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+Project Gutenberg's Five of Maxwell's Papers, by James Clerk Maxwell
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org/license
+
+
+Title: Five of Maxwell's Papers
+
+Author: James Clerk Maxwell
+
+Posting Date: February 25, 2014 [EBook #4908]
+
+Release Date: January, 2004
+
+[This file was first posted on March 24, 2002]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK FIVE OF MAXWELL'S PAPERS ***
+
+
+
+
+Produced by Gordon Keener
+
+
+
+
+
+
+This eBook includes 5 papers or speeches by James Clerk Maxwell.
+
+The contents are:
+
+   Foramen Centrale
+   Theory of Compound Colours
+   Poinsot's Theory
+   Address to the Mathematical
+   Introductory Lecture
+
+
+
+
+On the Unequal Sensibility of the Foramen Centrale to Light of
+different Colours.
+
+James Clerk Maxwell
+
+
+[From the _Report of the British Association_, 1856.]
+
+
+When observing the spectrum formed by looking at a long ve rtical slit
+through a simple prism, I noticed an elongated dark spot running up
+and down in the blue, and following the motion of the eye as it moved
+_up and down_ the spectrum, but refusing to pass out of the blue into
+the other colours.  It was plain that the spot belonged both to the
+eye and to the blue part of the spectrum.  The result to which I have
+come is, that the appearance is due to the yellow spot on the retina,
+commonly called the _Foramen Centrale_ of Soemmering.  The most
+convenient method of observing the spot is by presenting to the eye in
+not too rapid succession, blue and yellow glasses, or, still better,
+allowing blue and yellow papers to revolve slowly before the eye.  In
+this way the spot is seen in the blue.  It fades rapidly, but is
+renewed every time the yellow comes in to relieve the effect of the
+blue.  By using a Nicol's prism along with this apparatus, the brushes
+of Haidinger are well seen in connexion with the spot, and the fact of
+the brushes being the spot analysed by polarized light becomes
+evident.  If we look steadily at an object behind a series of bright
+bars which move in front of it, we shall see a curious bending of the
+bars as they come up to the place of the yellow spot.  The part which
+comes over the spot seems to start in advance of the rest of the bar,
+and this would seem to indicate a greater rapidity of sensation at the
+yellow spot than in the surrounding retina.  But I find the experiment
+difficult, and I hope for better results from more accurate observers.
+
+
+
+
+On the Theory of Compound Colours with reference to Mixtures of
+Blue and Yellow Light.
+
+James Clerk Maxwell
+
+
+[From the _Report of the British Association_, 1856.]
+
+
+When we mix together blue and yellow paint, we obtain green paint.
+This fact is well known to all who have handled colours; and it is
+universally admitted that blue and yellow make green.  Red, yellow,
+and blue, being the primary colours among painters, green is regarded
+as a secondary colour, arising from the mixture of blue and yellow.
+Newton, however, found that the green of the spectrum was not the same
+thing as the mixture of two colours of the spectrum, for such a
+mixture could be separated by the prism, while the green of the
+spectrum resisted further decomposition.  But still it was believed
+that yellow and blue would make a green, though not that of the
+spectrum.  As far as I am aware, the first experiment on the subject
+is that of M. Plateau, who, before 1819, made a disc with alternate
+sectors of prussian blue and gamboge, and observed that, when
+spinning, the resultant tint was not green, but a neutral gray,
+inclining sometimes to yellow or blue, but never to green.
+Prof. J. D. Forbes of Edinburgh made similar experiments in 1849, with
+the same result.  Prof. Helmholtz of Konigsberg, to whom we owe the
+most complete investigation on visible colour, has given the true
+explanation of this phenomenon.  The result of mixing two coloured
+powders is not by any means the same as mixing the beams of light
+which flow from each separately.  In the latter case we receive all
+the light which comes either from the one powder or the other.  In the
+former, much of the light coming from one powder falls on particles of
+the other, and we receive only that portion which has escaped
+absorption by one or other.  Thus the light coming from a mixture of
+blue and yellow powder, consists partly of light coming directly from
+blue particles or yellow particles, and partly of light acted on by
+both blue and yellow particles.  This latter light is green, since the
+blue stops the red, yellow, and orange, and the yellow stops the blue
+and violet.  I have made experiments on the mixture of blue and yellow
+light--by rapid rotation, by combined reflexion and transmission, by
+viewing them out of focus, in stripes, at a great distance, by
+throwing the colours of the spectrum on a screen, and by receiving
+them into the eye directly; and I have arranged a portable apparatus
+by which any one may see the result of this or any other mixture of
+the colours of the spectrum.  In all these cases blue and yellow do
+not make green.  I have also made experiments on the mixture of
+coloured powders.  Those which I used principally were "mineral blue"
+(from copper) and "chrome-yellow."  Other blue and yellow pigments gave
+curious results, but it was more difficult to make the mixtures, and
+the greens were less uniform in tint.  The mixtures of these colours
+were made by weight, and were painted on discs of paper, which were
+afterwards treated in the manner described in my paper "On Colour as
+perceived by the Eye," in the _Transactions of the Royal Society of
+Edinburgh_, Vol. XXI. Part 2.  The visible effect of the colour is
+estimated in terms of the standard-coloured papers:--vermilion (V),
+ultramarine (U), and emerald-green (E).  The accuracy of the results,
+and their significance, can be best understood by referring to the
+paper before mentioned.  I shall denote mineral blue by B, and
+chrome-yellow by Y; and B3 Y5 means a mixture of three parts blue and
+five parts yellow.
+
+       Given Colour.     Standard Colours.          Coefficient
+                          V.    U.    E.           of brightness.
+
+         B8    , 100  =   2    36     7   ............   45
+		 
+         B7  Y1, 100  =   1    18    17   ............   37
+		 
+         B6  Y2, 100  =   4    11    34   ............   49
+		 
+         B5  Y3, 100  =   9     5    40   ............   54
+		 
+         B4  Y4, 100  =  15     1    40   ............   56
+		 
+         B3  Y5, 100  =  22   - 2    44   ............   64
+		 
+         B2  Y6, 100  =  35   -10    51   ............   76
+		 
+         B1  Y7, 100  =  64   -19    64   ............  109
+		 
+             Y8, 100  = 180   -27   124   ............  277
+
+The columns V, U, E give the proportions of the standard colours which
+are equivalent to 100 of the given colour; and the sum of V, U, E
+gives a coefficient, which gives a general idea of the brightness.  It
+will be seen that the first admixture of yellow _diminishes_ the
+brightness of the blue.  The negative values of U indicate that a
+mixture of V, U, and E cannot be made equivalent to the given colour.
+The experiments from which these results were taken had the negative
+values transferred to the other side of the equation.  They were all
+made by means of the colour-top, and were verified by repetition at
+different times.  It may be necessary to remark, in conclusion, with
+reference to the mode of registering visible colours in terms of three
+arbitrary standard colours, that it proceeds upon that theory of three
+primary elements in the sensation of colour, which treats the
+investigation of the laws of visible colour as a branch of human
+physiology, incapable of being deduced from the laws of light itself,
+as set forth in physical optics.  It takes advantage of the methods of
+optics to study vision itself; and its appeal is not to physical
+principles, but to our consciousness of our own sensations.
+
+
+
+
+On an Instrument to illustrate Poinsot's Theory of Rotation.
+
+James Clerk Maxwell
+
+
+[From the _Report of the British Association_, 1856.]
+
+
+In studying the rotation of a solid body according to Poinsot's
+method, we have to consider the successive positions of the
+instantaneous axis of rotation with reference both to directions fixed
+in space and axes assumed in the moving body.  The paths traced out by
+the pole of this axis on the _invariable plane_ and on the _central
+ellipsoid_ form interesting subjects of mathematical investigation.
+But when we attempt to follow with our eye the motion of a rotating
+body, we find it difficult to determine through what point of the
+_body_ the instantaneous axis passes at any time,--and to determine its
+path must be still more difficult.  I have endeavoured to render
+visible the path of the instantaneous axis, and to vary the
+circumstances of motion, by means of a top of the same kind as that
+used by Mr Elliot, to illustrate precession*.  The body of the
+instrument is a hollow cone of wood, rising from a ring, 7 inches in
+diameter and 1 inch thick.  An iron axis, 8 inches long, screws into
+the vertex of the cone.  The lower extremity has a point of hard
+steel, which rests in an agate cup, and forms the support of the
+instrument.  An iron nut, three ounces in weight, is made to screw on
+the axis, and to be fixed at any point; and in the wooden ring are
+screwed four bolts, of three ounces, working horizontally, and four
+bolts, of one ounce, working vertically.  On the upper part of the
+axis is placed a disc of card, on which are drawn four concentric
+rings.  Each ring is divided into four quadrants, which are coloured
+red, yellow, green, and blue.  The spaces between the rings are white.
