602 



NATURE 



[April 27, 1893 



produce a given increase of velocity in the combined 

 system, it appears by our assumption that, as the relative 

 velocity is much greater after the second blow given to 

 m than after the first, the increase of velocity of the 

 system produced by this indirect method of applying 

 the second blow will be much greater than by the first, 

 and consequently much greater than the velocity that 

 could be given to the system by applying the blow 

 directly. By reducing the system to its otherwise pro- 

 duced velocity Vj, we could obtain a certain amount of 

 energy, and then repeat the process ad infinitum, thus 

 obtaining a continual supply of energy. 



An investigator without a mission would be led by 

 this curious result to assume that there must be some 

 mistake in his arguments, and " Waterdale " evidently 

 has some lurking doubts. He sees that it is impossible 

 in the simple case of bodies having only one direction of 

 velocity. Impact can never reduce two bodies of a system 

 to move with the same velocity and conserve energy. 

 We cannot have momentum and energy both conserved. 

 Unless M = o we cannot have 



mv-^ = (M + w)Vi 

 \mv^ = i(M + m)N{'. 



In order to divide the energy \mv^- between the two 

 bodies and reduce them both to a common velocity, we 

 require a third body, and then what becomes of the 

 principle that seemed so plausible, that the increased 

 velocity that tn could impart to M depended on their 

 relative velocity only? " Waterdale " sees the hitch all 

 right in the simple case, and consequently, in order to 

 cheat nature by inventing a complicated case in which 

 he hopes that she will get as muddled as himself, he 

 interposes bent channels, a third and fourth body to re- 

 ceive the blows, springy arms to absorb energy, and 

 smooth surfaces to divert the motion. He evidently has 

 some doubts about all this, for, notwithstanding his 

 assertion that "Appendix II. is a mechanical demon- 

 stration to prove that by the principleoft/-?/^'^/// of force, 

 a saving in mechanical work, . . . can be effected," and 

 that " there is no speculation about this, but simple 

 fact," yet he gives only a series of suggestions and vague 

 ts,\Xv\2Xt,'s,2L's, unspeculative proof s,\.\i2X the energy spent 

 in bending his springs, in jumping his bodies about, and 

 so forth, is negligible, while in reaUty it is an important 

 part of his system. That it is so necessarily is proved 

 conclusively by the impossible result he obtains by 

 neglecting it. This is the really interesting principle in 

 the whole matter, that it is not possible to give energy 

 to a system of bodies by giving a series of impulses to 

 some particles of it, to be transmitted to the rest of the 

 system by actions within the system without some part 

 of the energy being spent on internal motions in the 

 system. It is here that the example touches upon the 

 second law of thermodynamics, Boltzmann's hypothesis, 

 and so forth. In order to minimize the effects of these 

 internal vibrations, &c., "Waterdale "argues thus : "Loss 

 No, 2" (giving rise to internal vibrations of his system) 

 "if it arises" (he himself shows that it would, though 

 he overlooks a more important loss), " would be of the 

 nature of internally asserted work." ..." This loss of 

 work could not be great, for we see by the diagram that 

 the span of work already done when the ball arrives at 

 NO. 1226, VOL. 47] 



o is small compared with what it has to do." Notwith- 

 standing his profession of calculating everything he 

 does not calculate here, nor does he calculate with what 

 velocity the ball would rebound after it hit the body B, 

 which ultimately stops it ; in fact he omits this important 

 question altogether, and goes to the " third factor, the 

 bending of the arm of the system," which he goes on to 

 say, without calculation, "can be almost neglected if we 

 take the tension of elasticity of the arm to be small." 

 " I should say that one-eighth internal loss of work 

 would certainly more than cover everything." This 

 blessed " I should say ! " Is it thus that " Waterdale " 

 gives " a mechanical demonstration to prove .... a 

 saving in mechanical work"? "There is no speculation 

 about this " ! It is " simple fact, if calculation by figures 

 can be accepted as true." Most people would agree that 

 " if calculation by figures can be accepted as true " the 

 velocity that could be given by any mechanism to the 

 system indirectly could not be greater than what would 

 give it kinetic energy corresponding to the work supplied. 

 If "Waterdale" will apply a system of levers, springs, 

 &c., acting on the fixed bodies of his system, so as to 

 reduce all the bodies to relative rest, and thereby gives 

 up as hopeless the task of inventing some method 

 by which he can by internal actions alone transfer kinetic 

 energy from one body of a system to the whole of the 

 system without wasting any of it in internal kinetic or 

 potential energy, then he will see how he has to give up 

 the apparently legitimate assumption that the velocity 

 one body of a system can give to the whole system 

 by being itself reduced to relative rest depends only 

 on the relative velocity of the body and the rest of 

 the system. He will see that it depends also on the 

 velocity of his system relative to those supposed fixed 

 bodies he will require as fulcrums for the mechanism re- 

 quired to transfer the energy of the one body to the rest 

 of the system. He sees that something is required to 

 keep his wedge moving forward. He arranges " that the 

 wedge is supported by a following force . . . during 

 this part." The amount of work required he without 

 calculation assumes to be small, and he is probably right 

 here ; but it is only one of several losses that he does not 

 calculate, and there are others, such as the conditions of 

 impact at the end of the flight of w, that he does not 

 even notice, though this is the very first that should strike 

 a person investigating the subject after he had clearly 

 seen, as "Waterdale" appears to do. that it is here, in 

 the laws of impacts, that the simple case of velocity in 

 one direction and direct impacts fails. It is interesting 

 how cases of this kind illustrate the warming of a gas by 

 compression, the vibrations produced in a bell when 

 struck, and other such cases where energy is given to one 

 part of a dynamical system for this part to distribute 

 amongst the whole, and also how it illustrates the way in 

 which the amount of this internal energy depends on the 

 mobility of the part originally moved. Of course it is all 

 plain enough when the subject is attacked by means of 

 general principles of conservation of energy and momen- 

 tum, but when the interactions of the different parts of 

 the system are individually considered and the mind dis- 

 tracted by the complexity of the problem, there is real 

 danger that what is important may be overlooked as 

 trivial, as has been done by " Waterdale." He is not to 



