1900.] LOWELL—MARS ON GLACIAL EPOCHS. 657 
a, and 4, the respective maximum and minimum for the northern 
cap. 
x the increased ratio of deposition, where « > 1: then 
a — 6 equals the amount of the southern cap melted during the 
summer. 
a, — 6, equals the same for the northern cap. 
xa — (a — 4) will then represent the size of the southern cap at its 
new minimum, and 
xa — (a — db) A ie Bd 
ln b 
mum to the new. The ratio of the old maximun to the new is 
Xa 
ee DEES 
a 
will be the ratio of the old mini- 
(e—1)at+s 
b 
Now > x, for if it were equal to it we should have 
@—i1)@¢+6= 6x; 
whence (x — 1) a = (x —1) dand since a> 6 the first member 
would exceed the second. 
Thus the minimum would increase at a faster rate than the maxi- 
mum with increased deposit. 
For the northern cap we have similarly 
(*#—1)44+4 
by 
The similarity of the expressions shows that the same result would 
hold here too. 
But furthermore we have for the ratio of the maximum—minimum 
ratio of increase in the two caps respectively : 
(*+—I1)a4+ 46 to (x«—1)a,+ 4, 
ona b, 
The first member exceeds the second, for 
(Ce tae a Pare Nad rr a) 
b 
Since 
