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LXXX. Construction of Cubic Crystals ivith Theoretical 

 Atoms. By Albert C. Crehore, Ph.D.* (From the 

 Department of Physiology of Columbia University.) 



| [Plate XL] 



IN a former paper upon this subject! there was developed 

 a general expression for the instantaneous mechanical 

 force which one electron revolving uniformly in a circular 

 orbit exerts upon a second electron revolving in a different 

 circular orbit. This is based upon the well-known equations 

 for the mechanical force that one moving electrical charge 

 exerts upon another ; but the velocity of transmission is 

 taken as infinite to simplify matters, and reasons were given 

 why it seems probable that the results obtained with these 

 simpler initial equations would not be different if the more 

 complicated general expressions were employed. The 

 mechanical force between two rings of electrons is shown 

 to be independent of the relative phase angles, and any re- 

 tardation of the transmission velocity would be likely to 

 affect only these phase angles, and not change the mechanical 

 force. 



In that paper the integral of the general equation was 

 obtained in one special case only, namely, when the axes of 

 revolution of the two electrons are parallel to each other and 

 the angular velocities o£ orbital revolution are identical J. 

 The work of integrating £ or average velocities has now been 

 completed in the most general case, when the two axes of 

 revolution make any angle a with each other, and the 

 frequencies of revolution are either incommensurable or 

 equal to each other. 



The General Equation. 



Using the same notation as in the paper referred to, the 

 total instantaneous mechanical force is expressed as the sum 

 of four vector components. The first or electrostatic com- 

 ponent is 



F '=-ii R c» 



Here e and e 1 denote the two charges, each having the same 

 sign, K the specific inductive capacity of the medium, and 

 R the scalar instantaneous distance between the two charges. 



* Communicated by the Author. 

 t A. C. Crehore, Phil. Mag. July 1913, p. 25. 



t Loc. cit. Equations (42) and (44). Note an omission in the co- 

 efficients B, corrected in a note, page 325, Phil. Mag. Feb. 1915. 



