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 CALORIMETRY 509 the reduction of the results to the absolute scale of temperature. Specific Heat of Water in terms of Unit at 20° C. 4-180 Joules. The agreement of his corrected results with those of Griffiths by a very diiferent method, left very little doubt with regard to t” C. Joules. h. Rowland. the rate of diminution of the specific heat of water at 20° C. The work of Bartoli and Stracciati by the method of mixture between 0° 4-208 1-0094 0 0 0° and 30° C., though their curve is otherwise similar to Rowland’s, 5° 4-202 1-0054 5-037 5-037 had appeared to indicate a minimum at 20° C., followed by a 10° 4-191 1-0027 10-056 10-058 rapid rise. This lowering of the minimum was probably due to 15° 4-184 1-0011 15-065 15-068 20° some constant errors inherent in their method of experiment. 4-180 1-0000 20-068 20-071 The more recent work of Liidin, 1895, under the direction of 25° 4-177 0-9992 25-065 25-057 30° Prof. Pernet, extended from 0° to 100° C., and appears to have 4-175 0-9987 30-060 30-057 attained as high a degree of excellence as it is possible to reach 35° 4-173 0-9983 35-052 35-053 40° by the employment of mercury thermometers in conjunction with 4-173 0-9982 40-044 50° the method of mixture. His results, exhibited in Fig. 1, 4-175 0-9987 50-028 60° show a minimum at 25° C., and a maximum at 87° C., the values 4-180 1-0000 60-020 being '9935 and 1‘0075 respectively in terms of the mean specific 70° 4-187 1-0016 70-028 heat between 0° and 100° C. He paid great attention to the 80° 4-194 1-0033 80-052 90° thermometry, and the discrepancies of individual measurements 4-202 1-0053 90-095 Shaw 100° at any one point nowhere exceed (P3 per cent., but he did not 4-211 1-0074 100-158 Regnault 120“ vary the conditions of the experiments materially, and it does 4-231 1-0121 120-35 12073 140° not appear that the well-known constant errors of the method 4-254 1-0176 140-65 140-88 160° could have been completely eliminated by the methods which he 4-280 1-0238 161-07 161-20 180° adopted. The rapid rise from 25° to 75° may be due to radiation 4-309 1-0308 181-62 182-14 200° error from the hot water supply, and the subsequent fall of the 4-341 1-0384 202-33 220° 4-376 curve to the inevitable loss of heat by evaporation of the boiling 1-0467 223-20 water on its way to the calorimeter. It must be observed, however, that there is another grave difficulty in the accurate between Rowland’s corrected result 4-181 and the value 4-179, determination of the specific heat of water near 100° C. by this deduced from the experiments of Reynolds and Moorby on the method, namely, that the quantity actually observed is not the assumption that the ratio of the mean specific heat 0° to 100° to specific heat at the higher temperature, but the mean specific heat that at 20 is 1"0016, as given by the formulse representing the over the range 18° to 100°. The specific heat itself can be results of Callendar and Barnes. This would indicate that deduced only by differentiating the curve of observation, which Rowland’s corrected values should, if anything, be lowered. In greatly increases the uncertainty. The peculiar advantage of the any case the value of the mechanical equivalent is uncertain'to at electi’ic method of Callendar and Barnes, already referred to, is least 1 in 2000. The mean specific heat, over any range of temperature, may be that the specific heat itself is determined over a range of 8° to 10° at each point, by adding accurately measured quantities of heat obtained by integrating the formulse between the limits required, to the water at the desired temperature in an isothermal enclosure, or by taking the difference of the corresponding values of the under perfectly steady conditions, without any possibility of total heat h, and dividing by the range of temperature. The evaporation or loss of heat in transference. These experiments, quantity actually observed by Rowland was the total heat. It which have been extended by Barnes over the whole range 0° to may be remarked that starting from the same value at 5°, for the 100°, agree very well with Rowland and Griffiths in the rate of sake of coniparison, Rowland’s values of the total heat agree to 1 variation at 20° C., but show a rather flat minimum of specific in 5000 with those calculated from the formulse. The values of heat in the neighbourhood of 38° to 40° 0. At higher points the the total heat observed by Regnault, as reduced by Shaw, also rate of variation is very similar to that of Regnault’s curve, but show a very fair agreement, considering the uncertainty of the taking the specific heat at 20° as the standard of reference, the units. It must be admitted that it is desirable to redetermine actual values are nearly 0‘56 per cent, less than Regnault’s. It the variation of the specific heat above 100° C. This is very appears probable that his values for higher temperatures may be difficult on account of the steam-pressure, and could not easily be adopted with this reduction, which is further confirmed by the accomplished by the electrical method. The writer has, however, results of Reynolds and Moorby, and by those of Liidin. Accord- devised a continuous method of mixture, which appears to be ing to the electric method, the whole range of variation of the peculiarly adapted to the purpose, and promises to give more specific heat between 10° and 80° is only 0’5 per cent. Compara- certain results. In any case it may be remarked that formula} tively simple formulae, therefore, suffice for its expression to 1 in such as those of Jamin, Henrichsen, Baumgartner, Winkelmann, 10,000, which is beyond the limits of accuracy of the observations. or Dieterici, which give far more rapid rates of increase than that It is more convenient in practice to use a few simple formulae, of Regnault, cannot possibly be reconciled with his observations, than to attempt to represent the whole range by a single com- or with those of Reynolds and Moorby, or Callendar and Barnes, and are certainly inapplicable above 100° C. plicated expression:— Below 20° C. s = 0-9982+ 0-000,0045 (i!-40)2-0-000,0005 (i(-20)3. § 16. On the Choice of the Thermal Unit.—So much, un2 From 20° to 60°, s = 0-9982+ 0-000,0045 (t - 40) (5). certainty still prevails on this fundamental point that it 2 Above 60° to 900° /s = = 0'9944 corrd.) cannot be passed over without reference. There are three toM)0 0-000,22 +0'000,0009 (*-60), (Bosscha corrd.) 1-ooo++-000,04* The addition of the cubic term below 20° is intended to possible kinds of unit, depending on the three fundamental represent the somewhat more rapid change near the freezing- methods already given : (1) The thermometric unit, or the point. This effect is probably due, as suggested by Rowland, thermal capacity of unit mass of a standard substance to the presence of a certain proportion of ice molecules in under given conditions of temperature and pressure on the liquid, which is also no doubt the cause of the anomalous the scale of a standard thermometer. (2) The latentexpansion. Above 60° C. Regnault’s formula is adopted, the heat unit, or the quantity of heat required to melt or absolute values being simply diminished by a constant quantity 0"0056 to allow for the probable errors of his thermometry. vaporize unit mass of a standard substance under given Above 100° C., and for approximate work generally, the simpler conditions. This unit has the advantage of being indeformula of Bosscha, similarly corrected, is probably adequate. The following table of values, calculated from these formulse, pendent of thermometry, but the applicability of these is taken from the Brit. Assoc. Report, 1899, with a slight modifica- methods is limited to special cases, and the relation of tion to allow for the increase in the specific heat below 20° C. the units to other units is difficult to determine. (3) The This was estimated in 1899 as being equivalent to the addition of absolute or mechanical unit, the quantity of heat equivalent the constant quantity 0-020 to the values of the total heat h of to a given quantity of mechanical or electrical energy. the liquid as reckoned by the parabolic formula (5). This quantity is now, as the result of further experiments, added to the values This can be very accurately realized, but is not so conof h, and also represented in the formula for the specific heat venient as (1) for ordinary purposes. itself by the cubic term. In any case it is necessary to define a thermometric unit of The unit of comparison in the following table is taken as the class (1). The standard substance must be a liquid. Water is specific heat of water at 20° C. for the reasons given below. This always selected, although some less volatile liquid, such as aniline unit is taken as being 4-180 joules per gramme-degree-Centigrade or mercury, would possess many advantages. With regard to on the scale of the platinum thermometer, corrected to the the scale of temperature, there is very general agreement that absolute scale as explained in the article Thermometry, § the absolute scale as realized by the hydrogen or helium ther23, which has been shown to be practically equivalent to the mometer should be adopted as the ultimate standard of reference. hydrogen scale. The value 4-180 joules at 20° C. is the mean But as the hydrogen thermometer is not directly available for
 * (Reg.