2. Is it not probable that _Avernus_, if not corrupted from [Greek: aornos], is related to _iffrin_, the Irish _inferi_? This derivation is at any rate more probable than that of Grotefend, who connects the word with [Greek: Acheron]. 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_, a flame? The word _Gallus_, 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 endeavour 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 (probably) ceases to be an axis. If this process can be indefinitely continued, the cuttings must become smaller and smaller, for the following reason. 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.