184 On Underground Temperature. [April, 
to, the geo-thermometer must have shown in the lower 
depths a temperature less than the true temperature of the 
rock of the earth’s crust existing at that depth. 
The reasons given above seem quite sufficient to account 
for the diminished rate of increase of temperature shown in 
the table ; and they would lead to the conclusion that in all 
observations made in bore-holes of a sufficient width to allow 
convedtive currents full play, the temperatures taken at the 
lower parts will — even with the geo-thermometer — be less 
than the true rock-temperature. The conclusion appears a 
legitimate one that the diminution in the rate of increase in 
a bore-hole, even when the convention currents are tempo- 
rarily shut off, does not necessarily imply that there is any 
such diminution of the rate in the body of the rock ; or, in 
other words, that the temperature curve within the rock may 
be a straight line, although that given by the geo-thermo- 
meter be concave to the axis of depths. It will also follow 
that the mean rate of increase for the whole depth within 
the rock will exceed that shown by the geo-thermometer. 
The mean increase, for instance, in the above table, between 
the temperature of the surface and that at 4042 feet, is 
i° R. for 129 feet, or i° F. for 5 7 feet ; and it is stated in the 
Association Report that, when the observations are corrected 
for pressure, the mean rate to 3390 feet is i° F. for 
51*5 English feet. This is about the usual average. We 
may therefore conclude that at Sperenberg the adtual rate 
of increase in the body of the rock is greater than this. 
The most important conclusion from the above is that, 
in spite of the decreasing rate shown at Sperenberg (and 
also at St. Louis, and perhaps other places), the old assump- 
tion may be corredt, that for such depths as have been 
reached the rate — if it could be truly observed, and setting 
aside local causes of disturbance — is probably a uniform 
rate, amounting to, or, as the above reasoning would lead us 
to infer, probably exceeding, T F. for 51 feet of descent. 
Are we, then, to conclude that this rate of increase obtains 
for all depths, however great ? If such be the case, as Sir 
William Thomson in his late Sedtional Address at the British 
Association (1876) sarcastically observed, “ by a simple 
effort of the geological calculus it has been estimated that 
i° per 30 metres gives iooo 0 per 30,000 metres, and 3333 0 
per 100 kilometres.” And since it has been considered that 
between the two last-named temperatures all — even the 
most refradtory — substances of the earth’s crust would 
melt ; therefore it has been concluded that at depths varying 
from 30 to 100 kilometres (or from about 20 to 60 miles) the 
temperatures are so great as to melt all known substances. 
