ON THE VARIATIOX OF TDE SPECIFIC HEAT OF WATER. 37 



final rise of temperature 0, we can easily eliminate h and Unci J. When 

 the flow is large, the heat loss 7irf is a small fraction, 1 or 2 per cent., of 

 the whole. The gradient of temperature in the flow-tube is then nearly 

 constant, but diminishes slightly as tlie temperature rises, owing to 

 increased rate of loss of heat. With smaller flows this efl"ect increases, 

 as the magnitude of the loss hQ becomes greater in proportion to the 

 whole. There is therefore a small systematic variation in the tempera- 

 ture distribution when the flow is changed, which may be calculated from 

 the differential equation representing the conditions of heat-loss and 

 supply. The efiect can be represented by adding to equation (5) a term 

 ll/i'-y/25 JQ, in which the numerical factor 11/25 depends on the relative 

 dimensions of the tubes of the calorimeter employed. At a temperature 

 of 30° C. h is 2 per cent, of JQ for the larger flows, and the correction 

 amounts to only 2 or 3 parts in 10,000. Dr. Barnes observed that the 

 results deduced from the smaller flows diff'ered systematically from those 

 given by the larger flows, but the differences were so small that he 

 thought they might be due to accidental errors of observation or some 

 defect of the method. I find, however, that these small systematic differ- 

 ences are almost exactly accounted for by the correction in question. This 

 is an excellent verification of the accuracy of the work. The importance 

 of the correction arises from the fact that the heat-loss increases nearly 

 as the fourth power of the absolute temperature, and the correction itself 

 increases as the square of the heat-loss. Although practically negligible 

 at ordinary temperatures, it reaches one part in 1,000 at the higher 

 points. The results published in the ' Proc. R.S.,' 1900, must be corrected 

 for this source of error. The corrected values are given in column (1) of 

 Table II. 



Reduction to the Hydrogen Scale. 



The observations were all taken directly with standard platinum ther- 

 mometers, and the temperatures were reduced by means of the difference - 

 formula 



t-pt=\-5Qt{t-\Q0) 1 10,000 ... (6) 



This gives a perfectly definite scale of temperature, which agrees very 

 closel)"-, according to the observations of Callendar and Griffiths,' with 

 that of the constant-pressure air-thei'mometer. It is really preferable 

 and express the results in terms of this scale, which has the advantage 

 that it can be reproduced with much greater accuracy than is attainable 

 in gas-thermometry. If, however, we assume that it coincides with the 

 scale of the air-thermometer, it would be desirable to reduce the results 

 to the hydrogen scale, as being a closer approach to the absolute thermo- 

 dynamic scale. 



In making this reduction it would be most natural to assume the well- 

 known formula for the diff"erence between the nitrogen and hydi'ogen 

 scales given by Chappuis, and quoted by Guillaume and other authorities : 



«„-i,=<(<-100)(-)-6-318 + 0-00889<-0-001323<2)xl0-« . . (7) 



This has been done by Griffiths,'^ who gives a table of our results so 

 reduced. There are, however, one or two objections to be considered. 

 (1) The formula of Chappuis makes the differences t^ — t,^ negative be- 

 tween 80° and 100°, so that the correction to the specific heat changes 

 from -2 in 10,000 at 80° to -|-6 in 10,000 at 100°. Chappuis himself 



' Phil, 1rans.,\%^<d, " Thervtal Measurement of Merffi/, Cambxidge, 1901. 



