362 ^ On the Resistance of Fluids. 



proof of it was one of the main points aimed at in my argument ; 

 for a given plane when it moves a given distance encounters a given 

 quantity of fluid ; and I showed that when it moves a^iven distance 

 it encounters a quantity of resistance which is as the square of the 

 velocity. 



In short, if Prof. K. will examine the subject with careful atten- 

 tion, he will find that not one of the objections which he urges against 

 my views is well founded, and that the logic of my argument is pure, 

 and its conclusions irresistible. 



I deem it unnecessary to say more in reply to' the strictures of 

 Prof. K. There are however among these strictures one or two in- 

 cidental remarks, which invite, or rather seem to demand an expres- 

 sion of my views on a point of great interest in mechanical philoso- 

 phy, and in reference to which, if I mistake not, a most fatal error 

 almost universally prevails among men of science. Prof. K. says, 

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

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

 city, and offers 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 consider- 

 ed an element in their calculations as variable, which the Newtoni- 

 ans as universally considered constant." 



Before commenting upon this remark, I will quote one from Greg- 

 ory, alluding to the same dispute. He says, in his Treatise of Me- 

 chanics, Vol. I. Article 214, — 



" We must not omit observing, that about a century ago there was 

 a warm dispute among the mathematicians, in order to determine 

 whether we ought to consider the force of bodies in motion propor- 

 tional to the velocity or to the square of the velocity ; it is easy 

 from what has preceded, to reduce this question to a simple enun- 

 ciation which will remove all difficulty. The word force, deno- 

 ting any cause of vi^hich the nature is unknown, and of which the 

 effects are the only things we can measure, it is evident that by the 

 term measure of force, we can only mean that of its effects: now 

 the effects may be considered under different aspects, each comport- 

 ing with a species of measure particular and conformable to its na- 

 ture. If we consider the effect of the force as consisting in the 

 destruction of a certain sum of obstacles or of quantities of motion, 



