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MOVING WITH DIFFERENT VELOCITIES. 363 
had published an experiment which he considered as proving Leibnitz’s assertion that the 
force of moving bodies is proportional to the square of the velocity, and not, as is com- 
monly thought, to the simple velocity. Dr. Pemberton saw its insufficiency, and drew up 
a refutation of it.” This being “ communicated to Sir Isaac, he was so well pleased with 
it, that he called upon Pemberton at his lodgings, and showed him a refutation of Poleni, 
by himself, grounded upon other principles." This refutation, as it is called, is pub- 
lished in the * Philosophical Transactions,” and is intended to support in its fullest extent 
the Newtonian measure of force, viz. that of the simple velocity, against the measure 
proposed by Leibnitz. Here then we have Sir David Brewster, one of the greatest of 
living names in mechanical science, in one of his latest works, asserting that the force 
of a moving body is commonly thought to be as its velocity simply, and that the assertion 
of Leibnitz that the force is proportional to the square of the velocity was refuted by 
Dr. Pemberton, and again by Newton himself. 
While a question of this vital character, affecting all the conceptions and many of 
the computations of force, is in this contradictory and cloudy state, ought scientific 
men to rest upon it, or to suffer it to rest, as a closed subject? The labor of pre- 
paring the following paper shows my own opinion upon this question. 
It may be well, perhaps, before opening the particular course of investigation pur- 
sued in this paper, to state briefly the precise matter that formed the subject of this 
renowned controversy. Suppose, then, a body, as a stone, A, of a certain mass, to 
be thrown in any direction in space, with a certain velocity, it must move onward with 
a certain force* Now if another stone, D, having twice the mass of A, be thrown 
with the same velocity that was given to A, it must move with twice the force of A ; 
for we may divide B so as to form two stones, each of which shall have a mass equal to 
that of A, and if thrown with the velocity of A, they must each.have the force of A, 
and if each separately has the force of A, both, united to form B, must have twice the 
force of A. This is substantially the mode of reasoning used by Galileo to show that 
the mass of a body could not alter the velocity with which it would descend by its 
weight, when unsupported, to the earth ; and it follows from this, that under a given 
velocity the forces of all bodies must be directly as their masses. If, however, instead 
of throwing different masses with one and the same velocity, we throw one and the 
same mass with different velocities, we search in vain for any reasoning of this simple 
* Force is the unknown cause by which a body resists change from, or produces change in, another body. 
Synonyme, Power. I shall avoid, if possible, the use of the words momentum, vis mortua, and vis viva, as 
they are often used and understood in such vague and indefinite senses as to obscure rather than to give any 
clearness to our conceptions in an inquiry like this. - 
