Friction. 139 



When heterogeneous bodies are made to slide upon one 

 another, as wood on metal, the friction increases slowly with the 

 time, and docs not arrive at its maximum in less than four or five 

 days. Iron on oak after ten seconds, is found to have a friction 

 of 74 per cent, and after four days it amounts to nearly 20 per 

 cent. In heterogeneous substances, too, the friction increases 

 sensibly with the velocity, nnd follows nearly an arithmetical, 

 while the velocity follows a geometrical progression. 



When the surfaces are smeared with some unctuous substance, 

 although the friction is diminished, a certain time is required in 

 order that the friction may attain its maximum. Oak rubbing 

 on oak, the surfaces being covered with tallow, has a friction 

 that continues to increase for five or six days, and becomes sta- 

 tionary at about 42 or 43 per cent. In the case of brass on iron 

 with fresh tallow between the surfaces, the friction is four days 

 in coming to a maximum, when it is 10 or 12 per cent, it being 

 9 per cent at the commencement. The increase where metals 

 are used, is much less considerable than in experiments with 

 substances more porous and yielding. 



236. The quantity of friction being determined for a partic- 

 ular kind of matter, ;et us now see if the effect upon a given ma- 

 chine, or given motion, may be thence deduced, friction being 

 considered as simply proportional to the pressure. 



Let us take, as the first example, the body p, situated upon Fi S- 126 - 

 a horizontal plane AB, and drawn by the weight of the body 9, 

 parallel to JiB. Suppose that the body q has a weight just suf- 

 ficient to put the body p in motion. The ratio of the weight q 

 to the friction is thus found. 



From the centre of gravity G of the body p, let fall the per- 

 pendicular GH upon the plane AB. The body p is urged by 

 gravity in the direction G//, and by the weight q in the direction 

 KM which meets GH in K. From the joint action of these two 

 forces, there will result an effort according to some line KI, 

 meeting in /, the horizontal plane AB ; and this effort must be 

 just counterbalanced, since we have supposed that the body p is 

 only upon the point of moving. Suppose the effort according 

 to KI or KIZ applied at the point 7, and decomposed into two 



