
PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 199 
overlooked by all observers previous to himself and M. Araco. It seems that 
M. Araco ascertains the expansion of the buried column of spirit by sinking, 
alongside of each thermometer, a stem similar to its own, having a scale above 
ground, but no bulb: the variations of bulk of the contained spirit being thus di- 
rectly shewn are eliminable from the readings of the adjacent thermometer. 
As far as regards the correction due to the portion of the stem buried in the earth, 
this mode of correction is ingenious and satisfactory ; but, when the ‘tubes are 
capillary, the reduction is so small that it may readily be obtained otherwise, with 
sufficient accuracy. It does not, however, apply to the portion of the scale above 
ground, since the quantity of alcohol, so exposed, varies with the degree shewn 
| by the thermometer. And this correction, as has been said, is, in our observations, 
the more important of the two. The method which I propose to employ is the 
| following :— 
| The distribution of the thermometers, in geometrical progression, enables us 
to employ the temperatures indicated by the thermometers, Nos. 2, 3, 
ae and 4, for the correction of the reading of No. 1 (that is, to reduce the 
temperature of the column ab to the temperature of the bulb); the 
“ temperature of Nos. 3 and 4 to correct No. 2; and of No. 4 to cor- 
rect No. 3. It was matter of consideration (1.), how this might be 
most correctly done; and (2.), to select a formula of sufficient (not 
superfiuous) accuracy, and adapted to calculation. 
The mode of doing this was partly arbitrary, and justified by ap- 
plication to cases where the variation of temperature in the stems was 
a maximum selected from the journals of observation. Thus, the 
depth of the successive thermometers being— 
0, a ; 2a 3 224 . 23a . ec. 
The intervals of depth are— 
a a 2a 22a Se. 
And the product of the temperature and depth must lie between 
two series, one of which supposes the temperature of any interval 
equal to the temperature of the thermometer at its superior limit, the 
other supposes the mean temperature equal to that at its inferior limit. 
It is evident that the truth must lie between these suppositions, or 
that denoting by T, the superficial temperature ; and ¢, ¢,, 4, the in- 
dications of each thermometer successively in descending, we must 
| have the product of the temperature and depth between the values of the two 
| series, 
Tat+t,a+2t,a+2°t,a 
| and ; t,a+ t,@+2 t,a+ 2%t,a 
| Farther, it will be nearer the latter result than the former, since the variation of 
_ temperature diminishes as we descend. 
