36 The Foundations of Dynamics. 



compressed strata of two impinging rods. Yet if the elastic 

 connexions of every stratum are attended to, and if these 

 be regarded as iriassless, I think it will be found that all 

 the transmitted kinetic has really passed through a momentary 

 existence as potential. The fact of necessary transformation 

 is not so obvious when you come to look into some of these 

 special cases ; but I would refer once more to the proof given 

 at the beginning of Part IV., which seems to me conclusive 

 as to essential fact. 



The difficulty arises because when an elastic body is struck 

 (say a massive molecule with a massless spiral spring con- 

 nexion) it begins to move a little directly the spring is the 

 least compressed, and is moving half speed when the spring is 

 fully compressed ; but I venture to say that on any view of 

 the identity of energy the bit of kinetic which it first attains 

 is a bit of energy that has been transmitted through the 

 elastic stress of the spring, and that just as the second half 

 of the energy must admittedly exist in the spring before it 

 can reach the mass, so the first half has already passed through 

 the spring and has reached the mass only after transmutation, 

 although the transformation is disguised while the trans- 

 ference is obvious. 



I have now written enough to emphasize what I want to 

 bring forward as the simple doctrine of energy. Some years 

 ago * I attempted it with brevity, but failed to make it clear 

 or to call proper attention to it. Now I have set it forth at 

 length, with illustrative cases, as matter for discussion. It 

 remains to try and formulate briefly and strictly the extended 

 laws of motion appropriate to our present knowledge. 



* Especially in Phil. Mag. for October 1879, page 278 et seq., for 

 January 1881, p. 37, and June 1881, p. 530, and for June 1885, p. 482. 

 Also in 'Elementary Mechanics' (Chambers), which was written in 

 1876 and revised about 1884, without change in the energy chapter so 

 far as I remember ; I am not responsible for dates on title-pages. 



My attention has just been called to a " Smith's Prize " essay by Mr. E. 

 F. Muirhead, communicated by Professor James Thomson to the Philo- 

 sophical Magazine for June 1887. This essay, both in itself and in its 

 numerous quotations and criticisms, is an instructive and useful summary 

 or exposition of nearly everything that is foggy, confusing, and utterly 

 unsatisfactory in the fundamental treatment of Dynamics. It is hardly 

 toomuch to say broadly that the entire order of ideas in that essay is 

 antipodal to the conceptions I am endeavouring to urge on the acceptance 

 of Physicists. 



