510 Tramactions. — Miscellaneous. 



What becomes of the "rule"? As Zumpt seems to have 

 felt, it is so overwhelmed with exceptions that mole ruit earum. 

 Having examined three hundred and fifty place-names, found 

 chiefly in the western section of the Orbis Eomanus, I am 

 not able to discern any " rule " applicable to the names of 

 towns. But the influence of the " rule " is very great. Even 

 Lewis and Short, s. v., are misled by it. In order to justify 

 Liv., xxi., 19, cited above, they allege that Liv. used Snzuntus. 

 But SagunUwi is in good prose the only form used, cf. Mayor on 

 Juv., XV., 114. Poets and -sn-iters like Mela and Florus use 

 Sazutitus. Juv., loc. cit., uses ZazyntJnis, a thinly- veiled form 

 of Zacyntlnis. 



Art. LXVIII. — Transcendental Geometry : Remarks sugyested by 

 Mr. Frankland's Paper, " The Non-EucUdi<in Geometry Vin- 

 dicated.''* 



By George Hogben, M.A. 



[Read before the Philosophical Institute of Canterbury, 1th October, 1886.] 



In the paper referred to, Mr F. W. Frankland implies that the 

 views he advocates are generally accepted by living mathe- 

 maticians — e.g., on page 59, paragraph 4 : " He [Professor 

 Cliftbrd] says, in common with most living mathematicians who 

 have studied this question, that space ynay be finite" ; and again, 

 on page 60, paragraph 6: "To the expression ' geometers of the 

 Euclidian school ' I take exception, believing that none such 

 are left, in the sense in which Mr. Skey uses the word. The 

 triumph of the non-Euclidian geometry, or, I will say, the 

 'general' geometry, has been complete. I can safely appeal, 

 on this point, to any distinguished member of any Mathematical 

 Society in Europe or America." 



Now, I am quite aware that, if this were an accurate 

 description of the state of mind of most living mathematicians 

 and distinguished members of Mathematical Societies, it would 

 be an extremely rash proceeding on my part to enter into the 

 controversy'. One could only gaze in wonder at those superior 

 beings who roamed at large in space of the (n-f- l)th degree, 

 while we poor mortals had to be content Avith three dimensions. 



I cannot think that Mr. Frankland is justified in demanding 

 a greater admission than this : that there are (or have been,) 

 distinguished mathematicians holding those views, and that 

 Mathematical Societies have, as in duty bound, allowed the 

 discussion of thom in their meetings and in their journals. 



* " Trans. N.Z. Inst," vol. xviii., p. 58 



