ON THE MATHEMATICAL THEORY OF FLUIDS. 2^7 



It was ascertained by the independent labours of these two emi- 

 nent philosophers, that different aeriform bodies, submitted to the 

 same constant pressure, receive equal increments of volume for 

 the same increment of temperature ; so that if the masses of any 

 two be of equal size at one temperature, they will be of equal 

 size at any other temperature, provided the pressure to which both 

 are submitted, be the same and constant. It was also found by 

 Gay-Lussac, that from the temperature of melting ice to that of 

 boiling water, a mass of air, the size of which at the former tem- 

 perature is expressed by unity, expands to a size expressed by 

 1'375. If the augmentation 0*375 be divided into 100 equal 

 parts, and each of these parts be assumed to measure a degree 

 of temperature, it will follow, from the theory enunciated above, 

 that every gas dilates by the fractional part 0*00375 of its size 

 at the temperature of melting ice for each degree of the centi- 

 grade air thermometer. Thus, v' being the volume when the 

 temperature is 6° above zero, and v the volume when the 

 temperature under the same pressure is at zero, the relation be- 

 tween the volume and temperature is expressed algebraically by 

 the efjuation, 



/ = V (1 + 0*00375 fl). 



Also if D', D be the densities corresponding to v', v, we have 

 D' v' = D V, as the quantity of matter is constant. If now the 

 pressure on a unit of surface be changed, without altering the 

 temperature, from the constant. Vcilue it has hitherto been sup- 

 posed to have, which we will call tsr, to the value jh the density 

 at the same time changing from D' to p, the law of Mariotte gives 



— = Y\r These three equations easily conduct to the following 



relation between p, p, and d ; 



where « is put for 0*00375. This formula is considered to ap- 

 ply to gases, to vapours, and to compoimds of both, or either. 



The value of « is the same for all, but yy differs for different fluids. 



If the unit of density for atmospheric air be assumed to be that 



at a particular place on the earth's surface at 0° centigrade, yr will 



plainly be the pressure there at that temperature. MM. Biot 

 and Arago found I he ratio of the specific gravity of mercury to 

 that of air at the temperature of melting ice, and under the ba- 



q2 



