based upon Electromagnetic Theory. 583 



Moreover, there is one other feature of the law of gravi- 

 tation which the equation (66) supports. The attraction 

 between crystals has been shown experimentally * to be 

 independent of the orientations of their axes. If it may 

 be assumed that the atoms in a crystal are divisible into 

 four equal groups, with each group of atoms having axes 

 parallel to the four medial lines of a regular tetrahedron, as 

 there is some reason to believe from an independent investi- 

 gation f , then the attraction between an atom and any group 

 of four atoms having axes parallel to the four medial lines 

 of the tetrahedron is, according to (66), proportional to the 

 sum of the squares of the four perpendiculars expressed by 

 (\ 72 + £ 2 )> i2 . This sum has been shown to be constant J inde- 

 pendent of the orientation of the group. Moreover, its value 

 is such that a factor 2/3 is obtained, which combined with 

 the 1/2 in (66) reduces the force between the crystals to the 

 form (65), showing there is no difference between the attrac- 

 tion of crystals and other matter, provided, of course, one 

 admits the possibility that crystals have the axes of their 

 atoms so arranged. 



The equation (65) also implies Newton's law of equal action 

 and re-action between bodies. It remains only to show that 

 the magnitude of the force agrees with that given by the 

 o-ravitational constant. Before undertaking to show that 

 there is also agreement m this respect, it seems oecrssary 

 to consider another important result obtained by means of 

 Saba's equation (3). 



VI. 



Application to Rings of Equally Spaced Electrons. 



Instead of giving the demonstration in full, let us content 

 ourselves with a statement of the. results obtained, which 

 have, however, been rigorously proved. In the problems of 

 rings of electrons regarded as point charges uniformly dis- 

 tributed around a circle, and revolving at a uniform rate 

 around the circumference, it has been shown § that the 

 tangential force upon any selected electron in the ring due 

 to all the others added together always takes the direction in 

 which the electron is moving in the ring by the Larmor- 

 Lorentz equation. The effect of this force is to accelerate 



* A. S. Mackenzie, Phys. Rev. vol. ii. Mar.- Apr. 1895, p. 321. 

 t Orehore, Phil. Mag-. June 19] 5, p. 7*50, tig-. 1; Phil. Mag-. Aug. 

 1915, p. 257. 



| Crehore, Phys. Rev. June 1917, p. 459, italics. 



§ G. A. Schott, ' Electromagnetic Radiation," p. 1 10, eq. (130), p. 186, 



