8 



MECHANICS. 



plained ; and therefore the increase of 

 the accelerating force with which C D 

 is moved, must necessarily proceed from 

 a decrease in the retarding force arising 

 from the friction. But again, this re- 

 tarding force depends on two things: 

 1st, on the proportion of the friction 

 to the pressure ; and 2d, on the pro- 

 portion of the weights of C D and 

 S. The latter remains unaltered, and 

 therefore we are compelled to infer, 

 that the former must be diminished ; 

 that is, that the friction does not increase 

 in proportion to the pressure, but in a 

 less ratio. 



[To express this mathematically, let 

 the accelerating force with which C D 

 is actually moved be C. We have 

 then 



* 



gm' fm 

 m + m 1 



m 



. + 1 



Let us suppose that upon increasing m 

 and m', in the same ratio C is increased. 



The first part m_ of the value of C, 



i ~T" * 



m' 



evidently remains of the same value as 



m 



before. Hence, the second part/ 



must necessarily be diminished. 

 m 

 m r 



But 



the factor 



remains the same, and 



therefore /must be diminished. But/ 

 expresses the ratio of the friction to the 

 pressure, which would, therefore, under 

 these circumstances, be diminished.] 



(12.) Such are the principles upon 

 which Professor Vince founded his ex- 

 periments. He found that when he 

 doubled and trebled the weights of C D 

 and S, the accelerating force with which 

 C D was moved, was continually in- 

 creased. Thus, when CD was 10 oz., 

 and S = 4 oz., the space moved through 

 in two seconds, was 51 inches. Upon 

 making C D = 20 pz., and S = 8 oz., 

 the space described in two seconds was 

 56 inches ; and when C D = 30 oz., and 

 S = 12 oz., the space was 53 inches. 

 Numerous other experiments were 

 made, all producing similar results. 

 Professor Vince therefore concluded, 



" that although the friction increased 

 with the increase of pressure, yet that it 

 increased in a somewhat less propor- 

 tion." Thus, when the pressure was 

 doubled, the friction was not quite twice 

 its former amount ; also, when the pres- 

 sure was trebled, the friction was less 

 than three times its former amount ; and 

 so on. 



Having established this conclusion, 

 at variance with former received doc- 

 trines, a consequence immediately fol- 

 lowed from it, also inconsistent with 

 what had been considered as an esta- 

 blished property of friction. We have 

 shewn, that if the friction be propor- 

 tional to the pressure, it will be inde- 

 pendent of the magnitude of the surface 

 of contact, and that on whatever face a 

 body is placed, the friction will be the 

 same. If, however, according to the 

 results of Professor Vince, the friction 

 increase in a less proportion than the 

 pressure, it will follow that, with the 

 same pressure, the friction will increase 

 when the surface of contact is in- 

 creased. 



To explain this, let us suppose, as in 

 the former case, that a block weighing 

 sixteen ounces, has a face whose mag- 

 nitude is sixteen square inches, and an 

 edge whose magnitude is equal to one 

 square inch. When the block is placed 

 upon its face, there will be a pressure 

 of sixteen ounces upon a surface of 

 sixteen square inches ; let the whole 

 friction be equal to eight ounces. 

 Hence, on each square inch there will 

 be a pressure of one ounce, producing 

 friction equal to half an ounce. Now 

 suppose the block to be placed upon its 

 edge. There will be in this case a pres- 

 sure of sixteen ounces upon a surface 

 of one square inch. The pressure of 

 one ounce upon a square inch produc- 

 ing a friction of half an ounce, and the 

 friction increasing in a less proportion 

 than the pressure, it follows that a pres- 

 sure of sixteen ounces upon one square 

 inch will produce a quantity of friction 

 less than eight ounces. Hence the 

 friction, when the block rests upon its 

 face, is greater than when it is placed 

 upon its edge. In the same way, it 

 follows generally, that, under the same 

 pressure, the friction is increased when 

 the surface of contact is increased. 



This conclusion being, like the for- 

 mer, contrary to the previously-received 

 opinions, Professor Vince submitted it 

 to the test of experiments conducted 

 upon the same principle as we have. 



