SECT. II.] 
PROPERTIES OF STEAM. 
57 
\ 
close vessel which it exactly fills ; and that in this state it is exposed to a high tem 
perature. Then, as the bulk when expanded is to the quantity the bulk is increased 
by expansion, without change of state, so is the modulus of elasticity of water of 
that temperature to the force of steam of the same density as water. If our rule 
therefore gives steam a greater force than this at the same density and temperature, 
it must be erroneous. With these limitations we must in a considerable degree be 
guarded against error, and the method followed is next to be explained. 
86. Let f be the elastic force of steam, in inches of mercury, and t the cor 
responding temperature ; and let a be the temperature at which the expansive force 
is 0. Consider f the abscissa, and t—a the ordinate of a curve, of which the 
equation is A f— (t—a) n , whence the coefficient 
, A _ (f—a)» 
/ 
Let the abscissa increase to f, and the ordinate to t'—a ; then 
(t—a) n _ (t'—a) n 
log- f ~ lo g- / 
/ /" log. (t'—a) — log. {t—a) 
Now, if these points be near one extremity of the range of experiment, and two 
other points be taken near the other extremity, then 
f \3'J — n a nd consequently 
log. (t —a) - log. (f-a) 4 * 
log, f" — log. /" _ log, (f-a) — log. (t"—a) _ 
log- /' — lo g- / log- (t'—a) — log. (t—a) 
From four results of Mr. Southern’s experiments on steam from water, we find 
that a——100 very nearly satisfies the conditions; and this value of a being 
inserted, we find ?z=6 and A=177, or its logarithm =2’24797. 
Therefore, for water, X) 
/= (q^) 6 ; ort=177</)* 
100. 
In logarithms, 
log. /=61 log. (t +100) - 2-24797 J . 
87. If the expansion of confined water, when its temperature is raised to 1150 
degrees of heat, be 0*9693 of its bulk, the force necessary to confine it to its bulk at 
60°, when exposed to a heat of 1150°, the modulus of water being 22100 atmo 
spheres at 60°, would be about 6925 atmospheres. 1 Our rule gives for the force of 
1 The expanding power of heat, and the decrease of the modulus of elasticity, must he in the 
same ratio ; and most probably both vary as the square of the central distances of the atoms, and 
H