164 On the Resistance of Fluids. 



Art. XV.— On the Resistance of Fluids; by Prof. George W. 



Keely. 



Watcnrillc Coll. Feb. 22, 1836. 





TO PROF- SILLIMAN- 



Sir } — Mr. Blake has obliged your readers with a communication 

 on the resistance of fluids. With your permission I will make a few 

 remarks upon it. It is not my intention, however, to follow him 

 through all his statements and reasonings. To save time, I propose 

 merely to examine a few essential points. 



Mr. B. asserts that the common theory assumes what is a funda- 

 mental error, viz., that the force of a fluid particle is as the velocity 

 of the plane which it strikes perpendicularly ; that the nature of the 

 resistance Prof. Wallace proposed to determine is different from that 

 of the resistance which I had in view, in my former communication ; 

 that Prof. Wallace's reasoning does not differ from that of the com- 

 mon theory, so far as I examined it ; and that, at the same time, we 

 are both wrong in our conclusions. 



' Whatever be the effect of Mr. Blake's reasonings on others, I am 

 not convinced by them. Each of the above assertions T hold to be 

 incorrect. I will consider them in order. 



When Mr. Blake denies that the force of a particle is as the ve- 

 locity of the plane, he must mean that momentum is not a measure 

 of the moving force ; a truth so obvious, that if we are to give it 

 up, we give up the whole theory of Mechanics. This truth Mr. B. 

 would not have denied, but for the supposed accuracy of his argu- 

 ment that the force of a fluid particle, in an indivisible instant, is as 

 the square of the velocity of the plane. Mr. B. defines Force of 

 resistance to be the action, "in an i7idivisible instant of time" and 

 he undertakes to prove that this force of resistance for a particle, is 

 as the square of the velocity of the plane. Now I mean to show 

 that, in attempting this, the force he determines is not the force of 

 resistance according to his own definition ; and, however surprising 

 it may seem, that Mr. B. has actually assumed the same fundamen- 

 tal proposition as the common theory, and that too in the very argu- 

 ment he uses to prove it is a fundamental error : this argument I will 

 now examine. It consists of three " analogies," which, for brevity, 

 I will state by symbols ; using v', v, f, and t, to express respectively 

 the velocity communicated to a particle, the velocity of the plane, 



