564 HEAT formuli (2) but with a different numerical coefficient, 1 agreed perfectly with the normal air thermometer from to 325. (3) The carbonic acid gas thermometer with pressure 46 c.m. at 0, and its indications calculated with the co efficient 271-59 (-003G82- 1 ), agreed perfectly with the normal air thermometer from O 3 to 308. ( !) Tli3 carbonic acid gas thermometer with pressure, at O 3 , 74 centimetres (or nearly 1 atmo), calculated with the coefficient 270 64 ( 003695~ 1 ) to make it agree with the normal air thermometer at 100, gave numbers some what too large for all temperatures from 200 to 323. The difference seemed to rise to a maximum at about 180, when it was about , and to diminish so as to be only about ^ at the highest temperatures of the comparison. Two sulphurous acid gas thermometers, with pressures 59 c.m. and 75 c.m. at 0, calculated with coefficients 263 G (003794- 1 ) and 2G1-4 (-003825- 1 ) respectively to make them agree at 100 with the normal air thermometer, each gave numbers too small for the higher temperatures by dif ferences increasing gradually from ^ at 140 to 3 at 320. (5) Air and gas thermometers calculated according to differences of pressure of the gas kept at the same apparent volume (that is to say, with the bounding mercury column at a constant mark on the glass stem of the thermometer) give numbers too small at the higher temperatures by differences gradually increasing up to 2 at 350 in the case of Choisi le Roi crystal, a hard glass without lead, and to as much as 3J in the case of ordinary glass. In connexion with these observations Regnault remarks that the greatest cause of uncertainty in his air ther- mometry is the allowance for expansion of the glass. It was only by most carefully made special experiments 2 on each particular bulb and tube, to determine its expansion throughout the range for which it was to be used, that he succeeded in obtaining the great accuracy which we find in his results, according to which the probable error, whether by his normal air thermometer, or by other air or gas ther mometers of those stated above to agree with it perfectly, was not more than from 1 to 15 of a degree for any temperature up to 350. (6) The mercury-in-glass thermometers which Regnault generally used for comparison with his normal air ther mometer were overflowing thermometers, because he found that with such he could more easily obtain the very minute accuracy at which he aimed than with the ordinary volu metric thermometers; but the formula by which he calcu lated temperature from the overflowing thermometer was adapted to give exactly the same result as would have been obtained by the ordinary thermometer with divisions on the stem corresponding to equal volumes of the bore. It must be remembered, however, that this perfect agreement between the volumetric and overflowing thermometers would not be found unless the expansion of the bulb and tube were uniform and isotropic throughout. (7) The general results of Regnault s comparisons of mercury thermometers with his normal air thermometer 1 Instead of the 003665 of his normal air thermometer, Kegnault states that for his hydrogen thermometer he used 003652 (which would make the coefficient in formula (2) be 273 82 instead of 272 85). But this must surely be a mistake, as he found 0036678 for the coefficient of dilatation" of hydrogen calculated from its increase of pressure in constant volume, and 0036613 for the coefficient of dilatation observed directly for hydrogen under constant pressures of from 1 to 4 atmos (pp. 78, 80, 91, 115, 116), and he nowhere speaks of having found any smaller value than 003661 for hydrogen.
- These experiments were made by finding the weight of mercury
contained in each bulb and tube at several different temperatures throughout the range through which it was to be used, and thence cal culating the bulks according to the density of mercury for the different temperatures found by his independent investigation of the absolute dilatation of mercury by the hydrostatic method, this method being independent of the expansion of the containing glass or other solid. ,
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_ Jo were given by himself in a diagram of curves from which the accompanying is copied on a reduced scale (fig. 3). It shows that at a temperature of 320 the independent mercury thermometer stands at 329 8, the thermometer of mercury in Choisi le Roi crystal at 327 25, and the thermometer of mercury in ordinary glass at 321 8; and that the independent mercury thermometer and the mercury in Choisi le Roi crystal ./ * * 3 2 i o stand 10 higher than the normal " air thermometer at the temperatures by it of 323 and 345 respectively. 26. The curve for the inde pendent mercury thermometer is merely Regnault s graphic repre sentation of his experiments on the absolute expansion of mercury (Relation ties Experiences, vol. i. p. 328). It shows that the addition of bulk given to the same mass of mercury under constant pressure by elevation of temperature is for the same difference of temperatures as indicated by his normal air thermometer regularly greater and greater the higher the temperature. 27. It is interesting to see by the diagram that at the high temperatures all the mercury ther mometers keep nearer to the air thermometer than does the inde pendent mercury thermometer, and ^- s 7 fi 5 4321 o " that the mercury in ordinary soft Fig. 3. glass keeps much nearer to the air thermometer than does the mercury in the hard Choisi le Roi glass. We infer that, still reckoning temperature by the air thermometer, we have regular augmentation of expansion at thehigh tempera tures in all the different glasses, each greater than the ^ augmentation of expansion of mercury, and that this Jjjj^ augmentation is greater in the soft ordinary glass than in the hard Choisi le Roi glass, being in the ordinary glass great enough to overcompensate in the resulting thermometric indication the augmenting expansion of the mercury from 100 to 245; while above 245 in the ordinary glass thermometer, and at all temperatures above 100 in the Choisi le Roi thermometer, the compensation is only partial. Between and 100 the independent mercury thermometer stands regularly lower than the air thermometer by as great a difference as 35 at 50, where it is a maximum. The curves for the mercury- in-glass thermometers are not shown between and 100, but it is clear from the diagram that the Choisi le Roi thermometer must, like the independent mercury thermometer, stand lower than the air ther mometer, but by a smaller difference, probably only about 2 at 50; and the ordinary glass thermometer higher than the air thermometer from to 100 by a difference which may be 2 or 3 at 50. This last inference from the diagram is confirmed by Regnault s table of results facing page 227 of his first volume. 28. In the best modern thermometers the graduations are actually engraved on the glass ; but (J in most popular thermometers, and in many for scientific investigation, they are on an attached scale Fl S- 4- of wood, or ivory, or brass, or paper. Some of the best popular thermometers are the German bath thermometers, in which the graduation is on a paper scale guarded by being enclosed in a wide glass tube hermetically sealed round the stem and over the bulb of the glass which contains the mercury, in the manner shqwn in fig. 4. Abso lute 70 pans of in cury then
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