274 Mr. Power on the Principle 
at the point m, ak 
PB+ PR ah Pp 
a! 
t . 
a 
at m’, 
PB+P'8 + P'S’ — PB+ PB 
a a 
” 
at m’, 
and so on. 
But the equilibrium will remain undisturbed, if for the two 
P P : ; . 
forces se and a2. (of which the former acts upon m in di- 
rection of a, and the latter upon m’ in the direction opposed 
to a’,) we substitute two strings stretched with these forces, 
and acting in the same directions: again, the strings so stretched, 
may be conducted over fixed pullies, in such a manner, that 
their other extremities may impel perpendicularly the arms of a 
straight lever, divided by its fulcrum in the ratio a: a’. The 
fulcrum will then re-act with a force equal to the sum of the 
two tensions, and the whole will remain at rest. Should 
PB be negative, the strings stretched with the positive forces, 
must proceed from the two points in directions opposite to 
what we have just supposed, and be attached to the lever 
as before. 
In the same manner we may substitate for the forces 
the re-action of a second lever, divided in the ratio @ : a’. 
If we make similar substitutions throughout the system, at 
the same time substituting for the normal part of the resolved 
forces the re-action of so many fixed surfaces intersecting them 
at right angles; there will at length remain a single tangential 
force, whose numerator is the sum of all the terms P6+P'B'+ 
P’p"+..., making equilibrium with the machine, which results 
