( ) 
and the Force requir’d, or Value of the additional 
Weight at A to reftore the jFlquiiibrium. 
D E : D F 0 f : p f 
/fx D C== a;. 
The fame Rule will ferve for the fecond Cafe, if the 
Quantity found be made negative, and the additional 
Weight fufpended at B. Or having found the Value 
of t he Perpendi cula r Force, th e ^Equation will (land thus • 
— ^p f X B X ^ — ^9 and confe- 
quently the additional Weight mufl: be hanged at B ^ 
becaufe — at A is the fame as -f- at B. 
Scholium If. 
Hence it follows alfo, that if, in the firft Cafe, the 
Point of Trufion be taken at C, the Force at B, (or 
Force whofe Value is requir’d) will be the whole Per- 
pendicular Force ; becaufe C D is equal to nothing: 
And if the Point D be taken beyond C towards A j 
the Perpendicular Force puftiing upwards at that 
Pointy multiplied into D C, mull be added to the fame 
Force multiplied into B C, that is 'p fx B C^-J- 
^/xcTc>= 
I'he Machine I made ufe of to prove this expert* 
mentally-^ voas as follows. Fig, z. The Brafs Ba- 
lance A B is IX Inches long, moveable upon the Center 
C, with a Perpendicular Piece £ h hanging at the 
End B, and moveable about a Pin at B, and Hopp’d at 
its lower End h (by the upright Plate GG) from be- 
ing thrull out of the Perpendicular by the pulhing Pipe 
F E, whofe lower Point being put into a little Hole at 
H, the upper Wire or Point (when put into another 
little Hole under the Beam at D) is by Means of the 
I Worm- 
