Lever. 91 



extremity B of which is attached to a weighty, we are able, I 

 say, to explain, why a moderate impulse of the breath suffices to 

 raise the weight p, although very considerable. Indeed, each 

 half a EB, a CB, of the vertical section of this bag may be con- 

 sidered as a cord, pressed at each point by a perpendicular force 

 equal to that exerted by the air. The resultant of all these 

 pressures must be directed according to FED, that is, it must 154< 

 pass through the point of meeting of the tangents belonging to the 

 extremities' of this cord, and must be to the effort made in the di- 

 rection BD, as the sine of a DB or of a D u, is to the sine of FD a. 

 Now the angle aDu is very smalL Therefore a very small ef- 

 fort in the direction FD produces a very great effect in the direc- 

 tion BD ; and accordingly the pressure exerted upon a EB will 

 cause a considerable effort in the direction BF, and the weight 

 will be drawn by two forces of considerable magnitude in the 

 direction BD, BF, which will have so much the greater effect, 

 according as the angle FBD is smaller, since their "resultant will 

 approach so much the nearer to the sum of the components, 



Of the Lever. 



156. By the lever, we understand an inflexible rod, of any 

 figure whatever, so fixed at some point F, as to admit of no other Fig. 68, 

 motion, by the action of the forces that are applied to it, but a 69 

 motion of rotation, that is, a motion, by which it turns about the 

 fixed point F. This point is called the fulcrum. 



We first consider the lever as an inflexible line without mass 

 and without gravity. In the case of an equilibrium, we can ea- 

 sily make allowance for the gravity of the parts, by supposing 

 it collected at the centre of gravity of this lever, and thus regard- 

 ing it as a new force applied at this point according to a ver- 

 tical direction. In case of motion, it is not at the centre of grav- 

 ity that we are to suppose the mass collected, but at some other 

 point to be determined hereafter. 



We shall proceed on the supposition, that the forces applied 

 to the lever, are all in the same plane with the fulcrum.. We, 

 shall treat in another place of equilibrium and motion when the 

 forces applied to the lever are in different planes. 



