HEAT 569 15 in the gauge is known by accurate independent experiments such as those of Regnault on the compressibility of air and other gases. 43. The water-steam thermometer may be used, but somewhat precariously, for temperatures below the freezing point, bacause water, especially when enclosed and pro tected as the portion of it in the bulb of our thermo meter is, may be cooled many degrees below its freezing point without becoming frozen : but, not to speak of the uncertainty or instability of this peculiar condition of water, the instrument would be unsatisfactory on account of insufficient thermometric sensibility for temperatures more than two or three degrees below the freezing point. Hence, to make a steam thermometer for such temperatures some other substance than water should be taken, and none seems better adapted for the purpose than sulphurous acid, which, in the ap paratus represented with figured dimen sions in the accompanying diagram (fig. 9), makes an admirably convenient and sensitive thermometer for temperatures from -f 20 to something far below 30, as we see from the results of Regnault s measurements (Table VI. below). 44. To sum up, we have in 39 . . 43 a complete series of steam-pressure ther mometers, of sulphurous acid, of water, and of mercury, adapted to give absolutely definite and highly sensitive thermometric indications throughout the wide range from something much below - 30* to con siderably above 520 of the centigrade j| scale. The graduation of the scales of these thermometers to show absolute [- temperature is to be made by calculation from formula (3) of 38, when the requi site experimental data, that is to say, the values of <r and pK for different values of p throughout the range for which each substance is to be used as thermometric fluid are available. Hitherto these requi sites have not been given by direct experi ment for any one of the three substances with sufficient accuracy for our thermo metric purpose through any range what ever. Water, naturally, is the one for which the nearest approach to the requi site information has been obtained. For it Regnault s experiments have given, no doubt with great accuracy, the values of p (the steam pressure) and of /c (the latent heat of steam per unit mass) for all temperatures reckoned by his normal air thermometer, which we now regard merely as an arbitrary scale of temperature, through the range from -30 to +230. If he, or any other experimenter, had given us with similar accuracy through the same range the values of p (the density of steam) and cr (the ratio of the density of steam to the density of water in contact with it), for temperatures reckoned on the same arbitrary scale, we should have all the data from experiment required for the graduation of our water-steam thermometer to absolute thermodynamic scale. For it is to be remarked that all reckoning of temperature is eliminated from the second member of formula (3), and that in our use of it Regnault s normal thermometer has merely been referred to for the values of pi< and of 1 - cr, which correspond to stated values of p. The arbitrary constant of integration, t , is truly arbitrary. It will be convenient to give it such a value that the difference of values of t between the freezing point of water and the temperature for which p is equal to one atmo shall be 100, as this makes it agree with the centigrade scale in respect to the difference between the numbers measuring the temperatures which on the centigrade scale are marked and 100. We shall see ( 56 below) that indirectly by means of experiments on hydrogen gas this assignation of the arbitrary constant of integration would give 273 for the absolute temperature C., and 373 for that of 100 C. Meantime, as said above, we have not the complete data from direct experi ments even on water-steam for graduating the water-steam thermometer ; but on the other hand we have, from experi ments on air and on hydrogen and other gases, data which allow us to graduate indirectly any continuous intrinsic thermoscope (19 above) according to the absolute scale; and we shall see that by thus indirectly graduating the water-steam thermometer, we learn the density of steam at different temperatures more accurately than it has hitherto been made known by any direct experiments on water-steam itself. 45. Merely viewed as a continuous intrinsic thermo scope, the steam thermometer, in one or other of the forms described above to suit different parts of the entire range from the lowest temperatures to temperatures somewhat above 520, is no doubt superior in the conditions for accuracy specified in 16 to every other thermoscope of any of the different kinds hitherto in use ; and it may be trusted more surely for accuracy than any other as a thermometric standard when once it has been graduated according to the absolute scale, whether by practical experi ments on steam, or indirectly by experiments on air or other gases. In fact, the use of steam-pressure measured in definite units of pressure, as a thermoscopic effect, in the steam thermometer is simply a continuous extension to every temperature of the principle already practically adopted for fixing the temperature which is called 100 on the centigrade scale ; and it stands on precisely the same theoretical footing as an air thermometer, or a mercury-in- glass thermometer, or an alcohol thermometer, or a methyl butyrate thermometer, in respect to the graduation of its scale according to absolute temperature. Any one intrinsic thermoscope may be so graduated ideally by thermodynamic experiments on the substance itself with out the aid of any other thermometer or any other ther mometric substance ; but the steam-pressure thermometer has the great practical advantage over all others, except the air thermometer, that these experiments are easily realiz able with great accuracy instead of being, though ideally possible, hardly to be considered possible as a practical means of attaining to thermodynamic thermometry. In fact, for water-steam it is only the most easily obtained of experimental data, the measurement of the density of the steam at different pressures, that has not already been actually obtained by direct experiment. Whether or not, when this lacuna has been filled up by direct experiments, the data from water-steam alone may yield more accurate thermodynamic thermometry than we have at present from the hydrogen or nitrogen gas thermometer ( 64 . . 60 below), we are unable at present to judge. But when once we have the means, directly from itself, or indirectly from comparison with hydrogen or nitrogen or air ther mometers, of graduating once for all a sulphurous acid steam thermometer, water-steam thermometer, or mercury- steam thermometer, that is to say, when once we have a table of the absolute thermodynamic temperatures cor responding to the different steam pressures of the sub stances sulphurous acid, water, and mercury, we have a much more accurate and more easily reproducible standard than either the air or gas thermometer of any form, or the mercury thermometer, or any liquid thermometer can give
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