A New Principle of Relativity in Klectromagnetism. 413 



homoeoid by adding to the interior until h is changed from 1 

 to R, 



W = - 2wWfiV f * tf(l - 7i) <ta f " — =. 



^2^ 2 «W{A-|H*(1-!H) f -^ ^^ (52) 



J v (a- + 1/.)(6- + u)(c 2 + w) 



I£ H = 0, this becomes the result for a solid ellipsoid. 

 For this case 



10 Jo ^(* 2 + M )(6 2 + w)(c 2 + «) 



In the particular case of a uniform sphere this becomes 



W— aM 2 



5 a 



if the unit of mass is gravitational (see § 6, footnote), or 



° a 



if the ordinary unit of mass is used and re is the proper value 

 of the gravitational constant. This is the result given by 

 Helmholtz, from which the rate of shrinking of the sun 

 necessary to supply the energy radiated may be calculated. 

 If the density vary from shell to shell (53) becomes 



W=27r 2 aW Cp~ \ \dk f " ' _^ * u rm (54) 



Jo r /* J* Jo >/ (a 2 + m)( 6 + w)(c 2 tm) 



as the reader may verify by finding the work done in building- 

 up a thick homceoid by adding shells of: varying density p, 

 and then varying the constant h of this homoeoid from 

 to 1. 



XXXII. On a lS~ew Principle of Relativity in Electro- 

 magnetism. By A. H. Bucherek, D.Sc, P rivatdocent 

 in the Bonn University*. 



§ 1. TT is needless to dwell on the serious difficulties which 

 JL the Maxwellian theory has encountered by the 

 well established experimental fact that terrestrial optics is 

 not influenced by the earth's motion. The endeavours of 

 some distinguished physicists, notably of H. A. Lorentz, to 



* Communicated by the Author. A short note on the same subject 

 was published in the Physik, Zeitschr. vii. p. 556 (1906). 



