88 Mr. J. Walker. Relative Retardation between Components 



Suppose now that the actual roots or the biquadratic are 



, 7T - />-f-/3, 7T ^> + 7, - 7T -|- p + C ; 



then 



= 0, 



/J7 + O-r/0 7 W 



+ (^ 2 -/> 2 )(/3-) (^-7) 

 -(^-/>) 2 {^ + (^-r/>) (/8- = 0, 



which, on reducing and simplifying, become 



2 = 0, 



= 0. 

 Let 



with similar expressions for /3, 7, B ; then the terms involving sinH'/t; 2 

 give 



a 2 + A + 72+c 2 = 0, a2 + 72 = o, 



. . 7 2 = a. z and ^ = /3 2 , 



and from the terras involving sin 3 V/u", we obtain 



7s +Pia 2 + 2 = 0, 



