410 Prof. Lorenz on the Theory of Light. 



sequences which could have been arrived at in no other way ? and 

 have these consequences always been correct ? 



The Theory of Capillarity can be developed equally well with- 

 out these hypotheses ; and the only result to which they have 

 led is the principle discovered by Laplace and Poisson, that the 

 height of liquids in capillary tubes at different temperatures is 

 proportional to the densities of the liquids. This principle, how- 

 ever, is false. The same assumption, applied to the doctrine of 

 Electricity, led Poisson to the determination of the relation 

 between the two electric constants ; but this conclusion also has 

 turned out to be incorrect. Poisson's calculation has been par- 

 tially altered, and the final deductions veiled under an unsummed 

 summation-formula ; but does such a result give us any right to 

 consider the accuracy of our previous hypotheses as established ? 

 This assumption led, in Cauchy's hands, to wonderful results 

 by its application to the theory of light. Originally it served to 

 explain the dispersion of light ; it was, however, at once found 

 that a materially vacuous space would disperse light, provided 

 that a definite hypothesis was made regarding the nature of force 

 as a function of the distance. One would have supposed that so 

 important a glimpse into the nature of molecular forces would 

 necessarily lead to further consequences ; but this was not the 

 case. On the contrary, it was found in this case as in others — 

 for example, in the cases of the hypotheses which it was neces- 

 sary to add in order to explain double refraction — that the new 

 hypotheses were serviceable for those purposes only for which 

 they had been invented : ulterior consequences could not and 

 might not be drawn from them. 



I will not, however, dwell upon objections of this kind, since 

 they have already been made, but still have not overthrown the 

 theory. They have on their side only a certain degree of pro- 

 bability, while against them are ranged all the important results 

 which have hitherto been deduced from the theory. On the 

 contrary, I will lay stress upon a new objection, inasmuch as 

 it in reality upsets the theory, while the great results of the theory 

 which can be opposed to the objection, are not so great but 

 that, as I shall show, they can be much more completely attained 

 by a different method. 



The phenomenon of circular polarization obliged Cauchy to 

 assume a periodicity in the internal structure of bodies. Against 

 this nothing can be objected ; for such a heterogeneity is precisely 

 the most general case, and homogeneity, on the contrary, a par- 

 ticular case. Cauchy, however, committed the fundamental 

 mistake of assuming that the mean values of the periodic dis- 

 placements of the particles of the sether were approximately 

 dependent merely on the mean values of the periodic coefficients 



