216 On Friction in Machinery. 



In perusing Mr. Tiedgold's papers in your Numbers for Janua- 

 ry and July, I was not a little surprised to find that he had ar- 

 rived at the singular conclusion of the friction in uniform mo- 

 tions being inversely as the velocity — a doctrine directly opposed 

 to by far the greater number of experiments I have ever heard 

 of; which, with a very few exceptions, mostly lying the other 

 way too, confirm the general opinion that, on hard bodies, fric- 

 tion is tlie same for all velocities. This led me to examine more 

 closely the different steps of his investigation, in order, if possi- 

 ble, to find whence tlie mistake had originated. In the former of 

 these papers, page 6, Mr. T. asserts that the depth of indenta- 

 tion is as the square of the time ; and in July Number, page 23, 

 he quotes the same, saying that " the dejjth of impression is as 

 the force, and as the square of the time the force acts." Why 

 he should have pitched on the square rather than any other 

 power of the time, he has not thought proper to inform us. It 

 may not, however, be altogether useless to show that it cannot 

 be as the square of the time : it is well known, that when a 

 heavy body meets with a resistance which still allows it to descend 

 through a space proportional to the square of the time, that re- 

 sistance must be uniform. In which case it is evident there 

 could be no such thing as a maximum of indentation or impres- 

 sion : because the one body resting on the other, and meeting 

 with no increase of resistance to impression, if it sunk at all, 

 would continue to do so, with a uniformly accelerated motion, 

 till it had got quite through the lower body — nor would it likely 

 be at rest on this side of the earth's centre if time sufficient only 

 were allowed. 



Such are the ridiculous consequences to which this doctrine 

 would lead. Nearly in the same way it might be shown that the 

 depth of impression can be as no constant power of the time 

 whatever. Indeed we have no data for determining the relation 

 which subsists between the time and depth of indentation. But 

 the resistance to indentation, v.'ithout doubt, increases rapidly 

 with the depth. This is abundantly evident from Mr. Rennie's 

 interesting experiments. 



In January Number, page 7, Mr. T. further states that '^the 

 space abraded will be as the square of the velocity." This I am 

 not disposed to contradict, as he, no doubt, means the entire 

 space abraded from the commencement of motion. But I con- 

 fess I do not see how it applies : for, it seems clear that it is not 

 the ivliole space passed over from the beginning, but only its 

 rate of increase that he has to do with, and which must be as 

 the. velocity simply . There is just as good reason for including, 

 the whole space, from the commencement of motion, in the fric- 

 tion of the uniform motion, as there is in the accelerated. For, 



however 



