1032 Dr. A. C. Crehore on 



equilibrium in the direction of the axis, but there is no 

 stability in a direction perpendicular to the ,z-axis at this 

 distance. Before there is stability on this axis the distance 

 must be greater than about 1*32 X 10~ 8 cm., where the 

 A'-curve crosses it. Indeed there is no point on the chart 

 where the x and z curves intersect, and it is requisite that 

 they should intersect for complete equilibrium, since the 

 whole force must be zero ; and there must also exist a 

 restoring force for small displacements. 



The hypothesis made above that P (26) is exactly zero is 

 not, however, necessary, and it is quite unlikely on the 

 theory of probability. All that has been shown is that it is 

 probably small. This small value is entirely unknown 

 unfortunately, so that the best that can be done is to assume 

 different values for it large enough to have some effect upon 

 the curves and see how the chart is thus modified. The 

 chart of fig. 3 is the result obtained by taking 



P = 3-78xl0- 35 (31) 



The value is given to three figures simply because this is 

 the particular value that happened to be used in making the 

 chart. It lies between b 2 and fr 3 , not far from 6 2 ' 65 , and is 

 such as to make the r~ 6 and r~ 8 terms of the series compare 

 in magnitude with the other two terms at these distances, 

 the r~ 2 and r -10 terms. To obtain a single point on one of 

 the curves shown now requires the solution by approximation 

 of a fifth degree equation, a much more tedious process than 

 that required to chart fig. 2. 



The result shows that there is now a definite position of 

 stable equilibrium for the two atoms at the point where the x- 

 and ^-curves intersect, at an angle of latitude whose sine 

 square is *41 and latitude A, = 39°49'. The distance between 

 two atoms in the stable position is *81 x 10" 8 cm. 



A very great change has thus taken place in the result, 

 changing fig. 2 into fig. 3 merely by using a value of P so 

 small that it does not appreciably affect the approximation 



that 2b 2 = pa 2 . 



Although no other complete chart has been computed 

 corresponding to another value of P than that used for fig. 3, 

 it has been proved that when this value of P is doubled, 

 nevertheless the angle or latitude at which the stable equi- 

 librium occurs is not perceptibly changed, but the distance 

 r is reduced from '81 X 10~ 8 to '57 X 10~ 8 cm. 



The conclusion of this investigation seems to be that, in 



