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CALORIMETRY 507 difference from the nitrogen scale is so small as to be within the five revolutions per minute on the speed. These variations, so limits of experimental error in this particular case. Rowland far as they were of a purely accidental nature, would be approxihimself considered his results to be probably correct to one part mately eliminated on the mean of a large number of trials, so in 500, and that the greatest uncertainty lay in the comparison of that the accuracy of the final result would be of a higher order the scale of his mercury thermometer with the air thermometer. than might be inferred from a comparison of separate pairs of The subsequent correction, though not carried out strictly under trials. Great pains were taken to discuss and eliminate all the the conditions of the experiment, has shown that the order of sources of constant error which could be foreseen. The results of accuracy of his work about the middle of the range from 15° to the light trials with 400 foot-pounds on the brake differ slightly 25° was at least 1 in 1000, and probably 1 in 2000. At 30° he from those with 600 foot-pounds. This might be merely acciconsidered that, owing to the increasing magnitude and un- dental, or it might indicate some constant difference in the concertainty of the radiation correction, there “might be a small ditions requiring further investigation. It would have been error in the direction of making the equivalent too great, and desirable, if possible, to have tried the effect of a larger range of variation in the experimental conditions of load and speed, with a view to detect the existence of constant errors ; but owing to the limitations imposed by the use of a steam-engine, and the difficulty of securing steady conditions of running, this proved to be impossible. There can be no doubt, however, that the final result is the most accurate direct determination of the value of the mean calorie between 0° and 100° C. in mechanical units. Expressed in joules per calorie the result is 4-1832, which agrees very closely with the value found by Rowland as the mean over the range 15° to 20 C. The value 4'183 is independently confirmed in a remarkable manner by the results of the electrical method described below, which give 4-185 joules for the mean calorie, if Rowland’s value is assumed as the starting-point, and taken to be 4-180 joules at 20° C. 4/380 § 11. Electrical Methods.—The value of the international electrical units has Fig. 1. by this time been so accurately deterthat the specific heat might go on decreasing to even 40° C.” The results considered with reference to the variation of the specific mined in absolute measure that they afford a very good, heat of water are shown in the curve marked Rowland in Fig. 1. though indirect, method of determining the mechanical § 10. Reynolds and Moorby {Phil. Trans. 1897, p. 381) have equivalent of heat. But, quite apart from this, electrical determined the mechanical equivalent of the mean thermal methods possess the greatest value for calorimetry, on unit between 0° and 100° C., on a very large scale, with a Froude- account of the facility and accuracy of regulating and Reynolds hydraulic brake and a steam-engine of 100 h.p. This brake is practically a Joule calorimeter, ingeniously designed to measuring the quantity of heat supplied by an electric churn the water in such a manner as to develop the greatest current. The frictional generation of heat in a metallic possible resistance. The admission of water at 0° C. to the brake wire conveying a current can be measured in various ways, was controlled by hand in such a manner as to keep the outflow correspond to slightly different methods. By Ohm’s nearly at the boiling-point, the quantity of water in the brake which required to produce a constant torque being regulated automatic- law, and by the definition of difference of electric pressure ally, as the speed varied, by a valve worked by the lifting of the or potential, we obtain the following alternative expresweighted lever attached to the brake. With 300 pounds on a sions for the quantity of heat II in joules generated in a four- foot lever at 300 revolutions per minute, the rate of time T seconds by a current of C amperes flowing in a wire generation of heat was about 12 kilo-calories per second. In spite of resistance R ohms, the difference of potential between of the large range of temperature, the correction for external loss of heat amounted to only 5 per cent with the brake uncovered, the ends of the wire being E — CR volts :— and was reduced to less than 2 per cent by lagging. This is the H= ECT= G2RT= EdTR . . (1). special advantage of working on so large a scale with so rapid a generation of heat. But, for the same reason, the method neces- The method corresponding to the expression C-RT was sarily presents peculiar difficulties, which were not overcome adopted by Joule and by most of the early experimentalists. without great pains and ingenuity. The principal troubles arose from damp in the lagging, which necessitated the rejection of The defects of the earlier work from an electrical point of several trials, and from dissolved air in the water, causing loss of view lay chiefly in the difficulty of measuring the current heat by the formation of steam. Next to the radiation loss, the with sufficient accuracy owing to the imperfect developmost uncertain correction was that for conduction of heat along ment of the science of electrical measurement. These the 4-inch shaft. These losses were as far as possible eliminated by combining the trials in pairs, with different loads on the difficulties have been removed by the great advances since brake, assuming that the heat-loss would be the same in the 1880, and in particular by the introduction of accurate heavy and light trials, provided that the external temperature standard cells for measurements of electrical pressure. and the gradient in the shaft, as estimated from the temperature § 12. Griffiths.—The method adopted by Griffiths {Phil. Trans. of the bearings, were the same. The values deduced in this 1893, whose work threw a great deal of light on the manner for the equivalent agreed as closely as could be expected failure p.of361), previous observers to secure consistent results, correconsidering the impossibility of regulating the external condition sponded to the last expression E^TIR, and consisted in regulating of temperature and moisture with any certainty in an engine- the current by a special rheostat, so as to keep the potential room. The extreme variation of results in any one series was E on the terminals of the resistance R balanced against only from 776-63 to 779’46 foot-pounds, or less than | per cent. adifference given number of standard Clark cells of the Board of Trade This variation may have been due to the state of the lagging, pattern. The resistance R could be deduced from a knowledge of which Moorby distrusted in spite of the great reduction of the the temperature of the calorimeter and the coefficient of the wire. heat-loss, or it may have been partly due to the difficulty of regu- But in order to obtain trustworthy results by this method he found lating the speed of the engine and the water-supply to the brake it necessary to employ very rapid stirring (2000 revolutions per in such a manner as to maintain a constant temperature in the minute), and to insulate the wire very carefully from the liquid outflow, and avoid variations in the heat capacity of the brake. to prevent leakage of the current. He also made a special experiSince hand regulation is necessarily discontinuous, the speed and ment to find how much the temperature of the wire exceeded that the temperature were constantly varying, so that it was useless to of the liquid under the conditions of the experiment. This cortake readings nearer than the tenth of a degree. The largest varia- rection had been neglected by previous observers employing tion recorded in the two trials of which full details are given, was methods. The resistance R was about 9 ohms, and the 4,9t> F. in two minutes in the outflow temperature, and four or similar potential difference E was varied from three to six Clark cells