Page:Philosophical Transactions of the Royal Society A - Volume 184.djvu/600

I. $\kappa _{t}=1.113-.00112t=1.113\left(1-.001t\right)$.

II. $\kappa _{t}=1.130-.00112t=1.130\left(1-.001t\right)$.

The mean value of these results gives

$\kappa _{t}=1.12\left(1-.001t\right)$.

Determination of Density and Value of $\left(sd\right)$, the Thermal Capacity of Unit Volume of Copper.

The density of the copper was found to be 8.907 at 0° $\mathrm {C}$. Taking this as 8.9, we may take the density of copper at $t$° $\mathrm {C}$, as given by $8.9\left(1-.000056t\right)$.

The specific heat of copper at $t$° $\mathrm {C}$. is given by Béde^[1] as $.0892+.000065t$. This result may be expressed as $.0892\left(1+.00073t\right)$, hence the value of $\left(sd\right)$ at $t$° $\mathrm {C}$. is

$8.9\left(1-.000056t\right)\times .0892\left(1+.00073t\right)$,

or

$.794\left(1+.000674t\right)$.

Value of $\kappa$, the Diffusivity of Copper, in Absolute C.G.S. Units.

From the results obtained above the value of $\kappa$ at $t$° $\mathrm {C}$ will be given by

$\kappa _{t}=\left(\kappa /sd\right)_{t}=1.12\left(1-.001t\right)\div .794\left(1+.000674t\right)$.

That is,

$\kappa _{t}=1.41\left(1-.001t\right)\left(1-.000674t\right)$,

or,

$\kappa _{t}=1.41\left(1-.0017t+.0000007t^{2}\right)$.

This result is probably represented with sufficient accuracy by the formula

$\kappa _{t}=1.41\left(1-.0017t\right)$.

It will be seen that the results of the experiments here described go to show that for both iron and copper the conductivity decreases with rise of temperature.

1. [Recent determinations of the specific heat of pure copper (probably identical with that used in these experiments) give the specific heat at 100° $\mathrm {C}$. as .0928. Béde's formula gives .0957, a value about 3 per cent. too high. The determinations here referred to were made by J. Joly, Esq, F.R.S., with his steam calorimeter, and were kindly communicated to me by Mr. James H. Gray, M.A., B.Sc., Glasgow University.—12.4.93.]