+When the top is in motion, it is easy to see in which quadrant the
+instantaneous axis is at any moment and the distance between it and
+the axis of the instrument; and we observe,--1st. That the
+instantaneous axis travels in a closed curve, and returns to its
+original position in the body.  2ndly. That by working the vertical
+bolts, we can make the axis of the instrument the centre of this
+closed curve.  It will then be one of the principal axes of inertia.
+3rdly. That, by working the nut on the axis, we can make the order of
+colours either red, yellow, green, blue, or the reverse.  When the
+order of colours is in the same direction as the rotation, it
+indicates that the axis of the instrument is that of greatest moment
+of inertia.  4thly. That if we screw the two pairs of opposite
+horizontal bolts to different distances from the axis, the path of the
+instantaneous pole will no longer be equidistant from the axis, but
+will describe an ellipse, whose longer axis is in the direction of the
+mean axis of the instrument.  5thly. That if we now make one of the
+two horizontal axes less and the other greater than the vertical axis,
+the instantaneous pole will separate from the axis of the instrument,
+and the axis will incline more and more till the spinning can no
+longer go on, on account of the obliquity.  It is easy to see that, by
+attending to the laws of motion, we may produce any of the above
+effects at pleasure, and illustrate many different propositions by
+means of the same instrument.
+
+* _Transactions of the Royal Scottish Society of Arts_, 1855.
+
+
+
+
+Address to the Mathematical and Physical Sections of the British
+Association.
+
+James Clerk Maxwell
+
+
+[From the _British Association Report_, Vol. XL.]
+
+[Liverpool, _September_ 15, 1870.]
+
+
+At several of the recent Meetings of the British Association the
+varied and important business of the Mathematical and Physical Section
+has been introduced by an Address, the subject of which has been left
+to the selection of the President for the time being.  The perplexing
+duty of choosing a subject has not, however, fallen to me.
+
+Professor Sylvester, the President of Section A at the Exeter Meeting,
+gave us a noble vindication of pure mathematics by laying bare, as it
+were, the very working of the mathematical mind, and setting before
+us, not the array of symbols and brackets which form the armoury of
+the mathematician, or the dry results which are only the monuments of
+his conquests, but the mathematician himself, with all his human
+faculties directed by his professional sagacity to the pursuit,
+apprehension, and exhibition of that ideal harmony which he feels to
+be the root of all knowledge, the fountain of all pleasure, and the
+condition of all action.  The mathematician has, above all things, an
+eye for symmetry; and Professor Sylvester has not only recognized the
+symmetry formed by the combination of his own subject with those of
+the former Presidents, but has pointed out the duties of his successor
+in the following characteristic note:--
+
+"Mr Spottiswoode favoured the Section, in his opening Address, with a
+combined history of the progress of Mathematics and Physics; Dr.
+Tyndall's address was virtually on the limits of Physical Philosophy;
+the one here in print," says Prof. Sylvester, "is an attempted faint
+adumbration of the nature of Mathematical Science in the abstract.
+What is wanting (like a fourth sphere resting on three others in
+contact) to build up the Ideal Pyramid is a discourse on the Relation
+of the two branches (Mathematics and Physics) to, their action and
+reaction upon, one another, a magnificent theme, with which it is to
+be hoped that some future President of Section A will crown the
+edifice and make the Tetralogy (symbolizable by _A+A'_, _A_, _A'_,
+_AA'_) complete."
+
+The theme thus distinctly laid down for his successor by our late
+President is indeed a magnificent one, far too magnificent for any
+efforts of mine to realize.  I have endeavoured to follow Mr
+Spottiswoode, as with far-reaching vision he distinguishes the systems
+of science into which phenomena, our knowledge of which is still in
+the nebulous stage, are growing.  I have been carried by the
+penetrating insight and forcible expression of Dr Tyndall into that
+sanctuary of minuteness and of power where molecules obey the laws of
+their existence, clash together in fierce collision, or grapple in yet
+more fierce embrace, building up in secret the forms of visible
+things.  I have been guided by Prof. Sylvester towards those serene
+heights
+
+    "Where never creeps a cloud, or moves a wind,
+     Nor ever falls the least white star of snow,
+     Nor ever lowest roll of thunder moans,
+     Nor sound of human sorrow mounts to mar
+     Their sacred everlasting calm."
+
+But who will lead me into that still more hidden and dimmer region
+where Thought weds Fact, where the mental operation of the
+mathematician and the physical action of the molecules are seen in
+their true relation?  Does not the way to it pass through the very den
+of the metaphysician, strewed with the remains of former explorers,
+and abhorred by every man of science?  It would indeed be a foolhardy
+adventure for me to take up the valuable time of the Section by
+leading you into those speculations which require, as we know,
+thousands of years even to shape themselves intelligibly.
+
+But we are met as cultivators of mathematics and physics.  In our
+daily work we are led up to questions the same in kind with those of
+metaphysics; and we approach them, not trusting to the native
+penetrating power of our own minds, but trained by a long-continued
+adjustment of our modes of thought to the facts of external nature.
+
+As mathematicians, we perform certain mental operations on the symbols
+of number or of quantity, and, by proceeding step by step from more
+simple to more complex operations, we are enabled to express the same
+thing in many different forms.  The equivalence of these different
+forms, though a necessary consequence of self-evident axioms, is not
+always, to our minds, self-evident; but the mathematician, who by long
+practice has acquired a familiarity with many of these forms, and has
+become expert in the processes which lead from one to another, can
+often transform a perplexing expression into another which explains
+its meaning in more intelligible language.
+
+As students of Physics we observe phenomena under varied
+circumstances, and endeavour to deduce the laws of their relations.
+Every natural phenomenon is, to our minds, the result of an infinitely
+complex system of conditions.  What we set ourselves to do is to
+unravel these conditions, and by viewing the phenomenon in a way which
+is in itself partial and imperfect, to piece out its features one by
+one, beginning with that which strikes us first, and thus gradually
+learning how to look at the whole phenomenon so as to obtain a
+continually greater degree of clearness and distinctness.  In this
+process, the feature which presents itself most forcibly to the
+untrained inquirer may not be that which is considered most
+fundamental by the experienced man of science; for the success of any
+physical investigation depends on the judicious selection of what is
+to be observed as of primary importance, combined with a voluntary
+abstraction of the mind from those features which, however attractive
+they appear, we are not yet sufficiently advanced in science to
+investigate with profit.
+
+Intellectual processes of this kind have been going on since the first
+formation of language, and are going on still.  No doubt the feature
+which strikes us first and most forcibly in any phenomenon, is the
+pleasure or the pain which accompanies it, and the agreeable or
+disagreeable results which follow after it.  A theory of nature from
+this point of view is embodied in many of our words and phrases, and
+is by no means extinct even in our deliberate opinions.
+
+It was a great step in science when men became convinced that, in
+order to understand the nature of things, they must begin by asking,
+not whether a thing is good or bad, noxious or beneficial, but of what
+kind is it? and how much is there of it?  Quality and Quantity were
+then first recognized as the primary features to be observed in
+scientific inquiry.
+
+As science has been developed, the domain of quantity has everywhere
+encroached on that of quality, till the process of scientific inquiry
+seems to have become simply the measurement and registration of
+quantities, combined with a mathematical discussion of the numbers
+thus obtained.  It is this scientific method of directing our
+attention to those features of phenomena which may be regarded as
+quantities which brings physical research under the influence of
+mathematical reasoning.  In the work of the Section we shall have
+abundant examples of the successful application of this method to the
+most recent conquests of science; but I wish at present to direct your
+attention to some of the reciprocal effects of the progress of science
+on those elementary conceptions which are sometimes thought to be
+beyond the reach of change.
+
+If the skill of the mathematician has enabled the experimentalist to
+see that the quantities which he has measured are connected by
+necessary relations, the discoveries of physics have revealed to the
+mathematician new forms of quantities which he could never have
+imagined for himself.
+
+Of the methods by which the mathematician may make his labours most
+useful to the student of nature, that which I think is at present most
+important is the systematic classification of quantities.
+
+The quantities which we study in mathematics and physics may be
+classified in two different ways.
+
+The student who wishes to master any particular science must make
+himself familiar with the various kinds of quantities which belong to
+that science.  When he understands all the relations between these
+quantities, he regards them as forming a connected system, and he
+classes the whole system of quantities together as belonging to that
+particular science.  This classification is the most natural from a
+physical point of view, and it is generally the first in order of
+time.
+
+But when the student has become acquainted with several different
+sciences, he finds that the mathematical processes and trains of
+reasoning in one science resemble those in another so much that his
+knowledge of the one science may be made a most useful help in the
+study of the other.
