Doppler's Factor and the Electron Theory. 279 



Mr. Earhart tested four liquids — olive oil, paraffin, trans- 

 former oil, and kerosene. For the first three of these direct 

 comparison can be made with my results. 



For paraffiu and transformer oil I found a breaking-down 

 of insulation (i. e. the equivalent of a ** knee ") at 175 volts 

 and 200 volts respectively, whereas for these as for the other 

 liquids Earhart obtained the change at 330 volts. These 

 considerable differences may be explained by the very different 

 conditions of the two methods. 



curlH = 4tt' --- + ±irpu (2) 



XVIII. On the Introduction of Doppler's Factor into the 

 Solution of the Equations of the Electron Iheory. By 

 L. de la Rive *. 



THE transformation of Maxwell's equations takes place as 

 follows. The equations are | : — 



curlD. = - 4 ^.-, (1) 



dt 



For regions of space not containing any electric charges, 

 div D = 0. 



For a volume- distribution of electricity of density p 

 measured in electromagnetic units, 



div D = p. 



The distribution of H being solenoidal, we put 



H = curl A ; (3) 



whence curlH = V div A-V 2 A (4) 



Putting curl A for H in (1), we have 

 dA 

 dt 



,dA 

 curl - 7 = — 47rr curl D ; .... (5) 



and, on integrating, 



„_. dA , 



47r y 2 D=-^-V<£, (6) 



V<£ being a constant of integration whose curl is zero. Let 

 the auxiliary vector A be arbitrarily connected with the 

 function (f> by the relation 



A7 A + '? = ° (7) 



« Communicated by Prof. J. H. Poynting-, F.R.S. 

 f Mathematische Binfuhrung in die Elektronmtheorie, von A. H. 

 Bucherer, p. 76. 



