MECHANICS. 



able consequence follows, which is, 

 that however the magnitude of the sur- 

 face of contact may vary, the friction 

 will remain the same so long as the 

 pressure is unchanged. Thus, suppose 

 the body, C D, to be a flat block of 

 wood, the face of which is sixteen square 

 inches in magnitude, and the edge of 

 which is equal to only one square inch, 

 it will have the same friction with the 

 plane, A B, whether it be placed upon 

 its face or upon its edge. To explain 

 this, let us suppose the weight of the 

 block to be sixteen ounces ; "and let us 

 suppose that when the body rests upon 

 its edge, the amount of the friction, de- 

 termined in the manner already ex- 

 plained, be eight ounces; it therefore 

 follows that then the friction of every 

 square inch of surface is equal to half 

 the pressure on that square inch. Now 

 let the block be placed upon its face, 

 and let us suppose that the magnitude 

 of the face is sixteen square inches ; 

 the whole weight of the block is sixteen 

 ounces, and therefore the pressure on 

 each square inch will be one ounce. 

 AVhen the pressure on a square inch 

 was sixteen ounces, the friction was 

 eight ounces ; and since by hypothesis, 

 the friction is proportional to the pres- 

 sure, it follows that in the present case, 

 in which the pressure is one ounce on 

 each square inch of surface, the friction 

 of each square inch of surface must be 

 half an ounce ; and since there are six- 

 teen square inches, the total friction 

 will be sixteen half ounces, or eight 

 ounces, which is exactly equal to the 

 friction when the block rested upon its 

 edge. 



It is evident that the same result 

 would be obtained had we supposed the 

 surfaces of any other magnitudes, and 

 the pressure of any other amount. It 

 may be satisfactoiy, however, to those 

 who are a little conversant with alge- 

 braic notation, to see a general proof 

 of this remarkable property. 



* [Supposing the unit of surface to be 

 one square inch, and the unit of pressure 

 to be one pound, let P be the pressure 

 upon a square inch of surface, expressed 

 in pounds or parts of a pound. Let S 

 be the number of square inches in the 

 surface of contact ; then S P will be 

 the total pressure. Let /be the friction 

 which one pound of pressure would 

 produce on one square inch of surface ; 



* Those readers not familiar with mathematical 

 reasoning will omit the paragraphs included within 

 brackets. 



then /P will be the friction produced 

 by the pressure, P, on one square inch 

 of surface, and/S P will be the friction 

 produced by the pressure, S P, upon 

 the surface, S. If F be this total fric- 

 tion, we shall have F=/S P. But S P 

 is the total pressure or weight of the 

 block. Calling this W, we have F=/W, 

 which is independent of the magnitude 

 of the surface of contact.] 



The result which we have here ob- 

 tained as a consequence of the propor- 

 tionality of the friction to the pressure, 

 is fully confirmed by the experiments 

 of Coulomb and Ximenes. They found 

 that when a block of any substance has 

 several faces of different magnitudes, 

 the friction will be the same on what- 

 ever face it is placed ; as in the former 

 instance there is an extreme case which 

 forms an exception to this law ; for when 

 the pressure is very small, and the sur- 

 face of contact very much increased, 

 the friction is found to be somewhat 

 greater than it would be with a smaller 

 surface. 



(8.) There is another method of 

 proving, experimentally, the proportion 

 of the friction to the pressure, which 

 depends on a property of the inclined 

 plane. Let the body W (Jig. 2), be placed 



Fig. 2. 



upon a plane, AB, which is hinged to 

 an horizontal plane, C B, so that it can 

 be raised to any proposed elevation. 

 Now let the plane, AB, be slowly 

 raised, until it acquires such an eleva- 

 vation that the force of the body down 

 the plane is just sufficient to overcome 

 the friction, and that the body will 

 therefore commence to move. In this 

 case, therefore, the force down the 

 plane will be equal to the friction. If 

 the length of the plane, A B, be taken 

 to represent the whole weight, W, the 

 height, AE, will represent the force 

 down the plane, and the base, B E, will 

 represent the pressure of the weight, 

 W, upon the plane. The proportion 

 of the friction to the pressure will then 

 be that of A E to BE. Now let the 

 weight be successively doubled, trebled, 

 &c. ; and it will be found that the same 

 elevation of the plane will continue to 

 overcome the friction, and put the body 



