310 WARMING AND VENTILATING OCCUPIED BUILDINGS. 



33. Mariotteh laic. — According to this familiar law, the temperature of 

 tlie air remaining constant, its volume varies inversely as the pressure 

 to which it is exposed, and its density is proportional to those pressures. 



34. General relation between the ])ressure, volume, temperature, and density 

 of air. — Calling — 



do, Vo, Po, ( The density, the volume, and the f 32 degrees, 



d, V, P, } pressure corresponding to the.^(^'— 32) degrees, 



d', Y', P', ( temperatures, ( {t —32) degrees, 



the following relations result from the combination of Mariotte's and Gay- 

 Lussac's laws : 



y-y/ [1 + 0.002036 (t-32)] P ^ 

 [1 + 0.UU203G (*'— 32)J P 



1 1+0.002030 (^^-32)] P 

 d-d ^i^(,.00203(} (f-32)J P' 



If we suppose that t'=0 and P= P'= one atmosphere, d'= 0.081 

 pounds, the last formula becomes — 



-, 0.081 



d= 



1+0.002036 (^-32) 



which has been found before. 



35. Frineiple of Archimedes, its effects. — Air, like all fluids, follows that 

 elementary principle of physics, according to which a body plunged into 

 a fluid loses a part of its weight equal to that of the displaced fluid. 



Thus, at the temperature of 32° and under the pressure of 30 inches, 

 every cubic foot of air in the atmosphere weights 0.000081 pounds ; and 

 as it occupies exactly the same space as every other volume of air of 

 the same weight, it remains wherever it is placed, unless disturbed by an 

 external force. 



If, on the contrary, the temperature of this cubic foot of air be reduced, 

 for example, in consequence of its contact with some cold body, as a 

 window-pane or a wall, it contracts, its volume is reduced, its density 

 increases, it becomes heavier than the volume of air which it displaces 

 in the mass, which is assumed to remain at about the same temperature. 

 Theu the excess of its weight over that of a similar volume tends to 

 make it descend. 



Thus, in a ijlace where the general temperature is 68°, if a portion 

 which was at first at that temperature, with a density of 0.0000750 pound 

 to the cubic foot, becomes cooled by contact with a cooler body, such as a 

 window-pane or the walls, at a temperature of 32°, its density will 

 become equal to 0.000081, and each cubic foot will tend to fall with a 

 force equal to the excess of its new weight over that of a cubic foot of 

 the surrounding air, or 0.000081— 0.000076=0.000005 pound. This effect 

 is constantly produced in winter, when the surfaces of windows and 

 walls are colder than the air of the warmed apartments. 



On the contrary, if the temperature of a part of the air be raised above 



