o08 Royal Society : — 



change, and in which, therefore, the aid of the Integral Calculus is 

 required. This chapter (which is written by Professor Crofton, of 

 AVoolwich) is demoted to the consideration of " a few of the less 

 difficult questions on these subjects," and is intended '^ to give at 

 least some idea of the methods to be employed." There is, of 

 course, a certain order in the arrangement of the questions, but 

 hardly what amounts to a systematic treatment of the subject ; in 

 fact the number and diversity of questions on probability is " so 

 great that no attempt seems to have been made to classify or con- 

 nect Ihem into a regular theory" (p. 311). So that, in fact, the 

 chapter consists of a number of explanatory articles of a more or 

 less general character, each article being followed by a few examples 

 fully worked out (in all about forty) of such a kind as might be 

 anticipated — e. g. " To find the mean distances between two points 

 within a given circle " (p. 304), or again, " Three points being taken 

 at random within a s])here, to find the chance, that the triangle 

 which they determine shall be acute-angled " (p. 327). It is need- 

 less to say that such questions are excellent exercises in the Integral 

 Calculus, are likely to interest an intelligent student, and that the 

 chapter containing them is a very useful and interesting addition 

 to an admirable elementary treatise. 



XLII. Proceedings of Learned Societies, 



ROYAL SOCIETY. 



[Continued from p. 234.] 



March 22,1877. — Dr. J . Dalton Hooker,C.B., President, in the Chair. 



^pHE following paper was read : — 



-*- " On Priction between Surfaces moving at Low Speeds." 



By Pleeming Jenkin, P.R.SS. L. & E., Professor of Engineering in 

 the University of Edinburgh, and J. A. Ewing. 



The common belief regarding friction, Avhich is based on the re- 

 searches of Coulomb and Morin, is that between surfaces in mo- 

 tion the friction is independent of the velocity, but that the force 

 required to start the sliding is (in some cases at least) greater than 

 the force required to overcome friction during motion ; in other 

 words, the static coefficient is usually considered to be greater 

 than the kinetic. It occurred to the authors that there might 

 possibly be continuity between the two kinds of friction, instead of 

 an abrupt change at the instant in M'hich motion begins. AYe 

 should thus expect that \vhen the relative motion of the surfaces is 

 very slow there will be a gradual increase of friction as the velocity 

 diminishes. AVhether any such increase takes place at Aery low 

 speeds is left an open question by the experiments of Coulomb and 

 Morin, whose methods did not enable dejfinite measurements of tlie 

 friction to be made when the velocity was exceedingly small. The 

 authors have succeeded in measuring the friction between surfaces 

 moving with as low a velocity as one five-thousandth of a foot per 



