72 REPORT—1840. 
been instituted at Bonn by Prof. Bischoff*, and at Freiburg in 
Saxony by Prof. Reicht; but of these, so far as I am aware, 
only imperfect notices have yet appeared. 
99. The epochal retardations for the annual curves at the depth 
of a few feet follow, generally speaking, asimple law, for they 
are propagated uniformly downwards with a velocity which is 
easily connected with the constants proper to the soil determined 
from the range at two given depths, as justexplained{. It must 
not be concluded, however, that the epochs of earth-temperature 
at the surface coincide with those of air-temperature in the ad- 
joining stratum. The difference of epoch may be obtained in 
terms of the conductivity and superficial characters of the solid 
stratum§. But the complete expression for the epoch at any 
depth in terms of the dates of maximum and minimum at some 
other depth, and of the constants of conductivity and surface, 
derived from two observed ranges, is so complex, that so far as 
I know, no attempt has been made to verify M. Poisson’s for- 
mule except in a single example by himself, taken from M. 
Arago’s observations]|. 
100. It is a matter of some practical difficulty to find the 
precise period of maximum and minimum temperature from ob- 
servations at or near the surface, on account of the accidental 
fluctuations which occur, especially near the time of minimum, 
and which, even at a depth of three feet, produce in this climate 
an uncertainty sometimes of a week or more. 
101. I have already stated, in the preceding table, the results 
* Warmelehre von G. Bischoff, 8vo, 1837, pp. 100, 392,507. The observa- 
tions were not made with long-tubed thermometers having their scales above 
ground, but by sinking bottles of water in-wooden tubes to a certain depth, 
drawing them up rapidly, and observing their temperature. The observations 
were carried to a depth of 36 feet. 
+ Bischoff, ibid, p. 512. 
t Poisson, p. 432. If X be the range at a depth x, and X! at depth a!, and 
a the retardation of epoch due to the increased depth from a to a’, the following 
relation holds, 
X'=Xer™ r 
m being a constant and e the base of Napier’s logarithms. 
Ibid. 
iP. 502-3. The coincidence is not so remarkable as a cursory inspection 
would suggest; there are not four coincidences but only two—the data and 
quesita being reversed. The coincidence, such as it is, perhaps proves too much ; 
for M. Arago’s observations are not corrected for the temperature of the stem 
(‘afin de pouvoir faire usage des observations non corrigées que M. Arago 
m’a communiquées, je supposerai que ces corrections soient peu considérables, ” 
p- 500); it is certain, however, that for the larger thermometers, where the 
range is /east, and the correction greatest, the epochs must be (perhaps most 
materially) affected. The scientific world anxiously looks for the extended and 
reduced observations of M, Arago. 
