396 Mr Murphy on the Inverse Method of 



But the least root of the equation 



« ■ = t . u . (1 — «) is 



a 



W = %^-^ 2 + a2 + 2a/Ml - 2/)i4 ' 



and therefore l ~ = ^ + „= + 2 ^.(l'-20}* ' 



, d I n y du\ _ a a' — (i" 



a,ld 3j3 I/* It) 7" 2/34- S/3 a + a 2 + 2«/3.(l-2/)^- 



Hence = coefficient of j in j| ./(J) . ( j3 » + a . + a 2 «/3.(l-ao*' 



If therefore we multiply the external tension by 



g 3 -/3 a 



{/3 2 +a 2 + 2a/3.(l-2/)P 



and divide by 4™ the coefficient of ^ in the product, the result 

 expresses the law of accumulation. 



Or if we multiply the internal tension by the same factor 

 and divide by — ^- the coefficient of - in the product, the result 

 will likewise give the law of accumulation. 



This may be expressed in a definite integral by the theorem 

 (Camb. Trans. Vol. ill, p. 438.) 



35. When the electro-motive causes are unknown, then the 

 application of the first of these rules to the observed law of 

 external attraction, or tension (which is the integral of the at- 

 traction) will determine the law of distribution. But when the 



