Bodies ajTecied by Friction, 
than the weight on an equal part of A, as A is greater than a ; 
if therefore the fridion was in proportion to the weight, cceteris 
paribus, it is manifed, that the fri&ion on a would be equal to 
the friction oil A, the whole friction being, upon fuch a fuppo- 
fit ion, as the weight on any given part of each furface multi- 
plied into the number of fuch parts or into the whole area, 
which produdts, from the proportion above, are equal. But 
from the lad: experiments it has. been proved, that the frihlion 
on any given furface increafes in a lefs ratio than the weight ; 
confequentlyAhe fri&ion on any given- part of a has a lefs ratio 
to the friftion on an equal part of A than A has to a, and 
hence the fri£lion on a is lefs than the friftion on A, that is, 
the fmalled furface has always the lead. fridtion. But as this 
conclufion 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 to recorm- 
mend to thofe, who may afterwards be induced to repeat them, 
the following cautions, which are. extremely necedary to be 
attended to. Great care mull be taken that the two furfaces 
have exadlly the fame degree of. roughnefs; in order to be 
certain of which, fuch bodies mud: be chofen as have no knots 
in them, and whofe- grain is fo very regular 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 
bed way will be to pade fome fine rough paper :on each lur~ 
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 
