540 
MR. J. T. BOTTOMLEY ON THE 
any time into the stratum of the liquid bounded by horizontal planes through the top 
and bottom of its bulb. 
When heat is being conducted downward through the liquid, the various parts of 
the integrating thermometer are at different temperatures, the temperatures decreasing 
from above downwards. On the whole, however, the temperature indicated by the 
integrating thermometer is the average temperature from top to bottom of the layer 
of liquid which contains the bulb of the thermometer. 
I have verified by experiments that the integrating thermometer does give with 
very considerable accuracy the average temperature from top to bottom of a cylindrical 
layer of liquid in which it is contained. For this purpose I placed the thermometer 
vertical in a cylindrical vessel, the bottom of the bulb being at the bottom of the 
vessel. The bottom of the vessel was plane and was horizontal. I then poured in 
an inch or two of cold water. On the top of that layer I deposited a layer of warmer 
water, then a layer of still warmer water, and so on, making a succession of layers 
of water of gradually increasing temperature till the level of the top of the bulb was 
reached. I then read off the temperature indicated by the thermometer as the average 
of the whole. I next stirred the whole from top to bottom so as to equalize the 
temperature throughout and read the thermometer again. Many such experiments 
were tried, and in every case I found that the alteration in the reading was very small, 
and was certainly not more than variation which could be accounted for by unavoid¬ 
able errors introduced by changes of temperature of the parts of the containing vessel 
and of the stirrer." These tests were so severe in comparison with the requirements of 
the present experiments on the conductivity of heat by liquids, that I am satisfied that 
no error of consequence, in comparison with uncertainties that I have not yet been 
able to get rid of, is introduced by want of perfect averaging by the integrating 
thermometer. 
From the description of the arrangements for these experiments, it will be seen that 
we have a layer of liquid, of known thickness, between the thermometers A and B 
kept with one of its sides hotter than the other. The thermometers A and B give the 
temperatures of the two sides of the layer. The heat conducted across it warms the 
liquid beneath, and the whole heat that flows across the layer between A and B in 
any given time is known from the readings of the integrating thermometer at the 
beginning and end of the interval. Now if the temperature of the layers at A and B 
could be kept constant during an experiment the calculation of the thermal con¬ 
ductivity of the liquid from these data would be of the simplest possible kind. 
The quantity of heat that passes across the stratum between A and B in any time is 
in simple proportion to the difference of temperatures between the two sides of the 
stratum; it is in simple proportion to the time; it is in simple proportion to the area 
of the stratum; it is inversely proportional to the cross-sectional area of the stratum ; 
* It is hardly necessary to say that alteration of specific heat of the water by change of temperature 
could not be taken into account in considering the results of experiments such as those described. 
