Friction, 158 



place. In this ease, if we would know the ratio of the weight/) 

 to the power q, we imagine the weight of p. directed according 

 to the vertical GK, passing through the centre of gravity G, 

 decomposed into two parallel forces, the one passing through the 

 point / in which the body rests upon the lever, arid the other 

 through a point of CD, situated in the plane of the two parallels 

 GK, 1M\ then the resulting force in / will be to p as EK to EM ; 52 - 

 and if from A we let fall upon IM the perpendicular AL, the 

 force q will be to the force at /, as AL to AB ; whence H ^ 



q : p : : AL X EK : AB x EM. 



In short, it is only on account of the friction at the point / that 

 we regard the force according to IM, as transmitted entirely to 

 the lever. The lever would otherwise receive only a part of 

 this force which would exert itself in the direction of a perpen- 

 dicular to AB. 



251. It is to friction and friction only, that we are to refer 

 the singular motion by which certain bodies in a state of rotation 

 are seen to elevate themselves contrary to the tendency of grav- 

 ity ; I speak of the phenomena of the top. It is well known that 

 when a body of this description, that is, one which is symmetri- 

 cal with respect to one of its axes, as A r Z), has received a rotato- Fig.lSa. 

 ry motion about this axis, and moves upon its point JV, over a 

 horizontal plane XZ ; it is well known, I say, that the smaller 

 the point JV, and the greater the divergency of the sides from it, 

 the greater is the tendency of this body to rise, and thus to place 

 the axis ND in a vertical position. We proceed now to show 

 that this phenomenon could not take place without friction ; we 

 shall speak, moreover, of the nature of this friction. 



To simplify the subject, let us consider only the axis JVD of Fig.139. 

 the top, and let us suppose the point N, and the horizontal plane 

 XZ, to be perfectly smooth. The only cause which opposes the 

 motion of the centre of gravity G, being the plane XZ, the resis- 

 tance which the centre of gravity meets with can have no other 

 direction than the line NK, perpendicular to XZ, whatever be 

 the rotatory motion about the axis JVD. Now it is evident that 

 this resistance takes place only because gravity urges the body 



Mech. 20 



