NATURE 



60 1 



THURSDAY, APRIL 27, 1893. 



DYNAMICS IN NUB I BUS. 



Waterdale Researches; Fresh Light on Dynamics. By 



" Waterdale." (London; Chapman and Hall, 1892.) 



WHEN St. Paul tried to convince the Athenians 

 that they were mistaken in their philosophy, he 

 probably spoke to them in Greek instead of expecting 

 them to learn Hebrew. " Waterdale " is trying to con- 

 vince nineteenth century philosophers that it is possible 

 to invent mechanism by which he can attain "the un- 

 doubted theoretical possibility of perpetual motion" and 

 he does not take the trouble of learning the language of 

 those whom he desires to convince, but insists that they 

 must learn his language, simply because he professes to 

 have invented a possible explanation of gravity. He 

 acknowledges that his work would require at least a 

 month's hard work to comprehend, and taunts the scien- 

 tific world for not gladly spending this time in refuting 

 what most of them have already spent weeks on — 

 namely, refuting the very ingenious inventions of cranks, 

 who think to cheat nature in the dark by some round- 

 about way of doing what simple considerations show to 

 be impossible. A good month's work to teach him ! 

 Let him pay somebody with a reputation whose time is 

 probably worth twelve hundred a year, say a month's 

 time, one hundred pounds, to explain and convince 

 him of the impossibility of his mechanical arrangement. 

 It would take more than a month, however. If human 

 experience is worth much it proves that there is very 

 little use in trying to convince people with missions 

 whether they are right or whether they are wrong. And 

 fortunately so ; for, if they are right they will ultimately 

 prevail, and if they are wrong after all they generally do 

 more good than harm by interesting the world in some- 

 thing outside and better than the selfish interests of 

 individuals. 



" Waterdale " attributes a good deal of importance to 

 this mechanism. He says in his preface : " Let the 

 scientific reader, I would ask, take the trouble first to go 

 through these calculations, and he will then have some 

 idea as to whether the rest of the book is worthy or not 

 of careful perusal." In the body of the work he invents 

 a very complicated hydrodynamic machine to effect his 

 purpose. He there refers to the very much simpler 

 arrangement described in the appendix, and says : 

 "Unless the possibility" (of perpetual motion) "is ad- 

 missible, then I must confess that the theory of equal 

 real ponderosity to all matter can ne-c'er be accepted." 

 He acknowledges at the same time " that with full know- 

 ledge of the liability to error when dealing with the 

 action of forces," all he can reasonably do is to ask 

 "that . . . pure mathematics be once more applied to 

 the subject." All the same, he asserts that " no disproof 

 can be, or has up to the present been given." " There is 

 no speculation about this, but simple fact, if calculation 

 by figures can be accepted to be true." There are so 

 many things touched on in the work that do not seem in 

 any w.iy necessarily connected with the question of 

 "equal real ponderosity," that it is desirable to show 

 how much interest " Waterdale" feels in this part of his 

 NO. 1226, VOL. 47] 



theory in order to justify the paying of any serious 

 attention to what can, on general principles, be so easily 

 disproved. It would certainly not be worth while in. 

 vestigating the question in a scientific journal in order to 

 convince the author of the paradox. He could only be 

 convinced by very painstaking and judicious personal in- 

 terviews of his error and of the unimportance of this 

 question of equal real ponderosities. It would hardly 

 be worth while investigating the question merely because 

 " Waterdale " attributes importance to it, but it is worth 

 while doing so because others may attribute importance 

 to it, and still more so because " Waterdale's" mechanism 

 is interesting and involves a principle that is intimately 

 connected with the second law of thermodynamics, Boltz- 

 mann's hypothesis, and a lot of recondite questions which 

 are puzzling the scientific world, so that it is not much 

 wonder that even a clever and ingenious person should get 

 involved in its meshes, especially when that person is 

 involved in a "mission." 



The general idea involved in "Waterdale's" me- 

 chanism is as follows : — Suppose a large body (he 

 objects to the word "mass") M and a small one ;«, 

 and a spring or other means by which kinetic energy 

 can be given to the bodies. If the spring exert a con- 

 stant force F through a space Jj, it would communicate a 

 velocity Vj to (M -t- iri), given by the equation — 

 F^i = 4(M + m)N^. 



If now it work through a distance s^ it will increase 

 this velocity to Vj, when 



Ys^ = ^(M -I- m){N^- - V,2). 



So far all is plain sailing. But we may proceed in 

 another way. We may let the spring work against m 

 alone, and then by suitable mechanism use w's kinetic 

 energy to make the combined system M + m move. In 

 this way we might expect to give ;« a velocity t/j, such 

 that Fj, = ^wiz/j^j and when this energy was spent on the 

 two bodies M + w, they would acquire a velocity Vi the 

 same as before, given by \7nv^' = ^(M + m)V^. Now 

 comes an important assumption, that if the relative velo- 

 city of jn and M be equal to v^, then by proper mechanism 

 it must always be possible to increase M's velocity by Vj, 

 while m's velocity is being reduced to Vi. 



Suppose now Wj, moving with velocity Vj, we act upon 

 m by means of the force F, again through the distance 

 ^2 we have for its final velocity z'™ — 



¥s^ = jw(7V - Vj^). 



Hence the relative velocity of M and m is v.^ - Vj. 

 By choosing s.^ = 3.C1, we can arrange that Vj = 2Vj, as it 

 simplifies the further argument. In this case 



Z,j2 - VjS = 3z/j2 or 2,^2 = 3»i2 -f- Vi2 ; 



and the relative velocity 



z., _ Vi = sJsv^^ + Vi2 - Vi, 

 which may be much greater than Vi, if Vi be much greater 

 than Vi, I.e. if m be much smaller than M. This shows 

 that the relative velocity after the second blow may 

 be much greater than after the first, even though 

 the two blows were so chosen as that if applied 

 directly to the combined body they would produce 

 equal increments of velocity in that body. As- 

 suming then that a given relative velocity can always 



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