[ I0 4 ] 
of his engines with as much certainty and fuccefs as 
he could do, was he thoroughly acquainted with 
the laws of motion, from which thefe principles may 
be ultimately derived. However, tho’ an enquiry into 
the true method of deducing the practical principles 
of mechanics from the laws of motion, fhould not 
perhaps contribute much to promote the progrefs of 
the mechanic arts, yet it is an enquiry in itfelf ufeful, 
and in lome meafure neceffary : for, fince late authors 
have ufed very different methods of treating this fub- 
jedt, it may befuppofed that no one method has been 
looked upon as fatisfadtory and unexceptionable. I 
fhould therefore wifh to contribute towards having this 
fubjedt treated with more accuracy than has been hi- 
therto done. 
The moft general and remarkable theorem in ma- 
chanics certainly is this, “ That when two weights, by 
“ means of a machine counterpoife each other, and 
“ are then made to move together, their quantities of 
u motion will be equal’*. Now an aequilibrium al- 
ways accompanying this equality of motions, bears 
fuch a refemblance to the cafe wherein two moving 
bodies flop each other, when they meet together with 
equal quantities of motion j that Dodtor Wallis, and 
after him mod of the late writers, have thought the 
caufe of an ^equilibrium in the feveral machines, might 
be immediately adigned : by faying, That, fince one 
body cannot produce in another a quantity of motion 
equalto its own, without lofing its own at the fame time; 
two heavy bodies, counteracting each other by means 
of a machine mud continue at red, when they are fo 
circumdanced that one cannot defcend, without cauf- 
ing the other to afcend,at the fame time; and with the 
fame 
