730 PROFESSOR TAIT ON THERMAL AND ELECTRIC CONDUCTIVITY. 
flux of heat by above 5 per cent. in both bars. |The omitted terms reduce this 
by one-fourth, at jirst.| In copper this is diminished to 1 per cent. (less than 
the errors of observation) in less than two minutes, so that it cannot be traced 
in any of the observations, as certainly two minutes must elapse after the 
heating before readings can commence. In iron the error is reduced to 
2 per cent. after about six minutes; so that to this cause is due a part, 
but only a small part, of the difference between Fores’ results and mine. 
For the initial sluggishness of cooling is exhibited by copper as well as iron, 
so that there must be another and more effective cause besides longitudinal 
cooling. 
I next tried (but without the least hope that it would help me) whether the 
discrepance might not be due to the fact that Fourier assumes / to be constant. 
If we assume (for the range of temperature employed) 
akg 
be aaa 

which is not far from the truth, the equation is no longer linear, even for the 
infinitely long cylinder.* But I found that this would not account for the 
result to be explained, and that no substitution of a more accurate law of cooling 
than that adopted by Fourier would remove the difficulty. 
Thus I was driven to seek the main cause of the phenomenon in the ther- 
mometer, not in the bar, and I traced it to the fact that the mercury in the 
bulb is all but fully heated almost at once, but that the final adjustment im the 
bulb and stem takes place more gradually. No previous heating of the bulb 
will much help in such a case. 
To test this explanation I heated the short iron bar, and immersed a 
thermometer bulb at once in one of the holes, reading it, as usual, every 
minute. After six minutes had elapsed, I inserted a second thermometer in 
a hole very near the first, and read it at half time between the continued 
readings of the first. After another period of six minutes a third thermometer 
was inserted close to the others. The result has fully verified the correctness 
of my conjecture. The following table, graphically calculated from the 
readings, explains itself. A refers to the first-mentioned thermometer, B 
to the second, C to the third. The thermometers were read as soon as they 
ceased to rise. 
* Tt is interesting, however, to know that it can be transformed into 
dip d\n ade 
ak Fe 4 5 ae) = ae 
which differs only by the factor e? on the right from the equation for constant conductivity. 

