154 Thermally excited Vibrations of an AtmospJiere, 
By means of (24), (25), and (30), (17) may be written 
( /.--l . 2?f )(Q 1 cos ft + Q/ sin A*) 
+ (4*»-2 . :>^ 2 )(Q 2 cos 2fa-f-Q 2 ' sin 2fa) 
4- (4F- 4 . 5 -^f )(Q 4 cos 2fa + Q,' sin 2fa) 
+ Uk*-Q . 7^)(Q G eos 2fa + Q 6 ' sin 2fa) 
+ 
= Si cos fa + S/sin fa + (S a + S 4 + S 6 + . . .) cos 2kt 
+ (S 2 ' + S 4 ' + S 6 '+...)sin2fa + (31) 
By equating terms in cos fa, sin Jet, ... we obtain 
(Qi cos Jet + QY sin li)(P-l . 2 ^)= - (7-l)/o(S 1 cosfa + S/ sin fa) 
= — i(7~ l)A/o& sin cos (fa — a>) 
by (24) ; with corresponding values for Q 2 cos 2fa -f Q 2 ' sin 2fa, 
&c. 
Substituting in (25) the values thus obtained, we have 
finally for the solution corresponding to (thermally) forced 
vibrations, 
S p = I . ^7' 1 l pr \ M sin 6 cos (fa - o> ) 
i Z lrr—&<yar K 
+ g.^^A2^in^sin2(fa-o,) 
+ A • ul^-l^ A2k * in2 " (7 cos2 *~ 1} siD m " w) 
+- M -4fcS^ A2/ ' Sin ^ 33 C ° S4 ^ 18 C0S ^ + 1 ) 8iU *<*-> 
+ (32) 
It is unfortunately very difficult to base any sort of nume- 
rical estimate on these tentative results. In agreement with 
Lord Bayleigh's investigation the denominator of the first 
term of Bp vanishes when k= ^Jya 2 \/2/r ; 7a 2 being here 
the quantity which Lord Rayleigh denotes by a 2 . Simi- 
larlv the denominator of the second term vanishes when 
2k= \/ya 2 \/i/r. It appears that both the denominators are 
small, corresponding to well-marked resonance- effects ; but 
we cannot even say with certainty what is the sign of each. 
