Mr. J. A. Wanklyn on the Movements of Gases. 213 



merit whatever, the want of cohesion in the gas permits move- 

 ment, which accordingly takes place, but with exceeding slowness, 

 and indeed (if certain theoretical conditions could be realized) 

 with infinite slowness. 



If we could place our gases in contact without occasioning 

 any current by the act of making them communicate, and be- 

 sides could realize — 



(1) The inferior surface of the gas a mathematically hori- 

 zontal superficies. 



(2) A vessel mathematically cylindrical and vertical ; 



(3) Molecules of the gas infinitely little and absolutely non- 

 adherent either to one another or to the glass ; 



then, these conditions being granted, an infinitely prolonged 

 time would be required for any finite fraction of the gas to fall. 

 At the beginning of the experiment it would be the lowest 

 stratum of molecules alone whose gravitation would tend to 

 cause motion. All the molecules, situated above the plane of 

 contact between our gas and the air, would be in equilibrium, as 

 the descent of one of them would involve the ascent of another. 

 During the first instant the lowest plane of carbonic acid 

 would change place with the uppermost plane of air. Thus a 

 plane of air-molecules would be interposed between the mass of 

 carbonic acid above and a plane of carbonic acid- molecules below. 



During instant the second, the isolated plane of carbonic acid 

 molecules would change places with the adjacent air imme- 

 diately below it, while simultaneously the lowermost stratum jn 

 the mass of carbonic acid would change with the isolated stratum 

 of air. 



We should thus have an isolated stratum of carbonic acid- 

 molecules of infinitely small thickness travelling downwards 

 through the air ; and if it could be shown that this isolated 

 lowest stratum would require eternity to traverse a finite vertical 

 distance, it will follow, a fortiori, that a finite fraction of the car- 

 bonic acid would require eternity to fall a finite distance. 



That a body of infinitely small vertical diameter requires an 

 infinite time to fall through a finite portion of a medium may 

 be thus proved. 



Assign any finite time, e. g. a second. In a second a body 

 falling in vacuo acquires a velocity of 32 feet per second. Let 

 our body be conceived to enter a medium being charged with a 

 velocity of 32 feet per second (which is consequently the pro- 

 duct of a greater force than the gravitation during a second). 

 In moving through any finite portion of the medium, the body 

 would encounter an infinite number of times its weight of the 

 medium. It would therefore have to communicate its motion to 

 its weight multiplied by infinity. 



