THomson.—Glacial Action in Otago. 331 
unconforming levels at different parts of their courses. This curve of deposit, 
as I may call it, was first tested by the properties of the ellipse, but found not 
to accord ; it was then tested by the parabola, with the following results :— 
Bv PARABOLA. By SURVEY. DIFFERENCES, 
At Outram Bridge з 00:0 0-0 
13:23 14:4 lI 
At intermediate points... ue ue de m 2 
At Adams' Accommodation House... 30:0 30:0 0:0 
Thus, the curve of deposit may be said to be identical with the parabola, 
varying from it, in a course of eleven miles, on an average of six-tenths of a 
foot. The theoretic course of a cannon ball is in a curve of the parabola, 
subject, as it is, to unequal resistance and deflection of the atmosphere and its 
currents ; it, in practice, does not excel water in its mathematical truth, as 
here displayed. 
Here, then, are two laws proved in the Taieri “tailings,” as the gold digger 
would term them. The law of scooping out is as the ellipse ; that of spreading 
out as the parabola. And what practical objects do these lead us to. Many, 
no doubt, will develop themselves in various minds ; one or two I may shortly 
state. 
The first is one of geological interest. When the plains were being covered 
by detritus to the parabolic curve, glacial action was, of necessity, in full 
force. The valleys were filled with moving ice and turbid water, grinding 
against the sides and bottom of the earth. At the time this was in process 
the torrents issuing on the plains would have no more certain beds than the 
sluice waters of the miner, but would diverge to and flow over 180° of the 
horizon, depositing its “sludge” where there was readiest outlet or lowest 
level. 
But as the cycle pursued its course, so, with the increase of temperature, 
the ice of the glaciers would melt or retreat in diminished bulk to the tops of 
the valleys; then the depositing power would virtually cease, and the opposite, 
or eroding action, by the torrents finding for themselves a confined channel, 
would take place. Thus we arrive at the present era. As it is with great, 
so it is with small, things. Мо sooner are the miners’ claims worked out than 
deposits, spread out in the parabolic curve, cease, and the clear water, now 
unused, seeks for itself a confined channel in the elliptic curve. 
The other question may be called an engineering one. If detritus is 
deposited as the parabola, and scooped out as the ellipse, then we may conclude 
that such rivers as the Waitaki, on whose outlet the sea is encroaching, will 
more and more adhere to a confined channel—the elliptic curve following a 
lower course than the parabola; but that such rivers as the Waimakariri, 
