THE (v,,!









"Nee aranearum sane textus ideo melior quia ex se fila gignunt, nee noster vilior quia ex alienis libaraus ut apes." Just. Lips. Polit. lib. i. cap. 1 . Not.







" Meditationis est perscrutari occulta ; contemplationis est admirari perspicua .... Admiratio generat quaestioneni, quaestio investigationem, investigatio inventionem." Hvgo de S. Victore.

"Cur spirent venti, cur terra dehiscat,

Cur mare turgescat, pelago cur tantus amaror, Cur caput obscura Phoebus ferrugine condat, Quid toties diros cogat flag-rare cometas, Quid pariat nubes, veniant cur fulmina ccelo, Quo micet igne Iris, superos quis conciat orbes Tam vario motu."

J. B. Pinelli ad Mazonium.






Prof. Oliver Lodge on the Foundations of Dynamics 1

Prof. Ludwig Boltzmann on the Methods of Theoretical

Physics 37

Messrs. W. H. Harvey and F. Hird on Brush Discharges in

G-ases 45

Prof. H. A. Eowland : New Table of Standard Wave-lengths . 49 Mr. C. Y. Boys on the Drawing of Curves by their Curvature.

(Plate I.) 75

Mr. A. P. Trotter on a new Photometer 82

Mr. M. Carey Lea on the Nature of certain Solutions, and on

a New Means of Investigating them 88

Prof. F. Y. Edgeworth : Exercises in the Calculation of Errors. 98 Mr. Spencer U. Pickering on the Hydrates of Hydrogen

Bromide Ill

Dr. Silvanus P. Thompson : Some Notes on Photometry .... 120

Lord Eayleigh on the Theory of Stellar Scintillation 129

Notices respecting New Books :

A Memorial of Joseph Henry 142

Dr. A. Macfarlane's Fundamental Theorems of Analysis

Generalized for Space, and The Imaginary of Algebra. 143 Prof. Otto Koll's Theorie der Beobachtungsfehler und die Methode der Kleinsten Quadrate, mit ihrer Anwendung

auf die Geodiisie und die Wassermessungen 144

Proceedings of the Geological Society :

Mr. George Barrow on an Intrusion of Muscovite-biotite gneiss in the South-eastern Highlands, and its accom- panying Thermo-metamorphism 145

Mr. Frank Eutley on the Dwindling and Disappearance

of Limestones 146

Dr. Charles Callaway on the Origin of the Crystalline

Schists of the Malvern Hills 146

Messrs. Harker and Marr's Supplementary Notes on the

Metamorphic Rocks around the Shap Granite 147

Prof. J. F. Blake on the Felsites and Conglomerates between Bethesda and Llanllyfni, North Wales 148


Messrs. P. Lake and Theo. T. Groom on the Llandovery

and Associated Rocks of the Neighbourhood of Corwen 148 Lieut.-General C. A. McMahon's Notes on Dartmoor . . 149 Mr. A. J. Jukes-Browne on some Recent Borings through the Lower Cretaceous Strata in East Lincolnshire . . t « 150 Some Corrections to a Paper on the Laws of Molecular Force,

by William Sutherland 150

On a Remarkable Phenomenon of Oxidation of Pure Alumi- nium when in Contact with Mercury ^ by E. O. Erdmann. . 151 On the Processes which take place at the Boundary between two Solutions of Different Concentration when a Current is Passed, by George H. Zahn 151


Mr. Alfred M. Mayer : Studies of the Phenomena of Simul- taneous Contrast-Colour ; and on a Photometer for Measu- ring the Intensities of Lights of different Colours 153

Mr. Alex. McAulay on a Modification of Maxwell's Electrical Theory 175

Dr. William Pole: Purther Data on Colour-blindness. No. IV 188

Mr. J. E. Myers on a new Volumenometer 195

Prof. G. M. Minchin on the Magnetic Pield close to the Sur- face of a Wire conveying an Electrical Current 201

Prof. Perry and Mr. H. A. Beeston on Long-Distance Tele- phony 222

Proceedings of the Geological Society :

Mr. S. S. Buckman on the Bajocian of the Sherborne

District 229

Dr. Andrew Dunlop on Raised Beaches and Rolled Stones at High Levels in Jersey 230

