110 Barrett, Brown, AND HaprreLp—Researches on the 
conductivity of some forty of these alloys. The difficulty of absolute determina- 
tion of thermal conductivity is well known, and various methods have been 
adopted by different experimenters.* What we have to find is the temperature 
gradient, or fall of temperature in degrees per unit length along the lines of flow 
of heat. The rate of transmission of heat by conduction, or the quantity of heat 
transferred in unit time through unit area of the cross-section of the substance 
perpendicular to the lines of flow, is proportional to the temperature gradient. 
The thermal conductivity of the substance is the constant ratio of the rate of 
transmission to the temperature gradient. If the flow of heat be steady, that 
is, if a constant difference of temperature be maintained for a sufficiently long 
time between two parts of the substance, the rate of transmission—in isotropic 
homogeneous solids—is everywhere the same, and the conductivity can thus be 
determined. 
The difficulties in the exact determination of this temperature gradient are 
increased by the varying emissivity of different specimens. This is affected by 
so many circumstances that it forms the greatest source of uncertainty in experi- 
mental investigations. By making the substance under experiment of uniform 
size and shape, and uniformly silvered or blackened, these difficulties are partly 
overcome. Butit is impossible in practice to realize exactly the theoretical condi- 
tions required for an absolute determination of thermal conductivity. Hence even 
the most recent determinations of the absolute thermal conductivity of the same 
metal vary considerably. The well-known classical experiments of Forbes on the 
thermal conductivity of iron, when repeated by Tait, and subsequently by Mitchell, 
with additional precautions, differ by from 10 to 26 per cent. in their respective 
values, though identically the same massive bar of iron was used, and the same 
method of experiment employed. 
In determining thermal conductivity various methods of experiment have 
been devised, of which Forbes’ method of steady flow, and Angstrém’s method 
of variable or periodic flow of heat, are the best known. The temperature gradient 
may be ascertained by means of thermometers placed in holes drilled at definite 
distances along the bar under experiment—a method only possible in bars of 
large cross-section; or by a thermo-electric couple sliding along the bar, as used 
by Wiedemann and Franz; or by a series of thermo-electric couples placed in 
small holes, or bound at definite distances, along the bar. The difficulty here 
is to be sure that the thermo-couple exactly attains the temperature of the 
particular section of the bar to which it is attached. 
* An excellent résumé of the whole subject and of recent methods of experiment will be found in an 
article by Professor Callendar, F.R.s., in the Encye. Brit., vol. xxvii., p. 188, e¢ seg. See also Lee’s paper 
on “ hermal Conductivity,” Phil. Trans., 1892, p. 481, e¢ seg.; and Preston’s ‘‘ Heat,” chapter vil. 
