126 



Dr. L. Silberstein on Molecular 



In both eases the amplitudes and the phases of r u r 2 , r 3 are 

 equal ; in the first case each of the three dispersive particles 

 oscillates parallel to the opposite side, and in the second, 

 along the straight line joining its position of equilibrium 

 with the centre of the triangle Oi0 2 3 . 



Fig. 3. 



Both roots are verified on actually dividing (46 a) by the 

 corresponding factors, which gives the identity 



Thus our sextic is reduced to the quartic equation 



which is easily solved. In fact, applying Euler's method, we 



find that it has the two equal roots ~ and the two 



_1 + v/13 

 equal roots ^ . 



Together with those given in (47) we have, therefore, all 

 the six roots of D = 0, 



g' = 2; </"=-§; g"'=-^P^ (double) 



t 



3 

 V13-1 



(48) 



(double), j 

 o / 



and the identity, which may be useful at a future 

 opportunity, 



D=-($y.(ff-g')< S -g")(g-ff"y(g- ff *y. . (49) 



