136 Statics. 



by taking the limit of the ratio of u to v. Now as this ratio is 

 constantly the same, and equal to the ratio of DE to circum. EG; 

 according to the preceding proportion, we shall have, in the case 

 of an equilibrium, 



q : p : : DE : circum. EG, 

 as before shown by a different process. 



Of Friction,, 



234. The surfaces of bodies, even the most smooth, are cov- 

 ered with elevations and depressions ; and when two bodies are 

 brought in contact with each other, the prominent parts of the 

 one enter the cavities of the other, and they cannot be moved 

 the one over the other, without employing a certain force. The 

 resistance arising from this cause is called friction. 



There are two sorts of friction, one which takes place when 

 the bodies in contact have simply a sliding motion ; the other 

 when one or both the bodies move by turning upon an axis. We 

 have an instance of the former in the motion of skates and sledg- 

 es, and of the latter in the action that exists between the wheels 

 of wheel-carriages and the ground. The resistance arising from 

 the second kind of friction, is much less than that of the first, 

 since a rotatory motion serves to disengage the parts in contact 

 without breaking down the eminences or lifting them out of the 

 cavities. 



When the rising up of one body over the other is complete- 

 ly prevented, the friction becomes very intense, as appears 

 in what may be accounted an extreme case, the drawing of 

 wire, and the rolling of bars of iron, copper, &c., into plates, 

 where the extension of the metal is the effect of the friction acting 

 all round or on two sides. 



If the asperities with which the surfaces of bodies are cover- 

 ed, were perfectly hard, and immoveably attached to these sur- 

 faces, it would be necessary, in overcoming the friction, to raise 

 the incumbent mass. If these asperities, on the other hand, were 

 perfectly flexible, there would be no resistance and no friction.. 



