I 



200 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 



Until after 5Iay 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 tempei-aturc 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 

 1 837, 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 assmning 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 t^ 



Mean temperature of stem = lTempe^^pj<depths 

 making 3 '2 feet = unit of depth, 



mean temperature = — * ^-g — ^ ' (1.) 



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 - (<.>-^) + 2(<o-<i) + 4(<,-<.) _ _ (2.) 



Farther, to adapt this to calculation, let the successive intervals of tempera- 

 ture of the series of thermometers be taken, and make 



the above expression becomes 



i{(« + 6 + c) + 2(rt + 6) + 4a} 

 = J {7 « + 3 6 + c} for thermometer No. 1, . . (3.) 



* 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 tlie first 9 inches of the liui'ied 

 stem. 



