On the Resistance of Fluids. 113 



meant the action in no time ; let them consider that " irrespective 

 of duration," sometimes means that time is constant, and that* at 

 any indivisible instant, is not void of that ambiguity to those who 

 know the different meanings attached to the differential element (dt) ; 

 and further, that what words mean is fixed as much by their use as 

 by formal definitions, and that if I had taken the meaning, in no 

 time, there followed, not only the gross error above pointed out, but 

 Mr. Blake's demonstration of the " force of resistance," was abso- 

 lutely without meaning as such. 



As ray object has been to defend the common theory, any remarks 

 on Mr. Blake's proof, that the " force of resistance" is as the square 

 of the velocity, must now be considered gratuitous : whether just or 

 not, they have now nothing to do with the point at issue between us, 

 viz. the truth of the demonstration above given of the law of resistance 

 on direct impulse. With my former understanding of Mr. B's " force 

 of resistance," it was a material point whether his proof, that it was 

 as the square of the velocity was correct, since he identified it with 

 the force in the common theory : hence I attacked it.f Mr. Blake 

 thinks that by insisting on his definition, he has saved his argument : 

 if he had regarded the true meaning of my objection to that argu- 

 ment, instead of the mere form of it, he would have seen that it re- 

 mains in full force. That objection is that the definition and the 

 argument are heterogeneous. This is true, considering as I did in 

 my last communication, that the action of Mr. B.'s force of resist- 

 ance, took place in an indefinitely small invariable element of time ; 

 it is true if, as we are now to understand, it takes place in no time 

 at all ; and Mr. B. may vary his definition as he pleases, the objec- 

 tion I urged against that argument will always be fatal to it, if used 

 to demonstrate any other than the value of a force which acts in 

 variable time. The two first of the " analogies," as Mr. Blake 

 terms them, in his argument, which express substantially the 2d and 

 3d of Newton's Laws of Motion, are not abstract conceptions which 

 will apply to determine the value of any thing, whether real or im- 



* It was through an error of the pen that I appear to have misquoted Mr. Blake, 

 putting the quotation marlis before the word in, instead of after it, as I have done 

 in all other cases, and they are numerous. 



1 1 again suggest that, though the common theory takes the force of a particle 

 to be as the velocity, it may, its action occupying time, be taken to be as the square 

 of ihe velocity ; and if these measures are rightly understood, the results will be 

 the same. 



Vol. XXXI.— No. 1. 15 



