256 Transactions of the South African Philosophical Society. 
are all nearly satisfied when x= 28:1. Whence it follows that the 
three points lie upon a rectangular hyperbola,* one of .whose 
asymptotes is the line of initial temperatures, and the other the line 
x = 28:1: That is upon the rectangular hyperbola— 
t(T — 28-1) = 170-4, 
where T is the initial temperature, and ¢ the rise of temperature. 
It is curious that the numerical value of the equation is just about 
the highest temperature likely to be registered at Kimberley by a 
black bulb 7m vacuo on a fairly clear day at the end of December. 
So far as can be ascertained from the as yet hmited materials, the 
corresponding values for other months, lying between the solstices 
and equinoxes, are points upon the same hyperbola. Yet it would 
be exaggerating the evidence to consider the asymptotic nature of our 
temperature changes demonstrated; because, for one thing, the 
Kenilworth hourly temperatures are read only at the whole hours, 
and thus it is not easy always to select periods in which an average 
rise of temperature can be estimated, for a decrease of zenith distance 
by 12 degrees, from somewhere near 65 degrees. 
Again, the equation is not generally true for temperatures falling 
outside the Kimberley limits. For imagine a still more elevated table- 
land whereon we might happen upon an initial temperature T = 28° 1 
for a solar zenith distance of about 65 degrees. This would clearly 
make ¢ infinite, which is as clearly impossible. . Moreover, the 
equation would give a value of t—small it is true—for the largest 
assigned value of T short of infinity, which is as clearly unthinkable. 
Perhaps the explanation is that a similar formula, but with different 
constants, would apply elsewhere, within the observed limits of 
temperature, to furnish—if no more—a very useful mnemonical aid. 
At Cordoba, for example, which lies in 8. Lat. 31° 24’, and very 
nearly on the central meridian of South America, but otherwise 
having no great advantages of geographical position, we get the 
following increases of temperature for decreases of zenith distance by 
12 degrees from somewhere near 65 degrees : 
IM aitcliss stole st awenel ee to, 122-2 Ce irom ls2-6OiC: 
SULTON ey ote ne aed 4°36 ay eons 
Decemiieee 2 occas 2:13 gr we OEY 
Forming the equations as hefore, and solving by the method of 
least squares, we deduce the very accurate equation, in Centigrade 
degrees— 
i(T oo 0-943) = 44°154, 
* C. Smith, Conic Sections, Art. 151. Casey, Treatise on the Analytical Geometry 
of the Point, Line, Circle, and Conic Sections, Sec. Ed., p. 269. 