+
+When he examines into the reason of this, he finds that in the two
+sciences he has been dealing with systems of quantities, in which the
+mathematical forms of the relations of the quantities are the same in
+both systems, though the physical nature of the quantities may be
+utterly different.
+
+He is thus led to recognize a classification of quantities on a new
+principle, according to which the physical nature of the quantity is
+subordinated to its mathematical form.  This is the point of view
+which is characteristic of the mathematician; but it stands second to
+the physical aspect in order of time, because the human mind, in order
+to conceive of different kinds of quantities, must have them presented
+to it by nature.
+
+I do not here refer to the fact that all quantities, as such, are
+subject to the rules of arithmetic and algebra, and are therefore
+capable of being submitted to those dry calculations which represent,
+to so many minds, their only idea of mathematics.
+
+The human mind is seldom satisfied, and is certainly never exercising
+its highest functions, when it is doing the work of a calculating
+machine.  What the man of science, whether he is a mathematician or a
+physical inquirer, aims at is, to acquire and develope clear ideas of
+the things he deals with.  For this purpose he is willing to enter on
+long calculations, and to be for a season a calculating machine, if he
+can only at last make his ideas clearer.
+
+But if he finds that clear ideas are not to be obtained by means of
+processes the steps of which he is sure to forget before he has
+reached the conclusion, it is much better that he should turn to
+another method, and try to understand the subject by means of
+well-chosen illustrations derived from subjects with which he is more
+familiar.
+
+We all know how much more popular the illustrative method of
+exposition is found, than that in which bare processes of reasoning
+and calculation form the principal subject of discourse.
+
+Now a truly scientific illustration is a method to enable the mind to
+grasp some conception or law in one branch of science, by placing
+before it a conception or a law in a different branch of science, and
+directing the mind to lay hold of that mathematical form which is
+common to the corresponding ideas in the two sciences, leaving out of
+account for the present the difference between the physical nature of
+the real phenomena.
+
+The correctness of such an illustration depends on whether the two
+systems of ideas which are compared together are really analogous in
+form, or whether, in other words, the corresponding physical
+quantities really belong to the same mathematical class.  When this
+condition is fulfilled, the illustration is not only convenient for
+teaching science in a pleasant and easy manner, but the recognition of
+the formal analogy between the two systems of ideas leads to a
+knowledge of both, more profound than could be obtained by studying
+each system separately.
+
+There are men who, when any relation or law, however complex, is put
+before them in a symbolical form, can grasp its full meaning as a
+relation among abstract quantities.  Such men sometimes treat with
+indifference the further statement that quantities actually exist in
+nature which fulfil this relation.  The mental image of the concrete
+reality seems rather to disturb than to assist their contemplations.
+But the great majority of mankind are utterly unable, without long
+training, to retain in their minds the unembodied symbols of the pure
+mathematician, so that, if science is ever to become popular, and yet
+remain scientific, it must be by a profound study and a copious
+application of those principles of the mathematical classification of
+quantities which, as we have seen, lie at the root of every truly
+scientific illustration.
+
+There are, as I have said, some minds which can go on contemplating
+with satisfaction pure quantities presented to the eye by symbols, and
+to the mind in a form which none but mathematicians can conceive.
+
+There are others who feel more enjoyment in following geometrical
+forms, which they draw on paper, or build up in the empty space before
+them.
+
+Others, again, are not content unless they can project their whole
+physical energies into the scene which they conjure up.  They learn at
+what a rate the planets rush through space, and they experience a
+delightful feeling of exhilaration.  They calculate the forces with
+which the heavenly bodies pull at one another, and they feel their own
+muscles straining with the effort.
+
+To such men momentum, energy, mass are not mere abstract expressions
+of the results of scientific inquiry.  They are words of power, which
+stir their souls like the memories of childhood.
+
+For the sake of persons of these different types, scientific truth
+should be presented in different forms, and should be regarded as
+equally scientific whether it appears in the robust form and the vivid
+colouring of a physical illustration, or in the tenuity and paleness
+of a symbolical expression.
+
+Time would fail me if I were to attempt to illustrate by examples the
+scientific value of the classification of quantities.  I shall only
+mention the name of that important class of magnitudes having
+direction in space which Hamilton has called vectors, and which form
+the subject-matter of the Calculus of Quaternions, a branch of
+mathematics which, when it shall have been thoroughly understood by
+men of the illustrative type, and clothed by them with physical
+imagery, will become, perhaps under some new name, a most powerful
+method of communicating truly scientific knowledge to persons
+apparently devoid of the calculating spirit.
+
+The mutual action and reaction between the different departments of
+human thought is so interesting to the student of scientific progress,
+that, at the risk of still further encroaching on the valuable time of
+the Section, I shall say a few words on a branch of physics which not
+very long ago would have been considered rather a branch of
+metaphysics.  I mean the atomic theory, or, as it is now called, the
+molecular theory of the constitution of bodies.
+
+Not many years ago if we had been asked in what regions of physical
+science the advance of discovery was least apparent, we should have
+pointed to the hopelessly distant fixed stars on the one hand, and to
+the inscrutable delicacy of the texture of material bodies on the
+other.
+
+Indeed, if we are to regard Comte as in any degree representing the
+scientific opinion of his time, the research into what takes place
+beyond our own solar system seemed then to be exceedingly unpromising,
+if not altogether illusory.
+
+The opinion that the bodies which we see and handle, which we can set
+in motion or leave at rest, which we can break in pieces and destroy,
+are composed of smaller bodies which we cannot see or handle, which
+are always in motion, and which can neither be stopped nor broken in
+pieces, nor in any way destroyed or deprived of the least of their
+properties, was known by the name of the Atomic theory.  It was
+associated with the names of Democritus, Epicurus, and Lucretius, and
+was commonly supposed to admit the existence only of atoms and void,
+to the exclusion of any other basis of things from the universe.
+
+In many physical reasonings and mathematical calculations we are
+accustomed to argue as if such substances as air, water, or metal,
+which appear to our senses uniform and continuous, were strictly and
+mathematically uniform and continuous.
+
+We know that we can divide a pint of water into many millions of
+portions, each of which is as fully endowed with all the properties of
+water as the whole pint was; and it seems only natural to conclude
+that we might go on subdividing the water for ever, just as we can
+never come to a limit in subdividing the space in which it is
+contained.  We have heard how Faraday divided a grain of gold into an
+inconceivable number of separate particles, and we may see Dr Tyndall
+produce from a mere suspicion of nitrite of butyle an immense cloud,
+the minute visible portion of which is still cloud, and therefore must
+contain many molecules of nitrite of butyle.
+
+But evidence from different and independent sources is now crowding in
+upon us which compels us to admit that if we could push the process of
+subdivision still further we should come to a limit, because each
+portion would then contain only one molecule, an individual body, one
+and indivisible, unalterable by any power in nature.
+
+Even in our ordinary experiments on very finely divided matter we find
+that the substance is beginning to lose the properties which it
+exhibits when in a large mass, and that effects depending on the
+individual action of molecules are beginning to become prominent.
+
+The study of these phenomena is at present the path which leads to the
+development of molecular science.
+
+That superficial tension of liquids which is called capillary
+attraction is one of these phenomena.  Another important class of
+phenomena are those which are due to that motion of agitation by which
+the molecules of a liquid or gas are continually working their way
+from one place to another, and continually changing their course, like
+people hustled in a crowd.
+
+On this depends the rate of diffusion of gases and liquids through
+each other, to the study of which, as one of the keys of molecular
+science, that unwearied inquirer into nature's secrets, the late Prof.
+Graham, devoted such arduous labour.
+
+The rate of electrolytic conduction is, according to Wiedemann's
+theory, influenced by the same cause; and the conduction of heat in
+fluids depends probably on the same kind of action.  In the case of
+gases, a molecular theory has been developed by Clausius and others,
+capable of mathematical treatment, and subjected to experimental
+investigation; and by this theory nearly every known mechanical
+property of gases has been explained on dynamical principles; so that
+the properties of individual gaseous molecules are in a fair way to
+become objects of scientific research.
+
+Now Mr Stoney has pointed out[1] that the numerical results of
+experiments on gases render it probable that the mean distance of
+their particles at the ordinary temperature and pressure is a quantity
+of the same order of magnitude as a millionth of a millimetre, and Sir
+William Thomson has since[2] shewn, by several independent lines of
+argument, drawn from phenomena so different in themselves as the
+electrification of metals by contact, the tension of soap-bubbles, and
+the friction of air, that in ordinary solids and liquids the average
+distance between contiguous molecules is less than the
+hundred-millionth, and greater than the two-thousand-millionth of a
+centimetre.
+
+[1] _Phil. Mag._, Aug. 1868.
