in Reply to Professor P. Tardy. 299 



motion in a givai element are in successive instants normals 

 to surfaces of continued curvature." The condition stated in 

 other words is, that a continuous surfaceof displacement may 

 be drawn through a given element in each of its successive 

 positions. This law is just as conceivable in steady motion, 

 in which the surfaces of displacement are fixed in space, as in 

 instances of motion in which they are not fixed. 



I come now to the argument by which Professor Tardy 

 obtains a peculiar form of 4/ by assuming that 



Rf R^ 



# and d^ ,. 



It rf^+^(^) 



are at the same time factors which render integrable udx+ 

 vdy + ivdzj R^ being substituted for 



^2 ^ ^ 



dx^ dy^ dz^' 

 It is true, as the investigation of equation (2.) has already 



shown, that the value of - generally expressed is 



R 



R2 



But, this being the value of -, d-^ is not the value of - ; and 

 as my investigation has regard only to the value of-, it 



A 



is not chargeable with the consequences of the particular 

 assumption, that another quantity renders udx-{-vdi/-\-'wdz 



integrable simultaneously with -. Such assumption may be 



A 



admissible and the consequences true, but they have no bearing 

 upon the question at issue ; besides which, I have anticipated 

 this argument by proving already, that the investigation which 

 conducted to equation (2.) in no respects limits the value of \|/. 

 Next follows an example which is thought to show evidently 

 the inconsistency of the new equation. The result which I 

 am called upon to justify is a legitimate deduction from my 

 equation ; and as Professor Tardy finds no fault with it, 

 neither do I. The meaning of the result 1 take to be this. 

 The two equations 



\ogxy+{t-\fl+{t+\f^^-^^0, 

 X2 



