^lf^i H iffio 9^^f2}j^^HJ ;^ Va p p ,aijif^Bdi.'Jo nobo9iib aril 



-uijpa 3f{j 4f?^£ ' narh 91b 89xjj arfj oJ I ! lo gsuljjy aril 



and similarly for Y and Z ; from which it is evident, thiPU> 

 tafilc*<^ the existence of ^xrlS'^'SP efastlcity in ever)' .system of 



-particJete acting on each other is mere absurdity. And hence 

 it appears, that the " proposition on which the whole theory 

 of double refraction depends" is altogether untrue. 



,). Will it be urged, however, that although the general pro- 

 position does not hold, there still may be particular systems 

 of particles for which it does hold ? 1 do not hesitate to state 

 my belief, that the existence of such a system is vnpossible ; 



^and at any rate would challenge any analyst whatever to sug- 

 gest any such. 



The case then stands thus : — A writer states a proposition 

 as the basis of a theory ; he offers a proof of the proposition, 

 which turns out to be fallacious; and not only is the proof 

 itself erroneous, but during the investigation there appears a 

 degree of evidence approaching to certainty, that the propo- 

 sition itself, after modifying it in every conceivable way con- 

 sistent with the case to which it is meant to apply, is untrue; 

 and there is moreover a jperfect certainty that it is incapable 

 of proof Thus we have a fundamental proposition of which 

 a false proof is given, a certainty that if true, it must always 

 remain a mere assumption incapable of independent proof; 

 and this in the face of the fact that there is every reason to 



, suppose it untrue. Such a combination of circumstances 

 would have decided the fate of any other theory; why is this 

 to be made an exception to the rule? But to return. 



Assuming the existence of the axes of elasticity, we are next 

 introduced to the surface of elasticity. Referring the co-or- 

 dinates to the axes of elasticity, we have , " - -- t- --- ' 



•^ lO ?3i0lJlfiq 9flJ 1o 



jj X = a8a? = ar cos cl\ -' - f-. ' -- - < , . 



! Y — bZy = hr, pos ^ >- where a, h, c are constants. , 

 7j = c'^ is = cr cos y J 



Ifhe rest I shall give in the words of Sir John Herschel (vide 

 Encyclopaedia Metropol., art. Light, 1004): " M. Fresnel 

 next conceives a surface, which he terms the ' surface of elas- 

 ticity,' constructed according to the following law : — On each 

 of the axes of elasticity, and on every radius r drawn in all 

 directions, take a lengtli proportional to the square root of the 

 "(elasticity exerted on the displaced molecule by the medium in 



