200 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 
Until after May 1838, no superficial thermometer (or one in the uppermost 
stratum of soil) was used. There was simply a thermometer suspended beside 
the scales in the box, to indicate the temperature of the part of the column ex- 
posed to the air. Fortunately, however, the correction for the temperature of the 
first interval a, or 3 feet, is very small indeed. The extreme excess of tem- 
perature of the air in the box above the highest thermometer, or (T—¢, during 
1837, was 20° Fahr. In the most capacious of the tubes employed, supposing that 
the temperature of 20° had been applied through the whole depth of 3 feet, an 
expansion would have been produced, which would have raised the alcohol on the 
scale of that thermometer by 0°:07; but the expansion could not possibly amount 
to half of this, seeing that the mean temperature of the 3 feet of soil would more 
nearly approach to that of the inferior limit of it, than to that of the air in contact 
with its surface. We can hardly err -01 (a quantity in this particular case much 
less than the errors of reading), by assuming that { of the column of 3 feet had 
the temperature of the air, and the remainder that of the thermometer bulb itself.* 
In both the other three-feet thermometers, the error, owing to the smaller capa- 
city of the three-feet capillary tube, would be but about half as great. 
Now, by reasoning by the method of limits as above, and applying the above 
correction to the upper 9 inches of all the tubes, I find the following formula to 
be a more than sufficient approximation in every case. For the deepest thermo- 
meter, No. 1, whose temperature is ¢, 
= Temperatures x depths 
depth 
making 3-2 feet = unit of depth, 
Mean temperature of stem = 
Lt, +2, 447,487 
ee ore eee 

mean temperature 
And as the reduction of the temperature of the stem to that of the bulb depends 
on the excess of the former above the latter, we have 
Mean excess of temperature = aid elle 1) ee) =) File A) (2.) 
Farther, to adapt this to calculation, let the successive intervals of tempera- 
ture of the series of thermometers be taken, and make 
f,—f,=a 
f,—t,=6 
t,—t,=c 
the above expression becomes 
3{(a+6+c¢)+2(a+b)+4a} 
=3{7a+36+c} for thermometer No.1, . . (8.) 
* The application of this correction becomes exceedingly easy, by considering the correction for air 
temperature to apply, not only to the exposed part of the tube, but also to the first 9 inches of the buried 
stem, 

