Steam of Maximum Density. 181 



By means of these two equations have been calculated the theo- 

 retical elastic forces given in all four of the Tables hereunto 

 annexed. 



On inspection of the last two columns of Table I. hereunto 

 annexed, it will be seen that my theoretical values of u t coincide 

 at the same temperature almost exactly with the values of ut 

 directly obtained from the adjusted Table of M. Kegnault for all 

 temperatures above +10 degrees of the Centigrade thermometer. 

 It is, however, to be remarked that my adopted theoretical value 

 of a for 100° C, which is "0358, differs more from M. Reg- 

 nault's experimental number at the same temperature than it 

 ought to do if the smaller differences between theory and expe- 

 riment existing before and after that temperature are to be taken 

 as a guide. This discrepancy, however, is easily accounted for 

 by the statement already made, that M. Regnault's adjusted 

 Table is a composite Table formed in three sections, two of which 

 touch one another, but do not unite together, at the temperature 

 100° C. 



The general equation for the ratio of the elastic force at tem- 

 perature f to elastic force at temperature 0° having been ob- 

 tained, there remains to be added for practical purposes a com- 

 mon multiplier to take the place of unity previously used to 

 express the elastic force at temperature 0°. The standard of 

 measurement of force usually adopted is either the height or the 

 weight of a vertical column of mercury which is in equilibrium 

 with the ordinary pressure of the atmosphere. The height of 

 the column of mercury adopted to represent one atmosphere is 

 760 millimetres, or 29*9218 English inches. The pressure or 

 weight of such a vertical column of mercury amounts to 2116*4 

 pounds avoirdupois on the square foot, or to 14*7 pounds on the 

 square inch. Either of the above four quantities may be called 

 H, and used as a multiplier in the general equation for the ratios 

 of P at different temperatures. The equation for practical use 

 will then become 



p^Hx/^-Kr^Hxio^'-Kn, - 



and using common logarithms, 



,o g P ( = Io g H + ^{l-(l + t)-"}. 



It is not difficult, though somewhat laborious, to calculate 

 from the general formula the value of log P for every degree of 

 temperature. The properties of the formula are, however, such 

 that all the desired results can be obtained without incurring 

 the labour of making a direct use of the formula, except for 

 obtaining the values of log P for two temperatures only. If a 



