February 22, 1894.J 



NA TURE 



39i 



gxis will be produced, and if x represent downward ac- 

 celeration, we get the equation of motion : — 



vix = - ing~. 

 s 



which is ready for solution, and gives the well-known 

 result. 



We greatly abbreviate the above statements by saying 

 that the upward " force " exerted by the spring in the first 

 case is vig, and in the second, from the experimental 

 result, vig{s-\- x)js. This gives at once -mg.vis as the 

 downward force on the particle, which being substituted 

 for X in the formal equation of motion, nix = X, puts the 

 latter into a form adapted for solution. 



Thus, though we may use, and do use constantly, the 

 language of cause and effect in this connection, it ought 

 to be remembered that when matters have been reduced 

 to the solution of a dynamical problem, we have a purely 

 mathematical process to carry out, by which we render 

 explicit only that which is already implicitly involved in 

 our equations. 



This does not exclude or do away with the considera- 

 tion of stresses as physical realities, it only states what 

 I believe is substantially involved in the application of 

 dynamics to physical problems. The objectivity, in the 

 metaphysical sense, of force does not concern us, and 

 discussions regarding it are, so far at least as physical 

 results are concerned, not likely to be profitable. 



1 have heard it said by more than one very competent 

 judge, that there is a certain vicious circle at the founda- 

 tion of dynamics which there is no avoiding. We define 

 force by mass, and mass by force. Thus it is sometimes 

 said in effect, "Equal forces are those which produce 

 equal accelerations in equal masses — equal masses those 

 in which equal accelerations are produced by equal 

 forces." But, as shown above, if we can assume con- 

 stancy of mass of a body, and of the physical proper- 

 ties — say of a spiral spring — there is no difficulty in 

 getting out of this circle of definition. These are 

 assumptions we are entitled to make as the result of 

 experience. 



It is to be observed that since the measure of force in 

 Newton's second law, namely, inx, is relative, the forces 

 considered must be also relative. This is noticed by 

 Prof. MacGregor in his address (p. 4), but he states that 

 as our idea of force is derived from sensation, force in 

 this sense is not relative. "Accordmg to this concep- 

 tion a body either is, or is not, acted upon by force." It 

 is possible that I have failed to follow Dr. MacGregor 

 here, but it seems to me that he has confounded r^rt/ with 

 absolute. Our muscular sense certainly tells us that a 

 force, that is a stress as distinguished from a mass- 

 acceleration, exists, but in no case can it inform 

 us as to what in any absolute sense are the forces 

 acting on the body considered. The force we feel 

 " does not depend upon our point of view," but the 

 force we regard as acting on the body certainly does. An 

 acceleration which we observe is also a perfectly real thing 

 in itself, but the acceleration of the particle is altogether 

 dependent for its value on the point of view from which 

 we regard it. 



The ordinary misunderstanding that continually crops 

 up with respect to the equality of action and reaction is 

 feelingly alluded to by Dr. Lodge in his paper, and per- 

 haps as a sympathiser I may be pardoned for devoting a 

 paragraph or two to its consideration. A recent dis- 

 cussion of precisely the same thing in another journal 

 has made it clear that the difficulty felt by the beginner 

 in this matter is not clearly appreciated by many who 

 endeavour to remove it. Because action and reaction 

 are equal and opposite in the case (to take Newton's 

 illustration) of a horse pulling a stone, the student (and 

 the would-be critic of dynamical processes !) imagines 

 NO. 1269, VOL. 49] 



that neither the horse nor the stone can get into motion. 

 Now the confusion arises from regarding the action 

 which is a forward force on the stone as being cancelled 

 by the (if for a moment we neglect the mass of the rope 

 or chain between the two bodies) equal and opposite force 

 which acts, and this is what is overlooked, 7iot upon the 

 stone, but upon tlic horse, and therefore cannot affect the 

 motion of the stone. 



There may be other forces acting on the stone, and 

 others again acting on the horse, and the motion of each 

 body is changed by the forces acting on that body, and 

 those forces alone. Thus there are two groups of forces, 

 one group acting on the stone, and the other on the horse, 

 and all that is asserted in the law of equality of action 

 and reaction, as applied in this illustration, is that that 

 particular force of the first group, which is the force 

 exerted on the stone by the horse, is equal to that force 

 of the second group which is the force exerted on the 

 horse by the stone. 



Action and reaction, however, are, I believe, most 

 properly regarded as applied at the same place, though 

 not to the same thing. Across any cross-section of the 

 rope in Newton's illustration a stress acts, one aspect of 

 which is a forward force on the part of the cord imme- 

 diately behind the cross-section, the other a backward 

 force on the part of the cord just in front of the cross- 

 section. An excellent example is the action and reaction 

 between two links of a chain, which are exerted across 

 the surface of contact between the links, the action being 

 a force on one link, the reaction a force on the other Imk. 

 Here, as in all other cases, the action and reaction do 

 not cancel one another, simply because they are applied 

 lo what are here regarded as entirely different things. 

 [Of course, if we are considering the motion which a 

 system consisting of different parts may have as a whole, 

 the actions and reactions between these parts do cancel 

 one another.] 



I agree with Dr. Lodge in believing that in a certain 

 sense we have nothing but contact action, that is, that 

 all radiation phenomena are propagated by contact 

 between portions of matter (not necessarily ultimately 

 discrete portions) fiUmg space. Thus at every place 

 where such propagation is going on, and consequently 

 changes of the motions of bodies are taking place, stresses 

 are set up, and just where we have one aspect of a stress 

 we have its other aspect. 



This view, if it is adopted, certainly seems to lead to the 

 conclusion that a process of transformation accompanies 

 transference of energy ; but it is not, so far as I can see,, 

 inconsistent with, and does not render in any way un- 

 tenable, the doctrine of conservation of energy as 

 ordinarily stated. 



The doctrine that all energy is kinetic in reality, and 

 that transformation consists in a passage of the energy 

 from being kinetic energy of the bodies whose velocities 

 can be observed and measured to being kinetic energy 

 of those parts of the system regarding which we cannot 

 have such knowledge, or T'ice versa, when it is more 

 familiar, and more clearly understood in the light of 

 further scientific progress, may possibly help to clear 

 away some of the many difficulties which crowd round 

 this subject. 



This article is long enough, and we must defer to some 

 other opportunity any further consideration of Dr. Lodge's 

 theory of the transference of energy. But both he and 

 Dr. MacGregor have done good service in discussing 

 from their several points of view this very difficult but 

 apparently for many minds exceedingly fascinating 

 subject. Nothing but good can come of "a revision of 

 the standards" in dynamics, provided it has no destruc- 

 tive object in view, but only the improvement and,, 

 if necessary, correction of the methods of presenting and. 

 teaching: the science. A. Gray, 



