Steam of Maximum Density. 1 75 



force, have been calculated for all temperatures differing by in- 

 tervals of 10° C, beginning at the absolute temperature 246°, 

 and ending at the absolute temperature 506°. These values are 

 exhibited in Table I. annexed hereto. They are placed side by 

 side with similar values for the same temperatures, which have 

 been deduced directly from M. Regnault's principal Table 

 printed at page 624 of vol. xxi. of the Memoires de V Academie, 

 &c. On inspection and comparison, it will be seen that the two 

 different series of results are in close coincidence with one another 

 in nearly all parts of the scale. The only exception worthy of 

 note occurs for temperatures below + 10° C. But in this part 

 of M. Regnault' s Table the elastic forces, as well as the incre- 

 ments of elastic forces, have lost the regularity and uniformity 

 of progressive increase or decrease which is remarkable at all 

 temperatures above 10° C. On account of the want of uniformity 

 at this part of the scale, very little weight can be attached to the 

 slight discrepancies here existing between M. Regnault' s adjusted 

 Table and my theoretical Table. The errors of observation 

 amount apparently to about one part in one thousand for any 

 temperature above 10° C, and about one part in one hundred for 

 temperatures below that point. The extreme error (when the 

 two compared at the same temperature are in opposite directions) 

 might thus amount to one in five hundred at temperatures above, 

 and one in fifty at temperatures below 10° C. It is only within 

 these limits that the present new theoretical Table differs from 

 M. Regnault's adjusted Table and the selected observations 

 adopted by him. 



M. Regnault informs his readers (page 589) that, in the ad- 

 justment of his chief Table, all his definitive calculations have 

 been executed by using only the formula of M. Roche or that of 

 M. Biot for purposes of interpolation. The formula of M. Biot 

 is this : 



log P = a + £*'+<?£*, 



the five constants contained requiring for their determination 

 five observed values of P separated from one another by equal 

 intervals of temperature. M. Regnault afterwards says (page 

 599) ihat the formula of interpolation (E) which he has used for 

 all temperatures below the freezing-point of water, or 0° C, is 

 ~P = a + bcc t , which formula is a modification of Biot's general for- 

 mula, obtained by cutting off the third term and substituting P 

 for logP. At page 598 M. Regnault states that he has used another 

 formula (D), wherein log P, for all temperatures between 0° and 

 100° C, is represented by the general formula of Biot. At 

 page 600 it is stated that another formula (F), wherein log P is 

 represented by the general formula of Biot, has been used for 

 all interpolations between 100° C. and 230° C. It thus appears 



