356 Hydrostatics. 



470. Let us now suppose that, the weight of the atmosphere 

 remaining the same, the temperature of the confined air is rais- 

 ed ; as this air expands, its bulk will be increased, and its densi- 

 ty diminished. JNow we know by the careful experiments of 

 M. Gay Lussac and others, (1.) That all the gases dilate uni- 

 formly, at least from 32 to 212, or from the freezing to the boil- 

 ing point of water. (2.) That the dilatation arising from the same 

 increase of heat is precisely the same for all the gases, vapours, 

 and mixtures of gases and vapours. (3.) That the bulk of con- 

 fined gas, at the temperature of 32, being considered as unity, 

 this common dilatation is 0,375, (or a little more than one third,) 

 for 180, the difference between the boiling and freezing points 

 of water ; which gives VH 5 = ^ or 0,00208 for the augmen- 

 tation of bulk answering to 1 of Fahrenheit. Accordingly, we 

 shall have for the bulk or space occupied by the portion of air 

 in question 1 -|- 0,00208 n at the temperature denoted by ?i, the 

 number of degrees above or below 32, the latter being consider- 

 ed as negative. This bulk or volume may be reduced to its 

 original limits, by bringing the temperature back to 32, or by 

 increasing or diminishing the weight which compresses it, with- 

 out altering the temperature. It would only be necessary, in this 

 latter case, to add to, or take from the weight TO, a portion equal 

 to w (0,00208) w, that is, to substitute for w the weight 



TO (1 4- 0,00208 71), 



which is the measure of the elastic force of the confined air re- 

 duced to its original density. Hence, the bulk and density re- 

 maining the same, the elastic force varies with the temperature, and 

 in the same ratio. 



If the elastic force is proportional to the density when the 

 temperature is the same, and varies with the temperature when 

 the density is the same, it will be easy to deduce the value of 

 this force in terms of the two elements, on the supposition that 

 they both vary together. Thus, putting A for the density of the 

 air in question, and n for the number of degrees which marks the 

 temperature, and/) for its elastice force or pressure exerted upon 

 the unit of surface, a being the ratio of the elastic force to the 

 density at the temperature of 32, we shall have 



