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 suggesting one or two
"links" that I do not remember 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
_amaimus_ into _amemus_?

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.