Friction. 141 



IH the pressure, and HZ or IL the force of friction ; hence 

 the triangles ///Z, ABC being similar, we have Geom 



HZ or IL : IH : : BC : O4, * 02 ' 



from which it will be seen, that the force of friction is to the 

 pressure as the height of the plane to its base. 



It will be perceived, in like manner, that 

 HZ : IZ :: BC : ./IB; 



that is, the force of friction is to the weight of the body as the 

 height of the plane is to its length. 



In order, therefore, to determine the friction in different sub- 

 stances, we have only to raise the plane JIB till the body p is 

 upon the point of moving ; then measuring the height and the 

 base, we shall have the ratio of the force of friction to the pres- 

 sure. 



238. By these two examples, it will be seen, that regard 

 being had to friction, the condition required in order that a body 

 may remain in equilibrium upon a proposed surface, and be in 

 a state approaching the nearest to motion, is, that the single 

 force which acts upon it, if there be but one, or the resultant of 

 all the forces, if there be several, have with respect to the sur- 

 face upon which it is to move, an inclination GIE or ZJZ, such 

 that IL shall be"///, as the force of friction is to the pressure. v 

 But IL is to LZ, as one is to the tang. LIZ, I being the radius 

 of the tables. Consequently the inclination LIZ must be such 

 that the radius shall be to the tangent of this inclination, as the 

 force of friction is to the pressure ; therefore, the ratio of the 

 force of friction to the pressure being once ascertained, it will 

 always be easy to determine the inclination belonging to the 

 resultant of all the forces which act upon the body, this body 

 being in a state of equilibrium approaching as near as possible 

 to motion. Hereafter we shall call the angle LIZ the angle of 

 friction. It is different for different substances, and for different 

 degrees of smoothness of the same substance. If the friction is 

 331 per cent, or one third of the pressure, which is nearly the 

 case with respect to a great many kinds of matter, the rubbing 

 surfaces being tolerably smooth, the tangent of LIZ will be triple 

 of the radius, that is, LZ will be equal to 3 IL. Now the angle 



