94 Transactions of the South African Philosophical Society. 
that, if the chimneys are to stand, the diurnal changes of wind-direc- 
tion cannot be due to an outflow beneath of air from a heated region 
and inflow to a cold. The following simple calculation (which may 
or may not be new) has some bearing on the problem :— 
Suppose the climatic and geographical conditions peculiar to 
Kimberley to prevail for the same latitude in a narrow zone com- 
pletely round the world; that is, let the temperatures and pressures 
throughout have the same maxima and mmima and the same daily 
variations. At any instant mark the twenty-four points at which 
the times are whole hours, and on each point imagine a cube of air, 
whose volume at 32° F. is 1,000 (in any small units), to be situated. 
By virtue of the expansions—supposed equal in all directions—due 
to the mean temperature at each point for the hour, the cubes will 
have expanded from the volumes at 32° F. to the volumes shown by 
column 2 in Table 20. For all temperatures below the mean these 
volumes may be regarded as contractions from the mean volume at 
mean temperature, and for all temperatures above the mean as 
corresponding expansions. Suppose the temperature and pressure 
to change, hour by hour, per sali, so that, for 74 degrees of arc on 
each side of the hour points, the temperatures and pressures are the 
same as that at the hours. Also let 2 of the cubes, at mean tem- 
perature, placed end to end, occupy each of the areas whose centre 
is at any hour. Column 3 shows the length of each base for the 
times indicated in column 1, column 4 the departure from the mean 
length, column 5 the base areas, and column 6 the departure from 
the mean area. 
Now, taking only statical conditions into account, of the total 
length of the bases (equal to 2x 244-8 units), 2 °*360 units will be 
pushed by expansion westward from the hot hemisphere into the 
cold; * and 2x ‘278 units eastward. The bases will cover 2 x 1255:1 
square units in the hot hemisphere, and 2x 1242-0 square units in 
the cold. Whence by comparing the whole pressures, in respect of 
the cubes of air in question, upon the bases in each hemisphere we 
have the mean pressures in the hot and cold hemispheres in the 
respective ratio of 1:00 to 1:02. But the mean barometric pressure 
in the hot hemisphere is 26°1337 inches, and in the cold hemisphere 
it is 26°153 inches, 7.e., in the ratio of 1:000 to 1:001. The result 
seems to show that in the given zone the hypothesis that the expan- 
sion is equal in all directions would require the transfer of more air 
into the cold hemisphere than barometric observations warrant. 
* Agreeing with the fact that the air-temperature begins to rise before sunrise. 
The most energetic expansion is in the direction of the primary barometric 
maximum, the least energetic expansion being towards the secondary maximum. 
