﻿756 Dr. A. C. Crehore on the Construction of 



F x , F y , and F 2 denote the three components of the force 

 along the rectangular axes i,j, and k, referring to the atom A, 

 k being along the line of the axis of rotation of the electrons 

 so that they appear to revolve in the clockwise direction when 

 viewed from the positive side of the axis, j and i are in the 

 plane of its equator, the positive direction of j, along the line 

 of intersection of the equatorial planes of the two atoms, 

 being the vector kxk'. a^ is the unit in centimetres in 

 which all the other distances are expressed, and c is the 

 velocity of light. The summation £m 2 &>, m being the radius 

 and (o the angular velocity of some electron in the atom A, 

 is to be extended to the P electrons in that atom; and 

 similarly ^n 2 ay' to the P' electrons in the second atom. 

 X, Y, Z are the direction cosines of the position of the 

 second atom referred to the i, j, and k axes at the centre 

 of the first atom, and a is the angle between the axes of 

 rotation of the two atoms, v is the distance between the 

 centres of the two atoms, measured in a% units. 



Up to this point no particular hypothesis as to the structure 

 of the atom has been introduced. The equations apply as 

 well to the central nucleus theory of the atom as to any other 

 theory where electrons are moving in circular orbits about a 

 common centre. The test of different theories is in the 

 results obtained when numerical values of the different 

 quantities are introduced, especially the radii of the orbits 

 and the frequency of revolution of the electrons. 



The nature of the equations shows that they are parti- 

 cularly well adapted to the equal moment of momentum 

 hypothesis for each and every electron, since *Zm 2 co in the 

 coefficient of v -4 is proportional to this moment of momentum, 

 and equal to it if multiplied by the mass of the electron. If 

 we denote by /?* the ratio of the velocity of the electron 

 in hydrogen or in the single electron atom to that of light, 

 and let the unit a% be the radius of its orbit, and co* its angular 

 velocity, then we have for each electron in every atom 



m 2 co = n 2 (o' = c0*, and 



2!fi'»=P»»; 2nV = P'«»; £m*a£nV = PP'a J . (26) 

 p p' p p' 



a 2 

 The coefficient -^-Xm 2 (oXn 2 co' in the equation may then be 



c p p' 

 replaced by the quantity PP'/3|, where fi% is a constant 



quantity, since j8| = * 2 * • The introduction of this hypo- 

 thesis therefore makes the equations more easily applicable 



