temperature difference equivalent to 1 centim. of the bridgewire, but would of course have the same relative values in any scale. p='000082. Let us assume that the value taken for Øy differed from the true value by as much as 1 bridge-wire degree (as will be seen when the experimental results are given this is an excessive estimate), then 0-0x=1, hence (supra) the value would differ from of dt plotted as ordinates with 0, as abscissa, the resulting straight lines were found to intersect not in one but in three points, which, however, were so near to each other that (except in one case) the probable error introduced by assuming that any one intersection gave the true value of ON was less than that above indicated. The triangle formed by joining the three points of intersection was almost invariably of one form and of nearly equal dimensions, indicating that its existence was not due to experimental irregularities but was connected in some way with the difference in the rate of rise with different values of n. I think that my impression that p and hence de, AN are functions of is thus confirmed. Ν at In any case the error caused by the assumption that es is the same with different rates of increase in temperature, must be less than the error resulting from the assumption that it is the same when the temperature is rising and when it is steady. Again, the null point finally selected for each group of experiments was always obtained in the same manner from the three points of intersection. Any error, therefore, is of the same nature in each case, and as the specific heat was obtained by the subtraction of one ordinate from another, the effect of any error is diminished considerably. True, when the absolute value of the ordinate is used in order to obtain the water equivalent of the calorimeter, any error in the position of ON, and therefore in the length of the ordinate, would produce its full effect, and might be appreciable, but as regards the determination of the specific heat by the method of differences it is almost certainly negligible. It would be represented by (P1—P2)(01—ON) where and P1 n2 P2 are the values of the masses of the liquid are M, and M,; and since P1(M1S1+w1)=p2(M2S1+w1), the limit of error is given by the expression ρ when error, and this would in no case amount to 10% of dt don dt I assume, therefore, that the values of given by the experiments are sufficiently approximate. If C is the value, in degrees C. of the air-thermometer, of the temperature difference equivalent to 1 centim. of the bridge-wire*, then dox R1 × Cb gives the rise per second in degrees C. with unit resistance and unit potential-difference. The reciprocal of the quantity thus found gives us T, time of rising 1o, when E=1 and R=1. Now T the Let the value of T be T, when M is M1, and T2 when M is M2. Then we get Phil. Mag. S. 5. Vol. 39. No. 236. Jan. 1895. F We can now find the value of S1M1, and therefore Thus both the specific heat of the liquid and the waterequivalent can be found if two groups of experiments with different masses of liquid have been performed at the same temperature. Since J=4.198 x 107* ergs, when the unit of heat is "the quantity of heat required to raise 1 grm. of water through C. of the air-thermometer at 15° C.," it follows that the results obtained at different temperatures are all expressed in terms of that unit, and are not dependent upon our knowledge of the changes in the specific heat of water. Corrections. Before proceeding to plot the results the following corrections had to be made : I. For changes in the temperature of the steel chamber during the time of an experiment. For temperatures below 26° C. a mercury-thermometer labelled A was used, situated as described on p. 56, and 1 millim. change in A was equivalent to 4.05 millim. in the bridge-wire reading. Thermometer II. was used for temperatures above 26° C., and 1 millim. change in II. was equivalent to 5.5 millim. of the bridge-wire. The resulting correction had to be added or subtracted from the bridge-wire value of de1, and it rarely exceeded 0.2 millim. II. The correction to the "mean bridge centimetre." This correction was given with great exactness by the table resulting from the calibration of the bridge-wire previously referred de1 to. It is applied as a factor to dt III. The normal rate of stirring during experiments 1 to 8 was 9.10 revolutions per second, for the remaining experiments 5.00. A considerable number of experiments gave tr2=800,000 approximately, where is the rate per second, and t the time of rising 1 centim. of the bridge-wire. The 2-p, 2 where r is correction to the normal rate therefore is the normal and r, the observed rate. 800,000' As the stirring rarely departed much from the normal this correction was always small, it in no case exceeded 00006, and rarely exceeded 00002; and as the values of tr2 given by the stirring experiments did not differ by more than 1 part in 50, the correction is sufficiently close. IV. The correction consequent on changes in the temperature of the bridge-wire. This is given with sufficient accuracy by the expression 0, being measured by a Fahrenheit thermometer. V. The correction for the temperature of the Clark cells. Assuming Lord Rayleigh's temperature-coefficient 00077, {1+·00154 (0—15)}; for the rate of rise varies d01 we get dt as E2. VI. The subsequent operations are simplified if some arbi trary value is assigned to R', and the consequent value of dt for that value of R' ascertained. As the resistance of the coil increased from about 8:45 to 8.6 ohms as 1 increased from 15° to 50° C., it was found convenient to take 8.5 ohms as do1 R1 the arbitrary resistance. The correction is X dt 8.5 The true value of R1, however, is not that obtained by merely taking the resistance in the usual manner with a small current. I have in paper J, pp. 404-7, published a full account of a method of finding the increase in R due to an increase in the potential-difference of 1, 2, &c. Clark cells. The increase, with this coil, was carefully determined, with the following results*: I have to thank Mr. F. H. Neville, Fellow of Sidney College, Cambridge, for his kindness in assisting me in this somewhat troublesome determination. The resistance of the coil was carefully determined for each group of experiments, at the mean temperature of the group, and also occasionally at a fixed temperature, in order to trace any change. During the first series a slight increase was observable (apart from the natural increase due to its temperature-coefficient). This was possibly a consequence of an oversight on my part, as I had forgotten to previously anneal the wire. After it had been raised to the highest temperature attained during these experiments the further change became negligible. pp. 9 The absolute value of R, was obtained by means of the dial-box described in paper j. 408-10. The errors of the separate coils and of the coils in the bridge-arms had been ascertained by a direct comparison, which had been made by kind permission of Mr. Glazebrook, with the B.A. standards in the autumn of 1892. VII. The value of at several points of the range (which dt d01 dt was usually about 15 centim. of the bridge-wire, i. e. about 104 C.) having been ascertained, the results were plotted (with 1 as abscissa) in order to ascertain the regularity &c. of the observations, which was generally found to be satisfactory. The values of at the readings 60 and 70 of the bridge-wire were then obtained and divided by n2. Three experiments having been performed at each temperature with three different values of n, the intersection of the three lines thus found gave ON, the ordinate for that abscissa giving the rate of rise due to the electrical supply alone. A plan of these intersections is given on Plate I. A glance at Plate I. will show that the null point in each case is not accurately defined. The intersection of the 3- and 4-cell lines is always to the left of the other intersections. |