236 Proceedings of the Royal Society 
where l is the number of elements in the period of the first fraction. 
This we may prove by deducing from the expression which is 
given by (XIV.) for the square of the right hand member, the 
expression also given by (XIV.) for the square of the left hand 
member. 
Similarly, we may show that 
A+ 1 1 1 1 1 ± 
cl b c 5 4~ a 4~ 2 A. -f- . . . 
* * 
_ ^ be + 2 1 1 be + 2 
(ibe -)- 2 n 4- c 4~ b 4- nbc -l - 2d 4* c 4- 2 A. 4- . . . 
* * 
and many other such identities. 
22. Lastly, it is easily demonstrated that the condition that any 
periodic continued fraction 
. a. 2 a n _ x a n 
b x 4- by 4- • . . 4- b n _ x + b n + . . . 
* * 
may represent a quadratic surd is 
and that this can be satisfied in other ways than by choosing the 
elements so that the diagonals of the one continuant when read 
forward may be the same as those of the other when read backward. 
3. Remarks upon the Footprints of the Dinornis in the Sand 
Rock at Poverty Bay, Hew Zealand, and upon its recent 
extinction. By T. H. Cockburn-Hood, F.G-.S. 
Impressions of the tracks of large birds from this locality have 
lately been objects of attraction to visitors to the museum at 
Wellington, New Zealand. To these Dr Hector, F.R.S., has affixed 
a label, stating that they are from the “ Sea shore sand ” at Poverty 
bay, a harbour on the east coast of the north island. “ Sand rock ” 
would have been a preferable term, as to most observers the descrip- 
tion is calculated to convey the idea that these footprints are but 
of yesterday’s date. Indeed, were it not probable that the moa was 
