and the Conservation of Momentum. G29 



which is absolutely self-contradictory and meaningless. This 

 mistake o£ placing the axes of reference on one of the reacting 

 bodies has hflen made twice by Dr. Toiman. 



The first case * occurs in an attempt to prove bv a different 

 method the same proposition, given previously by himself 

 and Prof. Lewis, which has been discussed above. There are 

 only two bodies mentioned, and the observer is placed on one 

 of them. They collide, and in discussing the collision the 

 author speaks of the velocity of the body on which the 

 observer is placed. The conclusion is then attained that the 

 variation of the mass of a body with its velocity can be 

 ascertained by one of the observers if he remembers that, 

 while he cannot determine his absolute velocity, he can 

 determine that velocity of his which occurs in (A). Of 

 course this velocity is precisely that absolute velocity which 

 he cannot, ex hypothesi, determine. If there are only two 

 bodies present, the only velocity which can possibly be 

 determined is their relative velocity ; it cannot be split into 

 one part which is the velocity of one body and another which 

 is the velocity of the other, unless there is present also a body 

 absolutely unaccelerated. 



6. The second case occurs in the attempt made in the March 

 number of this Magazine to apply the result to electro- 

 dynamics. A charged body reacts with the instruments 

 exciting electric and magnetic fields, which are measured by 

 an observer at rest relative to those instruments. That is to 

 say, that the axes of reference are placed on one of the reacting 

 bodies, and (1), which only applies when the axes of refer- 

 ence are placed on an absolutely unaccelerated body, is utterly 

 irrelevant. 



7. Of course the same logical error is committed every 

 day in the laboratory : it is committed, for instance, every 

 time that g is determined by pendulum observations. AYe 

 then measure displacements relative to the earth and identify 

 them with absolute displacements in equations based upon 

 Newton's principles, which deny that the earth, when re- 

 acting with a pendulum, can be absolutely unaccelerated. 

 The justification in this case is that the method turns out \o 

 yield consistent and satisfactory results. But practical truths 

 can be used legitimately only in practical circumstances : 

 Dr. Toiman is attempting to prove a proposition of the utmost 

 generality, and he is using in his attempt the consideration of 

 circumstances which can never be approached practically. 

 His results may be true : indeed his results are much more 



* riiys. Rew xxxi, p. 2G (1910). 



