observes: + +"Nothing remains but upon our bended knees to return most humble thanks +to the Father of Lights, in vouchsafing us this art by the writings of +his servants, and the high priests of Nature; without which, it would be +beyond the power of man to arrive at so great a degree of knowledge." + +Some notion of the extravagance of the language employed may be obtained +from his description of a Philosophical Wine, literally, rectified +spirits of wine, or alcohol. He assures us that, on opening a vessel of +it, "a wonderful scent" should arise: "so as that no fragrancy of the +world can be compared to it; inasmuch as putting the vessel to a corner +of the house, it can by an invisible miracle draw all that pass in to +it; or, the vessel being put upon a tower, draws all birds within the +reach of its scent, so as to cause them to stand about it. Then will you +have, my son, our quintessence, which is otherwise called Vegetable +Mercury, at your will, to apply in Magistery of the transmutation of +metals." + +How ardent an adept this Alchemist was may be gathered from his +exclamation:--"May the God of Heaven put prudence in the heart of +evangelical men, for whom I compose this book, not to communicate this +venerable secret of God to the reprobates." + +Among the remarkable discoveries made by Alchemists, due to the +carefully noted and carefully examined failures and accidents, as well +as successes, of their endless combinations of matter, under the +treatment of fire and water, the most distinguished is that of +gunpowder, noted in a recipe left on record by Roger Bacon, who died in +the year 1284. He clearly names the mixture of Saltpetre with Sulphur, +but the third ingredient, Carbon, is concealed in the form of an +anagram. + +Lord Bacon, Luther, Spinoza, Leibnitz, and many eminent moderns, were +impressed with a belief in the possibility of transmuting lead, tin, +copper, or other metals, into gold; in short, as it was supposed there +were only four elements, fire, water, earth, and air, it was probably +assumed that a fifth might be found in the Philosopher's stone. + +But if ever any pursuit was more open to fraudulent practices than +another, surely the pretended possession of a transmuting powder or +elixir afforded a grand arena for their exercise. In this enlightened +age, although we cannot fail to look with charity on the arduous labours +of those adepts who honestly mixed devotional exercises with laborious +experimental operations, selecting times and seasons for their +alchemical work, and noting with accuracy the hours and days of fusions, +sublimations, distillations, lixiviations, and so forth; still, it is +scarcely possible to refrain from smiling at the docile simplicity of +Ashmole in denouncing a certain class of Alchemists, as pretended +masters and adepts, seeing "they are mere practisers of legerdemain," +while he himself gave credence to the story of the warming-pan, already +named as being shown to Queen Elizabeth, which was clearly a flagrant +piece of fraud practised by Kelly, a common adventurer, and from his +youth remarkable only for his indifferent character. + +An easily performed trick was effected by means of nails, or other +light articles, made half of gold and half iron, but disguised, so as to +appear to be of one metal and colour. Sometimes these knaves employed +crucibles, having an interior false bottom, below which a small quantity +of gold was placed, which, being reproduced, as was pretended from base +materials, was offered as an example of success. Or, by having the gold +in a hollow rod, stopped at one end with wax, used to stir up the +materials, the gold would naturally enough appear in the crucible. Or, +their materials being conveyed into charcoal, a similar result would be +obtained on heating the crucible in a furnace. At other times, by the +employment of amalgams, or solutions in acids, they could perform a +species of electro-plating on common metals. The extent to which these +nefarious practices were carried might appear incredible, considering +the evident inconsistency of the owner of the pretended golden key to +countless wealth, being in such comparative poverty as to be indebted to +any one of moderate means for pecuniary assistance. But, it is some +apology for such credulity when we call to mind the state of public +morals, of education, of political institutions, and the prevalent +superstition, not only among common people, but also the higher classes +of all countries and creeds, down to the seventeenth century: +representing a phase of the human mind, liable to be overawed by +impostors, who boldly claimed supernatural aid in abetting their +impositions. And the trickery of the designing was further aided by the +close secrecy adopted by the adepts in their processes, their +conversations, and their writings. Ashmole freely admits that--"Their +chief study was to wrap up their secrets in fables, and spin out their +fancies in 'vailes' and shadows, whose radii seem to extend every way, +yet so that all meet in a common centre, and point only to one thing." +It was this very secrecy, this continual mystery from beginning to end, +that favoured deceptions of the grossest and most bungling character, as +viewed by the light of modern chemistry. + +Alchemy no doubt tended to improve Medical science, by the introduction +of many new mineral and vegetable preparations, but the healing art +treated after the manner of the Hermetic Art, was laid open to every +description of quackery. It is not our intention, however, to enlarge on +this department, which has steadily advanced at every stage of +improvement in chemical science. + + +SQUARING THE CIRCLE. + +Of Mathematical Problems, the most perplexing to ancient and modern +mathematicians, although of late years said to be satisfactorily +demonstrated, and no longer desiderata of Geometry, are-- + +1. The Quadrature or Squaring of the Circle;--2. The Duplication, or +doubling of the Cube;--and 3. The Trisection of the Angle. + +In his "Popular Astronomy,"[11] Professor Arago, treating on the surface +of a circle, observes that,-- + +It is mathematically equal to the product of the length of the +circumference, multiplied by half the radius. To square a circle of a +given diameter in mètres, is the same as giving the number of squares, +of a mètre in each side, of which the surface is the equivalent. If, the +diameter being given, the exact circumference were known by a sort of +inspiration, the superficial extent of the circular space would be +deducible from the two numbers, by the mere multiplication of the +numerical length of the circumference by the fourth of the diameter, or +half the radius. But, the circumference being deducible from the +diameter only by approximation, the surface alluded to cannot be +computed with mathematical rigour; yet the result can be obtained with +all desirable precision by the aid of the ratios usually given for such +purpose; for instance, the area of the space included within a circle of +thirty-eight millions of leagues radius, may be determined within such a +degree of precision that the probable error shall not exceed the space +of a mite. + +[11] See Translation, by Admiral W. H. Smith, and Robert Grant, M.A., in +2 vols. 8vo. 1855, Vol. I., page 10. + +"The sect of squarers then," Arago adds,--"are searching after a +solution which is proved to be impossible, and which, moreover, would be +of no practical use, even if their foolish hopes were crowned with +success." + +In the "Birds" of Aristophanes, the character is introduced of a +geometer, who is going to make a square circle, showing how early this +chimerical performance became an object of ridicule. + +Thales, Anaxagoras, Pythagoras, Hippocrates, Plato, Apollonius, Ptolemy, +with other ancient mathematicians, have given methods for approximating +to the area of the circle; and many also among the moderns. In 1775, the +Paris Academy of Science determined to discourage papers devoted to this +subject, and their course in this respect was soon after adopted also +by The Royal Society, it being found that there was among certain +geometers a complete mania for settling this and similar problems, the +solution of which was either unattainable, or if attained of very +questionable value. + + +DUPLICATION OF THE CUBE. + +The Duplication of the Cube it is asserted can readily be demonstrated. +It is usually called the Delian Problem, from its having been suggested +by the oracle of Apollo at Delphos, requiring that Apollo's cubical +altar should be doubled. + +It is something in its favour to say that the enquiry has had the +attention of Newton and of Huygens. + + +TRISECTION OF AN ANGLE. + +Lastly, we shall notice among problems of this class--the Trisection of +an Angle, which it is asserted can only be accomplished by means of the +conic sections and some other curves. + +A rule for the cubic equation by which the problem of trisection is +solved has been given by Cardan. + +The difficulty only arises when we attempt the trisection of any other +than a right angle, its trisection being easily effected with a pair of +compasses. + +On this subject it has been observed that, "there is no more trouble in +trisecting an angle, not a right angle, than in finding a cube root." + + * * * * * + +These three celebrated problems have received