+[2] _Nature_, March 31, 1870.
+
+These, of course, are exceedingly rough estimates, for they are
+derived from measurements some of which are still confessedly very
+rough; but if at the present time, we can form even a rough plan for
+arriving at results of this kind, we may hope that, as our means of
+experimental inquiry become more accurate and more varied, our
+conception of a molecule will become more definite, so that we may be
+able at no distant period to estimate its weight with a greater degree
+of precision.
+
+A theory, which Sir W. Thomson has founded on Helmholtz's splendid
+hydrodynamical theorems, seeks for the properties of molecules in the
+ring vortices of a uniform, frictionless, incompressible fluid.  Such
+whirling rings may be seen when an experienced smoker sends out a
+dexterous puff of smoke into the still air, but a more evanescent
+phenomenon it is difficult to conceive.  This evanescence is owing to
+the viscosity of the air; but Helmholtz has shewn that in a perfect
+fluid such a whirling ring, if once generated, would go on whirling
+for ever, would always consist of the very same portion of the fluid
+which was first set whirling, and could never be cut in two by any
+natural cause.  The generation of a ring-vortex is of course equally
+beyond the power of natural causes, but once generated, it has the
+properties of individuality, permanence in quantity, and
+indestructibility.  It is also the recipient of impulse and of energy,
+which is all we can affirm of matter; and these ring-vortices are
+capable of such varied connexions and knotted self-involutions, that
+the properties of differently knotted vortices must be as different as
+those of different kinds of molecules can be.
+
+If a theory of this kind should be found, after conquering the
+enormous mathematical difficulties of the subject, to represent in any
+degree the actual properties of molecules, it will stand in a very
+different scientific position from those theories of molecular action
+which are formed by investing the molecule with an arbitrary system of
+central forces invented expressly to account for the observed
+phenomena.
+
+In the vortex theory we have nothing arbitrary, no central forces or
+occult properties of any other kind.  We have nothing but matter and
+motion, and when the vortex is once started its properties are all
+determined from the original impetus, and no further assumptions are
+possible.
+
+Even in the present undeveloped state of the theory, the contemplation
+of the individuality and indestructibility of a ring-vortex in a
+perfect fluid cannot fail to disturb the commonly received opinion
+that a molecule, in order to be permanent, must be a very hard body.
+
+In fact one of the first conditions which a molecule must fulfil is,
+apparently, inconsistent with its being a single hard body.  We know
+from those spectroscopic researches which have thrown so much light on
+different branches of science, that a molecule can be set into a state
+of internal vibration, in which it gives off to the surrounding medium
+light of definite refrangibility--light, that is, of definite
+wave-length and definite period of vibration.  The fact that all the
+molecules (say, of hydrogen) which we can procure for our experiments,
+when agitated by heat or by the passage of an electric spark, vibrate
+precisely in the same periodic time, or, to speak more accurately,
+that their vibrations are composed of a system of simple vibrations
+having always the same periods, is a very remarkable fact.
+
+I must leave it to others to describe the progress of that splendid
+series of spectroscopic discoveries by which the chemistry of the
+heavenly bodies has been brought within the range of human inquiry.  I
+wish rather to direct your attention to the fact that, not only has
+every molecule of terrestrial hydrogen the same system of periods of
+free vibration, but that the spectroscopic examination of the light of
+the sun and stars shews that, in regions the distance of which we can
+only feebly imagine, there are molecules vibrating in as exact unison
+with the molecules of terrestrial hydrogen as two tuning-forks tuned
+to concert pitch, or two watches regulated to solar time.
+
+Now this absolute equality in the magnitude of quantities, occurring
+in all parts of the universe, is worth our consideration.
+
+The dimensions of individual natural bodies are either quite
+indeterminate, as in the case of planets, stones, trees, &c., or they
+vary within moderate limits, as in the case of seeds, eggs, &c.; but
+even in these cases small quantitative differences are met with which
+do not interfere with the essential properties of the body.
+
+Even crystals, which are so definite in geometrical form, are variable
+with respect to their absolute dimensions.
+
+Among the works of man we sometimes find a certain degree of
+uniformity.
+
+There is a uniformity among the different bullets which are cast in
+the same mould, and the different copies of a book printed from the
+same type.
+
+If we examine the coins, or the weights and measures, of a civilized
+country, we find a uniformity, which is produced by careful adjustment
+to standards made and provided by the state.  The degree of uniformity
+of these national standards is a measure of that spirit of justice in
+the nation which has enacted laws to regulate them and appointed
+officers to test them.
+
+This subject is one in which we, as a scientific body, take a warm
+interest; and you are all aware of the vast amount of scientific work
+which has been expended, and profitably expended, in providing weights
+and measures for commercial and scientific purposes.
+
+The earth has been measured as a basis for a permanent standard of
+length, and every property of metals has been investigated to guard
+against any alteration of the material standards when made.  To weigh
+or measure any thing with modern accuracy, requires a course of
+experiment and calculation in which almost every branch of physics and
+mathematics is brought into requisition.
+
+Yet, after all, the dimensions of our earth and its time of rotation,
+though, relatively to our present means of comparison, very permanent,
+are not so by any physical necessity.  The earth might contract by
+cooling, or it might be enlarged by a layer of meteorites falling on
+it, or its rate of revolution might slowly slacken, and yet it would
+continue to be as much a planet as before.
+
+But a molecule, say of hydrogen, if either its mass or its time of
+vibration were to be altered in the least, would no longer be a
+molecule of hydrogen.
+
+If, then, we wish to obtain standards of length, time, and mass which
+shall be absolutely permanent, we must seek them not in the
+dimensions, or the motion, or the mass of our planet, but in the
+wave-length, the period of vibration, and the absolute mass of these
+imperishable and unalterable and perfectly similar molecules.
+
+When we find that here, and in the starry heavens, there are
+innumerable multitudes of little bodies of exactly the same mass, so
+many, and no more, to the grain, and vibrating in exactly the same
+time, so many times, and no more, in a second, and when we reflect
+that no power in nature can now alter in the least either the mass or
+the period of any one of them, we seem to have advanced along the path
+of natural knowledge to one of those points at which we must accept
+the guidance of that faith by which we understand that "that which is
+seen was not made of things which do appear."
+
+One of the most remarkable results of the progress of molecular
+science is the light it has thrown on the nature of irreversible
+processes--processes, that is, which always tend towards and never
+away from a certain limiting state.  Thus, if two gases be put into
+the same vessel, they become mixed, and the mixture tends continually
+to become more uniform.  If two unequally heated portions of the same
+gas are put into the vessel, something of the kind takes place, and
+the whole tends to become of the same temperature.  If two unequally
+heated solid bodies be placed in contact, a continual approximation of
+both to an intermediate temperature takes place.
+
+In the case of the two gases, a separation may be effected by chemical
+means; but in the other two cases the former state of things cannot be
+restored by any natural process.
+
+In the case of the conduction or diffusion of heat the process is not
+only irreversible, but it involves the irreversible diminution of that
+part of the whole stock of thermal energy which is capable of being
+converted into mechanical work.
+
+This is Thomson's theory of the irreversible dissipation of energy,
+and it is equivalent to the doctrine of Clausius concerning the growth
+of what he calls Entropy.
+
+The irreversible character of this process is strikingly embodied in
+Fourier's theory of the conduction of heat, where the formulae
+themselves indicate, for all positive values of the time, a possible
+solution which continually tends to the form of a uniform diffusion of
+heat.
+
+But if we attempt to ascend the stream of time by giving to its symbol
+continually diminishing values, we are led up to a state of things in
+which the formula has what is called a critical value; and if we
+inquire into the state of things the instant before, we find that the
+formula becomes absurd.
+
+We thus arrive at the conception of a state of things which cannot be
+conceived as the physical result of a previous state of things, and we
+find that this critical condition actually existed at an epoch not in
+the utmost depths of a past eternity, but separated from the present
+time by a finite interval.
+
+This idea of a beginning is one which the physical researches of
+recent times have brought home to us, more than any observer of the
+course of scientific thought in former times would have had reason to
+expect.
+
+But the mind of man is not, like Fourier's heated body, continually
+settling down into an ultimate state of quiet uniformity, the
+character of which we can already predict; it is rather like a tree,
+shooting out branches which adapt themselves to the new aspects of the
+sky towards which they climb, and roots which contort themselves among
+the strange strata of the earth into which they delve.  To us who
+breathe only the spirit of our own age, and know only the
+characteristics of contemporary thought, it is as impossible to
+predict the general tone of the science of the future as it is to
+anticipate the particular discoveries which it will make.
+
+Physical research is continually revealing to us new features of
+natural processes, and we are thus compelled to search for new forms
+of thought appropriate to these features.  Hence the importance of a
+careful study of those relations between mathematics and Physics which
+determine the conditions under which the ideas derived from one
+department of physics may be safely used in forming ideas to be
+employed in a new department.
