324 Mr. T. S. Thomson's Observations on Mr. Graham's 



with Mr. Dalton's law, it will affect the phaenomena of gases 

 under the same pressure, mutually diffusing through a porous 

 intermedium. For this purpose we shall consider any two 

 gases, g, g' representing their densities by d, d! ; the velocities 

 with which each would rush into a vacuum, under the same 

 pressures, by e, s' ; the volumes of each which would so escape 

 in the same times by v, v' \ and the comparative weights or 

 masses of v, v', by m, m'. By the known law, their relative 

 velocities into a vacuum are given by the proportion 



.= : s';: V~d>: */ d (1.) 



e*d = s' 2 d' (2.) 



Now s, e' evidently vary as e, v'; and as the weight or mass is 

 as the product of the density of each by its volume, we have 

 the equations 



vd — ed = m (3.) 



v/d' = e'd' = m' (4.) 



Combining equations (1.) (2.) with these, we obtain 



= m = s' ?n'. 

 Hence the mass multiplied into the velocity, of each issuing 

 stream is the same for both gases, whatever be their respec- 

 tive densities, or, in other words, the moving force of each 

 issuing current is the same\ a law most remarkable for its sim- 

 plicity and importance, and one which is not noticed in any 

 of the treatises on gaseous mechanics that I have met with. 



Instead of the gases issuing into a vacuum, let us now sup- 

 pose that they are permitted to diffuse through each other by 

 a small aperture, or system of apertures, such as is presented 

 by a plug of stucco, or any other porous substance. Know- 

 ing so little as we do of the ultimate corpuscular constitution 

 of gases, we cannot determine the precise manner in which 

 the opposing currents will act upon each other ; whether by 

 percussion, by friction, or in what other possible mode of 

 mechanical action. But one thing we may safely predict, 

 viz. that a partial obstruction will take place, a retardation 

 of the velocity of each gas will ensue ; and since, from the 

 equality of action and reaction, the quantity of motion lost 

 on each side is the same, the resulting momenta of the cur- 

 rents will necessarily be equal, and consequently, by the con- 

 verse of the equations (1.), (2.), (3.), (4.), tne resulting veloci- 

 ties will be inversely proportional to the square roots of the 

 densities. Hence it appears, if the data be correct, that the 

 initial velocities of diffusion ought to be exactly in the pro- 

 portion that Mr. Graham; has determined by experiment. 



