314 



Transactions. 



It will generally suffice to compute the first and second coefficients A t and 

 A 2 , B t and B 2 , which can readily be done by the method shown on form A. 



A scheme proposed by Professor Runge (" Zeitschrift fur Mathematik 

 und Physic") is given in Gibson's " Calculus," in which all the coefficients 

 are easily computed. 



The following is Runge's scheme slightly altered : — 



Cosine Terms. 



Sine Terms. 



Denoting by y lf y 2 , &c, the first, second, &c, harmonics, the equation to 

 the curve is 



y = - 24"-25 + y x + y 2 + &c. 



or y + 24"" 25 = y t + y 2 + &c, by changing the origin. 

 Now y t = — l" - 07 cos a — 8""65 sin a. 



The value of (a) when y ± vanishes is B, therefore 

 - 1"07 cos E - 8"- 65 sin E = 0. 



tan E = — 



1-07 



8-65 

 E = 1 72° 57'. 



