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 / 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/= (ta) n , whence the coefficient 



Let the abscissa increase to /', and the ordiuate to t'a ; then 



(t-a) n = (t'-a) . Qr log. /' - log. / = n 



f f 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 



log. /'" - log. /" 



, - g-^ - , J - = n. and consequently 

 log. (f"-a) - log. (t'-a) 



log, f" - log. /" = log, (f"-a) - log, (t'-a) 

 log. /' - log. / 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 n=6 and A=177, or its logarithm =2'24797. 



Therefore, for water, 



In logarithms, 



log. /=6 log. (t + 100) - 2-24797 . 



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 be in the 

 same ratio ; and most probably both vary as the square of the central distances of the atoms, and 



H 