+
+The figure of speech or of thought by which we transfer the language
+and ideas of a familiar science to one with which we are less
+acquainted may be called Scientific Metaphor.
+
+Thus the words Velocity, Momentum, Force, &c. have acquired certain
+precise meanings in Elementary Dynamics.  They are also employed in
+the Dynamics of a Connected System in a sense which, though perfectly
+analogous to the elementary sense, is wider and more general.
+
+These generalized forms of elementary ideas may be called metaphorical
+terms in the sense in which every abstract term is metaphorical.  The
+characteristic of a truly scientific system of metaphors is that each
+term in its metaphorical use retains all the formal relations to the
+other terms of the system which it had in its original use.  The
+method is then truly scientific--that is, not only a legitimate
+product of science, but capable of generating science in its turn.
+
+There are certain electrical phenomena, again, which are connected
+together by relations of the same form as those which connect
+dynamical phenomena.  To apply to these the phrases of dynamics with
+proper distinctions and provisional reservations is an example of a
+metaphor of a bolder kind; but it is a legitimate metaphor if it
+conveys a true idea of the electrical relations to those who have been
+already trained in dynamics.
+
+Suppose, then, that we have successfully introduced certain ideas
+belonging to an elementary science by applying them metaphorically to
+some new class of phenomena.  It becomes an important philosophical
+question to determine in what degree the applicability of the old
+ideas to the new subject may be taken as evidence that the new
+phenomena are physically similar to the old.
+
+The best instances for the determination of this question are those in
+which two different explanations have been given of the same thing.
+
+The most celebrated case of this kind is that of the corpuscular and
+the undulatory theories of light.  Up to a certain point the phenomena
+of light are equally well explained by both; beyond this point, one of
+them fails.
+
+To understand the true relation of these theories in that part of the
+field where they seem equally applicable we must look at them in the
+light which Hamilton has thrown upon them by his discovery that to
+every brachistochrone problem there corresponds a problem of free
+motion, involving different velocities and times, but resulting in the
+same geometrical path.  Professor Tait has written a very interesting
+paper on this subject.
+
+According to a theory of electricity which is making great progress in
+Germany, two electrical particles act on one another directly at a
+distance, but with a force which, according to Weber, depends on their
+relative velocity, and according to a theory hinted at by Gauss, and
+developed by Riemann, Lorenz, and Neumann, acts not instantaneously,
+but after a time depending on the distance.  The power with which this
+theory, in the hands of these eminent men, explains every kind of
+electrical phenomena must be studied in order to be appreciated.
+
+Another theory of electricity, which I prefer, denies action at a
+distance and attributes electric action to tensions and pressures in
+an all-pervading medium, these stresses being the same in kind with
+those familiar to engineers, and the medium being identical with that
+in which light is supposed to be propagated.
+
+Both these theories are found to explain not only the phenomena by the
+aid of which they were originally constructed, but other phenomena,
+which were not thought of or perhaps not known at the time; and both
+have independently arrived at the same numerical result, which gives
+the absolute velocity of light in terms of electrical quantities.
+
+That theories apparently so fundamentally opposed should have so large
+a field of truth common to both is a fact the philosophical importance
+of which we cannot fully appreciate till we have reached a scientific
+altitude from which the true relation between hypotheses so different
+can be seen.
+
+I shall only make one more remark on the relation between Mathematics
+and Physics.  In themselves, one is an operation of the mind, the
+other is a dance of molecules.  The molecules have laws of their own,
+some of which we select as most intelligible to us and most amenable
+to our calculation.  We form a theory from these partial data, and we
+ascribe any deviation of the actual phenomena from this theory to
+disturbing causes.  At the same time we confess that what we call
+disturbing causes are simply those parts of the true circumstances
+which we do not know or have neglected, and we endeavour in future to
+take account of them.  We thus acknowledge that the so-called
+disturbance is a mere figment of the mind, not a fact of nature, and
+that in natural action there is no disturbance.
+
+But this is not the only way in which the harmony of the material with
+the mental operation may be disturbed.  The mind of the mathematician
+is subject to many disturbing causes, such as fatigue, loss of memory,
+and hasty conclusions; and it is found that, from these and other
+causes, mathematicians make mistakes.
+
+I am not prepared to deny that, to some mind of a higher order than
+ours, each of these errors might be traced to the regular operation of
+the laws of actual thinking; in fact we ourselves often do detect, not
+only errors of calculation, but the causes of these errors.  This,
+however, by no means alters our conviction that they are errors, and
+that one process of thought is right and another process wrong.  I
+
+One of the most profound mathematicians and thinkers of our time, the
+late George Boole, when reflecting on the precise and almost
+mathematical character of the laws of right thinking as compared with
+the exceedingly perplexing though perhaps equally determinate laws of
+actual and fallible thinking, was led to another of those points of
+view from which Science seems to look out into a region beyond her own
+domain.
+
+"We must admit," he says, "that there exist laws" (of thought) "which
+even the rigour of their mathematical forms does not preserve from
+violation.  We must ascribe to them an authority, the essence of which
+does not consist in power, a supremacy which the analogy of the
+inviolable order of the natural world in no way assists us to
+comprehend."
+
+
+
+
+Introductory Lecture on Experimental Physics.
+
+James Clerk Maxwell
+
+
+The University of Cambridge, in accordance with that law of its
+evolution, by which, while maintaining the strictest continuity
+between the successive phases of its history, it adapts itself with
+more or less promptness to the requirements of the times, has lately
+instituted a course of Experimental Physics.  This course of study,
+while it requires us to maintain in action all those powers of
+attention and analysis which have been so long cultivated in the
+University, calls on us to exercise our senses in observation, and our
+hands in manipulation.  The familiar apparatus of pen, ink, and paper
+will no longer be sufficient for us, and we shall require more room
+than that afforded by a seat at a desk, and a wider area than that of
+the black board.  We owe it to the munificence of our Chancellor,
+that, whatever be the character in other respects of the experiments
+which we hope hereafter to conduct, the material facilities for their
+full development will be upon a scale which has not hitherto been
+surpassed.
+
+The main feature, therefore, of Experimental Physics at Cambridge is
+the Devonshire Physical Laboratory, and I think it desirable that on
+the present occasion, before we enter on the details of any special
+study, we should consider by what means we, the University of
+Cambridge, may, as a living body, appropriate and vitalise this new
+organ, the outward shell of which we expect soon to rise before us.
+The course of study at this University has always included Natural
+Philosophy, as well as Pure Mathematics.  To diffuse a sound knowledge
+of Physics, and to imbue the minds of our students with correct
+dynamical principles, have been long regarded as among our highest
+functions, and very few of us can now place ourselves in the mental
+condition in which even such philosophers as the great Descartes were
+involved in the days before Newton had announced the true laws of the
+motion of bodies.  Indeed the cultivation and diffusion of sound
+dynamical ideas has already effected a great change in the language
+and thoughts even of those who make no pretensions to science, and we
+are daily receiving fresh proofs that the popularisation of scientific
+doctrines is producing as great an alteration in the mental state of
+society as the material applications of science are effecting in its
+outward life.  Such indeed is the respect paid to science, that the
+most absurd opinions may become current, provided they are expressed
+in language, the sound of which recals some well-known scientific
+phrase.  If society is thus prepared to receive all kinds of
+scientific doctrines, it is our part to provide for the diffusion and
+cultivation, not only of true scientific principles, but of a spirit
+of sound criticism, founded on an examination of the evidences on
+which statements apparently scientific depend.
+
+When we shall be able to employ in scientific education, not only the
+trained attention of the student, and his familiarity with symbols,
+but the keenness of his eye, the quickness of his ear, the delicacy of
+his touch, and the adroitness of his fingers, we shall not only extend
+our influence over a class of men who are not fond of cold
+abstractions, but, by opening at once all the gateways of knowledge,
+we shall ensure the association of the doctrines of science with those
+elementary sensations which form the obscure background of all our
+conscious thoughts, and which lend a vividness and relief to ideas,
+which, when presented as mere abstract terms, are apt to fade entirely
+from the memory.
+
+In a course of Experimental Physics we may consider either the Physics
+or the Experiments as the leading feature.  We may either employ the
+experiments to illustrate the phenomena of a particular branch of
+Physics, or we may make some physical research in order to exemplify a
+particular experimental method.  In the order of time, we should
+begin, in the Lecture Room, with a course of lectures on some branch
+of Physics aided by experiments of illustration, and conclude, in the
+Laboratory, with a course of experiments of research.
+
+Let me say a few words on these two classes of
+experiments,--Experiments of Illustration and Experiments of Research.
