14 



NOTES AND QUERIES. 



[No. 219. 



CELTIC AND LATIN LANGUAGES. 



(Vol. viii., p. 174.) 



There was a Query some time ago upon this 

 subject, but though it is one full of interest to all 

 scholars, I have not observed any Notes worth 

 mentioning in reply. The connexion between 

 these two languages has only of late occupied the 

 attention of philologers ; but the more closely they 

 are compared together, the more important and 

 the more striking do the resemblances appear ; 

 and the remark of Arnold with regard to Greek 

 literature applies equally to Latin, " that we seem 

 now to have reached that point in our knowledge 

 of the language, at which other languages of the 

 same family must be more largely studied, before 

 we can make a fresh step in advance." But this 

 study, as regards the comparison of Celtic and 

 Latin, is, in England at least, in a very infant 

 state. Professor Newman, in his Regal Rome, 

 has drawn attention to the subject ; but his in- 

 duction does not appear sufficiently extensive to 

 warrant any decisive conclusion respecting the 

 position the Celtic holds as an element of the 

 Latin. Pritchard's work upon the subject is sa- 

 tisfactory as far as it goes, but both these authors 

 have chiefly confined themselves to a tabular view 

 of Celtic and Latin words ; but it is not merely 

 this we want. What is required is a critical ex- 

 amination into the comparative structure and 

 formal development of the two languages, and this 

 is a work still to be accomplished. The later 

 numbers of Bopp's Comparative Grammar are, I 

 believe, devoted to this subject, but as they have 

 not been translated, they must be confined to a 

 limited circle of English readers, and I have not 

 yet seen any reproduction of the views therein 

 contained in the philological literature of England. 



As the first step to considerations of this kind 

 must be made from a large induction of words, I 

 think, with your correspondent, that the pages of 

 " N. & Q." might be made useful in supplying 

 "links of connexion" to supply a groundwork for 

 future comparison. I shall conclude by sug- 

 gesting one or two *' links " that I do not re- 

 member to have seen elsewhere. 



1. Is the root of felix to be found in the Irish 

 fail, fate ; the contraction of the dipththong ai 



or e being analogous to that of ama'imus into 

 amemus? 



2. Is it not probable that Avernus, if not cor- 

 rupted from &opvos, is related to iffrin, the Irish 

 inferi f This derivation is at any rate more pro- 

 bable than that of Grotefend, who connects the 

 word with 'Axtpoov. 



3. Were the Galli, priests of Cybele, so called 

 as being connected with fire-worship ? and is the 

 name at all connected with the Celtic gal, aflame ? 

 The word Galhis, a Gaul, is of course the same 

 as the Irish gal, a stranger. T. H. T. 



GEOMETRICAL CURIOSITY. 



(Vol. viii., p. 468.) 



Mr. Ingleby's question might easily be the 

 foundation of a geometrical paper ; but as this 

 would not be a desirable contribution, I will en- 

 deavour to keep clear of technicalities, in pointing 

 out how the process described may give something 

 near to a circle, or may not. 



When a paper figure, bent over a straight line 

 in it, has the two parts perfectly fitting on each 

 other, the figure is symmetrical about that straight 

 line, which may be called an axis of symmetry. 

 Thus every diameter of a circle is an axis of 

 symmetry : every regular oval has two axes of 

 symmetry at right angles to each other : every 

 regular polygon of an odd number of sides has an 

 axis joining each corner to the middle of the 

 opposite sides : every regular polygon of an even 

 number of sides has axes joining opposite corners, 

 and axes joining the middles of opposite sides. 



When a piece of paper, of any form whatsoever, 

 rectilinear or curvilinear, is doubled over any 

 line in it, and when all the parts of either side 

 which are not covered by the other are cut away, 

 the unfolded figure will of course have the creased 

 line for an axis of symmetry. If another line be 

 now creased, and a fold made over it, and the 

 process repeated, the second line becomes an axis, 

 of symmetry, and the first perhaps ceases to be 

 one. If the process be then repeated on the first 

 line, this last becomes an axis, and the other (pro- 

 bably) ceases to be an axis. If this process can 

 be indefinitely continued, the cuttings must be- 

 come smaller and smaller, for the following rea- 

 son. Suppose, at the outset, the boundary point 

 nearest to the intersection of the axes is distant 

 from that intersection by, say four inches ; it is 

 clear that we cannot, after any number of cuttings, 

 have a part of the boundary at less than four 

 inches from the intersection. For there never is, 

 after any cutting, any approach to the intersection 

 except what there already was on the other side of 

 the axis employed, before that cutting was made. 

 If then the cuttings should go on for ever, or 

 practically until the pieces to be cut off are too 

 small, and if this take place all round, the figure 

 last obtained will be a good representation of a 

 circle of four inches radius. On the suppositions, 

 we must be always cutting down, at all parts of 

 the boundary ; but it has been shown that we can 

 never come nearer than by four inches to the 

 intersection of the axes. 



But it does not follow that the process will go 

 on for ever. We may come at last to a state in 

 which both the creases are axes of symmetry at 

 once ; and then the process stops. If the paper 

 had at first a curvilinear boundary, properly 

 chosen, and if the axes were placed at the proper 

 angle, it would happen that we should arrive at a 



