830 
:me. w, hopkixs’s expeebiextal eeseaeches 
and the temperature at the depth of fifty miles would be nearly 
=T+4400° 
Let us now conceive the 1000 feet of sedimentaiy mass of lower conductive power to be 
deposited upon the unstratified mass. The escape of the heat would at fii’st be impeded 
till the temperature of the bottom of the sedimentary mass should exceed the former tem- 
perature (T-l-16°) at the depth of 1000 feet, by a quantity which would compensate for 
the lower conductive power of the sedimentaiy portion. This would require the rate of 
increase of temperature in descending through this mass to be three times as gi'eat as in 
the unstratified mass, since the conductive power of the former is here assumed to be 
one-third of that of the latter. Thus, when the increase in descending 1000 feet should 
become 48° instead of 16°, the quantity of heat conducted through the upper stratum 
would be equal to that conducted to it through the lower mass, and the temperatui’es 
would again be stationary ; but the rate of increase of temperature in the sedimentary 
mass would be three times as great as in the unstratified mass either beneath the sedi- 
mentary portion, or in the surrounding region beyond its boundaries. This is the result 
which our general formula applied to this case immediately afibrds. 
In this explanation it has been assumed that the quantity of heat conducted through 
the sedimentary mass to the surface would be as great as that conducted to the suiiace 
immediately by the unstratified and more highly conductive mass. That this would be 
very approximately true is easily shoAvn. The quantity of heat conducted thi’ough the 
lower and unstratified mass, of which we have assumed the thickness to be fifty miles, 
will depend on the difference of temperatures at its lower and upper surfaces. Now if the 
sedimentary mass did not exist, the temperature of the upper sui’face of the imstratified 
mass would =T° ; and when it did exist, the temperature of the upper siuTace of the 
unstratified mass immediately below the sedimentary mass would =T+48° when the 
temperature of the Avhole should have become steady, as aboA'e explained. Hence the 
quantity of heat conducted through the lower mass without the sedimentary bed, aatII 
be, to that conducted through it with the sedimentary bed, in the ratio of 4400° — T° to 
4400° — (T°-)-48°), which is very nearly a ratio of equality. 
18. This numerical example may also enable us to explain A'ery simply the amoimt of 
lateral conduction. The temperature at the depth of 1000 feet at C would be nearly, as 
we have seen, T°-l-48°; while at the same depth beyond A and B, it AA'ould beT°+16°, 
the rate of increase there in descending being, by hypothesis, only one-thfid of that 
rate at C. Consequently the decrease of temperature in the horizontal distance CB, 
which we have supposed to be some 100 miles, would be about 32°; Avhile the decrease 
for half the same distance (50 miles) along the vertical line through C, would be about 
4300°. These two numbers enable us to judge how A'ery small must be the lateral con- 
duction of heat, in a case like that here considered, in comparison AAvtli the v ertical con- 
duction, and not only at the centre C of the area occupied by the stratum of smaller 
conductivity, but also throughout all the central portion of that area. 
