194 Prof. J. V. Jones. Calculation of the Coefficient of 



It is clear that M = M 2 M@ l5 



and we need therefore only consider the expression 



JAacos0 

 . -T 



where x = p = the axial length of the helix, reckoned from the 

 plane of the circle. 



We may now proceed in two ways either by expanding the 

 logarithmic expression in powers of x/a t which leads to a series of 

 limited application since it is convergent only so long as x < A a ; 

 or by integration by parts which leads to an expression applicable 

 for all values of x. 



3. The first method I developed in the paper above mentioned. 

 We have 



1.3.5. ... (2m 1) 1 



= A *~ r 1.3.5....(2 



' 





p ' 2.4.6 ____ 2m 2m + l ' 



- 1 ) 1 / 



2 . 4 . 6. . . . 2m 2m + l \A-f-a, 

 i + 1 _L_l^ m ~ gr 2 '?*Pt ... ( 3 ) 



2 \/Aa x 



where c = -_ , sr = - - , 



A + a 







or 



Let 



_ f 2 cos 2 



* - J (IZ^iia 



= P 



J (1-c-si 



The following properties of these elliptic integrals are perhaps 

 worthy of notice : 



?' 

 c 



