27 
1 879.] Relations to that of the Glacial Epoch . 
of necessity increase in thickness year by year, till the rate 
of discharge became equal to that of growth. We have 
just seen that it would require a thickness of not less 
than 1400 feet at the very edge of the cap to make the 
two rates equal, even although the ice was moving outwards 
with a velocity of a quarter of a mile per annum, a rate 
of motion greater than that of an Alpine glacier ; and, on 
the other hand, to produce such a rate of motion as this, a 
thickness in the interior enormously greater than 1400 feet 
is required. If, from an increase in the snowfall, or from a 
decrease in the quantity of snow and ice melted, or from 
both combined, the annual amount of ice requiring to be 
discharged were doubled, the velocity remaining the 
same, the thickness of the sheet would ultimately be- 
come doubled also. Or, if the thickness of the sheet 
remained the same the velocity would be doubled. The 
adtual result in such a case, however, would be that a 
restoration of equilibrium between supply and discharge 
would take place, by an increase both of thickness and 
velocity. As the quarter of a mile per annum of velocity 
would only be sufficient to discharge one-half the amount of 
ice being formed, the sheet would increase in thickness year 
by year. But this increase in thickness would produce an 
increase of velocity, and the increase both in thickness and 
velocity of motion would continue till the quantity of ice 
discharged would be equal to the 12 inches over the whole 
area, instead of the 6 inches as before. Equilibrium being 
now established, no further increase would take place either 
in the thickness of the sheet or in the velocity of its motion. 
If, on the contrary, the amount of ice being formed on the 
Antarctic continent were to become less than at present, 
both the thickness of the sheet and the velocity of its 
motion would become less. 
The following conclusions have now been established : — 
1. The Antarctic ice-sheet must be thickest at the centre 
of dispersion and thinnest at the edge. 
2. The rate of motion of the ice must be least at the 
centre of dispersion and greatest at the edge. 
3. The mean thickness of the edge of the sheet, other 
things being equal, must be proportional to the area 
of the sheet, and inversely as the rate at which the 
edge is moving outwards. 
