On the Motion of Badks affected ly Friciion. 53 



the surfaces A and a, the former being the greater, and the 

 latter the less. Now the weight on every given part of a is 

 as much greater tiian the weight on an equai pan of A, as 

 A is greater than a ; if therefore tlie friction was in propor- 

 tion io the weight, ccsleris parihusy it is manifest that the 

 friction on a would be equal to the friction on A, the whole 

 friction being, upon such a supposition, as the weight on 

 any given part of each surface multiplied into the number 

 of such paits, or into the whole area ; which products, from 

 the proporuon above, dre equal. But from the last experi- 

 ments it has been proved that^ the friction on any given 

 suitace increases in a less ratio than the weight; conse- 

 quently the friction on any given part of a has a less ratio 

 to the .^'riction on an equal part of A than A has to a; and 

 hence the friction on a is less than the friction on A, that 

 is, the smallest surface has always the least friction. But 

 as this conclusion is contrary to the generally received opi- 

 nion, I have thought it proper to contirm the same by a set 

 of experiments. But before I proceed to relate them, I 

 will beg leave to recommend to those, who may afterwards 

 be induced to repeat them, the following cautions, which 

 arc extremely necessary to be attended to. Great care must 

 be taken that the two suriaces have exactly the same degree 

 of roughness; in order to be certain of which, such bodies 

 nmst be chosen as have no knots in them, and whose grain 

 is so very regular, that when the two surfaces aie planed 

 with a fine rough plane their roughness may be the same, 

 which will not be the case if the body be knotty, or the 

 grain irregular, or if it happens not to run in the same di- 

 rection on both surfaces. When you cannot depend on the 

 surfaces having the same degree of roughness, the best way 

 will be to paste some fine rough paper on each surface, 

 which perhaps will give a more equal degree of roughness 

 than can be obtained bv any other method. Now as the 

 proof which I liave already given depends only on the mo- 

 lion of the bodv upon the same surface, it is not liable to 

 any inaecuraev of the kiiid which the preceding cautions 

 have been given to avoid, nor indeed to any other, and 

 therefore it must be perfectly conclusive. In the following 

 experiments the cautions mentioned above were carefully 

 attended to. 



ExH. 1. A bodv was taken whose flat surface was to its 

 edge as 29 : 9, and with the same moving force the body 

 tiescribed on its flat side 33 i inches in 2", and on its edge 

 47 inches in lhe same time, 



Kxi'. 2. A hccond i)ody was taken whose flat, surface was 

 J) 3 to 



