378 
MR. GEORGE W. WALKER ON 
OX and precisely twice the magnitude of the incident disturbance for all angles 
of incidence. 
(3) If the incident wave is transversal and the vibration in the plane of the paper 
we may assume that the incident disturbance is represented by 
(fi> Ci) = A ( — sin e, cos e)f{t + (cc cos e + z sin e)/V 2 }. 
This will give rise to a reflected transversal disturbance at an angle e on the other 
side of OZ, expressed by 
(£>, £>) = A 2 (sin e, cos e) j {t + (x cos e — z sin e)/V 2 }, 
and a reflected longitudinal disturbance at an angle e' on the other side of OZ, 
expressed by 
(4 Q = A 3 (— cos e', sin e')f{t + (x cos e'-z sin e')/Yi}. 
The vanishing of the stresses at the surface of separation leads to the relations 
A — A 2 = — mA 3 cos 2e/sin 2e, 
A +A 2 = — ju _ 1 A 3 sin 2e'j cos 2e, 
where 
/x = V 1 /V 2 and /j. cos e = cos e'. 
We note that the energy condition is satisfied by these equations. 
Solving the equations, we get 
A 2 /A 
a 3 /a 
_ {sin 2e sin 2F —/x 2 cos 2 2e} 
{sin 2e sin 2 e' + /u 2 cos 2 2 e] 
2/jl sin 2e cos 2e 
/ 
The resulting horizontal motion of the ground is H, where 
H/A 
2/ul 2 sin e cos 2e _ 
{sin 2e sin 2 e' + n 2 cos* 2e| 
and the resulting vertical motion is Y, where 
V/A 
2/ul sin e! sin 2e 
{sin 2e sin 2 e' + /u 2 cos 2 2e } 
For the ideal case /x 2 = 3, A 2 would vanish for e = 55° 44/ and e = 60°; but in our 
actual case /x = 1*788, A, does not vanish but falls to a small minimum near e = 58°. 
Tn the present case there is no real value of e' until e attains the value 56°. Thus 
in the range from e = 0° to e = 56° there is no reflected longitudinal disturbance, but 
there is a type of disturbance practically confined to the surface of separation and 
