62 



PROCEEDINGS OF THE AMERICAN ACADEMY 



The conductivity of iron, as determined by Forbes, varied from 

 .01337 at 0° C. to .00801 at 275° C. And the conductivity of sand- 

 stone, determined by burying thermometers from three to twenty-four 

 feet below the surface, was found to be .000G89. 



The conductivity which I found for glass, therefore, lies between 

 that of iron and that of sandstone. It also, like the conductivity of 

 iron, increases as the temperature decreases. It has not been deter- 

 mined how the conductivity of sandstone varies with the temperature. 



Conductivity of Sand. 



To determine the conductivity of sand I used the following method. 

 The sand is put in a thin metallic vessel ; inside of this is put an 

 exactly similar smaller metal vessel, which rests on the bottom of the 

 outer one. Thus the sand forms a layer, protected on each side by the 

 thin metal. These two vessels are entirely immersed in a larger vessel 

 containing a known volume of water. The interior of tlie inner ves- 

 sel is kept at a constant temperature (by means of steam). With a 

 thermometer we can find the temperature of the outside water every 

 minute, and thus construct a curve ; the abscissas being the times and 

 the ordinates the corresponding temperatures. In the next place, fill 

 the outside vessel with the same volume of water used in the preced- 

 ing experiment, heat it to a known temperature, and find the rate at 

 which it cools. For this purpose we construct a second curve, having 

 the times for abscissas and the temj^eratures for ordinates. Take any 

 ordinate t, of the first curve, and let d t^ ^ the gain of temperature in 

 time d T, then, if V= the volume of the water, d t^.V = the amount 

 of heat gained in time d T. Take the same ordinate <, of the second 

 curve, and let d t.^ =■ the loss of temperature in time d T, then 

 dt^. V = the loss of heat from the water, when the temperature is t, 

 in time d T. Hence the whole amount of heat that passes through 

 the layer of sand in time d T=: Q = d t^ . V-{- d t,^ . V. 



The formula for the quantity of heat that passes, in time T, through 

 a section of thickness x, and area A, is Q = K . A . — — 7\ In 



X 



the present case T= d T, and we have found the value for Q, 

 dt,.V-\-dt,.V—K.A. '-5^ d T; 



