380 



MR T. C. BAILLIE ON THE 



evaporated into steam). Also, by using an electrical heater, the heat supplied at the 

 hot end (subject to corrections for radiation) could be measured and the gradient of 

 temperature at that end. Such experiments, however, were not carried out in this case 

 because it was seen, in the manner described below, that the conductivity varied little 

 with temperature. 



§ 12. Change of Conductivity with Temperature. — Before the brass cap was 

 fitted on the end of the bar for the experiments just described readings were taken with 

 the bar losing heat only by radiation. After the distribution of temperature became 

 steady, the heat which passed any cross-section of the bar was lost by radiation from 

 the rest of the bar beyond. The following table gives the temperatures obtained, titer 

 mometric corrections being applied. 



Temperature 

 of Air. 



Corrected Mean Temperatures of Holes in Bar. 



No. 1. 



No. 2. 



No. 3. 



No. 4. 



No. 5. 



13-6 

 8-4 



14-3 

 9-2 



63-85 

 83-55 

 102-7 

 110-15 



68-9 



91-0 



112-75 



121-8 



78-7 

 107-35 

 132-8 

 146-2 



9535 

 13415 

 167-35 

 185-4 



119-5 

 174-4 

 219-1 

 248-3 



Curves were drawn from these readings, and differentiated. By supposing the bar 

 prolonged by an amount slightly over the length of the radius, and producing the 

 temperature curve to that point, one obtained the curve which would suit the bar if no 

 heat had been lost from the end, at which place d6/dx would then be zero. From the 

 first set of readings the value of d6/dx at the section which had the temperature 

 120 '6 5° C. was found to be 3*55, and its distance from the point at which d6/dx vanished 

 was 38 centimetres. The average excess of the temperature of those 38 centimetres of 

 the bar over the temperature of the surrounding air was 67 '45°. This gives the follow- 



ing relation 



KA x3-55 = Epx 67-45 x 38 ; 



where K is the conductivity at 120 *6 5° C. and E the average emissivity under the con- ! 

 ditions referred to. From the set of readings obtained on 31st December 1897, and , 

 given on page 19, the gradient at 120*65° C. was found to be 566, the gradient at 

 63-2° C. to be 433 ; and the distance between the points at these two temperatures was 

 11*72 centimetres. The average excess of the temperature of those 11*72 centimetres 

 of the bar over the temperature of the surrounding air was 76*0°. If we assume the 

 average emissivity to be the same in these two cases, we find that 1*23 is the value of 

 that part of the gradient which is required to account for the heat lost by cooling over; 

 the 11*72 centimetres in the latter instance. For if 



KA x 3-55 = Epx 67-45x38, 

 then 



KAx 1-23 = Epx 76-0x11-72. 