the attention of +mathematicians in every age and country, and led to many learned +discussions, and controversial writings. But in point of litigiousness +the Squarers of the Circle most decidedly carry off the palm, having +frequently laid and lost heavy wagers, and even appeared in a Court of +Justice to settle their monetary disputes. They are renowned for their +pamphlets, in which philosophers of every class are charged with +prejudice, conceit, and ignorance, and denounced for their want of +candour and consistency in not giving audience to the projector of the +last best demonstration. + + +PERPETUUM MOBILE. + +To conclude this Lecture we shall offer a few remarks on Perpetuum +Mobile, or the search for a means of obtaining a mechanical perpetual +motion. As a mathematical problem it dates back some 2000 years or +more, but we know nothing of any actual attempt earlier than the 14th +century to construct a machine intended to be self motive, by containing +within itself the means of continually overbalancing. External motive +agency such as the tides, magnetism, and the like are not included; the +only admitted agent being gravity. + +If we considered wear and tear the question would be settled at once, +but this is allowed as the single exception, and therefore any machine +constantly renewing the means that first moved it might be deservedly +called a perpetual motion. + +Until a history of the schemes invented by numerous ingenious mechanics +was published in 1861, inventors of this class were continually though +unconsciously reproducing obsolete contrivances, from taking up the +ordinary idea that a wheel may be kept constantly over-weighted on one +side, so as to raise the next weight which is to perform the same +miracle of art. It is singular to observe this particular coincidence of +the inventive faculty of man, and it shows next to a demonstration, that +if all mechanical inventions were swept from the face of the earth they +would be reproduced in some remote age. + +A common error with those who toil at perpetual motion machinery is +their aiming to produce a bottled-up power; or to apply the principles +of the ordinary scale or balance to a wheel, overlooking the simple +facts of friction on one side acting against their most ingenious +contrivances, and of non-production on the other. Sooner or later, +however, they discover the inertia of matter, that a pound will not +raise a pound, and that they cannot invent mechanism to move +independently of the laws of action and reaction. + +A ball descending a semicircular path, as suggested by Dr. Henderson, +will only rise to the same height as that from which it fell; and will +afterwards gradually diminish in velocity until it rests at the centre. +If it would ascend to a height greater than that from which it +descended, then indeed an inclined path might return the ball to repeat +such evolutions until quite worn out. + +And as regards the weighted wheels, it is always overlooked that they +come to rest from the same fact, that the vertical line of descent and +that of ascent are equal, however much the weights may on one side +recede from the centre, while on the other side the weights are +approaching the centre. (_See_ Plate 6, Fig. 1.) + +The most famous perpetual motive schemes were those of the Marquis of +Worcester made 1630-41; (_See_ Plate 6, Fig. 2,) and of Bessler, better +known as Orfyreus, between 1712-19. + +The Marquis gives a brief notice of his plan, in his "Century of +Inventions," a curious catalogue of his several ingenious schemes. + +But of Orfyreus's wheel we know nothing more than was communicated by +the eminent mathematician, 'S Gravesande, to Sir Isaac Newton, after an +external view of it, while it was rotating in a chamber of the residence +of the Prince of Hesse Cassel. + +The most singular part of this strange delusion is the fact of its +strong hold on the minds of its infatuated votaries. Once bewitched with +the idea of at last succeeding in the attainment of his grand design, +fortune, health, and reputation, are resolutely set at nought, in the +delirium of delight that follows; and more unreasonable creatures can +scarcely be found than such self-deluded individuals, for they cannot, +or will not, be convinced that their utmost efforts can at best but +produce an amazingly curious toy; and nothing can be more futile than to +expect any higher application, assuming such a discovery were possible. + +The best proof of the sincerity and earnestness of those who seek the +attainment of a mechanical perpetual motion, is afforded by the variety +and number of their patented schemes; the patentees having among them +divines, doctors, lawyers, civil engineers, carpenters, draughtsmen, +jewellers, watchmakers, shoemakers, confectioners, and all classes of +professions and trades. It is not, as is generally supposed, only the +wholly ignorant and designing who can be cajoled by these chimeras; +there is in them a spice of mystery, of wonder, of singularity, and of +simplicity combined with much subtle difficulty, which, being once fully +imbibed, acts like an opiate draught. + +We have thus reviewed summarily, chimeras which are mainly associated +with Astronomy, Chemistry, Mathematics, and Mechanics, and which have +swayed the human mind more or less from a period anterior to the +Christian era. The list of this species of deceitful systems of +pseudo-philosophy, and of profitless problems, might have been enlarged; +but what has been advanced may suffice as a warning to the uninitiated +to beware of blind guides and of visionary pursuits. Science has lost +nothing by its professors exercising that degree of caution, which all +classes of superficially learned men, affecting to possess original and +valuable views on certain matters, call _prejudice_: which, in such +cases, generally means no more than the natural aversion which the +learned have for all attempts to place specious dogmas on a level with +sound science. Such enthusiasts are generally men of no research or +depth of thought, who obtain an imperfect acquaintance with subjects +with which they are incompetent to grapple; and with whom it is, +therefore, hopeless to contend. Delusion will have its day, and will as +certainly decay, if not die out. Chimeras constantly spring up, and find +ardent professors and crowds of easily led proselytes, even up to this +very present time; so that although, undoubtedly with many--_Knowledge +is power_: yet it is to be feared that far too large a proportion of +mankind favour the delusion that--_Ignorance is bliss_. + + +EXPLANATIONS OF THE PLATES. + + +PLATE I.--FIGURE 1. + +_Of the Twelve Houses._--The 1st, 4th, 7th, and 10th +houses--_angular_.--These are of more durable signification than the +others, denoting the wife or husband--a situation under Government, &c. +&c. + +The twelve houses have signification of all the various concerns of +human life, and of nature at large. + +_For Example._--When the cusp of the first house is well aspected by, or +has the presence of Jupiter or Venus, and these are not afflicted by the +aspects of evil planets, they preserve life in infancy, and give health, +and often an agreeable person. + +But if their rays or presence (says Varley) should be thrown on the cusp +of the second house, then the native will have success in concerns of +property. The Sun in this house helps to disperse property; and if he be +peregrine, that is, in the sign of a contrary nature to his own, where +he has no dignities, and is without reception, then the native's +property is dispersed in vainglorious expenses; but if the Sun be in +Leo, his property in general will be ample enough to admit of instant +acts of bounty and benevolence. + +In a similar strain, Astronomers particularize the remaining eleven +houses. It would be impossible, in any reasonable space, to describe +further the operations of the planets in the several houses thus +assigned to them. + +_As to when the Planets are most powerful._--Barrett says:--The planets +are powerful when they are ruling in a house, or in exaltation, or +triplicity, or term, or face, without combustion of what is direct in +the figure of the heavens; but we must take care that they are not in +the bounds or under the dominion of Saturn or Mars. The angles of the +ascendant, and 10th and 7th are fortunate; as also the lord of the +ascendant, and place of the Sun and Moon. + +The Moon is powerful if she be in her house, in exaltation, in +triplicity, in face, or in degree convenient for the desired work, &c. +&c. + +FIGURE 2. + +VARLEY'S TABLE OF SIGNS, HOUSES, EXALTATION, AND TRIPLICITY. + +The falls of the Planets are opposite to their Exaltations, and their +Detriments opposite to their Houses. + + Aries and Scorpio are the house of Mars [Mars] + + Taurus and Libra are the house of Venus [Venus] + + Gemini and Virgo are under the dominion of Mercury [Mercury] + + Cancer is the house of the Moon [Moon] + + Leo is the house of the Sun [Sun] + + Sagittarius and Pisces are the houses of Jupiter [Jupiter] + + Capricorn is the house of Saturn [Saturn] + + And Aquarius is governed by the Herschel Planet [Uranus] + + +PLATE II. + +This table gives the usual symbols employed for indicating the several +planets, and which are still retained in Astronomy for simplicity of +expression, but which Astrologers venerate as possessing a cabalistic +character. + +Associated with these symbols are the names of certain principal angels, +spirits, or demons, forming, however, but a small proportion of such +airy nothings. + +The Astrological Symbols were also employed by the Alchemists to +indicate the seven metals then known. + + +PLATE III.