Friction. 1 55 



sure exerted upon .W, is by no means the effect of gravity only. 

 To have a just idea of this pressure, we must consider that by 

 gravity the parts of the point JV are at first urged against the 

 plane ; (2.) That by friction they are kept there with a certain 

 degree of force ; (3.) That by the rotatory motion they tend to 

 penetrate still further into the plane ; of this we shall be convinc- 

 ed by observing how readily instruments designed to pierce by 

 turning, are made to penetrate, when once introduced by means 

 of an opening however slight. Now all this is strictly applicable 

 to the top ; the parts of the point are attached by friction ; and 

 in this way the rotatory motion is aided in effecting an entrance 

 into the plane. This motion, moreover, being the more rapid 

 and the better fitted to bore and press upon the surface XZ, ac- 

 cording as the parts of the body diverge more from the axis JVD 

 in receding from the point JV, it must produce the effect which 

 takes place in the instruments abovementioned, that is, it must 

 urge forward so much the more forcibly the parts of the point in 

 question. From all this, it is evident that the more the figure of 

 the top diverges from the point JV, and the more rapid the rota- 

 tory motion, the greater will be the force GL compared with grav- 

 ity, and consequently the more will the resultant GE tend to raise 

 the centre of gravity above the plane. Now it is clear that in 

 proportion as the force by which the point is supported, and 

 at the same time the tendency of the centre to rise, become more 

 considerable, by so much will the tendency of the axis JVD to- 

 ward a perpendicular to the plane, be increased ; so that when 

 JVD becomes vertical, it begins, after a time, to incline more and 

 more, and if the inequalities of the surface are not too great, the 

 top will be seen to rise above the plane in very small, sudden, 

 vertical leaps ; and this we in fact observe when the point ter- 

 minates in a small plane surface cut very square and perpendic- 

 ular to the axis. 



We have sensible proof of the truth of this explanation deriv- 

 ed from the fact, that the pressure of the point upon the plane, 

 is much greater than that arising from gravity simply. Indeed, 

 when the top is put in motion upon a plane of jdelding matter, 

 the point works its way into the substance of the plane; and if it 

 be taken into the hand, the pressure will become much more 

 sensible than that which takes place when there is no motion. 



