446 Dr. J. Kerr on a new Relation between 



and, with these values of X and /ul } the expression for N becomes 



ivr- (l-w)(3 tt--5) (tt-l)(3tt-l w-1 



iN ~ 2 3 + 2 3 2 



= (»-l)(*=^)=0, . . . : . (13) 

 and N vanishes identically. 



14. Consequently, since ^ = \~T ) j we nn( ^ that 



( 



is equal to 



dr 2(w— 1) 2w— 2 y 



'rfa . 3/z — 1 3 ?z 



+ ^ TT« 2 - 



J*)* 8 ; 



W* 2(ra— 1) 2 7i 



and either of these equivalent expressions is a differential criti- 

 coid, which we may call a differential quadricriticoid. The for- 

 mulae fail when n=l or n=2, and primordinals and biordinals 

 have not such a criticoid. The differential varies from the ordi- 

 nary quadricriticoid in this, that the corresponding coefficients 

 of the former contain n } the order of the given differential equa- 

 tion, while those of the latter are free from n. 



"Oakwal" near Brisbane, Queensland, 

 Australia, June 11, 18/5. 



LI V. A new Relation between Electricity and Light : Dielectrified 

 Media Birefringent. (Second Paper.) By John Kerr, LL.D., 

 Mathematical Lecturer of the Free-Church Training College, 

 Glasgow*. 



L /E come now to the case of liquids. The principal results 

 are summed up in articles 33, 42. 



25. Plate-cell for Liquid Dielectrics. A well-made cell is in 

 these experiments indispensable. The piece which I call a plate- 

 cell, though simple enough in plan, is rather troublesome to 

 make, and very liable to fracture in the workman's hands ; but it 

 is the only cell which I have yet got to work satisfactorily, and 

 I have used no other in my latest experiments. I begin, there- 

 fore, with a full account of its construction. 



The reader will remember the large dielectric of plate glass 

 (2 inches wide and 6 long) which formed the principal subject of 

 my first paper. A new block of plate glass is taken similar to that 

 one in form, size, and mounting ; but the borings are different. 



* Communicated bv the Author. 



