
PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 201 
For the other thermometers, we have only to make a and 0 successively = 0, and 
substitute 4 and 2 for the depths, which give 
4{3 6+c} for No. 2. 
kc for No. 3. 
And the correction for No. 4 will be exclusively that derived from the observation 
of the thermometer in air T, and has for its argument 
SUE tae chen ien Met rakes Riel att AR yis-poen ia) CPAs) 
I should have observed, that, in order to ascertain that these formulee repre- 
sented the state of the instruments with sufficient accuracy, I first calculated how 
nearly the mean temperature of the whole column of each thermometer must be 
known, in order to entail no greater error than that of the reading, say of -01 de- 
gree. This, in the case of the deepest (26 feet) thermometer, with the widest bore, 
amounts to 1° of temperature, and in the three-feet thermometer to 3°. 
For the second or Air Temperature correction, the quantity of alcohol to be 
expanded, depends on the height at which the liquid stands in the tube, and the 
amount of expansion on the temperature to which it is subjected. 
Let us suppose, that in any thermometer the degree of temperature is known 
at which the surface of the column would just contract below the level of the 
soil. The number of degrees above this, which the thermometer at any time 
marks, points out the quantity to be corrected for expansion. If this correction 
is also to be applied to a part of the tube 9 inches lower, we have only to start 
from a degree of the scale corresponding to that point instead of to the surface. 
The number of degrees for which it is to be corrected, is the excess of the tem- 
perature of the air above that of the bulb, or T—Z,, ¢, denoting the temperature 
shewn by the nv“. thermometer in an ascending order. Table III. in page 198, gives 
the point on the scale of each thermometer, corresponding to a position 9 inches 
below the level of the soil; let that point be /,, /,, 7,, 7,, for each thermometer in 
| succession, then the number of degrees of temperature to be corrected for, will be 
Z—7., T—1,, &c. 
Thus, both the corrections required to reduce the observed readings amount 
| to finding by a table, the increased (or diminished) length of a given column of al- 
_ cohol (measured in degrees), for a given excess (or defect) of temperature, assigned 
| in degrees. Such a table I have constructed, and I have thought it advisable to 
_ employ the correct value of the expansion of alcohol at atmospheric tempera- 
| tures, instead of its mean amount between the freezing and boiling points. This 
latter quantity as given by Daron, and commonly employed, is ‘11 of the volume, 
from 32° to 212°, or 000611 for 1° Fahr. Now, it appears from Muncxe’s elabo- 
| rate experiments, that alcohol, of density -808, expands at common atmospheric 
| temperatures (viz. between 0° and 20° cent.), almost precisely -001 of its volume 
VOL. XVI. PART II. 3E 
