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XII. The Bakeeian Lectuee. — Exiierimental Besearckes io determine the Density of 
Steam at different Tempei'atures, and to determine the Law of Expansion of Super- 
heated Steam. By Williaii Faiebaiex, Esq.^ F.B.S., and Thomas Tate, Esq. 
Eeceived March 23, — Bead May 10, 1860. 
The object of these researches is to determine by direct experiment the law of the 
density and expansion of steam and other condensable vapours at all temperatures. 
Dumas determined with great accuracy the density of steam at 212°, but at this tempe- 
rature only. Gay-Lussac and other physicists since his time have deduced the density 
of steam at different temperatures from a theoretical formula, which assumes that steam 
follows the same law of expansion and contraction as a perfectly elastic fluid. 
The law which determines the relation between temperature, volume, and pressure, in 
the case of a perfect gas is expressed by the equation 
VP = + T 
V,P,-e + Tp ■ 
(10 
where V is the volume of the gas at P pressure and T temperature ; V, the volume at P, 
pressure and T, temperature ; s=a constant, the value of which, according to Regnault’s 
experiments, is for air 459. Xow, assummg that steam follows the gaseous laws, we 
have, according to the experiments of Dumas, Vi = 1669, the volume of steam raised 
from a unit of water at the temperature of 212°, and at the pressure of 14‘71bs. per 
square inch. Making these substitutions in equation (1.), we get for the volume of 
steam from a unit of water at any other temperature T and pressure P, 
459-l.T 
V = 1669xl4-7 
= 36-5 
459+T 
P ' 
(2.) 
From this well-known formula all the tables of the density of steam have hitherto 
been deduced, on which calculations of the duty of steam-engines have been founded. 
Although experimentalists have for some time questioned the truth of this theoretical 
formula, yet up to the present time no reliahle direct experiments have been made to test 
its truth. More recently, Dr. Joule and Professor Thomson announced as the result of 
the application of the dynamical theory of heat, that for temperatures above 212° Fahe. 
there would prove to be a considerable deviation from the gaseous laws in the case of 
steam. In 1855, Professor Rankine gave a theoretical formula for the density of steam 
confirmatory of Professor Thomson’s views. About the same time, and without any 
knowledge of Professor Rankine’s formula, Mr. Tate made some experiments Avith the 
mdccclx. 2 c 
