314 



Transactions. — Geology. 



in November, 1857. On plotting a section of the lower terraces, from the 

 summit of the Hawkclun Mountains to Alexandra, I found the curve approach 

 that of a conical 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 fiom 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 vi^ould 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 vc the distance of a point from v. Then VA 

 and vc abscisses, and ab an ordinate being given, to 

 find CD, the other ordinate; .". v/vl : v^vc '.'. 

 AB : CD .-. y 202,800 : ^35400 : : 5598 : 2054. 



The other ordinates having been calculated in 

 the same manner, as given below, afford us a comparison with the )'esults of 

 actual survey : — 





By Parabola. 



By Survey. 



Differences. 



At source 



{a) 0000 



0000 



000 





( (6) 2054 



3625 



1571 



Intermediate points 



{ (c) 3-272 



4307 



1035 





{ (d) 4172 



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 A^alley 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, h, c — the 

 intermediate points. The difference between the two curves B and (J has been slightly 

 exaggerated for the sake of clcai-ness. — Ei>. 



