316 Transactions. —Geology. 
mountain out of which it issues 8,500 feet. Testing the curve of the valley 
bed by the elliptic curve, in the same manner as given for the Manuherikia, 
we find the following result :— 
Bv ELLIPSE. By Survey. DIFFERENCES. 
At source i ... (a) 0000 Я 0000 р 
(6) 6672 es 7123 E 551 
j Í ? 7834 Fur 7725 i 109 
Ai mieoneduste points y ШЫ ы UNE C s ME 
(e) 8475 va 8291 bs 184 
Atexitintosea — ... (f) 8500 ` 
The Waitaki is about 140 miles in length, rising some miles to the north- 
east of Mount Cook, whose elevation is'12,460 feet, and a painting of which 
is lying on the table, the copy of a sketch that I made when exploring the 
country in December, 1857. The scenery is the most grand and rugged in 
New Zealand, and can scarcely be surpassed in barrenness and wildness in any 
part of the world. I, at that time, with the privilege of an explorer and 
surveyor, named the feeding waters of the Pukaki Lake “ Upper Waitaki," 
and their valley * The Valley of Sand." Dr. Haast, following me some years 
afterwards, has, no doubt inadvertently, altered these names to “ Tasman," and 
the great mountain next to Mount Cook, which I, appropriately I opine, named 
“Mount Stokes" he has altered to “Sefton.” From its alpine valley the 
Waitaki issues out on the Mackenzie Plains—named after a notorious sheep- 
stealer, by way of relief to the other good names in the Province— passing in 
its course through the Pukaki Lake; from thence it pierces the deep gorges 
of the Ben More and Kurow Mountains, after which it issues on the Waitaki 
Plains, near the sea. That one of the largest rivers in New Zealand, such as 
this, in passing over so many obstacles, should yet have its bed in such near 
conformity with the curve of the ellipse, was again striking, and wherein the 
divergences occur just where the mountain and rock obstructions are greatest. 
Thus a law of erosion of great power was again indicated, and so further 
enquiry stimulated ; and I may here remark that while one great abrasion of 
surface has undoubtedly taken place, another, of no less significance, is 
exhibited by the section in the upper valley and Pukaki Lake—the effect of 
the action of: mountain glaciers, whose effeets have already been pointed out 
by my friend Mr. MeKerrow (Trans. N.Z. Inst., Vol. IIL, p. 254), and to 
which subject I may recur. 
Leaving the Waitaki Valley, I then proceeded to investigate the levels of 
the bed of the Shag River. This river has a short course of about 39 miles, 
having its source in Kakanui Peak, whose elevation is 4,978 feet above the sea. 
The river has a course through very rugged country ; it is very tortuous, yet 
the section proves another very close approximation to the ellipse. For the 
calculation of the ordinates, we have : length of valley equal to 199,700 feet, 
