166 On the Resistance of Fluids. 



duced a quantity of a very different nature. But I have not yet 

 done with this analogy, v ccft; is (t) constant ? In other words, 

 does the time of the action of the force on the particle vary accord- 

 ing to the velocity of the plane ? Mr. B. must say that it does, for 

 if not, we have v cz f, the conclusion he takes so much pains to 

 avoid. Indeed he does say so, by giving the ratio of the variation 



in the third analogy, i a: ~ ; which means that the times of the 



V 



action, on a particle, of planes moving with different velocities, are 

 inversely as the velocities : so here we have another difficulty ; this 

 " indivisible instant" (t) not only consists of an infinite number of 

 indivisible instants, but varies with every varying velocity of the 

 plane. 



But disregarding the conflict between the definition and the argu- 

 ment, and admitting that the kind of action on a particle, imphed in 

 the argument is possible, and takes place, the conclusion is true and 

 important that the force (not Mr. Blake's force of resistance) is as 

 the square of the velocity. The following is a question to the solu- 

 tion of which that very argument may be applied. Suppose a plane 

 to act with different velocities, and perpendicularly to its line of mo- 

 tion on a fluid mass of constant or given amount, how would the re- 

 sistances be? The answer is, as the squares of the velocities. In- 

 deed this is the very question which Mr. B. has unconsciously sol- 

 ved ; he may and does call his fluid mass a particle, or stratum of 

 the thickness of a particle, but if this particle or stratum acts (as I 

 have shewn he virtually admits) as a uniformly retarding force, it un- 

 questionably has the property of a fluid constant mass of any extent. 

 The truth is, when Mr. Blake calls the measure of the simple velocity 

 a fundamental error, affirms it to be the square of the velocity, and of- 

 fers the above argument to prove it, he raises the very question which 

 unaccountably agitated all scientific Europe for forty years about the 

 measure of forces, whether it was the velocity or the square of the 

 velocity, and which at length died away by a tacit admission of the 

 parties, that the Leibnitzians universally considered an element in 

 their calculations as variable, which the Newtonians as universally 

 considered constant. 



Mr. B. moreover asserts, that Prof. Wallace and the common the- 

 ory determine two very different things. " Prof. Wallace considers 

 the number and effect of the particles at any (given) instant." 

 "Vrof. Keely and the common theory consider the effect and num- 



