192 The Rev. S. Haueuton on the Equilibrium and 
Let the case considered be that of two indefinitely extended homogeneous 
and uncrystalline solids, separated by a plane (which is assumed the plane «, 7), 
then the six conditions to be satisfied at the limits are, as in (46), 
& = fee ay! = ni”, ¢ = Gs 
ee Ce he a= =f 
which become, by means of equations (52), 
a -: > C=05 
Aus or) Seale Sie ee dé" a) 
ete tga" Cet eta) 
4 (OM vy AEN Only wae! 
x ‘Geta Sh (fe +5) 
(d¢! dé dc’ de” 
nae oS bieette dz] 
The incident vibration may be either transversal or normal; but as the 
transverse vibration may be resolved into two vibrations, one perpendicular to, 
and the other in the plane of incidence, we must finally, in order to include all 
the possible varieties, discuss the three following cases : 
1. Incident vibration transversal, and perpendicular to plane of incidence. 
2. Incident vibration transversal, and in the plane of incidence. 
3. Incident vibration normal, and in the plane of incidence. 
The plane of separation is the plane of x, y; z being perpendicular to this 
plane, and the intersection of the plane of incidence with the separating plane 
being the axis of 2. 
(57) 
Ist. The incident vibration transversal, and perpendicular to the plane of 
incidence. In this case we shall have € = 0, ¢= 0; and since the vibration is 
similar along the front of the wave-plane, we shall also have » independent of ¥. 
The differential equations (50) will therefore be reduced to 
en (ery dr! dy" plan . dy" 
mee “ — HT hate Z 58 
7 eps (a Ie Ta) hfe. (ae! Zi Za) (98) 
and the equations (52) will become 
