the English alphabet is treated in the way in practice: when the child is taught that a = ae, and no symbol is given for the broad a; that i = ai; that u = iu, &c. Let the reform begin at the fountain head, by a re-arraugement of the alphabet.
One or two Scotch names give good examples of the difficulties in spelling brought about by the want of system in English orthography. Let us take the name MacNeil. We find this variously spelt McNeil and McNeal. Although apparently a Celtic name, I suspect that it came from Scandinavia, where we have to this day the frequent Christian name of Nil, Nils. The French could make nothing of Neil, so changed the spelling to Niel, in the case of the celebrated marshal. The McNeils and Neals should do the same, and the name would then be written phonetically.
We find the name Mackay spelt the same, whether the owner of it comes from the Highlands or from Galloway; but the pronunciation is different. In the former case it is Mackai, in the latter Māckae; and at San Francisco I found another variation, viz., Mackāe, the accent being on the last syllable.
In looking up the Scandinavian languages, I have been struck with the similarity in some respects to broad Scotch, and I suspect that the language of the old kingdom of Northumbria, extending from the Humber to the Forth, has been more influenced by Scandinavian immigrants than is generally supposed. Such words as baru for bairu are suggestive; and in Norwegian I found a sentence, viz.: "Qua sae?" meaning "What do you say?" which one may hear any day in the streets of Edinburgh or Glasgow.
Art. VII.—The Non-Euclidian Geometry Vindicated: a Reply to Mr. Skey.
By F. W. Frankland F.I. A.
[Read before the Wellington Philosophical Society, 13th February, 1884.]
The following observations are an abridgment of a series of letters addressed to Mr. Skey, the author of the paper entitled "Notes upon Mr. Frankland's Paper 'On the Simplest Continuous Manifoldness of two Dimensions and of Finite Extent,'" read before the Wellington Philosophical Society on 26th June, 1880, and contained on pages 100–109 of the thirteenth volume of the Transactions of the New Zealand Institute. By Mr. Skey's kindness and courtesy these letters were made available to me for the preparation of a printed reply to his criticisms. I make no apology for the form in which this reply appears. I have taken, seriatim, the main points which Mr. Skey raised, and replied to each of his contentions in detail. Mr. Skey's own words are in each case placed at the commencement of the