On the Critical Point, and some Phenomena which accompany it, by G. Zambiasi 230

The Critical Point, and the Phenomenon of the Disappearance of the Meniscus when a Liquid is heated under Constant Volume, by G. Zambiasi 231


Prof. J. G. MacGregor on the Hypotheses of Dynamics .... 233 Mr. James Wimshurst on a new Form of Influence-Machine . 264 Mr. W. R. Pidgeon on an Influence-Machine 267


Profs. Dewar and Fleming on the Electrical Eesistance of Metals and Allovs at Temperatures approaching the Abso- lute Zero. (Plate II.) 271

Mr. A. A. C. Swinton : Experiments with High Frequency Discharges 300

Hon. Charles A. Parsons : Experiments on Carbon at High Temperatures and under Great Pressures, and in Contact with other Substances 304

Notices respecting New Books :

Prof. J. A. Ewing's Magnetic Induction in Iron and other Metals 308

On the Annual and Semi- Annual Seismic Periods, by Charles Davison, M.A 310


Prof. J. J. Thomson on the Effect of Electrification and Chemical Action on a Steam- Jet, and of Water-Vapour

on the Discharge of Electricity through Gases 313

Profs. Liveing and Dewar on the Refractive Indices of Liquid

Nitrogen and Air 328

Lord Kelvin on the Piezo -electric Property of Quartz 331

Mr. John Trowbridge on the Oscillations of Lightning Dis- charges and of the Aurora Borealis. (Plate III.) 343

Prof. F. T. Edge worth on the Calculation of Correlation

between Organs .... 350

Mr. M. Carey Lea on Endothermic Reactions effected by

Mechanical Force 351

Lord Bayleigh on the Flow of Viscous Liquids, especially in

Two Dimensions , 354

Dr. Sophie Bryant on an Example in " Correlation of

Averages " for Four Variables , 372

Proceedings of the Geological Society :

Prof. J. W. Judd on Composite Dykes in Arran 377

Mr. J. Postlethwaite on an Intrusive Sheet of Diabase and Associated Rocks at Robin Hood, near Bassen-

thwaite 379

Mr. Herbert R. Wood on the Dykes of Hope, Idaho . . 379 Dr. Robert Sieger on the Rise and Fall of Lake Tan- ganyika 379

On a Photometric Method which is Independent of Colour,

by Ogden N. Rood 380

Experimental Investigations on Dielectrics, by Dr. G. Benischke 383


Page On the Use of Cupric Nitrate in the Voltameter, and the

Electro-chemical Equivalent of Copper, bj E. E. Beach . . 384 Note by Lord Kelvin on Electric Molecules for the Explan- ation of the Piezo-electric and Pyro-electric Properties of Crystals 384


Mr. T. Proctor Hall on New Methods of Measuring the Surface-Tension of Liquids 385

Lord Kelvin on the Elasticity of a Crystal according to Bos- covich 414

Mr. J. H. Michell on the Highest Waves in Water 430

K. Tsuruta on some Thermal Properties of a Mixture of Carbonic Acid and Nitrogen 438

Lord Kelvin on the Theory of Pyro-electricity and Piezo- electricity of Crystals 453

Dr. A. Richardson and Mr. J. Quick on a Modified Eorm of Bunsen and Roscoe's Pendulum Actinometer 459

Notices respecting New Books :

Mr. J. Payne's Practical Solid Geometry, and Mr. J. J. Prince's Graphic Arithmetic and Statics 463

On the Strength of the Electrical Waves when the Spark passes in Oil, by H. Bauernberger 464


Dr. Harry C. Jones on the Dissociation of Compounds in Water as Measured by the Lowering of the Ereezing-Point, and some Investigations with Organic Compounds.

