176 On the Measure of 
difficulty in finding what part of the whole 
moving force is expended in producing the 
progressive, and what in ee the rota- 
tory motion. 
Let E be the centre of gyration of Aand B 
around G. Draw GF, DH and EI perpen- 
diculars to AB. On ET take two points K 
andI,sothatEK:KI::GE:G@D. Through 
K draw K F parallel to A B, and through F 
and I draw MN. Then if we take GF to 
represent the progressive velocity produced in 
G by any force acting at D, K I will represent. 
the rotatory velocity produced in E in the same 
time; DH will be the whole space through 
which the pressure has acted ; D L will repre- 
sent 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 GF?: 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 
effects, 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 deseribed by the pressure during 
its action, and if the pressure be uniform, that 
space, however small it may be, must consist 
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