1 76 Prof. P. Tardy 's Observations o?i a 



would give 



iog.,,+(.-.)«|+(.+ ,)»£--L_.'MO=o. 



a result which we would beg Professor Challis to justify. 



I have anxiously searched in the memoirs of Professor 

 Challis for an instance of applying the new equation, and I 

 must confess that I remained quite astonished when, in the 

 Cambridge Philosophical Transactions, vol. viii. part 1, I 

 found the following example. If 



u^=zmx^ v^—myi ttj=0, 

 we have 



udx-\-vdy — m{xdx—ydy) (8.) 



Professor Challis takes for the integral of this, or for the 

 general equation of the surfaces of displacement. 



Hence from equation (7.) 



da 

 ""dt 



But, adds Professor Challis, by the equation (8.) we have 



dx dy da 

 x-j- —y-77—a-j- =0; 

 dt ^ dt dt 



and since 



dx dy 



do. , a Ok 



therefore, substituting A= ^j which value, he says, makes 



11 v 



-dx-\--dy an exact differential, and the equation (7.) is there- 

 fore verified. I can scarcely conceive how such an illogical 

 process has escaped the sagacity of the learned Professor. 

 And indeed what does Professor Challis do but take the value 

 of X from the equation (7.), 



d^ 

 dt 



\— 



Jx) '^\dy) "^ \dz) 



