378 On the Motion of a Pendulum affected by the Earth's Rotation. 



Eliminating k, 



7wH(B+B'-AA'K+BB'=0. 



Denote the roots of this equation by 



mV-1, -mV-l,m'V-l, -mV-1; 

 and let the corresponding values of ^ be 



ZJ JJ Lit ^Vf 



lij "-"/l J A, f —A. * 



The complete solution is 



The constants R-i, R-g* B-s, B4 may be determined from the initial 

 circumstances of the motion, namely when /s=0, in which case 

 we shall also have 



dD. ^ d^!r ^ 



Let Hp a|rj be the initial values of fl, i/r. We shall have 

 Oi=Bi + R2+B3 + B4, 



, . 0=RX-R2m' + R3m''-R4m", 



* ' 0=:RiA/m' + Ra/tW + RgFm" + R4^"m". 

 Whence 



___ m"f n,k" ti \ 



p m^T a,F ^^ y 



^3- 2 \k'm''-k"m"'^kV-k'm" ]' 

 m' f a,k! jr, \ 



*^'»"" "2 LA/m'-AV k"m'^k'm"J' 

 And therefore, 



n^ 



2{k!m'-k"m") 



^k^^{^rn"(e^n^^^^^ 



