painted for their hall. An inquiry was
then made of all the members of his family; but no portrait of any
description could be found. I have heard my father say that Gilbert White
was much pressed by his brother Thomas (my grandfather) to have his
portrait painted, and that he talked of it; but it was never done.

A. HOLT WHITE.

_"A Tub to the Whale"_ (Vol. viii., p. 220.).--In the Appendix B. to Sir
James Macintosh's _Life of Sir Thomas More_ is the following passage:

"The learned Mr. Douce has informed a friend of mine, that in Sebastian
Munster's _Cosmography_ there is a cut of a ship, to which a whale was
coming too close for her safety; and of the sailors throwing a tub
{305} to the whale, evidently to play with. The practice of throwing a
tub or barrel to a large fish, to divert the animal from gambols
dangerous to a vessel, is also mentioned in an old prose translation of
the _Ship of Fools_. These passages satisfactorily explain the common
phrase of throwing a tub to a whale."

Sir James Macintosh conjectures that the phrase "the tale of a tub" (which
was familiarly known in Sir Thomas More's time) had reference to the tub
thrown to the whale.

C. H. COOPER.

Cambridge.

_The Number Nine_ (Vol. viii., p. 149.).--The property of numbers
enunciated and illustrated by MR. LAMMENS resolves itself into two.

1. If from any number above nine be subtracted the number expressed by
writing the same digits backwards, the remainder is divisible by nine.

2. If the number nine measure a given number, it measures the sum of its
digits.

As the latter is proved in most elementary books on Algebra, I confine my
proof to the former.

Let the number in question be--

_a__0 + _a__1 . 10 + _a__2 . 10^2 + ... + _a__{_n_-1} . 10^{_n_-1} +
_a__{_n_} . 10^{_n_}

Then

_a__{_n_} + _a__{_n_-1} . 10 + _a__{_n_-2} . 10^2 + ... + _a__1 .
10^{_n_-1} + _a__0 . 10^{_n_}

is "the same number written backwards." The difference is--

(_a__{_n_} - _a__0)(10^{_n_} - 1) + (_a__{_n_-1} - _a__1)(10^{_n_-2} - 1)
. 10 + ...
+ (_a__{_n_/2+1} - _a__{_n_/2-1})(10^2-1) . 10^{_n_/2-1} if _n_ be
even, but
+ (_a__{(_n_+1)/2} - _a__{(_n_-1)/2})(10-1) . 10^{(n-1)/2} if _n_ be
odd.

And every term of this difference, as involving a factor of the form (1 -
10^{_n_}), is divisible by 9; and therefore the difference is divisible by
9.

C. MANSFIELD I