116 Mr. 0. Heaviside. [June 15, 



1*0625 

 giving u = 0'8123, v = -, r , 



requiring , r = 0'76. 



Of course with such a small value of #, we cannot expect more 

 than a very rough agreement, because the convergence of the v series 

 is confined to the first and second terms, and we may expect an error 

 of magnitude of the ratio of the second to the first term. 



36. Now take n . We have 



1.3.7 / 1 . 3 . 7 . 11 aj\* 



|4 |4 



(53) 



J2 (I6a?) 2 '_3 (16#) 3 ' / ' 



and in case of x = 1 we have 



which make u = 1*2109, v = -p ; 



ljL 



and therefore j T =l'024. 



Now this shows a large error, for the value is about I'll. This 

 excess in v is, however, made a deficit by not counting the smallest 

 term in the v series (the third term). Omitting it, we make 



1-0625 1 



v = p[ and rj T14. 



Again, with x = 2, we have 



1-0399 

 making u = T365, v = vy X 2*. 



This makes n = -- = I'll, 



[i 1-04 X 1-18 



which is very good. 



