Motion of Solid and Fluid Bodies. 195 
é cea ore ‘(3 3s ne 2) ee "(3 ee oe 2 ON 
a ar 
dt dx? dadz a > dx Zz) 
(63) 
C5 ae BG OG cg Oe je a? s oe dP BY 
de 5 af dz ae iis a) ie "(3G Ee ie dadz/ 
Ge ade 
Also, since Aga aa in consequence of the vibration being transversal, 
we shall have the equations 
_ dp OE tke Df. 
ie dq LY ae. dG dé > 
2= 7% n= a=x(E+2) (64) 
BE Nhs ROCN. dé Leer a sh, 
1= ae n(3E+ a) me aeaic 
which prove that the first transversal lies in the place of incidence, and that the 
second is perpendicular to it; and also that the equations of condition at the limits 
are the four following : 
e = rate G = ree 
Wale GEN 3d" dé” ne 
c ee 7 ae 0 c dz a Kee) 
d. di! el Le!” 
ze (= a dz = v ae fi ra) 
which are exactly equal in number to the unknown quantities, which are the four 
intensities of the two reflected and two refracted vibrations; one reflected and 
one refracted wave having its vibration normal to the wave plane, and the other 
two waves having their vibrations transversal. If the incident vibration had been 
normal, it is easy to see that the equations of motion would be the same as 
in the present case, and also that the equations of condition at the limits (65) 
would remain unaltered; but, in the case of normal vibration, the equation 
= -b == = 0 does not hold; the equations (64) will therefore be different, and 
become the following : 
