290 



NATURE 



{Jan. 24, 1889 



of radial acceleration that is at the bottom of this whole 

 " new theory." The puzzle was solved completely long 

 ago, in the clearest possible manner, and the " Principia " 

 is the witness to it ; but it is still felt to be a difficulty by 

 beginners, and I suppose there is no offence in applying 

 this harmless epithet to both Mr. Grant Allen and Mr-. 

 Clodd, so far as the truths of dynamics and physics are 

 concerned. 



"Energy" and "Force" are always opposed to one 

 another, and the meaning of the author is well illustrated 

 by the following quotation : — 



" Again, when two masses are in a state of aggregation, 

 the Force of gravitation resists any attempt to sever them. 

 If a cannon-ball lies upon the ground, it cannot be raised 

 without an expenditure of Energy, and the amount of the 

 Energy required to lift it to a given height is the measure 

 of the resistance offered by Gravitation." 



That is to say, the energy required to lift a body to a 

 given height is a measure of the force of gravitation. 

 This reminds one of some of the sentences in Tyndall's 

 " Heat." 



The next chapter, " The Species of Energy," classifies 

 energy as molar, molecular, atomic, and electrical, just 

 as in the case of force. " Of Molar Energies employed 

 in resistance to aggregation, the most familiar instance 

 is that of orbital movement " — moon and earth, S:c. 



Now we come to the crux of how horizontal motion 

 can be an " energy " in the sense defined by Mr. Allen. 



" On a smaller scale, the Energy of a bird in flying, or 

 of a cannon-ball fired horizontally, is largely employed in 

 counteracting gravitation " ! ! 



May I inform the author of an elementary fact 1 A 

 cannon-ball fired horizontally falls just as quickly, and 

 reaches the ground (if flat) in precisely the same time, 

 as if it were merely dropped ; its energy of motion 

 has no power of counteracting gravitation. The same 

 is really true of the moon : it falls towards the earth 

 just as much in each second as if it had no orbital 

 velocity ; in no case does motion influence^the effect pro- 

 duced by a given force. But this is just the fact which, 

 if he had been able to recognize it, would have saved him 

 the trouble of writing this treatise. 



I said I would charitably omit reference to the mole- 

 cular, chemical, and electrical statements, but I cannot 

 resist one quotation from the next page : " Large masses 

 of water before freezing part with their Energy in the 

 visible form of heated mist." 



Chapter VII. is headed "The Kinds of Kinesis," by 

 which is meant apparently the varieties of motion. Motion 

 is subdivided, not into rotation and translation^ but thus : — 



" Motion has three Kinds ; ... it may be separative, 

 or it may be aggregative, or it may be continuous and 

 neutral. Each species of Kinetic Energy has a form of 

 each kind." 



The author now finds it necessary to grapple with the 

 difficulty which we guessed he would sooner or later feel, 

 viz. how it is possible to bring falling motion, or motion 

 of bodies towards one another, under his category of 

 "Energies or separative Powers." A body thrown up^ 

 and a body thrown horizontally, he has already tackled by 

 simply committing some convenient errors of fact. He 

 surmises that such bodies fall less than they would if 



dropped, and thus that their energy of motion counteracts- 

 gravitation ; but the case of a body thrown down is not to- 

 be thus managed, so he proceeds to get over the difficulty 

 in three ways. First, by raising a cloud of words ; second, 

 by asserting that when a body strikes the earth, althoujjh 

 its potential energy of separation has disappeared, yet the 

 heat of its collision separates atoms just as much, and 

 results in the same ultimate amount of separation again 

 (a statement which in no sense can be considered true), 

 so that the motion which intervened between the start and 

 stop of the falling body " we are justified in regarding 

 as essentially a transitory form of separative Power." 



"Throughout we see that aggregative Energy" {i.e. 

 energy apparently aggregative) "is merely Potential 

 Energy in course of transformation to another form. While 

 the really aggregative Power of Force is causing these 

 bodies to combine, the Energy of their motion represents 

 for a while their original separateness, and is finally 

 transformed into a similar separateness between other 

 bodies." 



So, while motion /r^;y/ the earth is true kinetic energy, 

 motion tozuards it is a transitory form of potential energy^ 

 and represents for a while the original separateness of the 

 bodies I 



When a doctrine requires a statement like this to 

 bolster.it up, it is wise to take the need as a sure 

 indication that we are somewhere off the track, and had 

 better get back to the turning whence the path which has 

 led us into such a jungle diverged. It is a pity the author 

 did not take the hint thus clearly vouchsafed to him. His 

 difficulties about understanding normal acceleration and 

 the generality of Newton's second law were natural and 

 excusable, though hardly the subject to write a book 

 about ; but after encountering and being worsted by this 

 last thicket, it was very unwise to go on plunging madly 

 forward, and exhibit his scratches as signs of victory. 



But he has not yet made his last struggle into still more 

 hopeless entanglement. Here is his third attempt at 

 extrication : — 



" We see that the Energy of a falling body does 

 not consist in its mere downward movement, but rather 

 in that accelerating motion which is capable of being 

 transformed into heat when the masses aggregate." 



If this statement means anything, it means that the 

 kinetic energy of a down-moving body consists, not in its- 

 velocity, as is the case with an upward-moving body, but 

 in its acceleration, and that it is this acceleration which 

 ultimately gets turned into heat ! 



" So the Energy of Kinesis is seen to be a mere trans- 

 ferential mode from one kind of separation to another.'' 

 " Motion is the redistribution of Separations." 



One may at least acknowledge the ingenuity as well as- 

 the gallantry with which the author endeavours to get I 

 clear of his impenetrable jungle. 



In passing, here is a curious definition of friction, givett 

 in an explanatory note. 



" From the point of view of the Force involved, friction 

 means the cohesion which must be overcome ; but from 

 the point of view of the Energy employed, friction means- 

 the separative power of heat which overcomes." 



j Next we come to the extraordinary but fortunately 

 I short chapter entitled "The Persistence of Force," which 



