I02 



NATURE 



[June i, 189c 



mount and abandon ourselves whithersoever they lead, quite 

 irrespective of dim suspicions about unacceptable consequences. 



Some doubt seems also felt concerning the wisdom of attempt- 

 ing to pack important laws into small compass ; but to this I 

 plead that the axioms already stated by me are most of them 

 purely Newtonian, and that for the attempt thus to summarise 

 science in as few and simple statements as possible we have the 

 high encouragement of his example. It is true that Newton 

 issued his axioms in a form as perfect as it was reasonable or 

 possible then to make them, and did not bring them out as 

 matter for discussion. But to this two pleadings may be put 

 in: — 



(i) That their perfect form did not by any means /r«'««/ dis- 

 cussion, nor would it have been desirable if it had ; it only made 

 the inevitable discussion painful to him instead of pleasant. 



(2) That in his day he was minting fresh coins, complete in 

 design and workmanship, for the use of a race which possessed 

 nothing of the kind ; whereas now one is partly trying to rub off 

 a little tarnish and furbish up old currency in more modern style, 

 and partly trying to put into circulation a few fresh coins at a 

 time when everybody feels that they have quite as much money 

 as they want. 



The step in advance which I believe has now to be made is 

 the explicit introduction of the Ether into the scheme of physics. 

 Newton knew well enough that a connecting medium was a 

 philosophic necessity, but he did not see his way to asserting 

 its physical existence and discovering its properties. Conse- 

 quently his philosophy was all stated in terms of action at a 

 distance. 



But science has progressed since then, and the ether has be- 

 come accessible in many then undreamed-of ways. It appears 

 to me, therefore, that the time has come for enlarging the New- 

 tonian axioms, on the basis of the labours of Faraday and Max- 

 well and of other men now living, and for fearlessly following 

 up any consequences to which the new axioms may lead us. 



My philosophic creed runs somewhat thus : — First that by 

 our senses we become aware of motion ; I don't much care 

 by what sense it is, it seems to me by the muscular sense — ' 

 partly eye muscles perhaps, mainly arm or leg muscles — but 

 it may be by a succession of tactile sense-perceptions as 

 some modern physiologists and psychologists believe. But 

 none of these questions belong to pure physics : somehow 

 or other we are aware of Motion and Time and Space. We 

 had already erected the structure of Geometry without invoking 

 motion and time, we now erect Kinematics. And by motion, 

 which is a usefully vague term, I mean nothing less than the 

 whole of kinematics. 



Next in order of complexity we become aware of /o?vv plainly 

 through our muscular or our tactile sense, and thus, indirectly, 

 we gain the tremendously important idea of "matter."' The 

 ratio of force to motion is inertia ; one of the most constant 

 and fundamental qualities in the apparent universe. The 

 product of force and motion is activity, whence arise the com- 

 plex but brilliantly useful ideas associated with the \e.xvci energy . 

 In elaborating these we erect the whole science of Dynamics. 



Thus far the scheme is essentially Newtonian, and the New- 

 tonian axioms may be held to summarise its essentials in the 

 briefest and clearest way. If I presume to restate them it is be- 

 cause the modern terms "acceleration" and "stress," which 

 were not available for Newton's use, assist the expression, so 

 that by their aid some minor difficulties, such as those caused 

 by the phrase "uniform velocity and direction" disappear; 

 this phrase need not have been introduced had a vector ac- 

 celeration been a thing of easy apprehension or of common 

 knowledge in Newton's time. 



Prof. Minchin urges the explicit retention of the first law, 

 not as a measure of time only, but as a qualitative statement 

 introductory to the quantitative assertion of the second ; and I 

 fully agree. I should like to take the opportunity of thanking 

 both Prof Minchin and Prof Henrici for their careful criticism 

 of my Physical Society paper. 



Premising that the necessary definition of terms must be 

 understood or supplied, I now repeat from my former article the 

 essence of the Newtonian laws. 



Axiom I. Without force there can be no acceleration of 

 matter. 



Axiom 2. The inertia of matter is unconditionally constant. 