+The aim of an experiment of illustration is to throw light upon some
+scientific idea so that the student may be enabled to grasp it.  The
+circumstances of the experiment are so arranged that the phenomenon
+which we wish to observe or to exhibit is brought into prominence,
+instead of being obscured and entangled among other phenomena, as it
+is when it occurs in the ordinary course of nature.  To exhibit
+illustrative experiments, to encourage others to make them, and to
+cultivate in every way the ideas on which they throw light, forms an
+important part of our duty.  The simpler the materials of an
+illustrative experiment, and the more familiar they are to the
+student, the more thoroughly is he likely to acquire the idea which it
+is meant to illustrate.  The educational value of such experiments is
+often inversely proportional to the complexity of the apparatus.  The
+student who uses home-made apparatus, which is always going wrong,
+often learns more than one who has the use of carefully adjusted
+instruments, to which he is apt to trust, and which he dares not take
+to pieces.
+
+It is very necessary that those who are trying to learn from books the
+facts of physical science should be enabled by the help of a few
+illustrative experiments to recognise these facts when they meet with
+them out of doors.  Science appears to us with a very different aspect
+after we have found out that it is not in lecture rooms only, and by
+means of the electric light projected on a screen, that we may witness
+physical phenomena, but that we may find illustrations of the highest
+doctrines of science in games and gymnastics, in travelling by land
+and by water, in storms of the air and of the sea, and wherever there
+is matter in motion.
+
+This habit of recognising principles amid the endless variety of their
+action can never degrade our sense of the sublimity of nature, or mar
+our enjoyment of its beauty.  On the contrary, it tends to rescue our
+scientific ideas from that vague condition in which we too often leave
+them, buried among the other products of a lazy credulity, and to
+raise them into their proper position among the doctrines in which our
+faith is so assured, that we are ready at all times to act on them.
+
+Experiments of illustration may be of very different kinds.  Some may
+be adaptations of the commonest operations of ordinary life, others
+may be carefully arranged exhibitions of some phenomenon which occurs
+only under peculiar conditions.  They all, however, agree in this,
+that their aim is to present some phenomenon to the senses of the
+student in such a way that he may associate with it the appropriate
+scientific idea.  When he has grasped this idea, the experiment which
+illustrates it has served its purpose.
+
+In an experiment of research, on the other hand, this is not the
+principal aim.  It is true that an experiment, in which the principal
+aim is to see what happens under certain conditions, may be regarded
+as an experiment of research by those who are not yet familiar with
+the result, but in experimental researches, strictly so called, the
+ultimate object is to measure something which we have already seen--to
+obtain a numerical estimate of some magnitude.
+
+Experiments of this class--those in which measurement of some kind is
+involved, are the proper work of a Physical Laboratory.  In every
+experiment we have first to make our senses familiar with the
+phenomenon, but we must not stop here, we must find out which of its
+features are capable of measurement, and what measurements are
+required in order to make a complete specification of the phenomenon.
+We must then make these measurements, and deduce from them the result
+which we require to find.
+
+This characteristic of modern experiments--that they consist
+principally of measurements,--is so prominent, that the opinion seems
+to have got abroad, that in a few years all the great physical
+constants will have been approximately estimated, and that the only
+occupation which will then be left to men of science will be to carry
+on these measurements to another place of decimals.
+
+If this is really the state of things to which we are approaching, our
+Laboratory may perhaps become celebrated as a place of conscientious
+labour and consummate skill, but it will be out of place in the
+University, and ought rather to be classed with the other great
+workshops of our country, where equal ability is directed to more
+useful ends.
+
+But we have no right to think thus of the unsearchable riches of
+creation, or of the untried fertility of those fresh minds into which
+these riches will continue to be poured.  It may possibly be true
+that, in some of those fields of discovery which lie open to such
+rough observations as can be made without artificial methods, the
+great explorers of former times have appropriated most of what is
+valuable, and that the gleanings which remain are sought after, rather
+for their abstruseness, than for their intrinsic worth.  But the
+history of science shews that even during that phase of her progress
+in which she devotes herself to improving the accuracy of the
+numerical measurement of quantities with which she has long been
+familiar, she is preparing the materials for the subjugation of new
+regions, which would have remained unknown if she had been contented
+with the rough methods of her early pioneers.  I might bring forward
+instances gathered from every branch of science, shewing how the
+labour of careful measurement has been rewarded by the discovery of
+new fields of research, and by the development of new scientific
+ideas.  But the history of the science of terrestrial magnetism
+affords us a sufficient example of what may be done by Experiments in
+Concert, such as we hope some day to perform in our Laboratory.
+
+That celebrated traveller, Humboldt, was profoundly impressed with the
+scientific value of a combined effort to be made by the observers of
+all nations, to obtain accurate measurements of the magnetism of the
+earth; and we owe it mainly to his enthusiasm for science, his great
+reputation and his wide-spread influence, that not only private men of
+science, but the governments of most of the civilised nations, our own
+among the number, were induced to take part in the enterprise.  But
+the actual working out of the scheme, and the arrangements by which
+the labours of the observers were so directed as to obtain the best
+results, we owe to the great mathematician Gauss, working along with
+Weber, the future founder of the science of electro-magnetic
+measurement, in the magnetic observatory of Gottingen, and aided by
+the skill of the instrument-maker Leyser.  These men, however, did not
+work alone.  Numbers of scientific men joined the Magnetic Union,
+learned the use of the new instruments and the new methods of reducing
+the observations; and in every city of Europe you might see them, at
+certain stated times, sitting, each in his cold wooden shed, with his
+eye fixed at the telescope, his ear attentive to the clock, and his
+pencil recording in his note-book the instantaneous position of the
+suspended magnet.
+
+Bacon's conception of "Experiments in concert" was thus realised, the
+scattered forces of science were converted into a regular army, and
+emulation and jealousy became out of place, for the results obtained
+by any one observer were of no value till they were combined with
+those of the others.
+
+The increase in the accuracy and completeness of magnetic observations
+which was obtained by the new method, opened up fields of research
+which were hardly suspected to exist by those whose observations of
+the magnetic needle had been conducted in a more primitive manner.  We
+must reserve for its proper place in our course any detailed
+description of the disturbances to which the magnetism of our planet
+is found to be subject.  Some of these disturbances are periodic,
+following the regular courses of the sun and moon.  Others are sudden,
+and are called magnetic storms, but, like the storms of the
+atmosphere, they have their known seasons of frequency.  The last and
+the most mysterious of these magnetic changes is that secular
+variation by which the whole character of the earth, as a great
+magnet, is being slowly modified, while the magnetic poles creep on,
+from century to century, along their winding track in the polar
+regions.
+
+We have thus learned that the interior of the earth is subject to the
+influences of the heavenly bodies, but that besides this there is a
+constantly progressive change going on, the cause of which is entirely
+unknown.  In each of the magnetic observatories throughout the world
+an arrangement is at work, by means of which a suspended magnet
+directs a ray of light on a preparred sheet of paper moved by
+clockwork.  On that paper the never-resting heart of the earth is now
+tracing, in telegraphic symbols which will one day be interpreted, a
+record of its pulsations and its flutterings, as well as of that slow
+but mighty working which warns us that we must not suppose that the
+inner history of our planet is ended.
+
+But this great experimental research on Terrestrial Magnetism produced
+lasting effects on the progress of science in general.  I need only
+mention one or two instances.  The new methods of measuring forces
+were successfully applied by Weber to the numerical determination of
+all the phenomena of electricity, and very soon afterwards the
+electric telegraph, by conferring a commercial value on exact
+numerical measurements, contributed largely to the advancement, as
+well as to the diffusion of scientific knowledge.
+
+But it is not in these more modern branches of science alone that this
+influence is felt.  It is to Gauss, to the Magnetic Union, and to
+magnetic observers in general, that we owe our deliverance from that
+absurd method of estimating forces by a variable standard which
+prevailed so long even among men of science.  It was Gauss who first
+based the practical measurement of magnetic force (and therefore of
+every other force) on those long established principles, which, though
+they are embodied in every dynamical equation, have been so generally
+set aside, that these very equations, though correctly given in our
+Cambridge textbooks, are usually explained there by assuming, in
+addition to the variable standard of force, a variable, and therefore
+illegal, standard of mass.
+
+Such, then, were some of the scientific results which followed in this
+case from bringing together mathematical power, experimental sagacity,
+and manipulative skill, to direct and assist the labours of a body of
+zealous observers.  If therefore we desire, for our own advantage and
+for the honour of our University, that the Devonshire Laboratory
+should be successful, we must endeavour to maintain it in living union
+with the other organs and faculties of our learned body.  We shall
+therefore first consider the relation in which we stand to those
+mathematical studies which have so long flourished among us, which
+deal with our own subjects, and which differ from our experimental
+studies only in the mode in which they are presented to the mind.
