550 MR A. CRICHTON MITCHELL ON THE THERMAL CONDUCTIVITY 



points (or four, as the case may be), cannot be received and adopted without 

 involving the possibility of occasional large error. 



Some assistance may be obtained from the graphic representation of the 

 value of dvjdx for different values of v. It sometimes gives a means of casting 

 out untrustworthy estimates, and at all events prevents the entrance into the 

 calculations of any great error. Diagram 3 illustrates its use in the case of 

 the iron bar. 



Curves of Cooling. — In the reduction of the observations, the same methods 

 were employed as in previous work. The deduction of the rates of cooling was 

 performed mainly by constructing a curve whose ordinates represented succes- 

 sive differences of temperature of the cooling bar (or -^, ^, &c. difference, where 

 the interval of observation was 2, 3, &c. times the time-unit), and whose 

 abscissas represented the mean temperature excesses during the interval. It is 

 not accurate to say a curve was thus constructed ; in reality, there was thus 

 obtained (as is shown in Diagram 4) a number of irregularly disposed points, 

 through which was drawn a smooth curve, the ordinates of which were the 

 rates of cooling at the temperature excess given by the respective abscissae. 

 In order to check the results derived in this manner, the following method of 

 " grouped " readings was adopted. Six readings of the cooling bar were 

 selected, taken at equal intervals. Correcting for thermometric errors, and 

 subtracting the air temperature, we obtain six successive temperature excesses. 

 Divide their sum by six, and there results the mean temperature excess during 

 the five time-intervals which elapse between the reading of the first and last. 

 Next take the five successive differences of temperature observed by the six 

 readings ; divide their sum by five, and we get the mean rate of cooling at the 

 mean temperature excess during the interval. We thus have obtained, by 

 taking many such groups of readings, a series of estimates of the rate of cooling 

 at different excesses of temperature. "When so plotted, the points nearly all 

 lie on a smooth curve which may easily be drawn through them. 



It was usual to go over each cooling experiment twice in this manner. 

 All the readings were grouped into sets of six, and the results deduced. Going 

 over them a second time, the readings were again placed in groups, so that one 

 group in this second reduction overlapped equally two groups in the first; thus 

 giving a second series of intermediate points on the curve. 



In Diagram 5 is shown the curve thus obtained, in the case of one of the 

 cooling experiments on iron at the higher temperatures. In order to show 

 how satisfactory is this method, the following comparison, made between the 

 ordinates (i.e., rates of cooling) of this curve, obtained from "grouped" 

 readings, and those of the curve obtained from "single" readings, may be 

 considered : — 



