By means of this equation Table II. has been computed, in which the pressures per square inch are given for every five degrees of temperature, beginning with forty degrees below the zero of Fahrenheit's scale, and ending with 150 degrees above. The formula does not represent the experiments with sufficient accuracy above the latter temperature.

TABLE II.

POUNDS PER SQUARE INCH CORRESPONDING TO DEGREES F. OF TEMPERATURE OF SATURATED ANHYDROUS AMMONIA.

The solution of the problem of the ammonia engine and of the ammonia refrigerating machine requires a knowledge of the specific heat of liquefied ammonia, and its latent heat of evaporation. Both these quantities were determined by Regnault, but the records of the experiments were destroyed during the reign of the Commune in 1870. Rel. des Exp. Vol. II. p. 609; Comptes Rendus, Vol. 104, p. 897. These constants have not since been determined so far as known. Regnault observed that the specific heat of liquid ammonia is considerable, and the latent heat of evaporation is also very great. Rel. des Exp. Vol. II. p. 608. Ledoux, a French scientist, by the use of a formula established by Zenner, deduced an approximate value for the latent heat of evaporation and other unknown values. But Zenner's formula was founded on hypotheses not warranted by the science of thermodynamics, and which are contradicted by his resulting equations. For instance,

he assumed that the specific heat of the gas is constant under constant pressure, and variable at constant volume; but the error of this assumption is easily disproved by the use of his equations. Ledoux also made an arbitrary assumption in regard to the coefficient of expansion of this gas; but with such data he made an ingenious thermodynamic analysis deducing expressions for the latent heat of vaporization, total heat of steam and of the liquid, and, consequently, the specific heat of the liquid.

Notwithstanding the theoretical errors in Zenner's assumptions, it must be admitted that his resulting equation

-represents with considerable accuracy the curve of saturation, and also the few experiments upon superheated steam reported by Hirn. The fact is, the specific heat of steam is so nearly constant at constant pressure-as shown by Regnault-that the error resulting from assuming it to be strictly constant will not seriously affect the result. But it is also true that the specific heat at constant volume will be more nearly constant than that at constant pressure—as may be shown from the equations and the general theory. In the preceding equation p is in kilograms per square metre, v is the volume in cubic metres, and 7 is the absolute temperature on the centigrade scale.

I intend in another paper to give the results of my investigation with another formula, somewhat similar to the above, founded upon an hypothesis of Rankine.

Ledoux assumed 0.0039 for the coefficient of expansion per degree centigrade.

This coefficient for the permanent gases is.

This coefficient for sulphurous acid

This coefficient for cyanogen.

This coefficient for steam..

0.00366

0.00390

0.00387

.00425

These values show that one is somewhat restricted, but not very closely, in the choice of an arbitrary value. At the temperature of the melting point of ice, at which state the saturated vapor will be under a pressure of about 60.4 pounds to the square inch, Ledoux found the latent heat of vaporization to be 564 British thermal units per degree Fahr. We find it to be about 484.

It has been shown by Mr. Frederick Trouton (Phil. Trans., 1884, (2), p. 54), that

Latent heat of vaporization x Density
Absolute temperature of boiling-point

= a constant, nearly.

The density here referred to is that resulting from the chemical equivalents. We have NH, = 14 + 3 = 17, and to make it correspond to Mr. Trouton's analysis it must be divided by 2, giving 8.5. The boiling-point is that attained under the pressure of one atmosphere. The smallest value of the constant is 10.30, and the largest 13.17; so that if ammonia falls within the limits of the substances given, its latent heat of vaporization will exceed 522 B. T. U., and be less than 671, under the pressure of one atmosphere. Again, the latent heat of vaporization is given by the formula

where p is pounds per square foot, agrees better with Regnault's experiments within the range of ordinary practice than equation (2), and will be used in the following investigation.

For the state where the temperature is that of melting ice under the pressure of one atmosphere we have

To find R, Regnault gives, for the theoretical density of the gas, 0.5894 (Rel. des Exp., Vol. II. p. 162), but he also says: "The real density of ammonia gas is certainly higher than the theoretical; the only experimental density of which I have knowledge gives 0.596" (Ibid. Vol. III. p. 193).

Vol. of a gramme of air at 0°C., 760m....1.293187 litres,

or vol. of a kilog. of air at 0°C., 760m....1.293187 cu. metres,

(Ibid. Vol. I. p. 162.) Hence the weight of one litre of the gas at 0°C., 760mm. will be

1.293187 × 0.596 = 0.770739 grammes,

and the volume of one gramme of the gas will be

Reducing this to the equivalent of one pound and cubic feet

British thermal units. This would be the latent heat of vaporization of ammonia at the temperature of melting ice under the pressure of one atmosphere, if the vapor were saturated at that state. But it is superheated at that state; and according to the theory of imperfect gases, the ratio of pressure to absolute temperature is

(8)

less for a given volume at lower temperatures; hence for the volume 20.7985 the latent heat of evaporation cannot exceed 580.66 B. T. U. Ledoux gives about 600 B. T. U. for this volume; hence his values are too large in the vicinity of this volume, and we will find that all his values are too large within the limits used in practice. We now proceed to find a general value for pv 7. eral equation of imperfect gases is, according to Rankine,

The gen

where ao, a1, etc., are inverse functions of v. The first two terms of this equation are generally sufficient to represent a fluid within the ordinary range of experiment, hence we write

This may be tested for steam. For any fluid we would have for any two states of same volume,

From Hirn's experiments and a table of Saturated Steam we have: