Mr KELLAND, ON THE TRANSMISSION OF LIGHT 



22 T —] sm- -— =((. 



Sx' . „/eSp 

 '2S^sin-— ^ =m, 

 /■' 2 



and calling 



„Sir . „kSp 

 22 -4- sin-— p- =71, 



r 2 



r 





3^y'\ ._„A-d/j 



sni- -— ^ = ". 



9 





62 — r- sin' — - = 1 , where a + o + c = 0. 



r 2 



62-^ sm'— ^ =X, 



2 



.62 — ^sin'— i- =Z, 

 r 2 



multiplying the equations by P, Q and i? respectively, and adding 

 them, we may put the result under the form 



,rf' 



.d'l3 



provided we make 



{a-A)P=QZ + RV, 



(b-A)Q = PZ+RX, 



{c-A)R = PY+QX. 



By eliminating P, we obtain 



\{a-A){b-J)-7/\ Q=\YZ+{a-A)X}R, 

 {{a-A){c-A)-Y'\R={YZ+{a-A)X\Q, 

 and finally 



i^ci- A) {b - A) {c- A)- X' {a- A)-Y' ib- A)- 7/ {c - A)-2XYZ=0, 



or {A-a) {A-b){A-c)- X\A-a)-Y' {A-b)- Z-" {A-c) 



+ 2XYZ^0, (2); 



an equation which it may be readily shewn gives tliree possible values 

 of A. 