--SQUARING THE CIRCLE. + +Mr. James Smith, of Liverpool, the most laborious among recent workers +in this field of enquiry, claiming to have propounded several simple and +exact methods, offers the following as sufficiently demonstrative:-- + +I construct my diagrams in the following way:--I draw two straight lines +at right angles, making O the right angle. From the point O, in the +direction OA, I mark off four equal parts together equal to OA, and from +O, in the direction of OB, I mark off three of such equal parts +together, equal to OB, and join AB. It is obvious, or rather +self-evident, that AOB is a right-angled triangle, of which the sides +that contain the right angle are in the ratio of 4 to 3, by +construction. With A as centre and AB as interval, I describe the circle +X, produce AO and BO to meet and terminate in the circumference of the +circle at the points G and C, and join AC, CG, and BG, producing the +quadrilateral ACGB. I bisect AG at F, and with O as centre, and OF as +interval, describe the circle Z. The line OF is the line that joins the +middle points of the diagonals in the quadrilateral ACGB; and it follows +that, {AG^2 + CB^2 + 4(OF^2)} = {AC^2 + CG^2 + BG^2 + AB^2.} + +When AO = 4, we get the following equation:-- + +{5^2 + 6^2 + (4 × 1'5^2)} = {5^2 + sqrt(10^2) + sqrt(10^2) + 5^2,} or, +{25 + 36 + 9} = {25 + 10 + 10 + 25} = 70. From the points B and C, I +draw straight lines at right angles to AB and AC, and therefore +tangential to the circle X, to meet AG produced at D, and join BD and +CD, producing the quadrilateral ACDB. I bisect AD at E, and with O as +centre, and EO as interval describe the circle XY, and with E as centre, +and EA or ED as interval describe the circle Y. + +Now, to square the circle, or, in other words, to get exactly equal in +superficial area to the circle X, I will show how to find it. From the +point G draw a straight line--say G _m_--perpendicular to ED, making G +_m_ equal GD. Produce GA to a point _n_, making G _n_ equal to 2AG - GD, +and join _n m_. The square on _n m_ will be the required square. (I have +indicated this square by dotted lines.) For example:--If AO = 4, then AG += 5, and GD = 1'25; therefore {2 AG - GD} = {10 - 1'25} = 8'75 = Gn: and +Gm = 1'25; therefore, Gn^2 + Gm^2 = 3-1/8 (AB^2); that is, {8'75^2 + +1'25^2} = 3-1/8 (5^2), or, {76'5625 + 1'5625} = {3'125 × 25}; and this +equation=Area of the Circle X; and area of the square on _n m_ :: and it +follows, that the area of every circle, is equal to the area of a square +on the hypotenuse of a right-angled triangle, of which the sides that +contain the right angle are in the ratio of 7 to 1, and the sum of these +two sides equal to the diameter of the circle. In many ways I have +proved this fact, by practical or constructive geometry. + + +PLATE IV. + +_Duplication of the Cube._--In his "Young Geometrician; or, Practical +Geometry without Compasses," 1865, Mr. Oliver Byrne's 40th Problem is as +follows:-- + +Let AB be the side of a given cube BD. It is required to find AC, the +side of another cube CE, so that the solid contents of the cube CE are +double the solid contents of the cube BD. + +Ancient and modern mathematicians (says Mr. Byrne) have in vain +attempted to solve this problem geometrically, that is, by the ruler and +compasses only. + +Let AB = BG = GR = RQ = QP = QO = OR = VZ. The length of the shortest +side of the lesser set square; a line of any other given length may be +applied. Draw OP and VR parallel to it; then apply the set squares in +close contact, the edge OV of OVT passing through the point O, while the +points of V and Z of ZSV fall exactly on the lines RV, RZ. Then draw the +line ZBC, cutting FA produced in C; then the cube on AC is double the +cube on AB. + + +PLATE V. + +_Trisection of an Angle._--In his work entitled _Young Geometrician_, +1865, Mr. Oliver Byrne gives as the 39th Problem: To divide a given +angle BAC into three equal angles:-- + +The line A _m_ is made = _p q_, the least side of the lesser triangular +ruler; by (II) _p m_ is drawn parallel, and _m n_ perpendicular to AB. +Then both rulers are kept in motion, and at the same time in close +contact, as represented in the figure, until _p_ falls on the line _p +m_, and _n_ on the line _m n_; _r n_A passing through the angular point +A. + +Then the angle DAB is one-third of the angle CAB. Mr. Byrne asserts that +this problem is not capable of solution by the straight line and circle. +Mathematicians have in vain attempted to solve it geometrically, that +is, by the ruler and compasses only. + + +PLATE VI.