luded, and very very improperly.

HORNER'S METHOD.

I think it may be admited that the indisposition to look at and encourage
improvements of calculation which once {188} marked the Royal Society is no
longer in existence. But not without severe lessons. They had the luck to
accept Horner's[325] now celebrated paper, containing the method which is
far on the way to become universal: but they refused the paper in which
Horner developed his views of this and other subjects: it was printed by
T. S. Davies[326] after Horner's death. I make myself responsible for the
statement that the Society could not reject this paper, yet felt unwilling
to print it, and suggested that it should be withdrawn; which was done.

But the severest lesson was the loss of _Barrett's Method_,[327] now the
universal instrument of the actuary in his highest calculations. It was
presented to the Royal Society, and refused admission into the
_Transactions_: Francis Baily[328] printed it. The Society is now better
informed: "_live and learn_," meaning "_must live, so better learn_," ought
to be the especial motto of a corporation, and is generally acted on, more
or less.

Horner's method begins to be introduced at Cambridge: it was published in
1820. I remember that when I first went to Cambridge (in 1823) I heard my
tutor say, in conversation, there is no doubt that the true method of
solving equations is the one which was published a few years ago in the
_Philosophical Transactions_. I wondered it was not taught, but presumed
that it belonged to the higher mathematics. This Horner himself had in his
head: and in a sense it is true; for all lower branches belong to the
higher: but he would have stared to have been told that he, Horner, {189}
was without a European predecessor, and in the distinctive part of his
discovery was heir-at-law to the nameless
Brahmin--Tartar--Antenoachian--what you please--who concocted the
extraction of the square root.

It was somewhat more than twenty years after I had thus heard a Cambridge
tutor show sense of the true place of Horner's method, that a pupil of mine
who had passed on to Cambridge was desired by his college tutor to solve a
certain cubic equation--one of an integer root of two figures. In a minute
the work and answer were presented, by Horner's method. "How!" said the
tutor, "this can't be, you know." "There is the answer, Sir!" said my
pupil, greatly amused, for my pupils learnt, not only Horner'