239 



log { a(v-l)+pv i-logpv 



By the first method \ a (v'— 1) + p } • { - =— '- 



J I J log v. 



a (v' — 1) (a— p) 

 By the second metliod ^ -j-a. 



Prom this comparison it follows that when money can be invested at 5 per 

 cent., and the Sinking Fund is less than 7 per cent, of the loan, the first is the 

 more economical method ; and the smaller the Sinking Fund, and the higher 

 the rate of interest, the greater will be the saving effected by investing the 

 fund in other securities, than by using it to buy up annually part of the loan. 



This however is only the mathematical or pecuniary view of the question ; 

 from the political point of view many reasons can be given why the second 

 method should be preferred, and the difference pecuniarily is not sufficiently 

 great to override them. 



Art. LXI. — List of Plants found in the Northern District of the Province of 

 Auckland. By J. Buchanan and T. Kirk. 



[In the course of the geological survey of the above district in 1865-6, an 

 extensive collection of plants was made by Mr. Bxichanan, and forwarded to 

 Dr. Hooker, at Kew. They were, however, unfortunately, distributed by an 

 assistant without being examined, so that a complete list was not obtained, and 

 any few novelties escaped notice in the appendix to Vol. ii. of the " Handbook 

 of the New Zealand Flora." 



From the portion of the collection retained, and from notes made on the spot, 

 Mr. Buchanan compiled the greater part of the following list, with the exception of 

 the natural orders, Juncese, Restiaceaa, Cypei'acese, and G-raminese, the lists of 

 which are furnished altogether by Mr. Kirk. As Mr. Buchanan collected in 

 the months of November and December, and Mr. Kirk went over most of 

 the same ground in April, the latter observer was also able to add largely to 

 the number of plants, the results, as combined in the following lists, should 

 give a tolerably complete Flora of each locality indicated. 



An account of the chief plants of interest obtained by Mr. Kirk is given 

 in a paper published in the "Transactions" for last year (p. 140) ; along with 

 which his contribution to the following tables was to have been printed, had 

 not circumstances prevented it. 



For the characteristic plants of the district, and a comparison of its botany 

 with that of other parts of New Zealand, the reader is referred to Mr. Colenso's 

 Essay, also in Vol. i. of the "Transactions." — Ed.] 



Introductory Remarks by J. Buchanan. 



The above area may be divided into eight districts, viz. : — 



1. Wangarei, 



2 . Bay of Islands, 



3. Wangaroa, 



4. Stephenson's Island, 



the latter as showing the comparative botany of a portion of land detached 

 from the Main Island. 



5. Mount Camel, 



6. North Cape. 



