252 Transactions of the South African Philosophical Society. 
The rise of temperature during the day depends mainly upon 
radiation from the sun; the fall during the night depends mainly 
upon radiation from the earth. Leaving the latter for future dis- 
cussion, let us consider the course of the former as given in the 
daily and monthly averages. At the outset we detect the fact, 
differentiating Kimberley from most places in other countries, that 
the greatest and least values of the maximum temperature curve 
for Kimberley are nearly synchronous with the solstices. This 
suggests some possible simplification of the difficulties that other- 
wise might reasonably have been expected in the framing of a 
formula involving some direct function of the Declination. It is | 
a legitimate argument, ad priorz that 
y= cos Ze Be 
where y is the required daily average maximum temperature : 
A a constant defining the amplitude of the curve ; 
B the distance from the base line of reference ; 
Z the sun’s zenith distance. 
Applying the equation, as a test, to the Kimberley maximum 
values, we find— 
y = 79 cos Z + 14 
a very good approximation to the observed facts—much better in 
every way than the simple sine curve. 
The philosophy of this formula is evidently based upon the law 
that the quantity of heat fallmg upon any given surface for a given 
time will vary as the cosine of the inclination of the incident rays to 
the normal. But there is a factor, not to be neglected, arising out of 
the eccentricity of the earth’s orbit. The sun’s distance changes, 
being greatest early in July and least in January, and the amount of 
solar heat intercepted by the earth’s full disk is less or greater 
accordingly. The sun’s apparent area varies inversely as the square 
of its distance ; the solar heat and light received also vary inversely 
as the square of the same distance; the quantity of heat received, 
then, at any time will be in proportion to the sun’s apparent area. 
This last, multiplied by some suitable constant, we shall for the 
present call the heat coefficient, and denote by S*. The formula 
therefore takes the amended form— 
y = AS? cos Z + B,* 
* Compare L. W. Meech, ‘‘On the relative intensity of the Heat and Light of 
the Sun upon different latitudes of the earth” (Smithsonian Contributions to 
Knowledge). He argues thus :— 
