9f>0 MR A. CEICHTON MITCHELL ON THE 



either at its cooler end, or near its middle, on the cooler side of the fifth thermometer. 

 This was suggested by Professor Tait in his paper on "Thermal and Electric Conductivity,"* 

 and first carried out in my experiments " On the Thermal Conductivity of Iron, Copper, 

 and German Silver, "t The advantages of this improvement were noticed in the latter 

 paper. 



The thermometers employed in the experiments were, with one exception, the same, 

 and were used in the same way as in Professor Tait's and my own previous work. The 

 single exception was that of the thermometer in hole A (i.e., that nearest the source of 

 heat). This instrument was broken at the beginning of the experiments, but was replaced 

 by another of exactly similar make and dimensions, and whose error was carefully ascer- 

 tained. 



Of the eight holes in the bar, only five were used, those being first five reckoned from 

 that end of the bar towards which they are closer together. These holes were, for con- 

 venience, named A, B, C. D, E. The first four were separated by intervals of three 

 inches ; the fourth and fifth by one of six inches. The cooling bath, through which a 

 stream of water was kept steadily passing, was placed close to hole E. 



In all other respects the experiments were conducted on exactly the same lines as 

 formerly, so that nothing remains to be said so far as details of experiment are 

 concerned. 



Deduction of Conductivity. — The manner in which the readings of the thermometers 

 are reduced, and from them the curve of stationary temperature excess constructed, has 

 already been fully described in my paper quoted above. It has also been pointed out 

 that this curve furnishes, so far, a test of the extent to which the experiments made on 

 different days agree among themselves. Judged in this way, the experiments were very 

 successful ; the only discrepance being in connection with the readings of the thermometer 

 next to the cooling bath. But that this should be so is not at all surprising. 



The curve of stationary temperature excess being obtained, the next step is to find 

 the value of the tangents to it at different points corresponding to different sections of 

 the bar. This is best done by finding an equation between v (temperature excess) and 

 x (position along the bar, reckoned from some arbitrary origin), which will represent the 

 curve, and by differentiation finding the value of the tangent of inclination which is simply 



that of -y-. In my previous paper, two formulas were given which have been used 

 for this purpose. These were — 



log* = loga- j-^ (A) 



\ogv = log a + ~T^~ ex ■ .... (B), 



where v and x have the above meaning, and where a, b, c, and e are constants. But for 

 the present case, while either would with tolerable accuracy represent any small portion 



* Trans. Roy. Soc. Edin., vol. xxviii. t Trans. Roy. Soc. Edin., vol. xxxiii. 



