FOR THE MEAN TEMPERATURE OF A STRATUM OF SOIL. 27 



The annual term in the expression for the temperature at the depth of 12 feet in 

 the same locality, as derived from direct observation, is — 



2-31 siii(^+l79n5') 



Hence the annual term in the expression for the mean temperature of the first 



24 feet will be — 



2-31 X 1-08 sin {t + 179° 15' + 35° 42') 



= 2-50 sin (i;+ 214° 57'). 



14. To correct for difference between temperature of bulb and that of stem, 

 the following method may be adopted : — 



Let the observed temperatures be represented by the expression 

 V = A(, + Pj cos < + Qi sin t + Pg cos 2t + Qg sin 2t, 

 and the mean temperature of the stem by the expression 



v=-aQ+p^ cos t + q^ sin l + 'P2 cos2^ + g2 sin 2^. 

 Then if r denote the ratio of the capacity of the stem to that of the bulb, and U 

 the corrected value of V, 



we have U + rt;=(l + r) V, or U = V + r (V-i;). 



Hence the correction for A is .... 7(Ao-ao) 



Pi is ... . r(Pj-pi) 



Qiis . . . • ''(Q,-gi) 

 and so on for the other terms. 



A different mode of correction is described in Principal Forbes's paper, " Ac- 

 count of some Experiments on the Temperature of the Earth," &c.. Trans. Roy. 

 Soc. Edin., Vol. XVI. Part II. 



15. For the theory of underground conduction, and the use of harmonic 

 functions in connection therewith, reference may be made to two papers on 

 " Underground Temperature," by Professor W. Thomson and the Author, 

 Trans. Roy. Soc. Edin. ,Vol. XXII. Part II. (April 1860). 



