100 Dr. G. J. Stoney on the Proof of 



am preparing, and which I hope shortly to have ready for 

 publication. It will, I trust, effectually rescue from oblivion 

 at least one method of proof of great value; and I shall 

 endeavour sufficiently to go back to first principles to meet 

 all Mr. Preston's difficulties and remove his scruples. It 

 may be hoped that others with more leisure than the present 

 writer will devote some of it to recovering other parts of the 

 distinctively Dublin work* in Mathematical Physics of the 

 above-mentioned period, which after MacCullagh's death was 

 far too much left to the chances of tradition. 



A few words suffice for the rest of Mr. Preston's letter. 

 In his second paragraph, on p. 458, he says u I fear Dr. 

 Stoney has misunderstood my communication. What I in- 

 tended to convey was &c." What Mr. Preston did convey 

 was not merely tbat he was making the artificial analysis he 

 proceeds here to set forth, but, to use his own words on p. 238, 

 " This then " (viz. an equation furnished by Mr. Preston's 

 artificial analysis) " is the analytical expression of the general 

 theorem enunciated by Dr. Stoney" (which dealt with the 

 analysis effected by nature) ; and what I pointed out is that 

 this is an entire delusion. 



The contrast between the two is well shown by the case 

 discussed by Mr. Preston at the foot of p. 459 of his letter 

 and top of the following page. To give the problem definite - 

 ness let us suppose that what we have to deal with is the 

 radiation by which we see an object which is illuminated by 

 monochromatic light. Here all the luminous waves emitted 

 by the object are of one wave-length, and all have trans- 

 versals lying in the wave-fronts. The analysis of this light 

 under my theorem is into trains of plane waves which have 

 both these characteristics. The plane-wave components have 

 all of them the one wave-length of the monochromatic light, 

 and the transversals everywhere lie, as they should, in the 



* Another feature which then distinguished the teaching of the Uni- 

 versity of Dublin in Mathematical Physics was the almost exclusive 

 study of great writers — Newton, Lagrange, Laplace, Poisson, Gauss, 

 MacCullagh, Ampere, &c— instead of re-castings of their work by com- 

 pilers of text-books; and all were illuminated by incorporating into 

 them the geometrical methods peculiar to the University, wherever this 

 was practicable. The great achievements of the fifty years that have 

 since elapsed — Thermodynamics ; the Kinetic Theory of gas ; Spectroscopy ; 

 the Electricity of Faraday, Clerk-Maxwell, and Lord Kelvin; the Electro- 

 magnetic Theory of light — were then unknown ; but while the teaching 

 of the University has since gained so immensely, something has been lost, 

 and especially in regard to the methods which were distinctive of a 

 Dublin training and which in a marked degree tended to produce original 

 thinkers. 



