VOL. XLV.] PHILOSOPHICAL TRANSACTIONS. SGS 



with falshood, for no definition can be false, yet I say in the first place, it is less 

 simple than the other ; for why should a duplicate ratio be used where the simple 

 ratio will do as well ? In the next place, this measure of force is less agreeable 

 to the common use of the word force, as has been shown above ; and this in- 

 deed is all that the many laboured arguments and experiments, brought to over-' 

 turn it, do prove. This also is evident, from the paradoxes into which it has 

 led its defenders. 



We are next to consider the pretences of the Leibnitzian, who will undertake 

 to prove by demonstration, or experiment, that force is as the square of the ve- 

 locity. I ask him first, what he lays down for the first measure of force ? The 

 only measure I remember to have been given by the philosophers of that side, 

 and which seems first of all to have led Leibnitz into his notion offeree, is this: 

 the height to which a body is impelled by any impressed force, is, says he, the 

 whole effect of that force, and therefore must be proportional to the cause : but 

 this height is found to be as the square of the velocity which the body had at the 

 beginning of its motion. 



In this argument I apprehend that great man has been extremely unfortunate. 

 For, 1 st, whereas all proof should be taken from principles that are common to 

 both sides, in order to prove a thing we deny, he assumes a principle which we 

 think farther from the truth ; namely, that the height to which the body rises is 

 the whole effect of the impulse, and ought to be the whole measure of it. 2dly, 

 his reasoning serves as well against him as for him : for may I not plead with as 

 good reason at least thus ? The velocity given by an impressed force is the whole 

 effect of that impressed force ; and therefore the force must be as the velocity. 

 Sdly, Supposing the height to which the body is raised to be the measure of the 

 force, this principle overturns the conclusion he would establish by it, as well as 

 that which he opposes. For, supposing the first velocity of the body to be still 

 the same ; the height to which it rises will be increased, if the power of gravity is 

 diminished ; and diminished, if the power of gravity is increased. Bodies descend 

 slower at the equator, and faster towards the poles, as is found by experiments 

 made on pendulums. If then a body is driven upwards at the equator with a given 

 velocity, and the same body is afterwards driven upwards at Leipsic with the same 

 velocity, the height to which it rises in the former case will be greater than in 

 the latter ; and therefore, according to his reasoning, its force was greater in the 

 former case ; but the velocity in both was the same ; consequently the force is 

 not as the square of the velocity any more than as the velocity. 



Reflections on this Controversy. — On the whole, I cannot but think the con- 

 trovertists on both sides have had a very hard task ; the one to prove, by mathe- 

 matical reasoning and experiment, what ought to be taken for granted; the other 



