B^dth affccfcd by Fn'^lion, 1 73 



than the weight on an equal part of A, as A is greater than a ; 

 if therefore the fridtion was in proportion to the weiglit, CiVte^ris 

 paribus^ it is inanifefl, that the fridion on a would be equal to 

 the friction on A, the whole fri£lion being, upon fuch a fuppo- 

 fition, as the weight on any given part of each furface multi- 

 plied into the number of fuch parts or into the whole area, 

 which produdls, from the proportion above, are equal. But 

 from the laft experiments it has beeji proved, that the fridlion 

 on any given furface increafes in a lefs ratio than the weight ; 

 confequently the fridion on any given part of ^ has a lefs ratio 

 to the fridion on an equal part of A than A has to a^ and 

 hence the friftion on<^ is lefs than the friflion on A, that is, 

 the fmalleft furface has always the leaft fridion. But as this 

 conciufion is contrary to the generally received opinion, I have- 

 thought it proper to confirm the fame by a fet of experiments. 

 But before I proceed to relate them, I will beg leave tC'recom-^ 

 mend to thofe, who may afterwards be induced to repeat them, 

 the following cautioijis, which are extremely neceflary to be 

 attended to. Great care muft be taken that the two furfaces- 

 have exactly the fame degree of roughnefs ; in order ta be 

 certain of which, fuch bodies mufl be chofcn as have no knots 

 in them, and whofe. grain is fo very regylar that when the 

 two furfaces are planed with, a fine rough plane, their rough- 

 nefs may be the fame, which will not be the cafe if the body 

 be knotty, or the grain irregular, or if it happens not to run 

 in the fame direction on both furfaces. When you cannot de- 

 pend on the furfaces having the fame degree of roughnefs, the 

 beft way will be to pafte Ibme fine rough paper on each fur- 

 face, which perhaps will give, a more, equal degree of rough- 

 nefs than can be obtained by any other method. Now as the- 

 proof which I have already given depends only on the motion'. 



of^ 



