373 
1898-99.] Lord Kelvin on Reflexion and Refraction. 
and in the lower medium 
£ = bl f(t - ax + by) + ajf (t -ax + cy ) 
r] = alj(t - ax + by) - efl J(t - ax + cy) 
where I, I', I y , J', J /5 denote five constant coefficients. The 
notation J' and J, is adopted for convenience, to reserve the 
coefficient J for the case in which the incident wave is condensa- 
tional, and there is no incident distortional wave. There would 
he no interest in treating simultaneously the results of two 
incident waves, one distortional (I) and the other condensa- 
tional (J). 
§ 11. We may make various suppositions as to the interfacial 
conditions, in respect to displacements of the two mediums and in 
respect to mutual forces between them. Thus we might suppose 
free slipping between the two : that is to say, zero tangential 
force on each medium; and along with this we might suppose 
equal normal components of motion and of force ; and whatever 
supposition we make as to displacements, we may suppose the 
normal and tangential forces on either at the interface to he those 
calculated from the strains according to the ordinary elastic solid 
theory, or to be those calculated from the rotations and con- 
densations or dilatations, according to the ideal dynamics of ether 
suggested in the article referred to in the first footnote to § 1. 
We shall for the present take the case of no interfacial slip, that 
is, equal values of £, rj on the two sides of the interface. Remark- 
ing now that where y = 0, the argument of / for every one of the 
five waves is i t -ax we see that the condition of equality of dis- 
placement on the two sides of the interface gives the following 
equations : — 
b(l - 1 ) + aJ = 61 + aJ ) 
. ( 22 ) 
a(l + 1') + cJ = al , - cfl i 1 > * 
§ 12. As to the force-conditions at the interface, I have already 
given, for ordinary elastic solid or fluid matter * on the two sides 
* The force-conditions for this case are as follows : — 
Normal component force equated for upper and lower mediums, 
(Tc - §rc)5 + 2 n^ = (Jc t - 1^)5, + 2n,(^) ; 
dy \dy/i 
and tangential forces equated, 
d + !§)- re '( 
dr] 
+ d -i) 
dx dy ) , 