 {Or, Acceleration of matter is proportional to unbalanced or re- 

 sultant force.] 



NO. I 23 I, VOL. 48] 



Axiom 3. Every force is one component of a stress, and a 

 stress in a body or system does not accelerate it. 



Before proceeding, let me here intercalate a remark about the 

 kind of scholium with which, on page 62 (Nature, vol. xlviii., 

 May 18) I prelude the definitions and axioms. I do not intend 

 the "experimental results" there quoted to be used for teach- 

 ing purposes ; in fact, my present aim is in no respects peda- 

 gogic, but more ambitious ; I quote them as affording some sort 

 of experimental basis for the Newtonian axioms. An experi- 

 mental basis is a necessity— in other words, an axiom must be 

 based on some sort of experience ; and the experience on which 

 the Newtonian laws are based can hardly be considered as of a 

 very commonplace type. 



It is easy to illustrate the second law with bits of elastic and 

 trucks on wheels, but it is not so easy to prove it with accuracy 

 — the sort of accuracy attempted, for instance, in the case of the 

 law of Ohm. It is customary to say that Astronomy proves it, 

 but as a logical procedure that would be a terribly circular one ; 

 and besides, the nature of gravitation is so singularly unknown 

 that it can hardly with satisfaction be used as a foundation 

 stone. 



Anyhow, the proof which by those experiments I suggest is, 

 first to establish Hooke's law for a spring, statically, by weights, 

 i.e., to prove that force is proportional to displacement ; next 

 to show that vibrations of the spring are isochronous, i.e., that 

 acceleration is proportional to displacement ; and thus to 

 deduce that force and acceleration are proportional (in this case 

 at any rate) to a high degree of accuracy. The difficulties, 

 such as they are, of this proof are of a merely mathematical 

 order, and are hence entirely unimportant. 



The third "experimental result" quoted is only to suggest 

 the impact experiments which Newton himself considered 

 desirable as a basis for his third law. 



Oneotherpoint before proceeding. With regard to the claim 

 for obviousness, or prima-facie certainty, sometimes set up in 

 connexion with a long-known law of nature, on any such 

 ground as that it is a mere assertion that Cause equals Effect : — 

 may I say once for all, and quite impersonally, that such a 

 claim appears to me to be metaphysical nonsense of the worst 

 kind — the kind which has tended to bring real Metaphysics 

 into unmerited disrepute. Is it not plain that everything 

 depends on what is cause and what is effect, and that the inler- 

 pretatioii of nature essentially consists in the discovery and 

 accurate specification of what in any given case the true cause 

 and the true effect are ? 



Now comes the new departure, or extension of the Newtonian 

 axioms, so as definitely to include the medium which it has been 

 one of the chief works of the present century to discover. 



The chief axioms I intend to propose and trace the conse- 

 quences of are : — 



Axiom 4. A stress cannot exist in or across empty space. 



Axiom 5. Material particles (atoms of matter) never come 

 into contact. 



Axiom 6. A stress must extend from one material particle to 

 another : it cannot end in ether. 



This last is hardly axiomatic, but it is based on special 

 experimental evidence (Phil. Trans., 1893). 



From these laws and from the law that stress is essential to 

 activity (which last does not need a separate statement, being 

 deducible from the Newtonian axioms), a series of what appear 

 to me fundainentally important deductions may t)e made. 



Some of these deductions relate to already known and ad- 

 mitted facts, while others introduce some as yet unknown or 

 unadmitted : the former set are mostly referred to in my paper 

 to the Physical Society, the others must be dealt with here- 

 after. 



Oliver Lodge. 



May I make through your columns some criticisms on Prof. 

 Lodge's views of dynamics, which I am afraid I failed to render 

 intelligible to him during the discussion on his paper before the 

 Physical Society ? 



It would be useless to say anything about his theory of 

 " Contact Action," for he has rendered the whole discussion 

 upon that point nugatory by saying in his reply to the criticisms 

 that he does not admit that any two bodies can ever come into 

 contact at all, i.e., that the contact action he contemplates is 

 something that takes place only between " the bodies '' and an 

 "ether" which exists between them. It follows that his own 



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