(Plates IV.-IX.) 465

Mr. Sidney J. Lochner on the Elongation produced in Soft

Iron by Magnetism 498

Mr. William Sutherland on the Viscosity of Gases and Mole- cular Eorce 507

Mr. G. Udny Yule on the Passage of Electric Wave-trains

through Layers of Electrolyte 531

Notices respecting New Books :

Dr. J. Casey's Treatise on the Analytical Geometry of

the Point, Line, Circle, and Conic Sections 545

Dr. J. Traube's Practical Chemical Physics (Physikalisch-

chemische Methoden) 546

Dr. Lassar-Cohn's Arbeitsmethoden fiir Organisch- chemische Laboratorien 547


Proceedings of the Geological Society :

Mr. W. J. Chmies Eoss on the Geology of Bathurst,

New South Wales 548

Dr. J. W. Evans on the Geology of Matto Grosso (par- ticularly of the region drained by the Upper Paraguay). 549

Aberration Problems, by Prof. Oliver J. Lodge 549

On a Simple Method of Investigating the Con ducting-Power

of Dielectric Liquids, by K. R. Koch 550

On the Emission of Heated Gases, by E. Paschen 551

On the Condition of Matter near the Critical Point, by B.

Galitzine 552

Note on the Atomic Weight of Carbon, by J. Alfred Wanklyn 552

Iudex , 553


I. Illustrative of Mr. C. V. Boys's Paper on the Drawing of Curves by

their Curvature.

II. Illustrative of Profs. Dewar and Fleming's Paper on the Electrical

Resistance of Metals and Alloys at Temperatures approaching the Absolute Zero.

III. Illustrative of Mr. John Trowbridge's Paper on the Oscillations of Lightning Discharges and of the Aurora Borealis.

IV.-IX. Illustrative of Dr. Harry C. Jones's Paper on the Dissociation of Compounds in Water as Measured by the Lowering of the Freezing-Point.






JULY 1893.

I. The Foundations of Dynamics. By Olivek Lodge, F.R.S., Professor of Physics in University College, Liverpool*.

Paet I. The Nature of Axioms .

IT is a matter of congratulation with me that a critic who has devoted so much thought to Newton's laws of motion and similar fundamental doctrines should have begun a dis- cussion of my papers on the subject of Energy ; and I shall willingly consider his objections in order to see what modifi- cations, if any, should be made in my original statements. But Dr. MacGregor's temporary attitude towards Physical problems is exhibited rather strikingly in a treatise on " The Fundamental Hypotheses of Abstract Dynamics," which he published as a Presidential Address to a section of the Royal Society of Canada (Transactions 1892) . Hence, before replying to his criticisms on my writings, as made in your February issue, page 134, I should like to make a few general observa- tions suggested by this other deliverance of his, so as to indi- cate what seem to me the rather different points of view from which we, or if not we some other writers, approach these fundamental doctrines of Mechanics and Physics. The dif- ference in attitude may be briefly summarised thus : Some philosophers seek to advance truth by detecting or inventing complications in what was apparently simple ; whereas others aim at making simple statements concerning things which are apparently or really complicated. A generalization like this is

* Communicated by the Physical Society : read May 12, 1893. Phil Mag. S. 5. Yol. 36. No. 218. July 1893. B

2 Prof. Oliver Lodge on

not one which will bear pressing into individual cases, but if it contains an element of truth it has reference to no personal detail, as it seems to me, but to a difference in type ; and I sometimes think that most minds, except those few of the very highest order who are above classification, may be said to fall into, or at least to lean toward, one or other of these categories*. Each type of mind performs its service, and each type has its appropriate danger.

The detection of a real complication is a service to truth ; the invention of a needless complexity is a disservice and temporary obstruction. The reduction of apparently complex facts to a simple statement in commonplace language is, I believe, a service ; the over-simple and incomplete summary of what is really complex is not an equal service, but I do not perceive that it is likely to be any serious obstruction : it seems to me rather of the nature of a first approximation, which is often temporarily helpful.

When Ohm stated his law that current is proportional to E.M.F., he did not know that it was really true. It has turned out to be precisely true for copper and for sulphate of copper the only substances for which it has been seriously tested ; but even if it had not been so accurate, its statement was a service, since it enabled half a century to walk in the light instead of in the dark. There is no evidence that it is accurately true for every variety of solid and liquid conductor, but by this time it is the fashion to assume its truth in ordinary simple cases. And rightly so, as it seems to me ; the burden of proof rests now with the enterprising experimenter who can detect a flaw in it. His evidence will be listened to, but till it is forthcoming vague doubts can be legitimately ignored.

