PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 201 



For the other thermometers, we have only to make a and h successively = 0, and 

 suhstitute 4 and 2 for the depths, which give 



\{2,b + c} for No. 2. 



\ c 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 



HT-^J (4.) 



I should have observed, that, in order to ascertain that these formulae 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 eiTor than that of the reading, say of 'Ol 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-^„, 4 denoting the temperature 

 shewn by the ?i*. 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 l^, l^, l^, l^,, for each thermometer in 

 succession, then the number of degrees of temperature to be corrected for, wiU be 

 T-^,, T-l„_, &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 Dalton, and commonly employed, is -11 of the volume, 

 from 32° to 212°, or 000611 for 1° Fahr. Now, it appears from Muncke'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. 3 E 



