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XVIII.—On a Method of Reducing Observations of Underground Temperature, 
mith its Application to the Monthly Mean Temperatures of Underground 
Thermometers, at the Royal Edinburgh Observatory. By Joseru D. Evrrert, 
M.A., Professor of Mathematics, &c., in King’s College, Windsor, N.S., and 
late Secretary to the Meteorological Society of Scotland. 
(Read 30th April 1860.) 
A few years since I was engaged in the performance of some calculations under 
the direction of Professor W. Taomson of Glasgow, having reference to the obser- 
vations of underground temperature made at the Royal Edinburgh Observatory. 
In this paper I propose to describe a modification of Professor THomson’s method, 
which, while retaining a sufficient degree of accuracy, will be simple enough for 
general adoption. The objects proposed are— 
1st, To express the variations of temperature at a given depth in terms of the 
time of year. 
2d, To deduce the conducting power of the soil. 
In the calculations performed for Professor THomson, the temperatures at 32 
equal intervals in each year were required as the basis of calculations; and as 
the observations had been made only once a-week, it was requisite to interpolate, 
either by graphical projection (which was the method employed) or in some 
other way. 
A Report of the Royal Edinburgh Observatory having recently passed through 
my hands, containing the mean temperature of each of the underground ther- 
mometers for each month of each year during a period of seventeen years, I have 
adapted Professor THomson’s method to a computation from 12 (instead of 32) 
| points in the year, and have applied the method thus modified to the means on 
| the seventeen years’ observations. The present paper embodies the results, which 
| will be found to agree pretty closely with those obtained by the more elaborate 
method. The monthly mean temperatures printed in the Observatory Report, on 
the averages of which, for the seventeen years, the following results are based, 
are simply the arithmetical means of the weekly readings taken in each calendar 
month. 
For the sake of making the paper intelligible, it will be necessary to premise 
a few principles which are common to both methods. 
The form of expression to which the temperature of each thermometer is to 
be reduced, is 
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