PROFESSOR MOSELEY ON THE THEORY OP MACHINES. 293 



of contact. We know, however, by daily experience, that the resistance of no two 

 surfaces is limited to this single direction. Friction presents itself wherever the re- 

 sistance of the surfaces of solid bodies is exerted, and is, in fact, but the resolved part 

 of that resistance in a tangent plane to the surfaces at their point of contact. And 

 from the laws which have been proved by experiment to obtain approximately in 

 respect to it, it follows that within the surface of a certain cone, called the cone 

 of resistance, whose apex is at the point of contact of the surfaces, whose axis coin- 

 cides with the normal, and whose angle is twice that which has for its tangent the 

 coefficient of friction, every direction that can be taken is one in which the mutual 

 resistances of the surfaces of contact is exerted as perfectly as in the normal direction ; 

 in fact, that any pressure (less than that which produces abrasion) being applied to 

 the surface of an immoveable solid body by the intervention of another body move- 

 able upon it, is sustained by the resistance of the surfaces of contact, whatever be 

 its direction, provided only the angle which that direction makes with the perpen- 

 dicular to the surfaces of contact do not exceed a certain angle, called the limiting 

 angle of resistance of those surfaces. This is true, however great the pressure may 

 be, within the limits of abrasion. Also, if the inclination of the pressure to the per- 

 pendicular exceed the limiting angle of resistance, then this pressure will not be sus- 

 tained by the resistance of the surfaces of contact ; and this is true however small 

 the pressure may be. 



Let P Q represent the direction in which the surfaces of two 

 bodies are pressed together at Q ; and let Q A be a perpendicular, 

 or normal to the surfaces of contact at that point ; then will the 

 pressure P Q be sustained by the resistance of the surfaces, how- 

 ever great it may be, provided its direction lie within a certain given 

 angle, A Q B, called the limiting angle of resistance ; and it will not be sustained 

 however small it may be, provided its direction lie without that angle. For let this 

 pressure be represented in magnitude by P Q, and let it be resolved into two others, 

 A Q and R Q, of which A Q is that by which it presses the surfaces together perpen- 

 dicularly, and R Q that by which it tends to cause them to slide upon one another ; 

 if therefore the friction F produced by the first of these pressures exceed the second 

 pressure R Q, then the one body will not be made to slip upon the other by this 

 pressure P Q, however great it may be ; but if the friction F, produced by the per- 

 pendicular pressure A Q, be less than the pressure R Q, then the one body will be 

 made to slip upon the other, however small P Q may be. Let the pressure in the 

 direction of P Q be represented by P, and the angle A Q P by ^, the perpendicular 

 pressure in A Q is then represented by P cos ^, and therefore the friction of the sur- 

 faces of contact by fV cos 6, f representing the coefficient of friction. Moreover, the 

 resolved pressure in the direction RQ is represented by P sin 6. The pressure P will, 

 therefore, be sustained by the friction of the surfaces of contact, or not, according as 

 P sin 6 is less or greater than/P cos &\ 

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