124 



Dr. L. Silberstein on Molecular 



simplest case of equal atoms, forming an equilateral triangle, 

 or of what may be called a regular triatomic molecule. 

 Such would be the molecules of ozone. The case of any- 

 isosceles triangle (with the limiting case of collinear 

 atoms), which would correspond to water or to the im- 

 portant group GH 2 , may be left to the reader. 



Regular Triatomic Molecule.— -In this case we have 



<i — a 2 — a 3— 2> 



further. 



and, finally, 



Ri = R, 7t = 7o, Bi = B = e 2 /m, 



Thus the system of six equations (41) becomes, with a 

 convenient rearrangement of their order, 



^23—^(^3— 2 r i2) = — -Gi3> 



etc. 



— ^12—2^3) = — -G-12, etc. 



^5 



(44) 



where Gr 23 , etc. are homogeneous linear functions of the 

 components of E, as defined above, and g is an abbreviation 

 for (yQ—y)/p, so that 



Let us consider the first line of (44) as the 1st, 2nd, and 

 3rd equations, and the second line as the 4th, 5th, and 6th 

 equations. Let this be the order of the rows, and let the 

 columns correspond to r 23 , r 31 , r l2 , r S2 , r l3 , r 2 i. Then the 

 determinant of the system (44) will be 



D = 



1 







gt% 







-9 



9I2 



1 



















gl* 



1 



-9 















-9 



1 



?/2 



-9 















1 







-9 







g/2 











-9 





 



ff/2 

 1 



(46) 



