181 
MOVING FORCK. 
Bat Iiow can these two motions be independent of each difti 
culty 111 till* 
other, when they are both produced by the same force ) The doctriiirs of 
pressure can neither be increased nor diminished without in*’"“'"'S *«rce 
creasing or diminishing, at the same time, the rotatory as well 
as the progressive motion ; and if we attend to the space 
through which the pressure acts, we shall have no difficulty in 
finding what part of the whole moving force is expended in 
producing the progressive, and what in producing the rotatory, 
motion 
Let E be the centre of gyration of A and B around G. Draw 
GF, DH, and El perpendiculars to AB. On El take two 
points K and I, so that EK : KI : : GE : GD. Through K 
draw KF parallel to AB, and througii F and I draw MN. Then 
if we take GF to represent the progressive velocity produced 
in G by any force acting at D, KI will represent the rotatory 
velocity produced in E in the same time ; DH will be the 
whole space through which the pressure has acted ; DL will 
represent that portion of the moving or mechanical force which 
has produced the progressive velocity ; and LH that portion 
which has produced the rotatory velocity, and we shall have 
GP : KI* : : DL : LH. These results are so well known, 
that it would be superfluous in me to give a demonstration of 
them here. The same relations of the moving force to the 
eft'ects, and of the effects to each other, take place whether the 
force be communicated by impulse or by gradual pressure. 
For, however sudden the impulse may be, a determinate space 
must be described by the pressure during its action, and if the 
pressure be uniform, that space, however small it may be, must 
consist of two parts, as described in the figure, having the ratio 
to each other of GP : KI*. If the pressure be not uniform, 
the fluent of the pressure into the space will bear the same re- 
lation which DH bears to the sum of the products of the masses 
into the squares of their velocities. 
(To le continued-) 
METE- 