Take another example : The characteristic equation of gases in the simple form pv = RT has done good service, though it turns out to be untrue for every actual substance. Without it, however, we should have been unnecessarily floundering in the dark. Even now it is more used in dealing with gases

* I see no reason in Dr. MacGregor's book on Dynamics for including him in the first category : it is his Presidential Address on the Laws of Motion that alone suggested it. I do not intend the classification as in any way offensive : I should think that Prof. Karl Pearson, for instance, would willingly enrol himself under the first head rather than under the second, judging by his ' Grammar of Science.' But very likely MacGregor has stated the laws of motion in their simplest conceivable form if attraction and repulsion across a distance are to be contemplated. That is the essential difference between us : he is willing to base Physics on action at a distance ; I am not. From the action-at-a-distance point of view his statements are in many respects admirable, especially those near the conclusion of his essay. The remarks in the text are in- tended to have only a general and impersonal application.

the Foundations of Dynamics. 3

than any other equation. The improved statement of Van der Waals, adding a term to p and subtracting one from v, was another distinct service, and enabled a mass of experi- mental evidence concerning the structure of liquids to be conveniently and simply smnmarised. In its turn, however, it has had to give place to more complex empirical statements, and the complete law has not yet appeared.

The examples I have chosen, one of a precise, the other of an approximate, simple statement, are not indeed of the nature of axioms ; and it may be held that it would be unsatisfactory to base our axioms on such a tentative sort of footing.

And yet what other course is open ? Truly axiomatic state- ments can only be effectively made concerning things of which the race has had a long course of experience, things to which they have grown familiarly accustomed. If they can be actually proved, they are theorems, not axioms.

The setting forth of an axiom I regard as a kind of challenge, equivalent to the statement: "Here is what seems to me to be a short summary of a universal truth ; disprove it if you can. I cannot prove it, it is too simple and fundamental for proof, I can only adduce hundreds of instances where it holds. I have indeed critically examined a few special cases and never found it fail, but a single contrary instance will suffice to overthrow it; hence, though it be hard to prove, yet if not true its disproof should be easy : find that contrary instance if you can." If no disproof is forthcoming for a few generations, the axiom is likely to get accepted. Meanwhile its undeniable simplicity is a practical advantage, even though in the course of centuries a flaw or needful modification in its statement may be discovered.

This is the kind of basis on which such a law as that of the Conservation of Energy or the Conservation of Matter rests. That the perpetual motion is impossible, that matter is in- destructible, that energy never diminishes in the act of transfer, all these must be regarded as generalizations based on a great series of experiments, some consciously directed to the upset- ting of one or other of the laws if possible, some aimed at establishing them, but most of a non-contentious and collateral character. If we are challenged to produce direct evidence that in any given chemical reaction the mass of the reagents is unchanged, not only in the initial and final stages but at every stage of the process, the proof may be exceedingly difficult. Heat is liable to be developed which would inter- fere with delicate weighings, and the reaction challenged may be an explosive or otherwise inconvenient one. But we do not attempt the proof, we shift the burden on to the shoulders


4 Prof. Oliver Lodge on

of the doubter and say to him, Disprove it if you can ; and so we practically say for all our axioms, and for all laws which are so simple and fundamental as to be hardly distinguishable from axioms.

Experiments are often made or adduced in support of a law as if they were part of its foundation : thus Newton tried experiments on impact before stating his third law, but the experiments did not really prove it with accuracy even for the particular case examined. All they could show was that there was nothing obviously wrong with it. He saw no reason for supposing it wrong, and so after consideration stated it as an axiom, to be hereafter challenged and found inaccurate if so the progress of experience turned out.

I should say that an axiom or fundamental physical law is a simple statement, suggested by familiar or easily ascertained facts, probable in itself, readily grasped, and not disproved or apparently liable to disproof throughout a long course of experience.

If a statement is capable of exact examination and verifica- tion, either by reasoning or by experiment, it is called a law, but not a fundamental law ; i. e. it is no longer part of the foundation, it is supported on something else. If it has no support, except the absence of evidence against it, it is an axiom. Far be it from me to decry the use of experiments of verification. The necessity for them whenever feasible is conspicuous and universally admitted, and much ingenuity may be usefully spent upon them ; but I do say that in time a theory can become established by processes other than direct experimental verification ; and in fact that really valid and flawless experimental verification is frequently an impos- sibility.

