ON THE SPECIFIC HEAT OF WATER. 233 



13. Determination of Mean Values of J for Various Intervals. In the deter- 

 mination of the value of J at any point most experimenters have determined the 

 value for a small range of temperature, and have taken the mean value of J for the 

 interval as the value at the middle point of the interval. Where the slope of the 

 J curve is sut>stantially constant during the interval this gives a correct result ; 

 where, however, this is not the case, the curve obtained for the values of J must be 

 slightly distorted. We have endeavoured to obtain the mean value of J for 

 consecutive intervals, and by the aid of the values so obtained to construct a curve 

 which should represent the values of J ', i.e., the mean value of J from zero to any 



temperature 0. The values of J are then given by the expression J = (0J *). 



(if) 



The course of these experiments has been already descritad in Section 9 by 

 reference to the notes of Experiment 125, which are given in Appendix D. We will 

 briefly indicate the method of calculation of the results also by reference to the notes 

 of this experiment. A graph was first plotted of the values of mi and m* to help in 

 getting the mean values for each of the five intervals into which this experiment is 

 divided. The mean values of Wi could be got with sufficient accuracy from the curve, 

 and the values of MI were then obtainable from the formula M! = r8117 + 0'0017mi. 

 The value of m a was obtained from the observed values by calculation. Thus, for the 

 third interval of 12 minutes (see Appendix D, from 10.58 to 11.10 a.m.), the observed 

 values of m, give * = 1.T65 + 0-30W, 



where t is time in minutes from beginning of interval. This gives for the middle ot 

 the interval m-j = 15 '49. From this figure the value of M 2 is calculated from the 



M a = 9-2208 + 0-02781m a +0'0001355m/. 



This gives for the total value of the mean resistance of the heater, including the 

 mercury leads, the figure 9'6839. From this has to be deducted the resistance of 

 the mercury leads above the obturator baffle-plate (which was 0'0045), giving for the 

 mean resistance of the heater during this interval the net figure 9'G794, which is 

 entered in the appropriate place in the column of the summary in Appendix D. 

 Ci being the current passing through the heater, C^Tl multiplied by time in seconds 

 gives the electrical joules expended in heating the water and calorimeter through A0. 

 To calculate the joules for heating the calorimeter the appropriate capacity figure for 

 the interval is taken as worked out in Section 12. The summary of the experiment 

 in Appendix D shows how the results are worked out. It should be noted that in 

 this summary the corrected temperatures a and b for the beginning and end of an 

 interval are given, and that the rise of temperature, due to heating by obturator, 

 stirring, &c., is deducted from the total temperature rise so as to give the value of A0, 

 which is due to electrical heating only. The results of Experiment 125, so far as 

 regards the interval from C. to 13 C., are set out in Appendix F. 



As the object of the point-to-point experiments was to determine the series of 



VOL. coxi. A. 2 H 



