59 



basis for applying efficient tests to the theories of variation and replace- 

 ment of species." Dr. Hector further suggests, as a subject for local 

 naturalists, the investigation of the eels and other fishes in the Otago 

 streams and lakes. 



Mr. Thomas Kirk, the Secretary of the Auckland Institute, also 

 writes, — "Have you any botanist, or even plant collector, who would 

 care to exchange a bundle of Otago plants, for the Herbarium, for one from 

 this district 1 Your west coast and alpine plants would be most valued, 

 but even your common kinds and naturalized species would be welcome. 

 The specimens need not be named if the collector does not chance to 

 have a good knowledge of them, although, of course, they woiild be of 

 greater value when named by the collector. The names of the localities 

 where collected shoiild always be given ; and in the case of naturalized 

 plants, it would be well to state their present extent of diffusion, so far 

 as the knowledge of the collector will admit. I need scarcely say this 

 is not imperative." 



Mr. Webb preferred a request that some gentleman should be 

 associated with him in the office of Honorary Secretary, and said that 

 Dr. Hocken had been so good as to say that he woiild assist him. 

 Subject to his acceptance of the office. Dr. Hocken was appointed 

 Honorary Secretary to the Institute, to act jointly with Mr. Webb. 



Second Meeting. March 16, 1870. 

 A. Eccles, F.R.C.S., Vice-President, in the chair. 



1. " On Modern Methods of Geometiy," by D. Brent. 

 (Abstract.) 



The object of this paper was to explain what is meant by modern 

 methods in geometry, to show that " Euclid " is not the best text-book 

 to put into the hands of beginners, and to point out some of the defects 

 in "Euclid." In France and G-ermany, where great attention has been 

 paid to the teaching of geometry, the modern text-books differ from 

 " Euclid" in many respects ; their distinctive features being — the intro- 

 duction of new principles, the tacit instead of the explicit reference to 

 axioms, the classification of the propositions according to their subject 

 matter, the separation of theorems and problems, the use of hypothetical 

 constructions, the introduction of new nomenclature, the adoption of 

 single and independent proofs wherever possible, the abandonment of 

 the detailed syllogistic form of reasoning, and the treatment of projjortion. 

 The main and only two serious arguments of those who still advocate 