An instructive example of the legitimate strength of a theory, even when opposed by apparent facts, is contained in an article by Lord Rayleigh in the Philosophical Magazine for March 1889, " On the History of the Doctrine of Kadiant Energy."

It appears that W. Herschel conceived the idea that the radiation which excites the sensation of light and the radia- tion which produces heat in black bodies are essentially different ; and this view, which was contrary to his original intuition, was based upon a crucial prismatic experiment, made for the purpose of ascertaining " whether the heat of the red rays is occasioned by the light of those rays " or not. A definite question, answered by experiment in the negative* On this Lord Ilayleigh remarks :

" I am disposed to think that it was this erroneous conclu-

the Foundations of Dynamics. 5

sion from experiment, more perhaps than preconceived views about caloric, that retarded progress in radiant heat for so many years. We are reminded of Darwin's saying that a bad observation is more mischievous than unsound theory. It would be interesting to inquire upon what grounds we now reject the plain answer which Herschel thought himself to have received from experiment. I do not recall a modern investigation in which the heat and light absorptions are proved to be equal for the various parts of the visible spec- trum. Can it be that after all we have nothing but theory to oppose to Herschel's facts V

Yes, that is all, and, as Lord Eayleigh well knows, it is amply enough. Whoever examines the facts again will do so not to substantiate our present theory but in the hope of up- setting it. Success is of course just conceivable, but, when it comes, there will be time enough to reopen the question. Lord Rayleiglr's words may be distorted, and may even suggest false meanings to minds with a crooked turn in them ; so may many of the apparent admissions about unprovableness in this paper of mine, but, whether it gives occasion to the enemy to blaspheme or not, it is true that a host of doctrines are believed because they form part of a consistent scheme rather than because of any seriously attempted, still less any really achieved, experimental proof. And to pull one of these neatly fitting blocks from its niche will demand the strength of more than one, of more than several, so-called crucial experiments. There comes a time indeed when the weight of experimental evidence suffices to uproot a portion of tightly fitting theory ; but seldom, as I think, without some looseness or uneasiness being first detected, and never without a betrayal of rottenness at the root.

Why do Physicists deny that matter can be moved by mental power from a distance without physical mechanism ? Why does modern science reject the whole of a certain class of miracles, in the teeth of an immense record of direct experimental evidence ? Solely because these things do not fit in with such coherent views of the universe as they have at present been able to frame.

Why, again, do we accept a multitude of unverified state- ments, such as, that every portion of radiation, whether it be of light or of sound, is intrinsically energy, and must, if absorbed, result in heat ; that every muscular contraction of an animal corresponds to the combustion of a portion of his food ; that a given gas consists of particles of approximately specified size and weight travelling at a certain average speed; that a medium connects every pair of bodies which are

6 Prof. Oliver Lodge on

perceived to exert force on each other ; and so on ? Solely because these things do fit into a coherent and self-consistent scheme of the universe.

Any scheme or doctrine sufficiently harmonious and consistent goes far thereby towards establishing itself as truth. So conspicuously is this the case, when one comes to reflect, that there are not wanting some who conjecture that by our thought we are, so to speak, constructing, or at least helping to construct, the cosmic scheme.

Some axioms the human race has now given up challenging, and by so abstaining has silently accepted as corresponding to the truth of things. Others it occasionally exercises its ingenuity in degrading or depreciating, not into untruths, but into special cases of a higher and super-sensuous gene- ralization. Varieties of space are imagined, and mathemati- cally treated, where more than one line can be drawn through a point parallel to a given line, where the shortest distance between two points is not straight, where the three angles of a triangle are not equal to half a revolution, where a closed surface is an incomplete boundary, and where more than three lines can be perpendicular to each other. These things are imagined, and for all I know they may in some occult fashion exist. To set bounds to the possibilities of the universe on the limited evidence of our few sense-organs would be absurd. But I say that any proof of their actual existence within our more developed ken rests with the experimentalist. As soon as facts are forthcoming which clearly and definitely are in- explicable on the basis of our present notions concerning space, I for one am willing to enlarge those notions and to con- template provisionally whatever hypothesis suggests itself as most simple and plausible. Till then there is plenty of work for a physicist in interpreting, systematizing, and clarifying the facts of the universe, as it appeals to him through the agency of his ordinary three-dimensional senses, aided by his undimensional common-sense.

