On the temperature of steam and its corresponding pressure

The author states that it is intended in this paper to propose a simple law to determine the pressure of steam corresponding to any given temperature, irrespectively of experiment , taking as the sole datum, that the vaporizing point of water under a given pressure is 100 degrees, that number being taken to correspond with the scale of Celsius; also to construct formulæ in accordance therewith; and afterwards to compare their results with the actual experiments of the Academy of Sciences of Paris. He further states that the rationale of the subsequent formulae is expressed as follows. Let it be conceived that a given quantity of water is vaporized under the condition that the pressure thereon is increased in the same ratio that the volume is increased, or that at intervals of temperature 1, 2, 8, &c. the volume is increased the same or in equal proportions; the temperature of the volume will be increased exactly as the square of the temperature indicated by the thermometer, supposing the instrument to be a true measure of temperature, and as the square of the volume ; and the same of the pressure . Steam being generated from an indefinite quantity of water and confined within a limited space, as in the usual boiler, he considers the foregoing case is reversed ; for the volume being constant, the action of the fire is entirely exerted in producing increased elastic tension of the vapour; therefore the temperature of the steam at the interval 1 to 2 degrees is increased inversely in the duplicate ratio of the ratio in the case first described; that is, the pressure is increased directly at the square of the square, or fourth power of the temperature; whence the following law. The pressure of steam generated in the usual steam-boiler is directly proportional to the fourth power of its temperature, when measured by a true scale.