32 KEPORT — 1873. 



Since the number of the molecules does not vary durinp: then- niotiou, this 

 quantity is zero, whatever the values of ^, rj, (. Hence we have in virtue of the 

 last term, 



^=0, !^=0, ^^=0, (18) 



d.c dy (l~ 



or A is constant througliout the whole region traversed by the molecules. 

 Next, comparing the first and second terms, we find. 



c=-2AM(^|.+ B) (19) 



We thus obtain as the complete form of (?N, 



^^^e-(AMi(f?+^5+^!+2^ii-B,)f/.ra'yffcrf|f/,,J^, . , , (20) 



where A is an absolute constant, the same for every kind of molecule in the vessel, 

 but Bi belongs to the first kind only. To determine these constants, we must in- 

 tegrate this quantity with respect to the six variables, and equate the re ult to the 

 number of molecides of the first kind. We must then, by integrating 



determine the whole energy of the system, and equate it to the oiiginal energy. 

 We shall thus obtain a sufficient number of equations to determine the constant A, 

 common to all the molecules, and Bj, B^, &c., those belonging to each kind. 



The value of A determines that of the mean kinetic energy of all the molecules 



in a given place, which is '^ — ; and therefore, accoi-ding to the kinetic theory, it 



also determines the temperature of the medium at that place. Hence, since A,, in 

 the permanent state of the SJ^stem, is the same for every part of the system, it 

 follows that the temperature is everywhere the same, whatever forces act upon 

 the molecules. 



The number of molecules of the first kind in the element dz dy dz, 



(5)' 



■"'■"*'*'''.l.,,l!,,k (21) 



The effect of the force whose potential is \f/i is therefore to cause the molecules 

 of the first kind to accumulate in gi-eater numbers in those parts of the vessel 

 towards which the force acts ; and the distribution of each different kind of 

 molecules in the vessel is determined by the forces which act on them in the 

 same way as if no other molecules were present. This agrees with Dalton's 

 doctrine of the distribution of mixed gases. 



On the Axis of least Moments in a EectanguJar Beam. By Jonx Nevit.t.k. 



On certain Phenomena of Impact. By Professor Osbokne Retnolds. 



On Ethereal Friction. By Professor Baifour Stewart, LL.D., F.R.S. 



Prof. J. G. ^laxwell has made a series of experiments on the friction of gases. 

 In these experiments a horizontal disk was made to oscillate in an imperfect va- 

 cuum near a similar disk at rest, and it was found tliat the motion of the oscilla- 

 tino- disk Wiis carried away by the residual gas of the vacuum at a rate depending 

 on the chemical character of "the gas, and depending also upon its temperature, but 

 nevertheless independent of its density. 



While the temperature of the arrangement remained constant, it was found by 

 Prof. Maxwell that this flLud friction was rather greater for atmospheric air than 

 for carbonic acid, while for hydrogen it was about half a-s great as for air. 



