. The London, Edinburgh and Dublin philosophical magazine and journal of science. ¢31772 â¢71433 40 0 420 772 47 20 â¢55749 102427 4] 0 374 758 51 32 â¢62515 â¢96763 42 0 324 745 56 26 â¢70197 â¢85838 43 0 264 732 62 22 â¢78S72 â 67868 44 0 187 719 70 18 â¢88745 â¢40338 44 30 132 713 76 1 â¢94190 â¢21999 45 0 0 707 90 0 1-00000 â¢00000 A1 = J47r«d« sin26>=2-6595,As=jW* sin2 26= 1-3682. ⢠⢠⢠(15). (16) Mr. J. C. Maxwell on the Dynamical Theory of Gases. 145 The paths described by mo-lecules about a centre of forceS, repelling inversely as thefifth power of the distance, aregiven in the
. The London, Edinburgh and Dublin philosophical magazine and journal of science. ¢31772 â¢71433 40 0 420 772 47 20 â¢55749 102427 4] 0 374 758 51 32 â¢62515 â¢96763 42 0 324 745 56 26 â¢70197 â¢85838 43 0 264 732 62 22 â¢78S72 â 67868 44 0 187 719 70 18 â¢88745 â¢40338 44 30 132 713 76 1 â¢94190 â¢21999 45 0 0 707 90 0 1-00000 â¢00000 A1 = J47r«d« sin26>=2-6595,As=jW* sin2 26= 1-3682. ⢠⢠⢠(15). (16) Mr. J. C. Maxwell on the Dynamical Theory of Gases. 145 The paths described by mo-lecules about a centre of forceS, repelling inversely as thefifth power of the distance, aregiven in the figure. The molecules are supposedto be originally moving withequal velocities in parallel paths,and the way in which their de-flections depend on the distanceof the path from S is shown bythe different curves in the figure. 3rd. Integration with respectto d~N±.We have now to integrateexpressions involving variousfunctions of £, rj, £ and V withrespect to all the molecules ofthe second sort. We may write the expression to be integrated n-5 QYn- ^M^VzQ^2d%d^. iff where Q is some function of £, rj, £, &c., already determined,and /2 is the function which indicates the distribution of velocityamong the molecules of the second kind. In the case in which n = 5, V disappears, and we may writethe result of integration where Q is the mean value of Q for all the molecules of thesecond kind, and N2 is the number of those molecules. If, however, n is not equal to 5, so tLat V does not disappear,we should require to know the form of the function/^ before wecould proceed further with the integration. The only case in which I have determined the form of thisfunction is that of one or more kinds of molecules which have bytheir continual encounters brought about a distribution of velo-city such that the number of molecules whose velocity lies withingiven limits remains constant. In the Philosophical Magazinefor January 1860, I have given an in
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