158 Intelligence and Miscellaneous Articles. 



of motion takes place only in the direction of: the common normal 

 to the two cylindrical atoms at the instant of the impact. The 

 atoms then behave like perfectly hard elastic spheres : no internal 

 motion takes place. First the number Sft of the collisions is cal- 

 culated (in the known manner) which the atom M experiences when 

 during a unit of time it moves through the atoms in with the con- 

 stant velocitv £2 ; and it is remarked that 9? is a minimum for 

 £2=0. 



It is then assumed that the velocity of M is continually altered 

 in quantity aud direction by the collisions, but at the same time a 

 certain mean velocity A, in the direction OX, prevails. Those de- 

 viations from the mean motion effected by the impacts the author 

 names the "oscillating motion" of the atom M. [To some extent 

 in this way behaves an atom of one kind of gas which is diffused 

 with a certain velocity through another. — The Reporter.] The 

 probability f v that the atom M has the velocity-components I7„, Y v , 

 W„ in the directions of the axes of coordinates the author finds by 

 a method first employed by O. E. Meyer. He first finds the pro- 

 bability that the atom, in n arbitrarily chosen time-elements, has 

 successively the velocity-components 



U 1 ,V 1 ,W 1 ,U a ,V 2 ,W a ,...F w Y„W a 



equal to the product 



/i. /..../■• 



As the most probable distribution of velocities he designates that 

 for which this product is a maximum. But now the sought-for 

 function / is not variated, but the differential quotients of the above 

 product with respect to the variables contained therein are, under 

 the corresponding accessory conditions, put equal to 0, which gives 



f^e-mv-aP+cr-PP+W-vW. 



By F the author denotes the ratio of the time during which the 

 velocity-components of the atom M lie between the limits U and 

 U+cW, V and Y+dV, W and W+dW to the whole time of the 

 motion of that atom ; and he finds from the above, putting 



U = £2cos0', V=£2sin0'cos©', W=£2sin 6' shirt', 



w = V/i-)/*£2, a=V&wA, k=j — 5 

 fern 



l , ^^AV KCiu2a ' "' 2cose,+a2) '"-(^sin6'(^'(^'. 



For the quiescent gas, Maxwell's distribution of velocities is 

 assumed : — the number of the atoms in the unit of space for which 

 the X component of the velocity lies between u and « + </" is 



v _ /hm 



' V7 



g-AwittS ,/„. 



