On the Resistance of Fluids. 165 



the force of resistance, and the time of the action of the plane on a 

 particle. (Note, that Mr* Blake applies these analogies, to deter- 

 mine the action on the plane, of a stratum of fluid, of the thickness 

 of a particle, and then infers the conclusion true of a particle, be- 

 cause the action of the stratum is as the action of a particle.) The 



analogies are these, v' oc v, v' cc ft, t cc _ ; hence v' 2 oc f; 



v 



from which it is inferred that the force of the particle is as the square 

 of the velocity of the plane. Now what do these analogies sepa- 

 rately mean as applied to determine the "force of resistance" of a 

 fluid particle. The first means that the whole velocity communica- 

 ted to the particle is as the velocity of the plane. This is very 

 true ; and, by the way, it is remarkable that Mr. Blake did not see that 

 as the force of the particle is as its velocity by its mass, it follows 

 that the force of the particle is as the velocity of the plane. But 

 what means the second analogy ? It is a dynamical relation between 

 velocity, accelerating force, and the time of the action of the force. It 

 expresses the fact, that the whole velocity communicated to the parti- 

 cle, is as the accelerating force (/) into the time (t) in which it acts. 

 Now, as a general truth how is that analogy obtained by the mathe-* 

 maticians ? Why by taking it for granted that the force (/) acting on 

 a body, produces, in any "indivisible instant" a certain velocity 

 which is its measure; that in the second "indivisible instant" 

 there is added another equal velocity which is the measure of the 

 second impulse, &c. &c. ; and thus they deduce finally that in any 

 time (t) consisting of an infinite number of indivisible instants v' cc 



ft. Now if Mr. B. uses this analogy, he must use it in the same 



force (/) 



f< 



velocity in the particle which is its measure ; and that, in the second 



Mr 



stop here, or go on ? If he stops, then the force is as the velocity, 

 and so indeed he acknowledges it is, if he goes on, as every one 

 must see ; but if he goes on, then the force of the particle which he 

 determines is not the "force of resistance" for it does not take 

 place in " an indivisible instant." But Mr. B. prefers to go on, and 

 now, what more, I would ask is necessary to prove what I proposed 

 to do, viz., that he has actually allowed to be true what he himself 

 styles the fundamental error of the common theory; and, moreover, 

 that setting out to determine the "force of resistance," he has de- 





