488 
ME, C. H. LEES ON" THE THERMAL CONDUCTIVITIES 
and then pouring melted sulphur into the paper cylinder. Since sulphur is an 
extremely poor conductor of heat, it may be assumed that the loss of heat from the 
ends of the bar is very small. 
The bar was suspended in the position occupied afterwards by the divided bar by 
means of threads. The temperature was determined by means of the platinum-silver- 
copper wires inserted into small holes amalgamated and filled with mercury, on oppo¬ 
site sides of a diameter at the middle of the bar. Observation of current, resistance, 
temperature of the cool junction, and of the enclosure, were made every two minutes 
during the experiments. From these observations the temperature of the bar at any 
time is determined, and curves drawn for each experiment showing the connection 
between time and temperature of bar and of enclosure. Of these curves that which 
corresponded most nearly with the mean of all was selected, and is referred to in 
what follows. 
If m is the mass of the bar, s its surface, c the specific heat of the material of the 
bar, v the excess of the temperature of the bar over that of the enclosure, which will 
be supposed constant, we have, as the connection between v and time, 
dv , 7 . . 
me — + sh v .v = 0.(1), 
where h v is a quantity which is generally assumed to be constant (Newton’s law), but 
which I have shown increases for a nickel-plated bar of the size used 70 or 80 per 
cent, for 100° C. rise of v* In the paper referred to this rise is expressed by writing 
h v = hv n where n is a small fraction = y about. In that paper v was always positive. 
As in the following work v is sometimes negative, in which case v n would require 
special interpretation, it is preferable to write h v = h{l + hv) where b is a small 
positive quantity. The foregoing equation becomes, then, 
me — -j- sh (1 + hv) v = 0.(2), 
the solution of which is 
^ fi- b = Ke iMcm)t .(3), 
where A is an arbitrary constant. 
The following table shows that this equation represents the cooling with a fail 
amount of accuracy for b = "008. The temperature of the enclosure has been assumed 
constant = 15 "2 C C., but in reality it varied from 15 '3° at the commencement to 15'4° 
at t = 10 minutes, and then down to 15'2 at 40 minutes, 15T8 at 60 minutes, 15T 
at 70 minutes. On this account no attempt has been made to determine b with 
greater accuracy; the value given above is determined by trial. 
* ‘Phil. Mag.,’ vol. 28, p. 429 (1889) 
