2i6 The Aiucrican Geologist. ^p--"- i^O'^- 
altitude. The mean sine of the altitude of the sun in latitude 
45° 30' N. the middle of the zone under consideration from the 
vernal to the autumnal equinox is approximately 0.919 and 
from the autumnal equinox to the vernal equinox it is ap- 
proximately 0.492. The heat incident upon a plane perpendic- 
ular to the sun's rays is sufficient to melt a layer of ice i .92 feet 
thick per day. Upon a plane over which the mean sine of the 
sun's altitude is 0.919, the amount of heat energy received in 
the 186 days from the vernal equinox to the autumnal equinox 
would be sufficient to melt a layer of ice 328 feet thick (1.92 x 
186.x 0.919 := 328). Similarly for the plane over which the 
mean sine of the sun's altitude is 0.492, the quantity of energy 
in the form of heat received in 179 days from the autumnal 
equinox to the vernal equinox would be sufficient to melt a 
layer of ice or snow 168 feet thick (1.92 x 179 x 0.492 = 
168). If this heat were uniformly distributed over the zone of 
the earth's surface lying between latitudes 41° and 50° N. it 
would be sufficient in amount to melt layers of ice approximate- 
ly 80 feet and 41 feet respectively. Assuming that the rate 
at which heat is received from the autumnal equinox to the 
vernal equinox is sufficient to keep the temperature up to the 
melting-point, the heat received in excess of that during the 
period from the vernal to the autumnal equinox might be taken 
as an approximate measure of the layer of ice melted during 
that period of the year, i.e. it would be sufficient to melt a lay- 
er 39 feet thick (80 — 41 = 39). This would still have to be 
decreased for the atmospheric absorption, for the loss by radi- 
ation, and for the low absorbing power of the ice surface : so 
that the actual melting would be much less than the thickness 
given above." 
But if we assume that the melting proceeded at one-third 
this possible rate, we should then have at least 500 cubic miles 
of water set free in the middle Missouri valley each year be- 
tween the vernal and autumnal equinoxes, all of which would 
have to pass through the constricted gorge in the lower part 
of the valley. Considering the decayed condition of the ice 
during the late stages of melting and the probable thin covering 
of accumulated dirt over large areas near the front, this rate 
would appear altogether probable. Supposing this gorge to be 
only two miles wide, as is really the case, and to be filled with 