+
+There is no more powerful method for introducing knowledge into the
+mind than that of presenting it in as many different ways as we can.
+When the ideas, after entering through different gateways, effect a
+junction in the citadel of the mind, the position they occupy becomes
+impregnable.  Opticians tell us that the mental combination of the
+views of an object which we obtain from stations no further apart than
+our two eyes is sufficient to produce in our minds an impression of
+the solidity of the object seen; and we find that this impression is
+produced even when we are aware that we are really looking at two flat
+pictures placed in a stereoscope.  It is therefore natural to expect
+that the knowledge of physical science obtained by the combined use of
+mathematical analysis and experimental research will be of a more
+solid, available, and enduring kind than that possessed by the mere
+mathematician or the mere experimenter.
+
+But what will be the effect on the University, if men Pursuing that
+course of reading which has produced so many distinguished Wranglers,
+turn aside to work experiments?  Will not their attendance at the
+Laboratory count not merely as time withdrawn from their more
+legitimate studies, but as the introduction of a disturbing element,
+tainting their mathematical conceptions with material imagery, and
+sapping their faith in the formulae of the textbook?  Besides this, we
+have already heard complaints of the undue extension of our studies,
+and of the strain put upon our questionists by the weight of learning
+which they try to carry with them into the Senate-House.  If we now
+ask them to get up their subjects not only by books and writing, but
+at the same time by observation and manipulation, will they not break
+down altogether?  The Physical Laboratory, we are told, may perhaps be
+useful to those who are going out in Natural Science, and who do
+not take in Mathematics, but to attempt to combine both kinds of study
+during the time of residence at the University is more than one mind
+can bear.
+
+No doubt there is some reason for this feeling.  Many of us have
+already overcome the initial difficulties of mathematical training.
+When we now go on with our study, we feel that it requires exertion
+and involves fatigue, but we are confident that if we only work hard
+our progress will be certain.
+
+Some of us, on the other hand, may have had some experience of the
+routine of experimental work.  As soon as we can read scales, observe
+times, focus telescopes, and so on, this kind of work ceases to
+require any great mental effort.  We may perhaps tire our eyes and
+weary our backs, but we do not greatly fatigue our minds.
+
+It is not till we attempt to bring the theoretical part of our
+training into contact with the practical that we begin to experience
+the full effect of what Faraday has called "mental inertia"--not only
+the difficulty of recognising, among the concrete objects before us,
+the abstract relation which we have learned from books, but the
+distracting pain of wrenching the mind away from the symbols to the
+objects, and from the objects back to the symbols.  This however is
+the price we have to pay for new ideas.
+
+But when we have overcome these difficulties, and successfully bridged
+over the gulph between the abstract and the concrete, it is not a mere
+piece of knowledge that we have obtained: we have acquired the
+rudiment of a permanent mental endowment.  When, by a repetition of
+efforts of this kind, we have more fully developed the scientific
+faculty, the exercise of this faculty in detecting scientific
+principles in nature, and in directing practice by theory, is no
+longer irksome, but becomes an unfailing source of enjoyment, to which
+we return so often, that at last even our careless thoughts begin to
+run in a scientific channel.
+
+I quite admit that our mental energy is limited in quantity, and I
+know that many zealous students try to do more than is good for them.
+But the question about the introduction of experimental study is not
+entirely one of quantity.  It is to a great extent a question of
+distribution of energy.  Some distributions of energy, we know, are
+more useful than others, because they are more available for those
+purposes which we desire to accomplish.
+
+Now in the case of study, a great part of our fatigue often arises,
+not from those mental efforts by which we obtain the mastery of the
+subject, but from those which are spent in recalling our wandering
+thoughts; and these efforts of attention would be much less fatiguing
+if the disturbing force of mental distraction could be removed.
+
+This is the reason why a man whose soul is in his work always makes
+more progress than one whose aim is something not immediately
+connected with his occupation.  In the latter case the very motive of
+which he makes use to stimulate his flagging powers becomes the means
+of distracting his mind from the work before him.
+
+There may be some mathematicians who pursue their studies entirely for
+their own sake.  Most men, however, think that the chief use of
+mathematics is found in the interpretation of nature.  Now a man who
+studies a piece of mathematics in order to understand some natural
+phenomenon which he has seen, or to calculate the best arrangement of
+some experiment which he means to make, is likely to meet with far
+less distraction of mind than if his sole aim had been to sharpen his
+mind for the successful practice of the Law, or to obtain a high place
+in the Mathematical Tripos.
+
+I have known men, who when they were at school, never could see the
+good of mathematics, but who, when in after life they made this
+discovery, not only became eminent as scientific engineers, but made
+considerable progress in the study of abstract mathematics.  If our
+experimental course should help any of you to see the good of
+mathematics, it will relieve us of much anxiety, for it will not only
+ensure the success of your future studies, but it will make it much
+less likely that they will prove injurious to your health.
+
+
+But why should we labour to prove the advantage of practical science
+to the University?  Let us rather speak of the help which the
+University may give to science, when men well trained in mathematics
+and enjoying the advantages of a well-appointed Laboratory, shall
+unite their efforts to carry out some experimental research which no
+solitary worker could attempt.
+
+At first it is probable that our principal experimental work must be
+the illustration of particular branches of science, but as we go on we
+must add to this the study of scientific methods, the same method
+being sometimes illustrated by its application to researches belonging
+to different branches of science.
+
+We might even imagine a course of experimental study the arrangement
+of which should be founded on a classification of methods, and not on
+that of the objects of investigation.  A combination of the two plans
+seems to me better than either, and while we take every opportunity of
+studying methods, we shall take care not to dissociate the method from
+the scientific research to which it is applied, and to which it owes
+its value.
+
+We shall therefore arrange our lectures according to the
+classification of the principal natural phenomena, such as heat,
+electricity, magnetism and so on.
+
+In the laboratory, on the other hand, the place of the different
+instruments will be determined by a classification according to
+methods, such as weighing and measuring, observations of time, optical
+and electrical methods of observation, and so on.
+
+The determination of the experiments to be performed at a particular
+time must often depend upon the means we have at command, and in the
+case of the more elaborate experiments, this may imply a long time of
+preparation, during which the instruments, the methods, and the
+observers themselves, are being gradually fitted for their work.  When
+we have thus brought together the requisites, both material and
+intellectual, for a particular experiment, it may sometimes be
+desirable that before the instruments are dismounted and the observers
+dispersed, we should make some other experiment, requiring the same
+method, but dealing perhaps with an entirely different class of
+physical phenomena.
+
+Our principal work, however, in the Laboratory must be to acquaint
+ourselves with all kinds of scientific methods, to compare them, and
+to estimate their value.  It will, I think, be a result worthy of our
+University, and more likely to be accomplished here than in any
+private laboratory, if, by the free and full discussion of the
+relative value of different scientific procedures, we succeed in
+forming a school of scientific criticism, and in assisting the
+development of the doctrine of method.
+
+But admitting that a practical acquaintance with the methods of
+Physical Science is an essential part of a mathematical and scientific
+education, we may be asked whether we are not attributing too much
+importance to science altogether as part of a liberal education.
+
+Fortunately, there is no question here whether the University should
+continue to be a place of liberal education, or should devote itself
+to preparing young men for particular professions.  Hence though some
+of us may, I hope, see reason to make the pursuit of science the main
+business of our lives, it must be one of our most constant aims to
+maintain a living connexion between our work and the other liberal
+studies of Cambridge, whether literary, philological, historical or
+philosophical.
+
+There is a narrow professional spirit which may grow up among men of
+science, just as it does among men who practise any other special
+business.  But surely a University is the very place where we should
+be able to overcome this tendency of men to become, as it were,
+granulated into small worlds, which are all the more worldly for their
+very smallness.  We lose the advantage of having men of varied
+pursuits collected into one body, if we do not endeavour to imbibe
+some of the spirit even of those whose special branch of learning is
+different from our own.
+
+It is not so long ago since any man who devoted himself to geometry,
+or to any science requiring continued application, was looked upon as
+necessarily a misanthrope, who must have abandoned all human
+interests, and betaken himself to abstractions so far removed from the
+world of life and action that he has become insensible alike to the
+attractions of pleasure and to the claims of duty.
+
+In the present day, men of science are not looked upon with the same
+awe or with the same suspicion.  They are supposed to be in league
+with the material spirit of the age, and to form a kind of advanced
+Radical party among men of learning.