--FIGURE 1. + +_Perpetuum Mobile._ Desaguliers demonstrated the absurdity of attempting +to raise weights enclosed in a cellular wheel, simply by providing for +their approach in succession nearer to the centre on the ascending side, +while they should be projected further from the centre on the descending +side. He remarks:-- + +Those who think the velocity of the weight is the line it describes, +expect that that weight shall be overpoised, which describes the +shortest line, and therefore contrive machines to cause the ascending +weight to describe a shorter line than the descending weight. + +For example, in the circle A B D _a_, the weights A and B being supposed +equal, it is imagined that, if by any contrivance whatever, whilst the +weight A describes the arc A _a_, the weight B is carried in any arc, as +B _b_, so as to come nearer the centre in its rising, than if it went up +the arc B D; the said weight shall be overpoised, and consequently, by a +number of such weights, a perpetual motion produced. + +Now the velocity of any weight is _not_ the line which it describes in +general, but the height that it rises up to, or falls from, with respect +to its distance from the centre of the earth. So that when the weight +describes the arc A _a_, its velocity is the line A C, which shows the +perpendicular descent, and likewise the line B C denotes the velocity of +the weight B, or the height that it rises to, when it ascends in any of +the arcs B _b_, instead of the arc B D: so that, in this case, whether +the weight B, in its ascent be brought nearer the centre or not, it +loses no velocity, which it ought to do, in order to be raised up by the +weight A. + +Indeed, if the weight at B, could by any means spring as it were, or be +lifted up to _x_, and move in the arc _x b_, the end would be answered, +because then the velocity would be diminished, and become _x_C. + + +FIGURE 2. + +In "The Life, Times, and Scientific Labours of the Marquis of +Worcester," 1865, page 454, will be found a full account of the present +diagram, which is intended to illustrate as far as possible, an approach +to the probable construction of the wheel by the Marquis in the 56th +article of his memorable "Century of Inventions." + +If any likely-looking method, could, more than another, render +hopelessness more hopeless, surely this mechanical demonstration must +prove most efficient for that purpose. For here, we actually produce a +wheel agreeing to the terms with which Desaguliers closes his +demonstration, when he suggests the only likely method to effect the end +proposed, namely, perpetual motion. We find the fallen weight is +absolutely "lifted up" as he desires, and "moves in the arc" he +describes, and yet although he declares that then "the end would be +answered"--it absolutely is _not_ answered in this instance. + +It is not requisite to calculate throughout the effect of the Marquis's +entire number of 40 weights; four will suffice, taking the vertical and +horizontal spokes _a a a a_, showing two rings _a_ and _b_; one, _b_, 12 +inches within the other, so that the wheel being, as the Marquis says, +14 feet diameter, the inner ring will be 12 feet diameter. Now let each +weight D be attached in the centre of a cord or chain _a_´, D, b´, 2 +feet long, and then secure one end, as _a_´, so the extreme end of each +spoke _a_´, and the other end of the cord, as b´, to place on one lesser +ring, as at _b_, or 12 inches from each spoke. + +We shall then find by admeasurement that the upper weight on the +vertical spoke is 7 feet from the centre, and the lower weight 6 feet; +while at the same time there appears to be a preponderance due to the +superior length of the horizontal arm A´; but against this latter we +have the rising weight _b_´D, 1 foot from the centre, which, added to +the 6 feet on the horizontal spoke, neutralizes the hoped-for effect, +and the wheel remains in _statu quo_. + + +THE END. + + * * * * * + +[Illustration: Plate 1. + +LONDON. E. & F. N. SPON. 48, CHARING CROSS.] + + * * * * * + +[Illustration: Plate 2. + +LONDON. E. & F. N. SPON. 48, CHARING CROSS.] + + * * * * * + +[Illustration: Plate 3. + +LONDON. E. & F. N. SPON. 48, CHARING CROSS.] + + * * * * * + +[Illustration: Plate 4. + +LONDON. E. & F. N. SPON. 48, CHARING CROSS.] + + * * * * * + +[Illustration: Plate 5. + +LONDON. E. & F. N. SPON. 48, CHARING CROSS.] + + * * * * * + +[Illustration: Plate 6. + +LONDON. E. & F. N. SPON. 48, CHARING CROSS.] + + * * * * * + + +OTHER WORKS BY THE SAME AUTHOR. + +One Volume 8vo., of 650 pages, illustrated with Steel Engravings of two + unpublished Portraits and 45 Wood Engravings, price 24_s_, + + THE LIFE, TIMES, AND SCIENTIFIC LABOURS OF + EDWARD SOMERSET, + SIXTH EARL AND SECOND + MARQUIS OF WORCESTER, + + To which is added, + + A REPRINT OF HIS CENTURY OF INVENTIONS (1663), + WITH A COMMENTARY THEREON. + +[Asterism] Thirty copies are printed on Large Paper, 1 vol. 4to. with +INDIA PROOFS before the Letters of the Portraits, price £3. 