454 



Royal Society : — Prof. J. Thomson on the 



expressed by his graphic curve with those got from the formula (H), 

 shows distinctly a re-entrant angle, or at least a flattened place, in 

 the curve at or about 0°. Several other like comparisons, by means 

 of his other formulae, give like indications ; but most of these may 

 for brevity be passed over without further mention here. The most 

 decisive indication comes out in the following way. We may ob- 

 serve that for temperatures adjacent to the freezing-point and ex- 

 tending bo'th ways from it, Eegnault finally adopted as fitting best 

 to his experiments the formula (E) for temperatures descending 

 from 0°, and the formula (D) for temperatures ascending from 0°. 

 He tried (at pages 598, 599 of his memoir) the continuing of the 

 application of his formula (D) beyond the inferior of the two limits 

 0° and 100°, for which he had specially aimed at adapting it to his 

 experimental determinations ; and he found that in calculating by 

 it the pressures which it would give for temperatures below 0°, 

 these pressures come out always slightly in excess of those which 

 were given by his experiments. I have developed this mode of 

 comparison in a more complete manner, and have arrived at remark- 

 able results. The formula (D) may be regarded as the formula for 

 giving the pressure p of steam with water, and (E) as that for 

 giving the pressure j?' for steam with ice. The following two Tables 

 show the pressures jo and jp' for temperatures, in each case, both 

 below and above the freezing-point, as calculated from these two 

 formulae ; and they show, also in each case, the consequent differ- 

 ences of pressure for 1° change of temperature at several different 



temperatures, or, what is the same, the values of -j— and -±- f p 



several temperatures slightly above and slightly below the freezing- 

 point. 



Table I. By Formula (D) ; Steam with "Water. 



Temperatures. 



Pressures =p. 



Differences for 1°, 



which are values of -4- 

 dt 

 for intermediate 

 temperatures. 



Temperatures to 

 which the values of 



-£ belong. 



-3° 



-2° 



-1° 



0° 



+ 1° 

 +2° 

 +3° 



3-703 

 3-983 

 4-281 

 4-600 

 4-940 

 5-302 

 5-687 



•280 

 •298 

 •319 

 •340 

 •362 

 •385 



oio 



~*2 



L 2 

 io 



2 



+ i° 

 +1*° 



+ 2i° 



