, and he
wants not grounds that doubts it." So thought Sir Thomas Browne, in his
_Vulgar Errors_, B. vii. Ch. 17. Gibbon, too, rejects it as fabulous.
"Till the Reformation," he says, "the tale was repeated and believed
without offence, and Joan's female statue long occupied her place among
the Popes in the Cathedral of Sienna. She has been annihilated by two
learned Protestants, Blondel and Bayle; but their brethren were
scandalized by this equitable and generous criticism. Spanheim and
L'Enfant attempted to save this poor engine of controversy, and even
Mosheim condescends to cherish some doubt and suspicion."--_The Decline
and Fall of the Roman Empire_, chap. xlix. Spanheim's work, _Joanna
Papissa Restituta_, was printed at Leyden in 1692.]

_The Well o' the World's End._--I am very anxious to find out, whether
there still exists in print (or if it is known to any one now alive) an old
Scotch fairy tale called "The Weary Well at the World's End?" Charles
Kirkpatrick Sharpe, Esq., who is unhappily dead lately, knew the story and
meant to write it down; but he became too infirm to do so, and though many
very old people in the hilly districts of Lammermoor and Roxburghshire
remember parts of it, and knew it in their youth, I cannot find one who
knows it entirely.

L. M. M. R.

[Some references to the story alluded to by our correspondent will be
found in Dr. Leyden's valuable introduction to _The Complaynt of
Scotland_; and the story itself in Chambers's admirable collection of
Scottish Folk Lore, _Popular Rhymes of Scotland_, p. 236. of the third
edition, which form vol. vii. of the _Select Writings of Robert
Chambers_.]

_Sides and Angles._--What is the most simple and least complicated method
of determining the various relations of the sides and angles of the acute
and obtuse-angled triangles, without the aid of trigonometry, construction,
or, in fact, by any method except arithmetic?

F. G. F.

St. Andrew's.

[The relations of sides and angles cannot be obtained without
trigonometry in some shape. A very easy work has lately been published
by Mr. Hemming, in which there is as little as possible of technical
trigonometry.]

_Meaning of Ratche._--In John Frith's _Antithesis_, published in 1529, he
says:

"The pope and bishops hunt the wild deer, the fox, and the hare, in
their closed parks, with great cries, and hor