+
+We are not here to defend literary and historical studies.  We admit
+that the proper study of mankind is man.  But is the student of
+science to be withdrawn from the study of man, or cut off from every
+noble feeling, so long as he lives in intellectual fellowship with men
+who have devoted their lives to the discovery of truth, and the
+results of whose enquiries have impressed themselves on the ordinary
+speech and way of thinking of men who never heard their names?  Or is
+the student of history and of man to omit from his consideration the
+history of the origin and diffusion of those ideas which have produced
+so great a difference between one age of the world and another?
+
+It is true that the history of science is very different from the
+science of history.  We are not studying or attempting to study the
+working of those blind forces which, we are told, are operating on
+crowds of obscure people, shaking principalities and powers, and
+compelling reasonable men to bring events to pass in an order laid
+down by philosophers.
+
+The men whose names are found in the history of science are not mere
+hypothetical constituents of a crowd, to be reasoned upon only in
+masses.  We recognise them as men like ourselves, and their actions
+and thoughts, being more free from the influence of passion, and
+recorded more accurately than those of other men, are all the better
+materials for the study of the calmer parts of human nature.
+
+But the history of science is not restricted to the enumeration of
+successful investigations.  It has to tell of unsuccessful inquiries,
+and to explain why some of the ablest men have failed to find the key
+of knowledge, and how the reputation of others has only given a firmer
+footing to the errors into which they fell.
+
+The history of the development, whether normal or abnormal, of ideas
+is of all subjects that in which we, as thinking men, take the deepest
+interest.  But when the action of the mind passes out of the
+intellectual stage, in which truth and error are the alternatives,
+into the more violently emotional states of anger and passion, malice
+and envy, fury and madness; the student of science, though he is
+obliged to recognise the powerful influence which these wild forces
+have exercised on mankind, is perhaps in some measure disqualified
+from pursuing the study of this part of human nature.
+
+But then how few of us are capable of deriving profit from such
+studies.  We cannot enter into full sympathy with these lower phases
+of our nature without losing some of that antipathy to them which is
+our surest safeguard against a reversion to a meaner type, and we
+gladly return to the company of those illustrious men who by aspiring
+to noble ends, whether intellectual or practical, have risen above the
+region of storms into a clearer atmosphere, where there is no
+misrepresentation of opinion, nor ambiguity of expression, but where
+one mind comes into closest contact with another at the point where
+both approach nearest to the truth.
+
+
+I propose to lecture during this term on Heat, and, as our facilities
+for experimental work are not yet fully developed, I shall endeavour
+to place before you the relative position and scientific connexion of
+the different branches of the science, rather than to discuss the
+details of experimental methods.
+
+We shall begin with Thermometry, or the registration of temperatures,
+and Calorimetry, or the measurement of quantities of heat.  We shall
+then go on to Thermodynamics, which investigates the relations between
+the thermal properties of bodies and their other dynamical properties,
+in so far as these relations may be traced without any assumption as
+to the particular constitution of these bodies.
+
+The principles of Thermodynamics throw great light on all the
+phenomena of nature, and it is probable that many valuable
+applications of these principles have yet to be made; but we shall
+have to point out the limits of this science, and to shew that many
+problems in nature, especially those in which the Dissipation of
+Energy comes into play, are not capable of solution by the principles
+of Thermodynamics alone, but that in order to understand them, we are
+obliged to form some more definite theory of the constitution of
+bodies.
+
+Two theories of the constitution of bodies have struggled for victory
+with various fortunes since the earliest ages of speculation: one is
+the theory of a universal plenum, the other is that of atoms and void.
+
+The theory of the plenum is associated with the doctrine of
+mathematical continuity, and its mathematical methods are those of the
+Differential Calculus, which is the appropriate expression of the
+relations of continuous quantity.
+
+The theory of atoms and void leads us to attach more importance to the
+doctrines of integral numbers and definite proportions; but, in
+applying dynamical principles to the motion of immense numbers of
+atoms, the limitation of our faculties forces us to abandon the
+attempt to express the exact history of each atom, and to be content
+with estimating the average condition of a group of atoms large enough
+to be visible.  This method of dealing with groups of atoms, which I
+may call the statistical method, and which in the present state of our
+knowledge is the only available method of studying the properties of
+real bodies, involves an abandonment of strict dynamical principles,
+and an adoption of the mathematical methods belonging to the theory of
+probability.  It is probable that important results will be obtained
+by the application of this method, which is as yet little known and is
+not familiar to our minds.  If the actual history of Science had been
+different, and if the scientific doctrines most familiar to us had
+been those which must be expressed in this way, it is possible that we
+might have considered the existence of a certain kind of contingency a
+self-evident truth, and treated the doctrine of philosophical
+necessity as a mere sophism.
+
+About the beginning of this century, the properties of bodies were
+investigated by several distinguished French mathematicians on the
+hypothesis that they are systems of molecules in equilibrium.  The
+somewhat unsatisfactory nature of the results of these investigations
+produced, especially in this country, a reaction in favour of the
+opposite method of treating bodies as if they were, so far at least as
+our experiments are concerned, truly continuous.  This method, in the
+hands of Green, Stokes, and others, has led to results, the value of
+which does not at all depend on what theory we adopt as to the
+ultimate constitution of bodies.
+
+One very important result of the investigation of the properties of
+bodies on the hypothesis that they are truly continuous is that it
+furnishes us with a test by which we can ascertain, by experiments on
+a real body, to what degree of tenuity it must be reduced before it
+begins to give evidence that its properties are no longer the same as
+those of the body in mass.  Investigations of this kind, combined with
+a study of various phenomena of diffusion and of dissipation of
+energy, have recently added greatly to the evidence in favour of the
+hypothesis that bodies are systems of molecules in motion.
+
+I hope to be able to lay before you in the course of the term some of
+the evidence for the existence of molecules, considered as individual
+bodies having definite properties.  The molecule, as it is presented to
+the scientific imagination, is a very different body from any of those
+with which experience has hitherto made us acquainted.
+
+In the first place its mass, and the other constants which define its
+properties, are absolutely invariable; the individual molecule can
+neither grow nor decay, but remains unchanged amid all the changes of
+the bodies of which it may form a constituent.
+
+In the second place it is not the only molecule of its kind, for there
+are innumerable other molecules, whose constants are not
+approximately, but absolutely identical with those of the first
+molecule, and this whether they are found on the earth, in the sun, or
+in the fixed stars.
+
+By what process of evolution the philosophers of the future will
+attempt to account for this identity in the properties of such a
+multitude of bodies, each of them unchangeable in magnitude, and some
+of them separated from others by distances which Astronomy attempts in
+vain to measure, I cannot conjecture.  My mind is limited in its power
+of speculation, and I am forced to believe that these molecules must
+have been made as they are from the beginning of their existence.
+
+I also conclude that since none of the processes of nature, during
+their varied action on different individual molecules, have produced,
+in the course of ages, the slightest difference between the properties
+of one molecule and those of another, the history of whose
+combinations has been different, we cannot ascribe either their
+existence or the identity of their properties to the operation of any
+of those causes which we call natural.
+
+Is it true then that our scientific speculations have really
+penetrated beneath the visible appearance of things, which seem to be
+subject to generation and corruption, and reached the entrance of that
+world of order and perfection, which continues this day as it was
+created, perfect in number and measure and weight?
+
+We may be mistaken.  No one has as yet seen or handled an individual
+molecule, and our molecular hypothesis may, in its turn, be supplanted
+by some new theory of the constitution of matter; but the idea of the
+existence of unnumbered individual things, all alike and all
+unchangeable, is one which cannot enter the human mind and remain
+without fruit.
+
+But what if these molecules, indestructible as they are, turn out to
+be not substances themselves, but mere affections of some other
+substance?
+
+According to Sir W. Thomson's theory of Vortex Atoms, the substance of
+which the molecule consists is a uniformly dense _plenum_, the
+properties of which are those of a perfect fluid, the molecule itself
+being nothing but a certain motion impressed on a portion of this
+fluid, and this motion is shewn, by a theorem due to Helmholtz, to be
+as indestructible as we believe a portion of matter to be.
+
+If a theory of this kind is true, or even if it is conceivable, our
+idea of matter may have been introduced into our minds through our
+experience of those systems of vortices which we call bodies, but
+which are not substances, but motions of a substance; and yet the idea
+which we have thus acquired of matter, as a substance possessing
+inertia, may be truly applicable to that fluid of which the vortices
+are the motion, but of whose existence, apart from the vortical motion
+of some of its parts, our experience gives us no evidence whatever.
+
+It has been asserted that metaphysical speculation is a thing of the
+past, and that physical science has extirpated it.  The discussion of
+the categories of existence, however, does not appear to be in danger
+of coming to an end in our time, and the exercise of speculation
+continues as fascinating to every fresh mind as it was in the days of
+Thales.
+
+
+
+
+
+
+
+
+End of Project Gutenberg's Five of Maxwell's Papers, by James Clerk Maxwell
+
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