364 a. H. KNIBBS. 



If x be varied, with q constant, we may write M»(q p - 1) 

 (qp + l)»2|a* instead of the final terms in the numerator 

 and 4 r log q in the denominator. If a* be fixed for eacb 

 set and q be varied, we shall have M-nxv S; f (q), as the final 

 term of the numerator. 



When w, n, and p are found, we have \r equations to 

 determine A : thus (25) gives 



log A = 4 »-2j log dhlhlhlh) ~ w-n a(q :, + q 2 + Q + l)} 



- M«2? ; .vj"(q : " + q->' + q" + l) } (59) 



The actual computation of the constants A, tn, w, and p is 

 thus seen to be direct and tolerably simple. 



10. Integral of the curve.— The indefinite integral 



fudx=fx™e™ v dx (60) 



will be required in several forms since it must, in general, 

 be expressed in a series, and since also a form suitable 

 when x is less than unity is ordinarily unsuitable when a is 

 greater than unity. 



Developing e ux ''' in a series by the exponential theorem, 

 we obtain, on integrating term by term 



ntegrating by parts, t 



This last expression might also be derived from (61) by 

 dividing the series in brackets by e nxr expressed as a series. 

 Or again putting nx? = z , so that 



