434 DK. T. It LYLE ON THE SKLF-IXDUCTAWK OF 



APPENDIX II. 



(Added October 1, 1913.) 



Since writing the above I have determined the sixth order term of the series for L. 



In order to do this it was necessary to extend to the sixth order MAXWELL'S series 

 formula (see l) for M, the mutual inductance of two unequal coaxal circles which 

 ROSA and COHEN* had already extended to the fifth order. 



Thus 



r { 2a 2*. a? 2 5 . a' 

 15,r 4 -42xy-17?/ 4 4 5.x '//- 3 (.).*-// 

 2 10 .a 4 2". a 6 



35s 8 -345a!V+ 45igy + 89/1 

 2 14 . a" 





2. a 2 4 .a 2 2 4 .3.a :i 

 93a: 4 -534xV-19?/ 4 



2 u .3.a* 2 12 . 3. 5. a 5 



1235x 6 -17445a:y+12045.ry-7371j/ r | 



When in M we substitute, as explained in 1, a + Y for a, the term of the sixth 

 order in the variables x, y, and Y becomes equal to U, where 



U = p + q Y + ?-Y 2 + S Y 3 + * Y 4 + M Y 5 + t'Y", 

 in which 



p = ^a |- log 



1235X-"- 17445./V + 12045^y-7371i/ >i 

 2*. 3. 5.0* 



g = 4 ^ a i XU+ V r/ -log-* + : X!/ <>ii\ f'% ~f 



^.Cc / A * D v Ci J 



4 -. , 



1) g " 



2. 1) g r " 2". a 6 J' 



? 2 5 .3.a 6 



* I 2 4 . a 8 ff 7 2 6 .3.a J 

 n = 4-rra . 



= 47T . 



2 . 5 . a 



1 

 2. 3. 5. a"' 



* ' Bull. Bureau Standards,' 2, p. 364, 1906. 



