On the Resistance of Fluids. 361 



to presume this is to presume that my piece was read inattentively, 

 1 think it fair to infer that the misunderstanding did not arise from 



o 



any defect in the definition, and therefore that further illustration of 

 my meaning, were it possible, would be unnecessary. 



The distinction here insisted upon between simple pressure and 

 the product of pressure by unity of time, is highly important to clear 

 and just views on the subject. Still however, the truth of the prop- 

 osition on which Prof. K. considers the question between him and 

 myself to turn, viz. that the force of a particle is as the square of 

 the velocity, does not depend on this distinction ; for although the 

 multiplication of a quantity of one species by unity of another 

 changes the nature of the quantity, it does not alter its numerical 

 magnitude ; and therefore, numerically measured, it will still retain 

 the same magnitudal relations to other quantities. The proposition 

 that the force of a particle is as the square of its velocity is true in 

 either sense of the term force. The fallacy of Prof. K.'s reasoning 

 in opposition to my views on this point, consists in his having hasti- 

 ly overlooked for a moment, the fact that the duration of the action 

 (if a given quantity of fluid is not given in my argument ; a fact 

 which he recognizes immediately afterward. 



If Prof. K. will reexamine the subject with more careful attention, 

 keeping in view that by force in every instance in which I used the 

 term, I meant precisely what I defined it to mean, he will see that 

 when I determined the force of a particle on the plane, I determined, 

 not its whole action, but only its action at any instant — he will see 

 that there is nothing in my argument which assumes that the whole 

 action of a particle takes place in an indivisible instant, or even that 

 it may not last for hours. He will see, therefore, that there is no 

 conflict between my definition and my argument, and that I have not 

 set out to determine one kind of force and determined another. He 

 will find that the "dilemma" into which he seems to himself to have 

 pursued my argument, will vanish when he calls to mind the fact that 

 velocity is not a measure of the force which generates it, except 

 when the time is given ; and that the time was not given in my ar- 

 gument. He will see that the truth that the resistance of a given 

 quantity of fluid is as the square of the velocity ; which truth he 

 takes some pains to show that I virtually admit, and which he says 

 that I unconsciously proved, is not deducible from the common the- 

 ory ; and that instead of supporting that theory it disproves it. He 

 will see also that instead of proving this truth unconsciously, the 

 Vol. XXX— .No. 2. 46 



