22 ART. G. — II. NAGAüKA : TUE INDUCTANCE 



lorj.l /r] = .15740313, %,„[ /.•'] = 2.8927890, 



lo(j,l 7,^«] =2.5337G81, %,o[ /.;'] = 2.283890G, 



log.llà''] = 2.0912009, %,o[/--''] = 3.9280777. 



The above series is only slowly convergent when the angular 

 aperture is large, so that its application is limited to small values 

 of o.. 



The second operation (19') above indicated can be applied 

 to the expression for E under the form given by Schlomilch. 



1 1111, 1 



where ,„=--_^ + -__+ -^ . 



Thus 



-l^l + 3.,)/.'-(lJ.|(l + 5(.,-|-.0)/'-"- j C^O') . 



This formula corresponds to that usually given for short solenoids. 

 The above expression can only be used for values of « close to 

 90°. 



§ 20. On account of the simplicity of calculation in series 

 proceeding according to powers of h or Ic, the two series (20) 

 and (20') above given will find special favour among practical 

 scientific men, but the limits within which the series may be 

 safely applied is so narrow that it is necessary to deduce other 

 series which can be easily used within a wide range in the value 

 of «. For this purpose, expansions in ç-series are speciall}^ to 

 be recommended. 



