294 On the Elastic Force of the Vapor of Mercury. 



temperatures, its density compared with that of air at 32° and at a 

 pressure of 29.94 inches may be found, if we know the ratio which 

 the two densities bear to each other, at any determined temperature 

 and pressure. For example, if we admit this ratio to be seven, as 

 it was given by the experiments of Dumas, the density of the vapor 

 of mercury at 212° F., the elasticity being according to the table 

 .0012 in., will be almost 0.0002 : that is, if the air were saturated with 

 the vapor of mercury at 212° this vapor would have a density 0.0002 

 of that of air at 32° and under a pressure of 29.94 inches ; and since 

 100 cubic inches of air weigh about 31 grains, there would be in 

 a space of 100 cubic inches about .0062 of a grain of mercury. 

 Similar calculations for ordinary atmospheric temperatures, may give 

 an idea of the relative danger of an exposure to mercury, in cases 

 when the space may become saturated with its vapor, at the assumed 

 temperature. 



The different forms of the expression for the elasticity of the 

 vapor of mercury, refer to the temperatures as given by the mercurial 

 thermometer ; they may readily be changed into others which shall 

 have reference to the air thermometer, corrected for the expansion 

 of glass. To make these changes, the approximate relation between 

 the temperatures shown by the two instruments, must first be ex- 

 pressed. This may be done by referring to the experiments of Du- 

 long and Petit on the subject of the comparative indication of the two 

 instruments. I find that if t denote the degrees of the mercurial ther- 

 mometer, and T those of the air thermometer, the relation, in degrees 

 of Fahrenheit's scale, will be ^=0.9845079r+0.000063492T2-{- 

 0.4307312,* or if the degrees be reckoned from the boiling point of 

 mercury downwards ^ = 1.0685714r — 0.00063492r- ;f if each 

 interval of one hundred degrees be considered as unity, this for- 

 mula will become /=1.0685714r- 0.063492^2. J ^ ^q^^ this 

 value of t be substituted in the formula log. e = — 0.35909^ 

 4-0.023443^2 —0.03164^3 Jt becomes, neglecting the powers of 

 T higher than the third,§ log. e = -0.38372T+0.02905r- — 

 0.03893'^='. From this formula a table might be constructed in 

 which the temperatures would refer to the air thermometer. 



* For the Centigrade scale f =:0.9885714t-|-0.000114286t2. 



t fz=1.0685714T — 0.0001142856r3, for the Centigrade thermometer. 



t f = 1.0685714T — 0.01142856T2. 



f Log. e=: — 69069T-i-0.0941irT2 _.0.22700iS: 



