436 PROFESSOR EVERETT ON A METHOD OF REDUCING 
The processes hitherto described are applicable not only to underground tem- 
peratures, but also to open-air temperatures, and, in fact, to any element that 
varies in a regular manner. 
It remains to show how the results which we have obtained can be applied 
for determining the conductivity of the soil. The mode of procedure will be 
exactly the same as that adopted in the calculations for Professor THomson. 
The conducting power of the soil may be inferred either from the diminution 
in the values of P, and P, as we descend in the soil, or from the diminution of 
E, and E,. In other words, it may be inferred either from diminution of ampli- 
tude, or from retardation of phase. 
Let x denote the difference in depth of any two of the thermometers; let 
a. E, denote the retardation of phase, or the excess of the value of E,, for the 
upper of the two thermometers above its value for the lower, E, being expressed 
not in degrees and minutes, but in circular measure; and let a . log, P,, denote the 
diminution of the Napierian logarithm of the amplitude, or the excess of log, P, 
for the upper thermometer above log, P, for the lower; the ratio of %, the 
conductivity of the soil, to ¢, the capacity of the soil, for heat, may then be deter- 
mined by either of the equations 
A.E, [nee A.loge P,_ [nae 
“@ NTE a Nak 

The manner in which these equations are deduced from the differential equa- 
tion for the flow of heat through the soil, 
dv_k dv 
dic. da” 
will be stated in a note at the end of this paper. At present we proceed to apply 
the equations to the numerical results above obtained. 
The values of E, and E, in circular measure, and of log, P, and log, P;, are as 
under :— 











Teta | eee By | 
3 feet thermometer 1:95 — ‘69 4:20 + ‘81 
6 feet % 1:56 a 1:15 3°85 + 39 
12 feet “ “84 — 2°25 3:15 — ‘92 
24 feet Ln — 47 =3'8l 1:76 — 2°98 
By comparing the thermometers two and two in every possible combination, 
the following results are oviained :— 

