1895-96.] Dr J. Halm on the Temperature of the Air. 273 
solar radiation, so that the change of the temperature of the soil 
during the instant dz , caused by the sun’s real radiation, may be 
represented by a formula — 
dt' — { — K cos <h cos S sin £ + dK. sin (2£ - u)}dz, 
where K is again the above-mentioned solar constant, £ the sun’s 
hour angle, dK. a quantity due to the influence of the daily change 
of clouds and moisture, and u the time of its maximum (cZK positive) 
or minimum {dK. negative). On introducing this term into our 
standard equations, we obtain — 
1 
I 
V 
dz v ' J 
whence we derive the following integral : — 
dt' 
— = - hit' - u) - hif - 1) - K cos <f> cos 8 sin £ -f cHv sin (2£ - u) 
t = t 0 + a cos cos S cos (£ - v) - da cos (2£ - u - w )" 
) da = cZK 
a — K- 
Jl +VP + W 
\/l6 + 28h 2 + id 
1 - h 2 4 
tgv== ~3hT’ tgw = ~ 
Id 
6h 
This is at last our final equation for representing the daily 
change of the air temperature from sunrise to sunset. We notice 
that there is no arbitrary constant, that every parameter bears its 
distinct theoretical significance, and can be determined directly 
from the observations. I need scarcely say that only stations at a 
distance from the sea can be considered, and even then we have to 
exclude in northern latitudes the extreme winter months, when 
the snow and the frozen water on and within the soil alter the 
physical conditions of our problem altogether. 
Let us first consider the constant of radiation h. It can be 
derived from the observations by means of the angle v. We 
have — 
h = - | tang v + ^ tang 2 v + 1 , 
h V 4: 
and by this equation I have derived from five trustworthy stations, 
for the eight months from March to October, the following values : 
0-363, 0-363, 0*370, 0-378, 0*366, 0*376, 0*385, 0*388 ; Mean:0-374, 
