[ 3 ] 
volving about a Center is as the quantities of matter 
into the fquares of the Brachia ; and in the prefent 
cafe, therefore, the whole Inertia of m and n is as 
m a 1 4 - nb z . Hence then, and becaufe the velocity 
generated in a given particle of time is as the Force 
diredtly and Inertia inverfely, we have - ---- - - n as 
J J ma 7 -f- nb 7 
the accelerating force, or the meafure of the angular 
velocity of the Power and weight at the end of the 
faid given particle of time. And I ufe the angular 
velocity, becaufe the arbitrary proportions in the 
lengths of the Brachia which may form an Equili- 
brium will not alter the expreffion. But again, the 
times of defcent by means of uniform forces, thro’ 
a given fpace, are inverfely as the fquare roots of the 
accelerating forces, or meafures of the velocities ge- 
nerated in a given particle of time ; and therefore 
I via 2 - + nb 7 
ma — nb 
is a general expreffion for the time of a 
ftroke. This being had, the folution is eafy ; for, 
fuppofing n only to be variable, fay as 
: 7 i :: i, a conftant or given time: n 
J 
j- 
ma 1 -f- nb 7 
ma — nb 
ma — nb 
tna 7 -f- nb 7 
the effedt in time i, ex hypoth. the greateil effedt 
which can poffibly be produced in the faid given 
time. Taking, then, as ufual, the Fluxion equal o, 
we have, after a proper reduction, 2 a 5 tn z — 3 a 1 mnb 
J- a mnb 1 — 2 n z b l = o, and n — “ 
1 b v b -r j 
— - an . 1 x 3 a Therefore, in thefe forts of En- 
4 b 7 
gines, when the Brachia are given, the weight : 
B 1 Power 
