PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 



199 



1. 2. 3. 4. 



overlooked by all observers previous to himself and M. Arago. It seems that 

 M. Aeago ascertains the expansion of the buried column of spirit by sinMng, 

 alongside of each thermometer, a stem similar to its o^ti, 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 bm-ied in the earth, 

 this mode of correction is iugenious 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 shewTi 

 by the thermometer. And this correction, as has been said, is, in om* obsei-vations, 

 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, 8, 

 and 4, for the correction of the reading of No. 1 (that is, to reduce the 

 temperature of the column a 6 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 

 superfluous) 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 , 2 a , 2"- a , 2=0 , Sfc. 



The intervals of depth are — 



a a 2 a 2= o §-c. 



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 Umit. 

 It is evident that the truth must lie between these suppositions, or 

 that denoting by T, the superficial temperature ; and t^, t^, t, ti, 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, 



T- a + t^a + 2t,a + 2" t„a 

 and t^a + t^a + 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. 







