Electrical Vibrations between Con focal Elliptic Cylinders. 225 

 Writing out and arranging 



x f + 44^.3 __ 340^2 _ 6000l , + 18000 = Qm 



Solving this equation graphically we obtain as the positive 

 finite value of x 



x = 2*7 mm 



which agrees very closely with that found by experiment. 



This consideration, however, by no means gives a complete 

 solution of the problem of the relative efficiencies of the 

 continuous and alternating current arc, but is only intended 

 to account to some extent for the phenomenon of continuous 

 and alternating current arcs of equal efficiency. 



A complete analysis of the subject could only be undertaken 

 on the basis of the evidence of a much more extended series 

 of experiments, of which the time at the author's disposal 

 would not allow. 



In conclusion the author wishes to thank Dr. J. A. Fleming, 

 F.R.S., for his many suggestions and constant advice, and 

 also for his kindness in placing the resources of the Pender 

 Laboratory at his disposal, and to express his indebtedness to 

 Messrs. J. S. Westerdale and H. 0. Bullman for the very 

 efficient assistance they have rendered him, at great personal 

 inconvenience, in making some thousands of electrical 

 measurements, without which the investigation would have 

 been impossible. 



XXVIII. On Electrical Vibrations between Confocal Elliptic 

 Cylinders, with special reference to Short Waves. By 

 J. W. Nicholson, B.Sc. (Loud. <y Vict.), Trinity College, 

 Cambr 



SOLUTIONS of the problem of electrical vibrations in 

 confined spaces, bounded by perfectly conducting sur- 

 faces, have hitherto been limited to the cases of the circular 

 cylinder (vide J. J. Thomson, ' Recent Res. in Elect, and 

 Magn/) and the sphere (Macdonald, ' Electric Waves '). In 

 the present paper, it is proposed to show that the case of the 

 elliptic cylinder, although in general devoid of simplicity, 

 will yet furnish results of great elegance,.when the solution is 

 merely carried to a close approximation. 



When the surfaces are perfectly conducting, they cause no 



* Communicated by the Author. 

 Phil. Mag. S. 6. Vol 10. No. 56. Aug. 1905. Q 



