l88 HINTS RELATIVE TO 



This being premifed, let M * be a weight placed at 

 the point X of a lever, moveable about an axis whofe 

 center is d, and radius dn ; and let N be the fuftaining 

 force acting at B : now it is evident that the preffure 

 on the axis d differs fo little from the weight, that it may 

 be fafely taken for it without any confiderable error, 

 except in feme remarkable cafes, which may be allowed 

 for from what has been faid already; and therefore the 

 friction which ought in ftrictnefs to be taken as the n 

 part of the preffure, will here be taken as the n part of 

 the weight upon the axis. Now if N be taken for the 

 force which, acting at B, would be juft fufficient to keep 

 the weight M at A in equilibrio, exclufive of fri&ion, 

 and if W be the additional force to be added to N fo as 

 to overcome the friction, then will M-f-P, M — P, and 

 P — M, be the weight upon the axis at d in the firft, 

 fecond. and third figures reflectively, (fuppofing the 

 J'um of M and N to be equal to P.) Now as the friction 

 is the n part of each of thefe quantities, and its effe6t is 

 to keep the lever in a ftate of reft, therefore in whatever 

 direction the force at N endeavours to draw the lever 

 by acting at B, the friction tends to counteract that force 

 by keeping the lever fteady, or acting in a contrary di- 

 rection at n; and as the effect, of the friction, and the 

 additional force W, are in equilibrio, and the friction 

 acts by means of the lever dn, and the force W by the 

 lever dB; therefore Bd is to dn as the fum or difference 

 of the n part of N-{-W and M is to W ; confequently 

 \\ r =zdn fM+NJ : (n, Bd — dn,) in the firft figure ; 

 Wz=zdn (M — N) : (n. Bd-\-dnJ in the fecond figure; 

 and in the third figure, W=zdn ( N — M) : (n.Bd — dn.) 

 All thefe are the expreilions for the moving forces. 



To find the fu fpending forces, or the forces which, act- 

 •ing at N, fhall be jufl fufficient to prevent the weight M 

 from defcending: Let M and N be the fame as before, 

 and let xo be the force which, taken from N, will leave 



a force 



* Fie. 12. 13. H. 



