1 50 Statics. 



tact /, and making with the plane an angle equal to the angle of 

 friction. 



246. We proceed in the same manner in determining the 

 second kind of friction, or that which is to be overcome in giving 

 a rolling motion to bodies terminated by curved surfaces ; I say 

 curved surfaces, since with respect to bodies terminated by 

 plane surfaces, as they cannot roll, except by turning on a point 

 or some angular part, we shall not treat of these, the laws and value 

 of friction m such cases not being sufficiently known. But as to 

 the friction of bodies terminated by curved surfaces, the method 

 is precisely the same as that above pursued. We have only to 

 suppose the angle of friction to approach more nearly to 90 ; 

 and it is to experiment that we are to look for the determination 

 of this angle in all cases. 



247. Friction may be the occasion of motions very different 

 from those which take place without this cause, some of which it 

 may be worth while to notice. 



186, &c. \y e nave already mentioned more than once, what must hap- 

 Fig.133. pen to a free body BO g, which receives an impulse in a direc- 

 tion not passing through the centre of gravity. But if the body 

 were struck externally according to any direction AB, it would 

 not receive the whole of this impulse. The impelling force is 

 to be decomposed into two others, one in the direction of a tan- 

 gent to the surface, and the other perpendicular to this surface. 

 When there is no friction, the impelling force would have no 

 effect in the direction of a tangent. It is only the force in the 

 direction BF, therefore, which would be transmitted to the body, 

 and this would not cause the body to turn, except when it hap- 

 pened not to pass through the centre of gravity G. It will hence 

 be seen that if the body were of a spherical form and homogene- 

 ous, it would never be made to turn in virtue of an external force 

 unaccompanied with friction, since in this case a perpendicular 

 to the surface would always pass through the centre of the figure, 

 which would, at the same time, be the centre of gravity. On the 

 supposition of friction, the case is different. The force in the 

 direction of a tangent would transmit itself by means of the as- 

 perities of the surface, and to a greater or less degree according 

 to the amount of friction ; so that in addition to the motion aris- 



