THERMAL CONDUCTIVITY OP WATER. 
541 
and it is in simple proportion to the thermal conductivity of the liquid. Now let 
T and T' denote the temperatures of A and B respectively—supposed for the moment 
constant—let a denote the thickness of the layer between A and B, let t denote the 
time in seconds, k the conductivity, and Q the quantity of heat conducted across the 
stratum whose area is A ;—then we should have 
T — T' 
Q=k- - At 
( 1 ) 
Again, taking as unit quantity of heat the quantity required to raise unit bulk of 
water one degree, and neglecting for the present differences of specific heat, in the 
different layers of the liquid column, due to differences of temperature, we have, if l 
be the length of the integrating thermometer, D the difference between the average 
temperature from top to bottom at the beginning and the average temperature from 
top to bottom at the end, and if c be the specific heat of the liquid per unit of bulk 
Q=A.kc.D 
Hence, equating (1) and (2), we have 
or 
and 
T—T' _ 
k -.A.£=AJ.c.D 
a 
k Dl 
a 
._ Die 
rp_rp / 
a 
t 
( 2 ) 
( 3 ) 
( 4 ) 
In calculating from the results of experiments on the conductivity of water I have 
taken its specific heat as being equal to 1. The experiments that I have made up to 
the present time do not permit of my being able to take into account either variations 
of specific heat in the different parts of the layer tested, or variations of the average 
specific heat in the layer from top to bottom from that of water at the temperature 
chosen for defining unit specific heat. The formula, therefore, which would be used for 
calculation, if the conditions mentioned above—namely, the constancy during an interval 
of time of the temperature at the levels A and B—were fulfilled, is 
k= 
Dl 
T-T 
■t 
4 A 2 
