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

Rh 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 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. Rh