X ITI. 
On the Measure of the Forces of Bodies moving with different Velocities. 
By DANIEL TREADWELL, 
VICE-PRESIDENT OF THE ACADEMY, AND LATE RUMFORD PROFESSOR IN HARVARD UNIVERSITY. 
[This paper was read to the Academy in March, 1854, as here printed, except a few sentences since added by 
way of illustration (as that from Brewster's “ Life of Newton”), and some trifling verbal alterations. ] 
ALTHOUGH the great controversy on the measure of the forces of moving bodies, 
which divided the investigators of mechanical science during a part of the seventeenth 
and eighteenth centuries, is no longer considered open, as a subject for scientific specu- 
lation or inquiry, by many of the leading writers of the present day, they having con- 
cluded that it has been exhausted, or rather that it had terminated in the discovery 
that the whole question was of a verbal rather than of a substantial character, I have 
. yet ventured to present to the Academy a paper touching it. I am not aware that any 
one has heretofore followed the course of experiment, and the particular reasoning from 
it, which will be found in this paper, though the force of the spring has often been ap- 
pealed to by partisans on both sides of the controversy, as proving the truth of the 
standard which each attempted to establish. I shall be very willing, however, to forego 
all claim to originality, if what is herein presented shall be found to assist any one to 
a clearer understanding of a subject on which Newton and Leibnitz were divided. 
Notwithstanding the high authority which, in more recent times, has decided that 
their disagreement was rather one of words than of things, I cannot but consider it 
as substantial and irreconcilable, not only affecting all just conceptions of mechanical 
force, but leading even those who thus attempt to reconcile the opposing theories 
into very grave practical errors and contradictions. 
Thus Dr. Lardner says (“ Mechanics,” chap. iv.): “If a cannon-ball were forty times 
the weight of a musket-ball, but the musket-ball moved with forty times the velocity 
VOL. VIII, 47 
