112 
PROFESSOR HUGH L. CALLEXDAR OX 
The constant of integration B is determined by the consideration that the tempera¬ 
ture-gradient vanishes at the centre of the tube. Putting this condition in (3), we 
find B = 0, which materially simplifies the solution of the equation. Integrating 
from the temperature 6 0 of the surface of the tube, we find 
~ 0 = Q 0' (r*/W - (r/r v f - })/2 nlk . . . 
The temperature 0 l at the axis of the tube where r = 0, is given by 
6 U — 6*i = 3Q 6' / Snlk 
(4 
( 5 ). 
The mean temperature of the flow, allowing for variation of velocity over the 
cross-section, is given by the expression 
6 0 — 0.-, = llQdy iSnllc 
( 6 ). 
(31.) Electrical Method of Measuring the Thermal Conductivity of a Liquid. 
The remarkable simplicity of this expression induced me to attempt a method of 
measuring the conductivity of a liquid, based on the observation of the difference of 
temperature 9 0 — 61, between the tube and the mean of the flow at any point ; the 
temperature 0 O of the tube and the gradient O'jl being deduced from observations of 
the changes of resistance of the flow-tube itself. Although this may appear at first 
sight a difficult and out of the way method, it possessed special attractions for me as 
an application of the electrical resistance method of measuring temperature, and it 
really offers several advantages which more than counterbalance the difficulty of the 
electrical measurements. The longitudinal distribution of temperature in the flow- 
tube was deduced from observations of the resistance of consecutive sections by the 
same method which I had already applied in 1886 to the determination of the 
conductivity of platinum. The difficulty of this part of the work was therefore 
largely discounted by previous experience. The advantage of the method is that 
the tube is its own thermometer; the temperature measured is that of the tube 
itself, and not that of a thermo-couple or water-bath assumed to be at the same 
temperature as the tube. This avoids the most common and insidious source of error 
in all conductivity measurements. 
As compared with the plate-method of measuring the conductivity of liquids, which 
has been practised by Weber and many other observers in different forms, the tube- 
method possesses several important advantages, (a) It avoids the difficulty of measuring 
accurately the small distance between the bounding surfaces of the liquid, or the 
thickness of the sheet, since the expressions (5) and (6) already given are independent 
of the radius of the tube, and contain only lengths and differences of temperature 
which are easily observed, (b) All uncertainties with regard to the area from which 
the heat is conducted, and all difficulties of boundary conditions, which cannot 
