516 Dr. J. W. Nicholson on the Bending of 



the theoretical curves fit the experimental results remarkably 

 closely, quite sufficiently closely indeed to justify the adoption 

 of this formula. 



To render the series more complete the theoretical curves 

 for 71=1*9 and n=2*0 have also been added. 



The results show that the resistance diminishes with an 

 increase in temperature, the amount of the variation with a 

 given temperature-difference increasing as the temperature 

 diminishes and also as n diminishes. Its value in the neigh- 

 bourhood of 65° F. with a polished brass disk (n = l'S) is 

 about one-third of one per cent, per degree Fahr. When 

 n=l'9 this falls to one-seventh of one per cent, per degree 

 Fahr., and when n = 2'0 it becomes inappreciably small. 



'TV, 



LYII. On the Bending of Electric Waves round a Large 

 Sphere : I. By J. W. Nicholson, M.A., JD.Sc* 



THE effect of an obstructing sphere upon incident waves 

 has been examined by Lord Hayleighf , more especially 

 when the waves are those of sound. When the character of 

 the obstacle differs only in a small degree from that of the 

 medium around it, a solution may be obtained, whatever its 

 size and form. But when the difference of character is very 

 marked, as for example in the case of electric waves, when 

 the permeability and dielectric constant are arbitrary, the 

 solutions of value relate only to the case of small spheres. 



In the general cases the entire motion outside the sphere 

 may be regarded as consisting of two parts, (a) the undis- 

 turbed motion which would exist in the absence of the 

 sphere, and (6) a secondary disturbance zero at infinity 

 radiating outward from the sphere. The motion may thus be 

 readily expressed in the form of an infinite series of zonal 

 harmonics, whose coefficients involve Bessel functions and 

 their derivates in a complex manner. This general series 

 cannot be summed, and it is comparatively of little utility. 



But the character of the secondary disturbance is deter- 

 mined by the ratio of the radius of the obstacle to the wave- 

 length of the incident vibration, and when this ratio is very 

 small, the terms of the series decrease rapidly in order of 

 magnitude, and any desired approximation to the solution 

 may be effected. This series therefore leads to the physical 

 solution of the problem of the small sphere. 



A case of equal, if not greater, importance is that in which 



* Communicated by the Author. 

 t ' Theory of Sound/ 1896, § 334. 



