Thomson. — Glacial Action in Otago. 



315 



i' Survey. 



Differences. 



5207 



431 



5251 



121 



bb'dS 



000 



By Parabola. 



Intermediate points < S'L rx.-ir, 

 1 1 (y ) 5 1 30 



At exit ((/) 55 D8 



Thus, as will he observed hj these differences, and the form of the 

 pai-abola, the curve of the valley bed does not conform to the same. 

 It was evident that the hyperbola would be yet more unconformable. 

 The ellipse was then tried with the following results : 

 — Let VA the length of the valley, ab its rise, and 

 vc the distance of any intermediate point from v be 

 given, to find CD. Let A be the centre of the 

 ellipse, then VA will be the semi-axis major, ab the 

 semi-axis minor, vc and cz will be abscisses to the 

 ordinate CD. .•. vz : be : : y vc x cz : cd. Again, vz 

 and BE being double of VA and ab, we have 525600:11196 :: ^35400 x 490200 

 :2804, the ordinate required. 



The other ordinates having been calculated in the same manner, afibrd the 

 following comparison : — 



At source ... • 



At intermediate points 



At exit 



As the data of the actual survey are given for the lower terraces close to 

 the river, I may state that these vary from 80 to 100 feet in difference of 

 level from the river surface. The point marked with an astei-isk, as stated 

 before, is also given, not for the terrace, but for the ford, which accounts for 

 so great a difference ; otherwise it will be seen that the actual curve of the 

 bed of the Manuherikia agrees surprisingly with that of the ellipse, and, 

 where it differs materially, such deviations are in the positions to be expected, 

 viz., where the ei-oding forces have had to expend themselves on the hard bai's 

 of schist rock already alluded to as crossing the valley. Here, then, we 

 have in our fii-st tried example a valley bed, whose length is 45 miles and 

 differ-ence of level 5,598 feet, conforming practically to the curve of the ellipse. 

 That such might be a rule with other valleys was then surmised, though, no 

 doubt, modifications would take place from peculiar contour of country and 

 other natural obstructions. 



The next valley, then, wlaich the data in the Survey Department enabled 

 me to test was the Waitaki. The length of the Waitaki, from its source in 

 the Mount Cook ranges to the sea, is 720,080 feet, and the altitude of the 



By Ellipse. 



By Sukvey. 



Differences 



{a) 0000 



0000 



000 



(&) 2804 



3625* 



821 



(c) 4212 



4307 



95 



{d) 5012 



4987 



25 



(e) 5384 



5207 



177 



(/) 5523 



5251 



272 



{g) 5598 .. 



5598 



000 



