540 PROFESSOR W. E. AYRTON, MR. T. MATHER AND MR. F. E. SMITH: 



in the design, and for the care and skill displayed in making the drawings of the 

 instrument ; to Messrs. E. FISHER and A. W. HARROLD, late of the Central Technical 

 College, for checking the initial calculations ; and to Professor A. G. GREENHILL, 

 F.R.S., for advice concerning the elliptic integrals involved. 



APPENDIX A. 



Values of coefficients (logs of) and constant terms in series* for complete elliptic 

 integrals of the first and second kinds (F and E) when k nearly =1. k' = y\ 1?. 



l a - 3 2 7, 4 /i 422 



*~7& \ g 'F~i72 3^ 



I 2 . 3 2 . 5 a 7 , 6 /i 4222 

 + oi-TT-gi *" ( lo S w - T-o - g-7 ~ g-j 



2) * 4: v A/ I m m Or v 1 



+ &c. 

 This may be written 



F (Jb) = log, J + A^^log, J -B 2 j + A^log. J -B 4 



+ A 6 F 6 (log e l-B 6 )+ &c. 

 \ / 



Similarly the corresponding series for E (&) may be written 



E(i) = l+A/F 2 (log i-B 2 ')+A/p(lo ge l-B 4 ') 



\ K I \ K / 



fcD-TV) + &C. 



Values of log A B , log A/, B B , and B B ', are given below : 



* CAYLEY, 'Elliptic Functions,' chiip. III., 77. 



