QUANTITY OF HEAT. SPECIFIC HEAT. 79 



gentler slope down from to 20, and a steeper slope up after that than 

 the water sets. Thus, at the metal mixtures gave 1 '00551, and the 

 water mixtures 1 -00777 ; while at 31 the metals gave 1 '00337 and the 

 water 1 '00145. The mean of these results gives a slope from to 15, 

 very nearly the same as those obtained by Rowland and Griffiths (see 

 Fig. 60), but Bartoli and Stracciati found a minimum at 20. 



Liidin in 1895 (Beibldtter, 1897) also used the method of mixtures, 

 and his results are represented on Fig. 60. 



Dr. Barnes has made the most complete series of experiments up to 

 the present (Phil. Trans., A. 199, 1902, p. 149). The method, that of 

 electric heating, was suggested by Prof. Callendar, and the apparatus was 

 devised by him (Phil. Trans., loc. cit., p. 55). But as Prof. Callendar, 

 with whom Dr. Barnes was associated at first, was unable to continue 

 the experiments, they were carried out by Dr. Barnes. In this method 

 a stream of water is led through a narrow tube t (Fig. 59), through which 

 passes a fine platinum wire. This wire carries an electric current intro- 

 duced and taken away by the thick wires cc. The temperatures of the 

 water on entering and leaving t are taken by the platinum thermometers 



c 



Water Jacket 



Vacuum Jacket 



v_^= _ 



-^pt/i 



FlG. 59. Callendar- Barnes Electric Heating Method of Determining the 

 Specific Heat of Water. 



pth, pth. t is surrounded by a vacuum jacket to diminish loss of heat by 

 cooling, and this again is surrounded by a water jacket. Let Q be the 

 quantity of liquid flowing through t per second, and let 6 be the tempera- 

 ture at entrance, 6 l that at exit. Let s be the mean specific heat of the 

 liquid between and O v and J the mechanical equivalent of heat ; then 

 the work value of the heat gained by the water is JQs(O l - 6 ). But if 

 E is the potential difference between the ends of the fine wire, and C 

 is the current in it, and if, for simplicity, we suppose all the heat given 

 by the current to remain in the water, the heat is EC in work measure. 

 Hence we have 



JQs(0!-0 ) = EC, 



and measuring Q, p , E and C, we can determine s. We must refer 

 the reader to the original papers for the account of the various 

 corrections and their determinations. There is a minimum value 

 at about 40 C. Callendar (Phil. Trans., A. 199, p. 142) gives the 

 following formula for the specific heat: From to 20 C., s='9982 

 + -0000045^ -40) 2 + -00000005(20 -t)*. From 20 to 60 C. the last 

 term is omitted and s= '9982 + '0000045(2 - 40) 2 . From 60 to 200 C 

 s= -9944 + -00004* + -0000009* 2 (Regnault's formula corrected). 