But I hold that with all these vague possibilities of ultimate development in front of him (not so vague but that they are in some sort conceivable, or at least tractable by reason), a natural philosopher need not confuse himself by endeavouring to complicate what is already transparently simple ; nor will he be wise to attempt an over-laborious scrutiny of his funda- mental axioms ; for the more neatly and quietly he can lay his foundations the more time will he have for building the super- structure, and the more gorgeous he may hope to make it. By all means let him avoid a rotten or insecure element in his foundation. It must be as sound and strong as possible ;

the Foundations of Dynamics, 7

but his underground work need not be decorated with fanciful and laborious conceits, it may be as plain as it is substantial, and he may leave its edges rough in order to connection with structures as yet unbuilt and unimagined.

Of this plain and substantial character would I seek to keep the laws of motion. If a statement like the first law of motion cannot be made in simple and readily intelligible language, I should despair of Physics. In that case the Physics of the future could be little better than a barbarous jargon of technicalities. There are plenty of really difficult places where technical language and unfamiliar modes of thought are for the present essential. The developments of the super- structure erected during the present century are indeed now so stupendous that for myself I should be satisfied if, without appreciably adding to them, I could by consolidation and restatement remove the necessity for some of this artificiality, and so make their harmony and beauty more readily appre- ciated. But in order to do this a simple and unlaborious foun- dation is a necessity. I hope to try before long to display the bold outlines of the foundation already laid by men of sur- passing genius, every unnecessary accretion being cleared away, and the whole simplified to the uttermost ; and then, if the attempt be not too ambitious, I should wish to extend the process to some portion of the superstructure.

Part II.

The First and Third Laivs of Motion,

So much for general preamble ; now turning to Dr. MacGregor's address, we find that he objects to the Newtonian statement of the first law of motion on the same ground that Prof. Karl Pearson, Prof. Mach, Mr. Macaulay of King's College, Cambridge, and several others'* have objected to it, on the ground, namely, that uniform motion is unin- telligible or meaningless unless you specify its direction and velocity with reference to a set of axes. And directly you try to specify axes you get into difficulties, for, although a uniform translation is permissible to them, any rotation or any acceleration of the axes is fatal to a simple state- ment of the behaviour of a body acted on by no force. It is useless to say that the axes must be stationary, because one cannot define what that means ; so the attempt is made to say that the axes must not rotate and must not be acted on by force ; but this last condition is of no use unless they possess

* See for instance a correspondent in ' Nature/ vol. xxxvi. p. 366.

8 Prof. Oliver Lodge on

inertia; so the axes are sometimes supposed to be generated by particles of matter projected in different directions and subse quently free from force *; or else the axes are made of infinite mass so that no finite force may be able to affect them.

Now I hold that all such notions as axes of reference are artificial scaffolding, necessary for the numerical specification of a velocity, but not at all necessary for the apprehension of what is meant by a uniform velocity. It is in the specification of any absolute velocity that the difficulties cited about an origin and axes of reference legitimately occur. It is in fact impossible to specify the absolute velocity of any- thing, because we have literally no criterion of rest. We shall, I believe, hereafter find it convenient to postulate the Ether as a body absolutely at rest; but none of these physical or geometrical complications should enter into an axiomatic statement.

All that the first law asserts is that the motion of a body not acted on by force is uniform in magnitude and direction. There is no need to attempt the impossible and say what that magnitude and direction absolutely are. Whatever they are they remain constant. If asked to prove this statement, we should at once decline, and throw the burden of disproof on the doubter. This is what Maxwell doesf when he says (virtually) : If the speed and direction of a freely moving body vary they must vary in some definite manner ; very well, tell me in what manner they are varying. You cannot, unless you can show me absolutely fixed lines of reference.

The fact is that the conception of uniform motion is based upon a simple primary muscular sensation, or at any rate upon a succession of such sensations ; everybody understands what it means, so far as it is possible to understand anything in this material universe, and the sense in which it is understood is amply sufficient as a basis for a physical superstructure. The first law is a true axiom, and its boldest and simplest form is not only the best, but is the only one that can with any justice be called axiomatic. How can one appeal to the experience of the human race with reference to coordinate axes of infinite or any other mass ? How can we utilize as axes the trajectory of particles free from force, without tacitly assuming the first law continually ? The whole attempt to complicate the statement of the first law of motion seems to me absurd.

