374 Proceedings of Royal Society of Edinburgh. [sess.. 
of the interface, a complete solution of the present problem in my 
paper * “ On the Reflexion and Refraction of Light ” in the 
Philosophical Magazine for 1888 (vol. xxvi.); nominally for 
the case of simple harmonic wave-motion, but virtually including 
solitary waves as expressed by an arbitrary function : and I need 
not now repeat the work. At present let us suppose the surface- 
force on each solid to be that which I have found it must be for 
ether,f if magnetic force is due to rotational displacement of ether, 
and the lines of magnetic force coincide with axes of rotation of 
etherial substance. According to this supposition the two com- 
ponents, Q (normal) and T (tangential), of the mutual force 
between the mediums, which must be equal on the two sides of 
the interface, are 
(di + dr,\ 
i -Jdi+'kh 
1 
\dx dy) 
\dx dy) 
/( 
(fq _ d£\ 
\dx dy) 
~ n \dx dy) 
J 
• • (23), 
where k denotes for ether that which for the elastic solid we have 
denoted by ( k + ^n ), and suffixes indicate values for the lower 
medium. If we begin afresh for ether, we may define n as 1/4GT 
of the torque required to hold unit of volume of ether rotated 
through an infinitesimal angle T3 from its orientation of equi- 
librium, and k as the bulk-modulus, that is to say, the reciprocal 
of the compressibility, of ether. Thus we now have as before in 
equations (15), (11), and (18) 
= 2 = a 2 + J ( S = «-* = ~'l 
B q . (24). 
a 2 + c 2 = v~ 2 = - : a 2 + o' 2 = v ~ 2 = — j 
k’ K , } 
Using (20) and (21) in (23) with y = 0 we find 
K (a 2 + c 2 )J' = K t (a 2 + c, 2 )J, ) 
n(a 2 + b 2 )(l + T) = n i (a 2 + b / 2 )I / j ' * ' • )y 
whence by (24) 
p(l + 1') =£,!,; (26). 
* In that paper B, A, and ( denote respectively the n , the k + %n, and the 
p of the present paper, 
t See first footnote to § 1. 
