156 Dr. WHEWELL'S SECOND MEMOIR ON THE INTRINSIC EQUATION, ETC. 



1 4,dm 2 1 m 2 4.6.m 4 e 2 



° = 1 . 2 . 3 . 3 + 3 ~ 1 . 2 . 3* ~ 1 . 2 . 3* . 5* 3.5 ' 



m° m* 



Taking the integral from <p = to (f) = m, it is = - mb. 



52. As already remarked, Art. 34, there is a certain value of m for which the whole 

 abscissa w, from = to = m, is 0. That is 



m 2 m* m e 



= 1 (- = + &c. 



2 2 2 2 .4* 2 2 .4 2 .6 2 



When w = 1, the series is evidently positive. 



1 1 1 



When m = 2, the series is l - 1 + — 2 - - t ^ g2 + ^ ^ $i ^ - &c. 



This is evidently positive ; therefore there is no value which makes the series between 



m = l and m = 2. 



2 1 1 



Let m* = 8 ; the series is 1 - 2 + 1 - - + ^-^ - g ^ g2 + &c. 



This is evidently negative ; therefore there is a value which makes the series between 

 m 2 = 4 and m 3 = 8 ; or between m = 2 and m = 2 -y/2. 



53. In like manner there is a certain value of m which makes 6 = 0, that is 



2 4 



wr m . 



W. WHEWELL. 



Trinity College, 



April 15, 1850. 



