1880.] 3Ir Glazehrook, On the Reflexion and Refraction of light. 329 



and therefore, since 



Alo(^) Al,(2/) = M:1(x + y) Al,^i [x-y)- 1<?M^I {x + y)Mp,{x-y), 



Ayi [a' + h') Al/i- {a'-h') - F Al^i {a! + V) M^l {a' - h') 

 Ai;i [a + h) A\^{a -b)- FAl/i {a + 5) Al/i (a - 6) 



AIq^Hc + d') Ai;i (c^ - (^') - F Al/i (c^ + c^Q Al/i (c^ - ^') 

 ^ Ai;i (c + d) Ai;i (c - cZ) - F Al/I (c + c^) Al/i (c - c?) ' 



whence, since 



A.\l{a^-h)K\ I (a - b) A\ i (g + d) A\ |- (c - d) 



= A]„i (a'+ 6') Al^i (a- b') Al,| (c'+c^') AloJ (c -tZ'), 



{1 - Fsn^-|(a'+ b') sn'^(a'- b')]{l- Fsn^| (c + ^')sn^l(c^- d')} 

 {l-Fsn^i(a + 5)sn^i(a-6)}{l-Fsn^i(c + (^)sn-'i(c-^)} ' 



and by combining the four formulae (i)'...(iv)' we obtain at once 

 the six theorems quoted at the beginning of § 10. 



(2) Mr R. T. Glazebeook, M.A. On the Reflexion and Re- 

 fraction of light. 



In his paper on the reflexion and refraction of light, Green 

 assumes that there are no forces acting on the ether but those 

 which arise from the relative displacements of its parts. Kirchhoff, 

 in a paper read before the Royal Academy of Berlin, considers the 

 problem of the reflexion and refraction of plane waves in crystal- 

 line media. He supposes there are impressed forces acting over the 

 bounding surface of the two media. 



These forces are such as to prevent the propagation of normal 

 waves either reflected or refracted, while at the same time they do 

 no work on the vibrating particles of the ether. On the same 

 assumptions I propose here to discuss at length the case of two 

 isotropic media, following Kirchhoff 's method. 



Let the forces be X, Y, Z, acting per unit area of the bounding 

 surface parallel to the axes. Let u, v, w be the displacements of a 

 particle whose position first is x, y, z. Then the rate at which 

 work is done per unit area is 



^du ^^dv ydw 

 dt dt dt ' • 



Let iVj, N^, N^\ T^, T^, T^ be the strains in one medium, 

 iV/, A";, N^; T/, T/, T/ in the other, p, p the densities. Let the 

 plane cc = be the bounding surface of the two media, and let x 

 be negative for the first positive for the second medium. 



