100 Transactions. — Miscellaneous, 



So far as I can judge from a somewhat cursory examination of works 

 on the spectroscope, it would appear that, when a variable or periodic star 

 is at its maximum of brightness, its spectrum is the ordinary spectrum of 

 the star with certain bright lines, those of hydrogen, added. Now in the 

 stars placed by Secchi in his first class, such as Sirius, the spectrum con- 

 sists also of a certain assemblage of bright and dark lines, with the charac- 

 teristic lines of hydrogen superposed. 



Art VII. — Notes xipon Mr. FranklancVs x><:iper, " On the SimjAest Contimcons 

 Manifoldness of tic o Dimensions and of Finite Exte7it."* 

 By William Skey, Analyst to the Geological Survey of New Zealand. 

 [Read before the Weltington Philosophical Society, 2Qth June, 1880.] 

 It may be still in your mind that, some time ago, one of our members, 

 Mr. F. W. Frankland, read a paper to us embodying a great deal of very re- 

 markable matter, and entitled, " On the simplest continuous manifoldness 

 of two dimensions and of finite extent."* Now, there is much in this paper 

 which I took great exception to at the time, and still do; but I have hitherto 

 refrained from informing you of this, as I had always the hope that a sub- 

 ject in itself so startling and profound, though possibly not new to you, 

 would, as presented to us, and championed in this way, have elicited some- 

 thing more than a mere verbal discussion thereon ; something more com- 

 prehensive and connected than such a discussion can well be ; something 

 commensurate with the importance of the matter treated, and which would 

 possibly represent my ideas thereupon better than I may ever attempt to do. 



My hope not being realized I can wait no longer, and I therefore beg 

 your kind attention for a short time, so that I may, as best I can, acquaint 

 you with the particulars of my dissent from the views in question, and my 

 reasons for it ; and if, in its turn, this paper should fortunately induce 

 Mr. Frankland to answer the objections which he will here find stated, or 

 to explain those parts of his paper which must appear somewhat obscure to 

 others besides myself, I am sure that, for such a boon, you will cheerfully 

 accord me the time and attention I ask for, and excuse all my short- 

 comings. 



Ere I proceed with this, I will refresh your memory by a synopsis of 

 Mr. Frankland's paper. 



It commences by a statement of the well-knoAvn fact that some geome- 

 tricians maintain that the axioms of geometry may be only approximately 



* See " Trans. N.Z. Inst." Vol. IX., p. 272, 



