5221 Mr. J. W. L. Glaisher on a Multiple 



Naturally the previous assumption -£ =L 2 (understanding 



^ 1 

 by L 2 a constant independent of the density) has for its con- 

 sequence the further — = % 2 = constant, from which then 

 follows 



and, at least for substances with a single absorption-streak, 



D' = C(n^-l) (K) 



The dependence hereby expressed between refraction and dis- 

 persion is in fact demonstrated by my experiments on gases. 

 They show, namely, that in a gas-spectrum the distance be- 

 tween two lines which are sufficiently distant from the middle 

 line, so that in equations (8) and (i) the wave-lengths I and \ 

 can be exchanged for one another, are proportional to their 

 prismatic deviation. 



Further, as regards the treatment of anisotropic media, 

 equation (h) for these should evidently be written thus, 



And thence it is obvious, not merely that the reasonings in 

 §§ 7-12 still retain their previous applicability, but also that 

 especially the more rigorous equations VII. and VIII., after 

 corresponding completion, would likewise remain valid. 



The same would be the case with respect to equations IX., 

 X., XI. of circularly polarizing media. 



The conclusive decision if k in reality differs from nil de- 

 pends, as it appears to me, on the answer given by experiment 

 to the difficult question whether the refraction-ratio of the 

 metals can or cannot be less than unity. 



LXIII. Further Note in regard to a Multiple Differentiation of 

 a certain Expression. By J. W. L. Glaisher, M.A., F.R.S.* 



THE present additional note contains a result of a similar 

 nature to that noticed in the September Number 

 (pp. 208-211), but which follows from the (n-l)ple integral 



Jo Jo Jo 



1 1 2 



exp 1 —x—y ... — t \xn yn 



t=i-i , , u (2tt)K«-D 



n ax dy . . . dt = - — '- e~ 



9 s/n 



* Communicated by the Author. 



