Spontaneous Ionization of Air and other Gases. 265 



while those of electric force are given by 



^ = n . n + 1 . D;;' T-n . Pr(ju) cos (mo + S£) 



V sm C7 



- D Jr- 1 j r (f*J) sin ^p cos (ma) + 8J) 



*ik> r7P m 



-— - = (J r *J . sm ^ — 7 - — cos (ma> + e„ ) 



V cfy/, 



-mDy-^(rJ).^sm(ma, + SZ), . . (24) 



where J may now be taken as J (kr) + X» J (At) . 



«+| — »— | 



When, in (as, y, z). or ("a, b, c), we add to PJ* an 

 arbitrary multiple of the associated harmonic of type Q™, and 

 perform a summation for all integral values of m and n, we 

 obtain the most general solution of" the circuital relations 

 corresponding to wave motion. In this form, the results are 

 more appropriate to electromagnetic problems involving- 

 spheres, than those ordinarily given, their main utility lying- 

 in the fact that they give the radial and transversal com- 

 ponents directly. For example, the period equations of free 

 vibration of the space between two conducting spheres may 

 be written down at once, and are seen to be independent of 

 the question as to whether the vibrations are symmetrical * 

 or tesseral. 



XVI. Diurnal Periodicity of the Spontaneous Ionization of 

 Air and other Gases in Closed Vessels. By Alexander 

 Wood, B.A., D.Sc. (Glas.), Lecturer, Emmanuel College, 

 Cambridge-, and Norman R. Campbell, M.A., Fellow of 

 Trinity College, Cambridge^. 



IF a stream of air be drawn through a metal vessel which 

 is subsequently sealed up, the spontaneous ionization in 

 the vessel undergoes a progressive change which has been 

 investigated by several observers. Since the conclusions 

 reached w r ere various and sometimes conflicting, a new and 

 careful series of experiments was undertaken. It was soon 

 found that the phenomenon was more complicated than had 



* Phil. Mag. May 1906 ; Macdonald, ' Electric Waves,' chap. 3. 

 t Communicated by Prof. J. J. Thomson. 



