1895 - 96 .] Dr J. Halm on the Temperature of the Air . 
269 
author deduces from the observations of Langley * a formula, 
founded on the ingenious mathematical researches of Clausius , 
giving the total amount of solar radiation which enters the earth’s 
surface at any altitude of the sun. This formula may be repre- 
sented in general terms by the equation : 
I = A cos Z - b , 
where I is the total radiation arriving at the surface, A and 5 
calorimetric constants, and Z the zenith distance of the sun. 
Zenker's investigations being the best and most extensive known 
to me, I accepted his final formula for the following deductions : — 
We know that if a body be exposed to the radiation of a 
constant source of heat, there will be produced — theoretically after 
an infinite, but practically after a comparatively short time — a 
state of thermal equilibrium in the body, it receiving from the 
source exactly the same quantity of heat as it transfers in the same 
time to its neighbouring elements by radiation or conduction. 
After once having established this final state, there is no more 
change in the temperatures of the body and its neighbourhood as 
long as we assume the source of heat to be constant. If we, for 
instance, could suppose the sun, a short time after having risen, to 
remain strictly in a fixed position, we would see that shortly after 
that moment the soil as well as the lowest elements of the atmos- 
phere had assumed a constant temperature, to be maintained 
during the whole time during which the sun is fixed in this 
constant position. But now, let the sun’s altitude increase for 
an infinitely short space of time, then naturally the earth’s 
surface receives more radiation at the end of that time than at 
the beginning, and it is obvious that the increase of its tempera- 
ture must be proportional to the difference of solar radiation in the 
two positions. So, by adding this term to our former equations, 
we obtain 
df 
dz 
dt 
dz 
- hit ' -u)- h{t' - 1) + ] 
- h(t - t') j 
* Researches on Solar Heat and its Absorption by the Earth's Atmosphere . 
A Report of the Mount Whitney Expedition. 