* Thomson and Tait, vol. i. Part I. (1879), § 249. But although these writeis do propose to use such axes to fix direction, or, better, the invariable plane of a rotating system, §§ 267, 245, they quite logically deduce these things from Newton's laws, and do not use them in the statement of those laws.

t Matter and Motion, art. xli, p. 36e

the Foundations of Dynamics. 9

The well-known other objection, that a statement of the first law is unnecessary because it is only a special case of the second, rests on a different footing. Thomson and Tait have pointed out that it acts as a definition of equal intervals of time. Prof. MacGregor denies that the first law gives us any more useful definition of time than the second does ; but seeing that every clock is an attempt at a uniform mover, and that the second law is concerned with the more complex notion of accelera- tion rather than with the simple idea of velocity, I do not imagine that he will seriously adhere to this view : and there- fore, fully admitting the obvious fact that the first law is a special case of the second, I still hold that its separate state- ment is desirable, because it is so simple, and because it does afford a clear practical definition of the mode of measuring time. But were this its intended meaning it could have been expressed more straightforwardly. Newton probably con- sidered it as a qualitative statement introductory to his second law : and as such it is entirely suitable.

None of the objectors to the first law have the slightest doubt of its truth, that is what makes their contentions so practically futile ; it would appear that it is too simple to please them ; they seem to wish to complicate its statement so as to make it look more like the difficult things with which they are accustomed to deal. I feel convinced that many mathematicians mistrust a simple statement in English, and hardly conceive that such a language can really express an important law ; their trained ability to deal with difficult con- ceptions leads them, as I think, astray.

I am not quite clear what the word logomachy means, but much of the discussion which has been bandied about con- cerning the statement of the first law seems to me to be rightly designated by some such opprobrious or perhaps complimentary epithet.

When Dr. MacGregor goes on to consider the third law, and to deny that it can properly be regarded as a deduction from the first, he is urging a very minor matter, if what 1 have said concerning axioms has any truth in it. Still the question has some interest. Whether it is deducible from the first law or not may be held to depend on how general the terms are in which that law has been stated. If it can be axiomatically asserted that the centre of mass of a rigid system moves uniformly until an external force acts on the system, and also that the system does not begin to spin, then the third law is established. For since zero accelera- tion means zero force, it follows that all the internal forces add up to zero, and have no moment ; and since the system

10 Prof. Oliver Lodge on

can be dissected bit by bit without ceasing to be a system within the scope of the first law, it follows that no stress can contain an unbalanced force or couple.

If the law be doubted for the case of a pair of bodies attract- ing each other from a distance, Newton says* (virtually): Jam the bodies apart with a rigid obstacle, then you have re- duced their action to contact action ; and since you have a balanced stress at each point of contact, and likewise between the ends of the introduced obstacle, it follows that the attract- ing forces of the distant bodies are also balanced.

Now Dr. MacGregor's objections are (1) that Newton's proof only aims at extending the law from contact action to actions across a distance, while for contact action he is con- tent to assume it as an axiom or to verify it by experiment ; and (2) that the proof breaks down for a particle or single body which cannot be analysed into parts.

It is quite possible that Newton thought it best to state his third law as an axiom ; because the fact that the centre of mass of a complex system of bodies obeys the first law is hardly an experience that can be confidently appealed to, even though all the bodies are in contact. That fact and the third law are intimately connected, but whichever is the simpler had better be stated as the axiom, and the other be made a deduc- tion from it. Thus the centre of mass statement follows from the third law, and so very likely Newton preferred to arrange it. It is frequently difficult to know which of two very simple statements is the more axiomatic ; and methods of proof are notoriously susceptible of considerable variation. The important thing is to notice the link or tie between two facts, to show that they mutually strengthen each other, not to pretend that one is beneath the other and supports it.

Attempts to build even so simple a structure as geometry in the form of a single column, stone upon stone, have been found artificial and in the long run impracticable. An en- larged basis of direct appeal to experience is not only necessary but desirable, and all fundamental matters should be kept low down, as nearly in contact with first principles as possible.

