[• 569 ] 



LXV. An Atomic Model based upon Electromagnetic 

 Theory. I. By Albert C. Crbhore *. 



IT is proposed in this paper to obtain an expression for the 

 mechanical force between two closed circular rings of 

 charge revolving at uniform velocity around the centres of 

 their respective circles, making use of the new electro- 

 magnetic theory of Saha. This problem for point charges 

 revolving in circles has been investigated! by means of the 

 J, J. Thomson electromagnetic equations, and later % by 

 means of the equations of Larmor-Lorentz. The force 

 between two neutral atoms, each supposed to be composed 

 of revolving rings and stationary charges, in equal amounts 

 so as to render the atoms neutral, comes out exactly zero at 

 great distances using either of the two latter theories. By 

 the use of the new Saha theory this is not the case, and the 

 result obtained is of interest. 



After obtaining an expression for the ponderomotive force 

 upon one point charge due to a second, each point moving 

 in the most general form of path, by means of the four- 

 dimensional analysis of Minkowski, Saha § states that "in 

 three dimensions the forces are equivalent to a force of 

 repulsion 



ee'^' 2 f uvcosO 



? X 3 /3 



(1-— ^jr (1) 



in the direction of the line joining the two points, and a 

 force 



ee'/3' 



;.(-?> w 



in the direction of the velocity of the second or attracting 

 point." The meaning of Saha in the words quoted must 

 have been that the directions of the force and the velocity 

 of the second point are parallel without regard to sign, for 

 the negative sign in his equation (13) before the last velocity 



* Communicated by the Author. 



t Crehore, Phil. Mag. July 1918, p. 58; he. tit. June 1915, p. 750, 



X Crehore, Phvs. Rev. June 1917, p 445; G. A. Schott. Phys. Rev. 

 Julv 1918, p. 89^ Crehore, Phvs. Rev. Feb. 1919, p. 89 ; he. rib Feb. 

 1921, pp. 249-255. 



§ Saha, Phys. Rev. Jan. 1919, p. 41. 



Phil. Mag. S. 6. Vol. 42. No. 250. Oct. 1921. 2 Q 



