any Function of Sines and Cosines. 127 



Calculation of B h or coefficient of cos 5 u in the development of 

 {1 — *5 cosa}-#, by the method of p. 10. 



If B 7 is neglected with every B which has a higher index than 7 ; 



(3) 1 =2<.3*.2.4.1cosl5i? 5 £ 6 = O0889 1st approximation. 



If B 9 is neglected with every B which has a higher index than 9 ; 



(4), = 2 6 .3.2.4.1 .6.1 cos 20 B & B 5 = -00924 2nd approximation. 



If B u is neglected with every B which has a higher index than 1 1 ; 



(5), = 2 6 .3.2.4.1.6.1.7.2 cos 25 B 6 



£, = -00934 



3rd approximation. 



The correct value of B 5 is -0093675. 



Calculation of the same coefficient by mechanical quadratures. 



yxcos 5 * 



7-47413 



-7-38981 



7-38981 



9) -08432 



•009368 



* 3 is written here for sin 3, 2 for sin 2, &c. 



