910 Dr. A. C. Crehore on 



That this series is so rapidly convergent at distances 

 comparable with 10~ 8 cm. that the first term of it represents 

 veiry approximately the whole force may be shown as 

 follows.- The approximate value of b/r is 10~ 13 /10~ 8 =10"" 5 , 

 so that 68/^ = 10" 40 , b w /r 10 = 10" 50 , etc., and so that 

 £s r -io_iO- 24 , 6 10 y-i2 :K= io~ 34 , etc., these values decreasing 

 in the ratio of 10 10 , In all succeeding terms the exponent 

 of b is always two less than the exponent of r but with 

 opposite sign. The numerical coefficients do not increase 

 at any such rate as 10 10 , and the r~ 12 and succeeding terms 

 are .of no value. The electrostatic force between these atoms 

 therefore varies as the inverse tenth power of the distance 

 between their centres, when (26) is satisfied. 



In a similar manner the condition that (26) is satisfied 

 reduces the force of the atom ABO on the positive charge c 

 (23) to 



F =^{-5(10-3/ /O )6 4 r- 6 +(-196 + 315/ /3 -35/ / Q 2 )6 6 r- 

 at °^ BC + (-486 + 1890/P-1260/V 2 



+ 126O/,0 3 )^- 10 ...}, . . . . ' (33) 



and reduces the force upon the two electrons (a-\-b) due to 

 ABC in (24) to 



2e 2 

 F = - F {5(10-3/ / o)//r- 6 4-(196-315/ /3 + 35/^)5V- 8 



on?a+?) C +(-31014 + 17010/ / )-1575/ /9 2 



-1260/p 3 )^- 10 ...} (34) 



These tw T o equations are exactly equal but of opposite sign 

 in both the r^ 6 and r~ 8 terms, and, since the first term 

 represents practically the whole of the force, it may be said 

 that the force upon the nucleus is one of repulsion equal to 

 the first term of (33), while that upon each electron is an 

 attraction equal to one half the first term of (34) electro- 

 statically. These forces are very large, varying as the 

 inverse sixth power in comparison with their sum which 

 varies as the inverse tenth power. It is this smaller force 

 which must be balanced by terms due to the rotation of 

 the positive nuclei, which will now be considered. 



Terms due to Rotation. 



Fortunately the solution for the mutual action of two 

 continuous rings of charge in rotation has been solved in its 

 generality, using the Saha equation so far as the inverse 

 square of the distance terms are concerned. At distances 



