638 
Proceedings of the Royal Irish Academy, 
where (3 = S5-5, and w', wi, n, are unknown. "We have, therefore, two 
equations and three unknown quantities. If we eliminate between 
the equations (4)' and (5)' we find, after some reductions 
92000 
«M(/3'-;8-l)»'» + 2/3a,'-;3M+-^^^ = 0. (6) 
This equation becomes numerically 
^Ml223'75o)'2 + 71o>'- 1260-25) + = 0. (6/ 
As # must be essentially positive the quadratic function of co' must 
be essentially negative ; now this quadratic has two real roots, viz. : — 
, / + 0-9862089 + &c., 
\- 1-0442273 4- &c. 
"We can show, from chemical considerations, that w'^ > 1, and 
therefore we must choose a negative value for w'> 1 < 1-0442273 + &c. 
The attraction of the hydrogen atom for the chlorine atom in the 
hydrochloric molecule must be greater than that of the hydrogen 
atoms for each other in the hydrogen molecule or than that of the 
chlorine atoms for each other in the chlorine molecule. In tlie 
hydrochloric molecule the distance between the atoms is 1 + — and in 
the hydrogen molecule the distance is 2 ; hence the attractions in the 
hydrochloric and hydrogen molecules are 
and f^. 
Substituting in these the values of /x and /x' already given (1)' and (2)' 
the first reduces to w'^ and the second to unity ; hence w'^ > 1 . Similar 
reasoning applied to the chlorine molecule gives the relation w'^ > ^wi^. 
It follows from all the preceding that the rotation of the chlorine and 
hydrochloric molecules is opposite to that of the hydrogen molecule, 
that the rotation of the hydrochloric molecule is comparable with that 
of the hydrogen molecule, and that they are both much more rapid 
than that of the chlorine molecule. The whole subject will be better 
understood by considering equation (6)' as a cubic curve, whose co- 
ordinates are and , 
