314 T'ransactions.—Geology. 
in November, 1857. Оп plotting a section of the lower terraces, from the 
summit of the Hawkdun Mountains to Alexandra, I found the curve approach 
that of a conienl section, excepting at that point below the mountains where 
the ford, instead of the terrace, had been given on the maps by the surveyors. 
This led me to surmise that—in the hollowing out or moulding, as may be, of 
a valley 45 miles in length, and 5,500 feet in depth from the apex of the 
culminating mountains to the lower river bed at its exit from the valley—there 
must be a law, a law that only the most obdurate materials can oppose. Thus 
the Manuherikia, in its course, crosses two great bars of schist rocks situated 
below the junctions of the Ida and Spottis, yet these bars appear to have had 
but a moderate influence in modifying the curve of the valley bed, as shown 
in the diagrammatic section.* 
The power of water alone could 
never have done this.. Then, 
if it were with the aid of 
moving ice, at first blush I 
anticipated that the conic sec- 
tion would be a parabola, for 
here we would have the gravity 
of the ice tending downwards perpendicularly, with the flow of water tending 
horizontally. 
Comparing, therefore, the curve of the Manuherikia Valley, as shown by 
actual survey, with the parabolic one, we have va the length of the valley, 
AB its rise from the exit to the source of its waters, 
and ve the distance of a point from v. Then vA 
and vc abscisses, and AB an ordinate being given, to 
find cp, the other ordinate; +. ./va : V VOR 
AB: CD 7. 4/262, 800: /35400 :: 5598:2054. 
The other ordinates having been calculated in 
the same manner, as given below, afford us a comparison with the results of 
actual survey :— 
Bv PARABOLA. By Survey. DIFFERENCES. 
At source... e. (a) 0000 MET 0000 sd 000 
( (b) 2054 e 625 1571 
Intermediate points - (co) 3272 iin 4507 1035 
| (9) 41727 ...- — 4987 815 
* Eleven sectional plans were appended to this paper, to illustrate the curves of the 
different valleys described. But as the same principle is repeated in each case, and the 
data for the construction of the valley curves are given in the text, the above general 
diagram has been substituted, in which S is source of river ; SE—length of valley ; A— 
parabolic curve ; B—the elliptic, and C—the actual curve from survey ; a 
intermediate points. The difference between the two curves 
exaggerated for the sake of clearness. —Ep. 
b, c—the 
3 and C has been slightly 
