180 The Rev. 8S. Haveuton on the Hquilibrium and 
pendiculars on tangent planes drawn at the six points where the normal of the 
incident wave-plane pierces the ellipsoids; the intercepts of the normal itself 
being (7, 7,.7,,> P» P)» P),,) 3 and let (a) denote the direction (a, 8, y) in which 
the real molecular vibration takes place; then we shall have the following geo- 
metrical meanings for the quantities (h, &c., k, &c.), 
rye cos(ap,) ae cos (az) 
nos PY, aK TP, 
one cos(ap,,) pe cos(a,,) (44) 
a Pi yy 4 Ty Py 
ha = cos(ap,,,) k= os (am,,,) 
uh Pula ti TyyPi 
Hence the equations for determining the direction of the two transversals become 
finally, 
Pin? 1 €08( ap,,) cosy, —p,,7,,.cos(ap,,,) cos“, = O 
Pp, .Cos(ap,,,)CosX, — p,,,7,,.CoS(ap,) cosy, = O 
P,,7 ,-COS(ap,) cos, — p,r,. cos(ap,,)cosA, = O 
(45) 
7, ,/P),,COS(A7,,) COSY, — 7,,p,.COS(Am,,,) COSu,, = O 
) cosA,, — 7 cos(a7,)cosv,, = 0 
7 ,p,. COS (am 
ws wus 
7, /P,, «COS (a7,) COSH,, — 7, p,. COS(am,,) COSA, = O 
The two transversals are thus completely determined in magnitude and direction, 
and are to be conceived as accompanying the rea/ vibration in its progress, de- 
pending upon its direction and velocity; and the equations of condition (40) at 
the limits are expressed by saying that, in passing from one medium into another, 
the first transversal preserves its value perpendicular to the separating surface, 
while the second transversal preserves its value parallel to the same surface: 
the real vibration preserving its value both perpendicular and parallel to the 
surface of separation, since the molecules composing it may be viewed as be- 
longing indifferently to either medium. It is important to observe that we 
have thus as many conditions as unknown quantities; for, the incident vibra- 
