168 Miscellaneous Intelligence. 



the number of degrees between the points of congelation and ebul- 

 lition, .9 the number of degrees at the boiling point, and cal. q the 

 degrees of the true augmentation of heat corresponding to the state 

 q of the thermometer, the following expression is correct : — 



Cal. qz=:q-i (q-s) 0.09 — 0.028 ~^- 



— Annal. der Physik und C hemic. 



11. Determination of the Mathematical Law, according to which 

 the Elastic Force of Steam increases with the Temperature. By 

 M. Roche, Recueil Indust. p. 285. — It has already been ascer- 

 tained — i. That a small increase of temperature augments consi- 

 derably the elastic force of vapour, ii. That this force increased 

 nearly in geometric progression, for each increase from 30° of 

 Fahrenheit's scale, or 13^ of Reaumur's, or 16§ of the centigrade 

 thermometer ; the elastic force doubling successively for the suc- 

 cessive augmentations of 16§ from the boiling point 100. 



Nevertheless, it appears, from experiments made both in France 

 and England, that the tensions of vapours depart from this law at 

 high temperatures, and different empirical formulae, more or less 

 exact, have been proposed to represent the law of the elastic force ; 

 that of M. Laplace, inserted in the Trait'e de Physique of M. 

 Biot, is of the form F = 760 m X 10 m + bi 2 + ci 3 + &c, in 

 which F denotes the elastic force estimated in millimeters : 760 m 

 the height of the column of mercury equivalent to the pressure of 

 the atmosphere, and a, b, c, &c, constant coefficients, which M. 

 Laplace endeavoured to determine by experiment; he found 

 a =0.154547, b = 0.00625826, &c. 



Such a formula is very complicated, and to apply it to high 

 temperatures, the terms i 3 , i 4 , &c, must be employed ; i represent- 

 ing the excess of the temperature above 100°. But a simple for- 

 mula may be obtained by observing that the elastic force of steam 

 increases for each element of temperature by a quantity, which is 

 in a ratio composed of the existing elastic force and of the in- 

 crease which I denominate the expansive heat, and which is pro- 

 portional to the product of the temperature by the density it would 

 give to the vapour, or to the quotient of this temperature, by the 

 volume which it tends to give to the vapour, according to Gay- 

 Lussac's law of dilatation. We see, then, that the true law will be, 

 that the elastic force increases in a geometrical progression when the 

 expansive heat increases in arithmetical progression, and as this 

 expansive heat, denoting by x- the excess of temperature above 

 100, would be proportional to 



100° +x 100 + tf 



or 



8 + 0.03 (100 +«r) 11+0.0307 

 (0°, f being the coefficient of the dilatation or the increase of 

 volume for each degree) ; and as 



