206 
Proceedings of Royal Society of Edinburgh. [sess. 
Thus (2) gives 
so that 
QPJdq = Ydr + xYq , 
Q n dq = (y + xYq) + dr . 
( 3 ), 
x and y being undetermined scalars. 
Substitute in (1), and again use (3), and we have 
Q„dq = dr + ^ri(Q „dr - 4>dr) , 
which is the complete solution. 
Note that this gives, by means of (1), for an equation satisfied 
by the linear function , 
Q„) = 0. 
The fact that this equation is of the second, instead of the fourth 
degree, is of course due to the very special form of </> as shown in (1) 
above. In fact the first factor kills any scalar, or any vector in the 
plane of q ; while the second kills a vector parallel to the axis of q. 
Additional Remarks on the Virial of Molecular Force, 
By Prof. Tait. 
(Read March 18, 1889.) 
(Abstract.) 
In my paper, read Jan. 21, I stated that I would not “for the 
present, insist on this point [the value of j3] further than to say 
that the main effect is merely to alter the value of the disposable 
quantity A, below.” 
The present paper contains the more complete investigation here 
promised, and shows that the Virial equation takes the form 
p(Y - f3) = kt- 
v(v-y) 
which, as a and y are noio at least nearly identical, is practically 
the same form as that previously given. 
