Royal Society, 567 



The constants ^ and h being thus determined from two observations, 

 the equation for the density at any other G temperature i^o'futmoq 



and for the pressure 



»\ axleijifi hi ^ ba£ <'iwoqfiv 



;t--'J?--rr -,;ft -■"^n'iT'.'nrYT. 



The several equations, with the numerical values of the constants 

 g and h, for the series of observations previously referred to and 

 represented on the chart, are then given, the G temperatures being 

 in degrees of Fahrenheit's scale, and the values of h being calculated 

 so as to give the pressure in inches of mercury. 



The author remarks that the observations on the vapour of water 

 below 80° show a small excess of density above what is required by 

 the line corresponding to those at higher temperatures ; and that it 

 is a curious circumstance that the law of expansibility of water also 

 becomes disturbed at about the same temperature. In proof of this, 

 the observations of M. Despretz (Ann. de Chim. vol.lxx.) being pro- 

 jected, by making the volume the ordinate to the square root of the 

 G temperature as abscissa, these observations above 25° C. or 

 77° F. give in the most exact manner a conic parabola ; but below 

 77° they no longer give that curve. 



The equation to the parabola for temperatures above 77° F. is 

 a(v— 0) = ( V^— <^)S in which v is the volume at the G temperature 

 t, in terms of its volume unity at 39°*2 F. or 4° C. (its point of 

 maximum density^ a=352-38, 0=-99872, and 9=21*977 or 

 02=483°. 



The law of the increase of density and temperature in saturated 

 vapours having a certain analogy with the law of increase of density 

 and temperature in air while suddenly compressed or dilated, the 

 author next discusses the latter subject in a manner similar to that 

 in which he had discussed the former. From this discussion he 

 draws the following conclusions : — 



1. When air is compressed or dilated, the G temperature varies 

 as the cube root of the density ; and the tension as the 4th power 

 of the G temperature, or the cube root of the 4th power of the 

 density. 



2. The mechanical force exerted by a given quantity of air while 

 expanding from one density to another, is proportional to the differ- 

 ence of the cube roots of these densities, or to the difference of their 

 G temperatures : hence the fall of temperature is proportional to the 

 force expended, 



3. The mechanical force exerted upon a given quantity of air, 

 while compressing it from one density to another, is proportional to 

 the difference of the cube roots of these densities, or to the differ- 

 ence of their G temperatures : hence the rise of temperature is pro- 

 portional to the force exerted. 



4. The total mechanical force exerted by a volume of air of a 

 given tension, while expanding indefinitely, is equal to that tension 

 acting through three times the volume. 



