1849.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



367 



The fifth column of the Table shows that, from 30° below the 

 freeziiia: point to 20° above it, wliere the minuteness of the pres- 

 sure makes the barometric errors of most importance, the greatest 

 difference between experiment and calculation is -^ of a mille- 



metre, or -^ of an inch of mercury, — a very small quantity in 

 itself, although, from the slowness with which the pressure varies 

 at low temperatures, the corresponding difference of temperature 

 amounts to -^ of a degree. 



Table I. — Vapour of Water. 



The sixth and tenth columns show that, from 20° to 830° above 

 the freezing point, the greatest of the discrepancies between e.x- 

 periment and observation corresponds to a difference of tempera- 

 ture of only yfij of a degree, and that very fevv of those discrepan- 

 cies exceed the amount corresponding to ^ of a degree. 



A comparison between the sixth and tenth columns shows that, 

 for four of the temperatures given, viz., 120°, 150°, 200°, and 210°, 

 the pressures deduced from M. Regnault's curve of actual elastici- 

 ties, and from his logarithmic curve respectively, differ from the 

 pressures given by the formula in opposite directions. 



If the curves represented by the formula were laid down on 

 M. Regnault's diagram, they would be almost undistinguishable 

 from those which he has himself drawn, except near the freezing 

 point, where the scale of pressures is very large, the heights of the 

 mercurial column being magnified eight-fold on the plate. In the 

 case of the curves of logarithms of pressures above one atmosphere, 

 the coincidence would be almost perfect 



The formula may therefore be considered as accurately repre- 

 senting the results of all M. Regnault's experiments throughout a 

 range of temperatures from 30° of the centigrade scale below the 

 freezing point to 230° above it, and of pressures from -.p^ of an 

 atmosphere up to 28 atmospheres. 



It will be observed that equation (1.) bears some resemblance to 

 the formula proposed by Professor Roche in 1828 — viz. : 



where T represents the temperature measured from the ordinary 

 zero point, and A, B, C, constants, which have to be determined 

 from three experimental data. It has been shown, however, by 

 M. Regnault, as well as by others, that though this formula agrees 

 very nearly with observation throughout a limited range of tem- 

 perature, it errs widely when the range is extensive. I have been 

 unable to find Professor Roche's memoir, and I do not know the 

 reasoning from which he has deduced his formula. 



The use in computation of the equations I have given, whether 

 to calculate the pressure from the temperature, or the temperature 

 from the pressure, is rapid and easy. In Table II. they are re- 



capitulated, and the values of the constants for different measures 

 of pressure and temperature are stated. 



In calculating the values of o, the specific gravity of mercury 

 has been taken as 13-596. 



Temperatures measured by mercurial thermometers are in all 

 cases to be reduced to the corresponding temperatures on the air- 

 thermometer, which may be done by means of the table given by 

 M. Regnault in his memoir on that subject. 



Table II. — Vapour of Water. 

 Formula for calculating the Maximum Elasticity of Steam (F), front 

 the Temperature on the Air-Thermometer., measured from the Abso- 

 lute Zero if) : 



LogP = o- J. 



Inverse Formula for calculating the Temperature from the Maximum 

 Elasticity of Steam : 



1 /a 



7=V " 



i-LorP (82 



-t- r^- 



7 4y 



■27 



Values of the Constants depending on the Thermometric Scale. 

 For the centigrade scale : — 



Absolute zero 274°-6 below the freezing point of water. 

 Log/3 = 3-1851091 Log 7 = 5-0827176 



■^ = 0-0063294 

 27 



472 



= 0-00004005 



For Fahrenheit's scale; boiling point adjusted at 29-922 inches : — 



Absolute zero 462°-28 beluw ordinary zero. 



Log = 3-4403816 Log 7 = 5-5932626 



;^ = 0-0035163 

 27 





= 0-000012304 



For Fahrenheit's scale; boiling point adjusted at 30 inches : — 

 Absolute zero 461°-93 below ordinary zero. 

 Log 3=3-4400625 Log 7=5-5926244 





0-0035189 



— =0-000012383 

 47^ 



