COEFFICIENTS OF SOLENOIDS. 21 



of tga = -Lep^th^- • These tables are given at the end of the 

 paper. 



§ 13. The coefficient 8 can be expressed in various ways. 

 Since ~^'^ir = -V -W=^^~^ ' 



and ^{K~E) + E=-'^ ^ + E 



IC K Ole 



_4_ 



The expression (19) can be conveniently used when the length 

 is very large as compared with the diameter of the solenoid, 

 while the second expression (19') will be found useful when the 

 said ratio is very small. 



By difierentiating the power series in k- for E 



7-_ ^U n ^' ^^' ( 1-3 V ^^ ( 1-3-5 V ^^' 1 



we find by (19) 



^~//r 'à- \2) 2' I ~\2-4:J 3 3 ~V 2.4-0 y 4 5 



/ 1-3-5-7 Y 9 7^^/^-3 .5.7.9 Y 11 ^^'' I (X)\ 



V2-4.6.8j*5 7 V2-4.6.8.IO7 6 9 ~ j ^^^ 



For convenience in calculating the coefficients, the following table 

 is added 



-^=0.42441318, %io- 3 - = 1.62778887. 



