52 DISSERTATION SECOND. [parti.. 



ters contending about the truths of their own science, and 

 opposing one demonstration to another. The spectacle 

 must have given pain to the true philosopher, but may 

 have afforded consolation to many who had looked with 

 envy on the certainty and quiet prevailing in a region 

 from which they found themselves excluded. 



Descartes had estimated the force of a moving body by 

 the quantity of its motion, or by the product of its velo- 

 city into its mass. The mathematicians and philosophers 

 who followed him did the same, and the product of these 

 quantities was the measure of force universally adopted. 

 No one, indeed, had ever thought of questioning the con- 

 formity of this measure to the phenomena of nature, when, 

 in 1686, Leibnitz announced in the Leipsic Journal, the 

 demonstration of a great error committed by Descartes and 

 others, in estimating the force of moving bodies. In this 

 paper, the author endeavoured to show, that the force of 

 a moving body is not proportional to its velocity simply, 

 but to the square of its velocity, and he supported this 

 new doctrine by very plausible reasoning. A body, he 

 says, projected upward against gravity, with a double ve- 

 locity, ascends to four times the height ; with the triple 

 velocity, to nine times the height, and so on ; the height 

 ascended to being always as the square of the velocity. 

 But the height ascended to is the effect, and is the na- 

 tural measure of the force, therefore the force of a mov- 

 ing body is as the square of its velocity. Such was the 

 first reasoning of Leibnitz ou this subject, — simple, and 

 apparently conclusive ; nor should it be forgotten that, 

 daring the long period to which the dispute was length- 

 ened out, and notwithstanding the various shapes which it 

 assumed, the reasonings on his side were nothing more 

 than this original argument, changed in its form, or ren- 

 dered more complex by the combination of new circum- 



