266 
Proceedings of Royal Society of Edinburgh . [sess. 
dd, dv denoting the changes of heat in equal elements of volume 
of the surface and the mass of air at temperature t, c x and c 2 being 
the specific heat of the soil and the atmosphere for unit of weight. 
Our differential equations for the changes of temperature in each 
element will therefore he : 
daft' - u) - daft' - t) 
daft - t ') , 
- 
da x being the quantity of heat absorbed, or radiated, by an element 
of volume of the earth’s surface from, or to, each of the two masses 
of air, the difference of temperature being 1° ; da 2 the same for an 
equal element of volume of the air. Applying the above-men- 
tioned relation : 
da x = —da 2 and putting 
P‘2 
Pi dV <r ’ 
we obtain 
dt' 
Cl dfz~ 
dt 
C ' 2 dz 
- ait' - u) - a(t' - t ) 
— a{t — t') 
1 
i 
I 
}• 
I 
I 
J 
which may be considered as the fundamental equations of our 
problem. 
blow, a considerable simplification of these equations arises from 
the curious fact that the average values of the specific heat of the 
ordinary soil and the atmosphere are practically the same. The 
well-known value for the air by Regnault is 0238, which has, of 
course, to be slightly enlarged on account of the presence of 
aqueous vapour in the atmosphere. On the other hand, very 
careful observations by Pfaundler have proved that, for the 
mineral part of the earth’s crust, whatever be its chemical con- 
stitution, we may assume the well-determined value 0*20. But, 
in most cases, a certain amount of humus will increase this number, 
and he has found that, for average conditions, the value of 0*25 
to 0*28 will be the proper quantity, which is indeed very close to 
the value for the air under ordinary circumstances. No doubt the 
amount of water in the soil will still influence its thermal capacity ; 
