On Friction in Machinery. 217 



however unknown the nature of friction may be, nothing seems 

 more certain than that the friction, for any given instant, depends 

 on the then value of, and relation which subsists at that instant 

 among, the quantities concerned in producing it. Present fric- 

 tion has really no more concern with past space, than we have 

 with " the years beyond the flood." 



Besides the consequents of the mistakes already noticed, there 

 are some other things in Mr. Tredgold's investigation, which, if 

 not erroneous, are at least fanciful enough. But be these as they 

 may, by combining mollia cum duris, he has luckily hit on the 

 truth in his (10) prop., which, however, contains the condemna- 

 tion of the (8). 



The mistake first noticed about the indentation being as the 

 square of the time, has no doubt given birth to his (S) prop, that 

 — in uniform motions friction is inversely as the velocity; and this 

 in its turn has been the fruitful parent of many strange incon- 

 sistences. For instance, if friction were inversely as tlie velocity, 

 it would necessarily follow that the thickness of an axle is a mat- 

 ter of total indifference as to the moving of the carriage : for, 

 as the axle's diameter increases, the relative velocity of sliding 

 at its surface, increases, and bv prop. (S) the friction diminishes. 

 But the effect of the power at the wheel's rim to turn it round, 

 or overcome the friction at the axle, is also, cceteris paribus, 

 inversely as the diameter of the axle. Consequently, the wheel 

 must hav€ the same disposition to turn, whatever be the axle's 

 diameter. Let, therefore, the axle's diameter become nearly 

 equal that of the wheel, which, if it turned b«fort, will, for the 

 same reason, turn still. The obvious conclusion then is, that on 

 a polished railing it is in the wheel's option whether to turn or 

 slide; or, that the use of wheels is merely to overcome the in- 

 equalities ^f the road. Mr. Tredgold has thus duly laid claim to 

 the very delusion which I exposed towards the end of my former 

 letter, though it be directly contrarv to what he teaches us on 

 page 21 of July Number. But the remaining pages of that pa- 

 per are sadly infected bv prop. (S) — the final conclusions, espe- 

 cially IV and VI, being quite contradictory. On these, however, 

 I shall not now enlarge, but only remark, that it is indeed no 

 small recommendation to any theorv, however vague, that it be 

 consistent with itself. Tills is at least a possible case ; yet, how 

 rarely do we meet u-ith an instauiie of the kind! 



Admitting that friction is constant for all velocities, it readily 

 follows that friction, when referred to the first mover, or, in other 

 words, that the waste of moving power in order to overcome fric- 

 tion, is, cceteris paribus, directly as the relative velocity of the 

 rubbing surfaces. It is on this princijjlc that friction wheels are 



(if 