The so-called deduction of the third law from the first or second is important as a clear and strong cross-connexion between the two things, and need not be considered as a rigorous proof. It is rigorous enough if the premisses are granted, but if not, then there is a certain outstanding axio^ matic or unprovable character to be shared between them ; but this outstanding portion is, by reason of the cross-connexion,

* Principia, Scholium to Axiomata,

the Foundations of Dynamics. 11

so slight as to remove all difficulty from what otherwise would seem, and indeed, strange to say, to many still does seem, an exceedingly tough morsel to swallow.

[I mean that one constantly finds examination candidates, and even Engineers, when catechized about a horse pulling a cart, though they may, some of them, politely admit that approximately the pull of the horse and the pull of the cart are equal (constituting the stress in the trace whose inertia we may agree to neglect), yet nevertheless assert that in reality the pull of the horse must be the least little bit bigger than the pull back of the trace, else the thing could not start. The fact is that the universal truth of the third law is not axiomatic, or at least is not obvious"*, and hence its deduction from the other two laws is really a useful deduction^

I do not see any point in Dr. MaoGregor's second objection that the proof is inapplicable to a body without parts. For if such a body anywhere exists, plainly its parts cannot act on each other, and so there are no actions or reactions in such a body worth troubling about.

The concluding portion of Prof. MacGregor's address has to do with the Conservation of Energy and the question of how far it can be deduced from the third law. But all these questions respecting energy we must fight out at greater length. Dr. MacGregor well knows that from the third law and the denial of action at distance together I claim to have deduced a law of conservation simpler and more precise than the ordinary law ; but his objection to thisf is that though such a law may come to be accepted as sufficient in the future, when the universality of contact-action is fully recognized, it is inadequate for the present, when action at a distance still holds a portion of the field ; by which I suppose he really only means that many mathematical methods of treatment are based at present on action-at-a-distance modes of expression. I have no fault to find with any convenient mode of attacking specific problems ; it is permissible to everyone to use the language of distance-action for practical purposes ; but when it comes to formulating fundamental laws I have no ambition to legislate for such cases until they can be shown actually to occur. 1 am open to experimental proof of their existence, but to none other. It is premature to legislate for them. If any action other than contact-action exists, we had better know more about it before formulating its laws. If the will-power of a " medium " for instance can really move a chair without

* See for instance ' Nature/ vol. xxxvii. p. 558 ; and see all recent volumes of 'The Engineer ' passim, especially about 1885 and 1891. t Expressed elsewhere, viz. Phil. Mag. February 1893.

12 Prof. Oliver Lodge on '

any kind of contact or physical connexion, it will be wise to look carefully for the seat of the other component of the stress, if there is one, and for the source of the energy concerned, but I myself should feel extremely hazy as to their probable locality.

When action at a distance does present itself in Nature (and if it ever does it is clearly going to be in connexion with the operations of Life), it will be very well to overhaul our axioms to see if they require modification. Till then I pro- pose to state them in terms of the facts we know. This I will attempt in another Part.

Part III. The Conservation of Energy and Universal Contact-action.

The ground is now clear, I think, for a reply to Professor MacGregor's criticism, as made in the Phil. Mag. (vol. xxxv. p. 134) for February 1893 ; and incidentally I may hope to answer or at least discuss the matter with some other critics, notably Mr. Heaviside in his paper in the Phil. Trans. 1892.

The first objection is that in my definition of energy I assume the ordinary law of conservation, because I say, in an early paper (Phil. Mag. Oct. 1879, viii. p. 278), "When- ever work is done upon a body, an effect is produced in it which is found to increase the working-power of that body (by an amount not greater than the work done) ; hence this effect is called energy, and it is measured by the quantity of work done in producing it/' " The words ' is found/ " says Dr. MacGregor, " indicate an appeal to experience/'' Most true, so they do. My position is this : Before making any definition it is desirable and only civil to show the reasonable- ness of it. To thrust a statement out without preamble or explanation, under cover of the contention that being only a definition or an enunciation one is at liberty to define or enunciate as one pleases, is I fear a thing frequently done, but it is barely polite, and it is apt to excite either resentment or else undue and slavish submission.

It is from no lack of love for Cambridge and the great men she has nurtured that I venture to hold that the typically Cambridge plan of text-book