3_s_. + +"A monument raised late, it is true, but not too late, to a great and +modest genius. A national biography which illustrates and elevates our +ideas of the past, and a contribution which the world will recognize to +the European history of Science." + + _Dublin University Magazine_, September, 1865. + +"A work which displays a high order of literary ability, careful +antiquarian research, much ingenuity, and withal thorough honesty of +purpose. + +"[Lord Worcester], his life, told as Mr. Dircks has told it, is one of +much interest. + +"Here we have an elaborate--although of course not a completely +exhaustive--account of his life; at any rate the most complete account +of him ever likely to be written--a work filled with abundant evidence +of the most painstaking research, a work written in a generous and +sympathising spirit, and with every attribute of conscientiousness." + + _Engineering_, 5th January, 1866. + +"The production of this volume is no common achievement; Mr. Dircks has +undertaken to write the life of a man about whom the public know very +little. + +"He has, we think, collected some curious information, and established +the claim of the Marquis to be the first constructor of a steam-engine. +The reprint of the celebrated _Century of Inventions_ adds greatly to +the interest of the volume."--_The Spectator_, 14th September, 1867. + + * * * * * + + One Volume, 8vo., price 21_s_, only 100 copies printed, + + WORCESTERIANA; + + A COLLECTION OF + + BIOGRAPHICAL AND OTHER NOTICES, ALPHABETICALLY ARRANGED, + RELATING TO EDWARD SOMERSET, SECOND + + MARQUIS OF WORCESTER, + + AND HIS IMMEDIATE FAMILY CONNECTIONS; WITH OCCASIONAL NOTES. + +"The present volume is, as it were, a supplement. [To. Mr. Dircks's +_Life of the Marquis of Worcester_.] It contains what the French call +'pièces justificatives,' on which that biography was founded; and such +other materials connected with the history of Lord Worcester's family +and his invention of the steam-engine as will prevent, as far as +possible, a repetition of the gross errors hitherto promulgated on these +subjects." + + _Notes and Queries_, February 3, 1866. + + * * * * * + + One Volume, post 8vo., with 130 wood engravings, price 10_s_ 6_d_, + + PERPETUUM MOBILE; + + OR, + + HISTORY OF THE SEARCH FOR SELF-MOTIVE POWER + DURING THE 17TH, 18TH, AND 19TH CENTURIES, + + WITH AN INTRODUCTORY ESSAY. + +"The literature of this subject [Perpetual Motion] is very extensive, +but scattered mainly through Patent Records and ephemeral pamphlets. We +would especially refer the curious reader to a recent work by Mr. +Dircks, entitled _Perpetuum Mobile_, to which we have been indebted for +historical notices. It is extremely complete and interesting as a +history." + + _Chambers's Encyclopædia_, Part 15, 1865. + +"A very useful collection on the history of the attempts at perpetual +motion, that is, of obtaining the consequences of power without any +power to produce them."--_Professor De Morgan's_ Budget of Paradoxes, +No. 28.--_Athenæum_, July 15, 1865. + + * * * * * + + One Volume, post 8vo., with portrait, price 3_s_ 6_d_, + + CONTRIBUTION TOWARDS A HISTORY OF + ELECTRO-METALLURGY, + ESTABLISHING THE ORIGIN OF THE ART. + +"In his Introduction, Mr. Dircks has clearly stated the claims of +invention, and fairly discussed the only just grounds that can give +claim to priority of invention."--_The Mining Journal_, February 7, +1863. + +"In the collection of chronological and other data for the history of +various branches and application of science, Mr. Dircks appears to be +indefatigable."--_The Electrician_, February 27. + +"It is a useful and clear digest of evidence, and apparently impartially +put together."--_The Practical Mechanics' Journal_ (_Glasgow_), July. + + * * * * * + + One Volume, post 8vo., with two portraits, price 4_s_, + + INVENTORS AND INVENTIONS, + + IN THREE PARTS. + + I. THE PHILOSOPHY OF INVENTION, considered strictly in relation to + Ingenious Contrivances tending to facilitate Scientific Operations, + to extend Manufacturing Skill, or to originate New Sources of + Industry.