FORCE. 
sate a if the two - a in the fame dire€tion, they 
ill increafe the effet of each other; but if they aa in 
Ronettes aaa. the point will only move in confequ 
of their difference, and it would remain at reft if the fae 
were equal. If the direétions of the two forces make an 
augle with each other, the refulting force will take a mean 
dire€tion, and it can be demonftrated geometrically ; that if, 
force thus determine 
o 
a" 
‘acd 
ci 
core forces which, accordin g to the above rule, would com- 
pofe that force. Any force therefore may be decompoled 
into two others parallel to two axes fituated in the fame 
age and perpendicular to each other. To do this, 
is fufficient ‘to draw from the firft extremity of the 
fee pe aia the force two lines parallel to thefe 
aXe3, form with thefe lines a rectangle, the 
dia coal of which will be the force required to be decom- 
é : ae fides of this rectangle or parallelogram will 
e forces into which the given b 
ha oad co-or 
Hence arifesa ery ; Geople method of having oat See 
= of ~~ nu soe forces, which are fup 
in each of their direGtions ; be taken pcos t them, 
0 point af eeteeios (called the crigia 
point. 
iy Maclau 
The eee of the compofition of forces is of the moft 
extenfive utility in mechanics; i it is fufficient alone to deter- 
mine the law of equilibrium in every cafe. For by compofing 
faltog foe all the forces two by two, and taking the re- 
ting force as a new force, we arrive at a force which muit 
be equivalent to all the reft, and hana in cafe of homed ee 
muft equal zero, when the nder confider 
o fixed point; but if there ee an immo sreable: point by 
e conditions of the problem, then the refulting force 
arifing from all the producing forces muft neceflarily pafs 
through that point. 
t is admitted by all writers on this fubject, that the 
mott abitrufe pros tion: relating to the doétrine of forces 
may be deduce fimple principles ; yet in the 
» few authors are found entire] 
and advantageous meth 
that in which the Giatn which fubfitts between en 
forces in a flate equilibrium is -firit oo and 
then es conlidera tion lure to-a ia 
action of the others ; ; a caeiie | effet of any 
force by unity, the effect of the other ‘ia! to this 
above, which he r 
ut this 
but of fi he 
fame principles, pa “oe that ie are eftablifhed in the 
moft farisfactory ma 
La Grange founds a whole doctrine of the equilibrium 
of forces on the well-known principle of the lever, on the 
compolition of motion, and on the principle vin tual - 
city. The principle of the lever may be derived from 
compofition of forces, and even from much lefs (complied 
confiderations 
Archimedes is the earlieft author upon record who 
attempted to demonftrate the property of the lever;-he 
aflumes the ne hea at . oa weights at equal diftances 
from the fulcrum as a in mechanics, and reduces 
to this fimple and primitive ae that of unequal weights, 
Py fuppofing thefe, w ey are commenfurable, divided 
to equal parts, Goad ae and placed pai points of 
e lever at equal diftances, fo that whole lever may 
be loaded with a are of {mall cae weights at equal 
diftances from the fulcr 
The principle of the iat and horizontal = er being 
admitted, the law of equilibrium i in other machines may be 
deduced from it: there is, however, fome difficulty 1 in re- 
ferring the inclined plane to this principle ; and the laws 
relating to it were, for a long time, unknown to mathema- 
ticians. 
Stevinus, a to prince Maurice of Naffau, was 
the firlt that gave a den 
art’ har 
a pended freely uridernedth, in the fame ver as if Aeehed 
to tre lower extremities of the bafe. He then ane in 
that if the chain is not in equilibrio, it will begin to flide 
along the plane, and the fame caufe fubfitting, it “Ihould 
continue to flide for ever, producing a perpetual motion ; 
but this implying a oo we mutt conchide it to 
be in equilibrio, and i ‘fince the efforts of all the 
weights applied ta ene fide exadtly eT - 
t 
