248 Dr. J. W. Draper's Remarks on the 



pass into a vacuum are inversely proportional to the square 

 roots of their densities respectively : moreover, the volumes 

 that so pass vary directly as the velocities, and therefore may 

 be taken as an index and measure of them ; but as the mass 

 of each gas is expressed by the product of its density into 

 its volume, it may be represented by the velocity multiplied 

 into the density; and as the square of the velocity of one 

 gas multiplied into its density is equal to the square of the 

 velocity of the other multiplied into its density, whatever may 

 be the difference of the specific gravity of the two gases, their 

 mechanical momentum will always be the same ; the resistance 

 they meet with in passing through the tissue is common to 

 both, and equal in both cases, and hence the initial velocities 

 of diffusion ought to be inversely proportional to the square 

 roots of the densities; and as during the progress of the ex- 

 periment the impelling force of the one gas is equal to the ex- 

 pelling force of the other, the resulting momenta of the two 

 currents is still equal, and the final volumes are such as are 

 found by direct experiment. 



In the second case. We have first to refer here to a fun- 

 damental proposition of dynamics, that when the moving 

 force and the matter to be moved vary in the same propor- 

 tion, the resulting velocity will be the same. An illustration 

 will show the application of this principle to the case in hand : 

 if a cylinder of air, fitted appropriately with a piston, com- 

 municates with a vacuum by means of a narrow aperture, it 

 is immaterial whether the air be allowed to flow into the void 

 without any pressure, or whether it be urged by a direct ac- 

 tion on the piston ; its velocity as it goes into the void will in 

 both cases be the same ; for if it be compressed, the immediate 

 action of the force exerted on the piston is to reduce the air 

 in the cylinder to such a density that its elasticity shall be 

 equivalent to the compressing force; and because the elasticity 

 varies as the density, the density of the air will increase with 

 the expelling force; the matter to be moved is therefore in- 

 creased in the same proportion with the pressure, and the 

 final velocity is therefore the same. Now what is here said 

 of a cylinder of compressed air, applies evidently to the action 

 of barriers, such as sheets of water or India-rubber, which 

 are nothing more than perpetual and equable condensing en- 

 gines. When one of these is employed, if it increases the 

 elastic force of a gas by compressing it, at the same time it 

 increases its density, and therefore the velocity of transit is 

 the same as though the gas had suffered no action of com- 

 pression. 



Such is the case whilst the gases are engaged with each 



