The values of the scale correction dt deduced from these formu lae agree with those experimentally determined by Chappuis in the case of carbonic acid within the limits of agreement of the observations themselves. The calculated values for nitrogen and hydrogen give rather smaller differences than those found experi mentally, but the differences themselves are of the same order as the experimental errors. The deviations of hydrogen and helium from the absolute scale between o° and ioo° C are of the order of -oof ° only, and beyond the limits of accuracy of experiment. Even at — 250° C (near the boiling-point of hydrogen) the cor rections of the constant volume hydrogen and helium thermome ters are only a tenth of a degree, but as they are of opposite signs, the difference amounts to one-fifth of a degree at this point, which agrees approximately with that observed by Travers. For a fuller discussion of the subject, together with tables of corrections, the reader may refer to papers by Callendar, Phil. Mag. v. p. 48 (1903), and D. Berthelot, Tray. et Mem. Bur. Int. Paris, xiii. (1903). Berthelot assumes a similar type of equation to that given above, but takes n= 2 in all cases, following the so-called law of corresponding states. This assumption is of doubtful validity, and might give rise to relatively large errors in the case of monatomic gases.
Limitations.—In the application of the gas thermometer to the measurement of high temperatures certain difficulties are encountered which materially limit the range of measurement and the degree of accuracy attainable. These may be roughly classi fied under the heads—(I) changes in the volume of the bulb; (2) leakage, occlusion and porosity; (3) chemical change and dissociation. The difficulties arise partly from defects in the materials available for the bulb, and partly from the small mass of gas enclosed. The troubles due to irregular changes of volume of glass bulbs, which affect the mercury thermometer at ordinary temperatures, become so exaggerated at higher points of the scale as to be a serious source of trouble in gas thermometry in spite of the twentyfold larger expansion.
The difficulties of leakage and porosity occur chiefly with por celain bulbs, especially if they are not perfectly glazed A similar difficulty occurs with metallic bulbs of platinum or platinum iridium, in the case of hydrogen, which passes freely through the metal by occlusion at high temperatures. The difficulty can be avoided by substituting either nitrogen or preferably argon or helium as the thermometric material at high temperatures. With many kinds of glass and porcelain the chemical action of hydro gen begins to be appreciable at temperatures as low as or 30o° C. In any case, if metallic bulbs are used, it is absolutely necessary to protect them from furnace gases which may contain hydrogen. This can be effected either by enclosing the bulb in a tube of porcelain, or by using some method of electric heating which cannot give rise to the presence of hydrogen. At very high temperatures it is probable that the dissociation of diatomic gases like nitrogen might begin to be appreciable before the limit of resistance of the bulb itself was reached. It would probably be
better, for this reason, to use the monatomic and extremely inert gases argon or helium.
On account of these and similar difficulties, it appears probable that the extreme limit of gas thermometry, even with the best metallic bulbs, must be placed in the neighbourhood of 1,600° C. A great deal of valuable work has been done in recent years in this direction, especially at the Reichsanstalt and the U.S.A. Bureau of Standards, by which tile limitations of our knowledge of the absolute scale in this region have been materially nar rowed. The methods employed in these researches do not involve any fresh questions of principle, and it would be impossible in the limits of the present article to give an intelligible account of the intricate details and results. But it may be doubted whether any advantage gained by the extension of the bulb method, as usually practised, from ,ioo° to 1,600° is not more than neutralised in point of accuracy by the subsidiary corrections, such as that for the expansion of the bulb, most of which increase in uncertainty more rapidly than as the square of t. At these and higher temper atures it would appear that the accurate extension of the absolute scale must rest primarily on improvements in the measurement of total radiation for which the fourth power law is now firmly established by comparison with the gas thermometer at lower temperatures over a very wide range. (See HEAT.) Other Methods.—Many attempts have been made to over come the difficulties of gas pyrometry by adopting other methods of measurement. Among the most interesting may be men tioned : (i.) The variation in the wave-length of sound. The ob jection to this method is the difficulty of accurately observing the wave-length, and of correcting for the expansion of the material of the tubes in which it is measured. There is the further objec tion that the velocity varies as the square root of the absolute temperature. (ii.) A similar method, but more promising, is the variation of the refractivity of a gas, which can be measured with great accuracy by an interference method. Here again there is difficulty in determining the exact length of the heated column of gas, and in maintaining the temperature uniform throughout a long column at high temperatures. These difficulties have been ingeniously met by D. Berthelot (Comptes Rendus, 1895, 120, p. 831). But the method is not easy to apply, and the degree of accuracy attainable is probably inferior to the bulb method. (iii.) Methods depending on the effusion and transpiration of gases through fine orifices and tubes have been put in practice by Barus and by the writer. The method of transpiration, when the resistance of the tube through which the current of gas is passed is measured on the Wheatstone bridge principle (Nature, 23rd March 1899), is extremely delicate, and the apparatus may be made very small and sensitive, but the method cannot be used for extrapolation at high temperatures until the law of increase of resistance has been determined with certainty. This may be successfully accomplished in the near future, but the law is apparently not so simple as is usually supposed.