214 



SCIJEJJS/CjHJ. 



[Vol. IX., No. 213 



experiment in ' frictional electricity ' — so called. 

 Given a lioiise heated by a hot-air furnace or by 

 steam, a floor covered with soft carpet which, in 

 virtue of the furnace heat, is dry and warm, a man 

 the soles of whose shoes are thoroughly dry, and 

 electrification will probably result from every brisk 

 movement of the man over the carpet. These condi- 

 tions are most likely to be met with during cold win- 

 ter weather, and it is then that the j^henomena are 

 generally noticed. It is not probable that Dr. Shu- 

 feldt's two friends can perform the feat of lighting 

 gas in this way ' at all times and under all circum- 

 stances.' His statement that the " electrical discharge 

 was considerably greater from the tip of the index 

 finger than from any of the others of the hand, and 

 gradually diminished in regular order as we pro- 

 ceeded to the little finger," is interesting, but needs 

 confirmation. I am sceptical as to the charging of 

 his entire system ' with this animal electricity,' and the 

 results which followed such a condition, and -particu- 

 larly so as to the otigin of the " sense of the most pro- 

 found relief, as if it were that all the electricity of 

 my system had been completely withdrawn by the 

 act," which he experienced when his hand toiTched 

 the back of the young mulatto girl. Is man one of 

 the extremely small number of animals having spe- 

 cialized electrical organs ? T. C. M. 

 Terre Haute, Ind., Feb. 22. 



Inertia-force. 



The importance of clear elementary ideas on the 

 teaching of dynamics justifies me, I think, in asking 

 space for a further discussion of Dr. E. H. Hall's 

 ' inertia-force.' 



In his letter published in Science of Feb. 18, Dr. 

 Hall expresses the opinion that our difference with 

 regard to ' inertia-force ' is based uj)on a difference 

 of interpretation of the term ' force.' That, I think, 

 is not the case. With all his statements as to force 

 in general I agree ; and the passage which he qiiotes 

 from Maxwell, as expressing his view of force with 

 sufficient accuracy, expresses also my view with com- 

 plete accuracy. Dr. Hall, indeed, says that this pas- 

 sage meets many of the points raised by me ; and it 

 would thus seem that it must be inconsistent with 

 many of my positions. But I am unable to detect 

 the inconsistency, and Dr. Hall merely asserts it 

 without giving any proof. 



I am in full agreement also with Dr. Hall, not in 

 opposition to him as he supposes, when, passing 

 from force in general to a particular case, he says 

 that a ball swinging in a circle at the end of a string 

 acts upon the string with a force directed from the 

 centre. The ball certainly does exert such a force. 

 I think it misleading to call that force centrifugal 

 force, as he and many writers do ; but that the force 

 which he calls centrifugal force is an actual force is 

 undoubted. 



But when Dr. Hall proceeds to expound his 'inertia- 

 force,' we seem to part company, perhaps because he 

 has not given a complete specification of this force. 

 He has told us its magnitude and its direction, but 

 its place of application, the body on which it acts, he 

 has left us to infer from the context, and my infer- 

 ence he calls in question. It would be useless for 

 me to justify my inference, because in Dr. Hall's 

 letter he modifies the statement of the , pamphlet 

 from which it was drawn, saying that what he meant 

 was that ' ' the inertia-force works [or acts] with the 



smaller applied force against the agent which exerts 

 the greater force." From this modified statement I 

 could not, of course, have made the inference re- 

 ferred to, — in fact, I could have made no inference 

 at all ; for it is couched in language which is not the 

 current language of dynamics, which is not defined, 

 and which I must confess I do not understand. 



Let us, however, take Dr. Hall's new illustration, 

 and see what light that throws on the place of appli- 

 cation of inertia-force. " A train is being started by 

 a locomotive. The forces applied to the train are 

 the pull of the locomotive, and the smaller, opposing, 

 force of friction. The pull of the locomotive pre- 

 vails, but In prevailing it must deal not only with 

 the resistance due to friction, but with the reaction 

 (which also I call resistance) due to the inertia of 

 the train," in other words, the inertia-force. Here, 

 again, Dr. Hall uses terms not current in dynamics, 

 and I do not understand what he means by the loco- 

 motive ' dealing with ' both the frictional resistance 

 and the inertia-force. Whatever may be the exact 

 meaning of that phrase, however, it seems clear that 

 if the inertia-force acts on the train, and if the pull 

 of the locomotive has to deal with this force in mov- 

 ing the train, it must he expected to have some effect 

 on the motion of the train. Yet if F is the pull of 

 the locomotive, R the frictional resistance, M the 

 mass of the train, and a its acceleration, we have 

 undoubtedly, by Newton's second law of motion, 



a = (F— R)-h M; 



and hence the inertia-force is quite without effect on 

 the motion of the train. It would seem, therefore, 

 that the inertia-force cannot act on the train. Does 

 it then act on the locomotive ? If so, it can only be 

 the force which the train exerts on the locomotive, 

 which is of course equal and opposite to the above 

 force F. But it cannot be this force ; for if the 

 brakes be put on the train, though the pull of the 

 locomotive on the train — and therefore the force 

 exerted by the train on the locomotive — may be kept 

 constant, the acceleration of the train will change ; 

 and, according to Dr. Hall, the inertia-force must be 

 proportional to this acceleration. Thus even this 

 new illustration does not enable us to determine on 

 what body the inertia-force acts. 



This difficulty in determining the place of applica- 

 tion of the inertia-force would be at once accounted 

 for if it should be found to have no place of appli- 

 cation at all, and I strongly suspect this to be the 

 true conclusion. Dr. Hall seems to me, in fact, to 

 have postulated a hypothetical force to account for 

 the supposed resistance of a body to the action of an 

 applied force, and to have thus fallen into the error 

 referred to by Poisson in the following sentences : — 



" Concevons qu'un corps soit pose sur un plan 

 horizontal, et qu'il n'y soit retenu par aucun grotte- 

 ment. Si je veux le faire glisser sur ceplan, il faudra 

 neanmoins, h cause de I'inertie de la matifere, que 

 j'exerce un effort quelconque. . . . J'aurai, dans 

 chaque cas, le sentiment de I'effortque je serai oblig6 

 de faire ; mais je ne devrai pas en conclure que la 

 matiere oppose aucune resistance k cet effort, et qu'il 

 existe dans les corps ce qu'on appelle tres impropre- 

 ment une force cVinertie. Quand on s'exprime ainsi, 

 on confond la sensation que I'on a eprouvee, et qui 

 resulte de I'effort qu'on a exerc6, avec la sensation 

 d'une resistance qui n'existe reellement pas" ( Traits 

 de mScanique, tome i. § 120). J. G. MaoGbegob. 



Halifax, N.S., Feb. 22. 