--II. THE RIGHTS AND WRONGS OF INVENTORS, Legally and + Politically Examined.--III. EARLY INVENTORS' INVENTORIES OF SECRET + INVENTIONS, employed from the 13th to the 17th Century, in + substitution of Letters Patent. + +"The author enters fully and effectually into the claims and grievances +of the inventor. He discusses the arguments for and against the concession +of patent right, and examines very ably leaders in the _Times_ on patent +monopoly; very clearly dissipating the sophism of the opponents of patent +right; also Sir William Armstrong's evidence regarding 'patent monopoly,' +&c., affording an interesting and useful publication from its many +excellences."--_The Scientific Review_, September 2, 1867. + +"The second part of the volume discusses the right of inventors to a +property in their inventions, and thus raises the question of the patent +laws, and the twofold issue, whether it will be better to retain them +and reform them, or to sweep them away altogether. We are bound to admit +that he treats this topic in a fair spirit, and without any taint of +bigotry. Mr. Dircks is a man whose opinions are entitled to a hearing." + + _The London Review_, September 21. + +"Mr. Dircks treats the real problem and discusses the comparative merits +of the existing system, and the advantages which he, together with many +others, hopes would follow on the establishment of some judicial council +of inventions. The difficulties of the question are enormous, and no one +will think the less of them after having gone through this volume. + +"The third part, or the lists of their inventions left by many great and +some ingenious persons, is interesting and curious." + + _The Westminster Review_, October. + + * * * * * + + One Volume, post 8vo., price 3_s_ 6_d_, + + A BIOGRAPHICAL MEMOIR OF + SAMUEL HARTLIB, + MILTON'S FAMILIAR FRIEND, + + With Bibliographical Notices of Works published by him; and a reprint + of his Pamphlet entitled + + "AN INVENTION OF ENGINES OF MOTION." + +"Mr. Dircks's is the first careful attempt to make posterity his +(Hartlib's) friend."--_The Examiner_, 18th February, 1865. + +"A scholar-like little monograph, giving all the information that can be +given about a man whose name occurs in the correspondence of almost +every eminent literary or scientific person of the time of the +Commonwealth."--_The Spectator_, 20th May. + + * * * * * + + One Volume, post 8vo., with engravings, price 2_s_, + + THE GHOST! + + AS PRODUCED IN THE SPECTRE DRAMA, + + POPULARLY ILLUSTRATING THE MARVELLOUS OPTICAL ILLUSIONS + OBTAINED BY THE APPARATUS CALLED THE DIRCKSIAN + PHANTASMAGORIA. + +"Mr. Dircks gives us the benefit of all his progressive discoveries in +the matter, from the paper first read at the British Association Meeting +at Leeds, in 1858, to the more recent improvements, with full +explanations of the machinery, apparatus, and processes adopted in these +ghost dramas, and further favours the public with a number of new +adaptations. As a curious description of these spectral illustrations, +the book is most interesting."--_The Technologist_, January, 1864. + +"A volume explanatory of the uncommonly clever and scientific "spectral +illusion" which has of late fairly turned the public head." + + _The Dublin Builder_, January 1. + +"A few months ago all London was rushing off to see Professor Pepper's +Ghost, as it was called, but which it now appears was the property of +Mr. Dircks, and from which his good name was filched in a very +unhandsome manner. Here then he tells us all about it, how the spectre +was raised, and how we may ourselves at pleasure call spirits from the +vasty deep."--_The Bookseller_, February 29. + + * * * * * + + +Transcriber's Notes + +Page 36: changed "Sorbiere" to "Sorbière" (15. Samuel Sorbière visited +the works at Vauxhall) + +Page 61: changed "Jupiper" to "Jupiter" (of cloves, &c. to Jupiter;) + +Page 83: changed "BD^2" to "BG^2" ({AG^2 + CB^2 + 4(OF^2)} = {AC^2 + +CG^2 + BG^2 + AB^2.}) + +Page 83: changed "sqrt(10^2 5^2)" to "sqrt(10^2) + 5^2" ( ... = {5^2 + +sqrt(10^2) + sqrt(10^2) + 5^2,}) + +Page 84: changed closing parenthesis to closing braces ( ... 9} = {25 + +10 + 10 + 25} = 70) + +Page 84: changed "tangental" to "tangential" (tangential to the circle +X) + +Page 84: changed "Q" to "2" (making G _n_ equal to 2AG - GD) + +Page 84: added missing opening parenthesis in "(I have indicated this +square by dotted lines.)" + +Page 84: changed "+ 1'25}" to "× 25" ({76'5625 + 1'5625} = {3'125 × 25}) + +Page 84: changed "hypothenuse" to "hypotenuse" (the area of a square on +the hypotenuse) + + + + + +End of the Project Gutenberg EBook of Scientific Studies, by Henry Dircks + +*** END OF THE PROJECT GUTENBERG EBOOK 43841 *** |