EDGE CORRECTIONS IN THE CALCULATION OF THE 



ABSOLUTE CAPACITY OF CONDENSERS BY THE 



SCHWARZIAN TRANSFORMATION. 



By J. G. CoFFiNv 



Presented by A. G. Webster, December 9, 1903. Received December 11, 1903. 



In the construction of an absolute condenser, consisting of two sil- 

 vered plane circular glass plates, it was found necessary to compute the 

 edge corrections for many cases which have not yet been determined. 



In the following pages will be found a number of such cases worked 

 out by means of the general conformal transformation due to Cristoflfel * 

 and Schwarz.| 



A very clear resume of the method will be found in the chapter on 

 conjugate functions of J. J. Thomson's Recent Researches in Electricity 

 and Magnetism. 



The method has been applied to problems of different kinds by Kirch- 

 hoffjt Potier,§ Michell,|| and Love.^ 



It will be noticed that in all the cases here presented, there is a 

 variable parameter which allows the correction for any relative position 

 or size of the edges to be given from the general solution. 



It then follows that a number of cases already solved by J. J. Thom- 

 son are but special cases of these the more general solutions. 



This is a great advantage, as it affords an excellent check upon tiie 

 accuracy of the more complicated results. 



In a number of cases the problem was solved in two distinct manners, 

 the more elegant being here presented, but the results in every case 

 asreeing with each other. 



* Annali fie Math.. 1, 89 (1867). § Frencli Trans, of Maxwell, Appendix. 



t Crelle, 70, 105-120 (1869). II Phil. Trans., A, 389 (1890). 



t Gesam. Abhand.,.p. 101. t Proc. Camb. Phil. Soc, 7, 175 (1891). 



