152 Account -of some Experiments on Friction. 



It is well known to mathematicians, that had the re- 

 sistances which opposed the motion of the stone hcen uiji- 

 form, and the observations correct, the second ditierence's, 

 or those contained in the fourth colunni of each experi- 

 uicnt, would have been the same, or a constant quaniity. 

 This it appears was not so, and several causes can \vt as- 

 signed why tliey mioht not be so, though friction itself be 

 an uniform resistance : First, when the stone v.as making 

 260 or 270 turns per minute, as it was at the beginning of 

 each experiment, the miimtc-hanJ would be passing over 

 4-i- minutes on the dial-plate per second of time, and conse- 

 qiieiitlv it was diliicult to observe the precise place of the 

 hand. ' ilcncc it is easy to see that A variation might arise 

 on this account, especially when it is considered that the 

 moment of calling by one person, and of attention of a se- 

 cond, might not be shnultaneous. Secondly, as the circum- 

 ference ol' the stone at the beginning of the experiments 

 was movins: with a velocity of upwards of 60 feet per se- 

 cond, some^ resistance from the air would necessarily arise, 

 wjiich would diminish as the stone revolved more slowly, 

 and this would create a dilfcrence in the uniformity of 

 resistance, and consequently in the second differences. 

 Thirdly, the mill being used for grinding, the principal 

 part of the apparatus was covered with siliceous dust ; arid 

 though the rubbing parts were protected from it as much as 

 possiule, some particles of it might, by the shaking of the 

 machine, fall between the rubbing surfaces, and thus occa- 

 sion a variation in the resisting force at different instants. 

 i am the more inclined to believe this was actually the case, 

 from observing in the table the variation of mean resistance 

 in the three experiments, notwithstanding tbey were made 

 under circimistanccs as precisely the same as possibly could 

 be; for in the second experiment the stone made 135 more 

 turns before it came to rest than it did in the first, although 

 tl>e initial velocities were not matei-ially different ; and in 

 the third experiment, notwithstanding the initial velocity 

 was greater than in the second, the whole number of revo-^ 

 lutions was 9f) less. 



If the second differences for each corresponding minute 

 of time in the three experiments be added together, and di- 

 vided by 3, the numbers 30|, 304-, 28^, 28-1-, 2fi, 261, 26i 

 ■will be 'obtained for mean second differences; and had the 

 experiments been verv numerous, I think tlie probability is 

 great that a set of means would have arisen which would 

 have shown a more steadily decreasing series. From these 

 few experiments, howeyerj it seems fair to infer, that the 



resistance 



