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to print it, and suggested that it should be withdrawn; which was done.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's method, but
the estimation it held at Cambridge. "Yes!" said the tutor, "there is the
answer certainly; but it _stands to reason_ that a cubic equation cannot be
solved in this space." He then sat down, went through a process about ten
times as long, and then said with triumph: "There! that is the way to solve
a cubic equation!"
I think the tutor in this case was never matched, except by the country
organist. A master of the instrument went into the organ-loft during
service, and asked the organist to let him _play the congregation out_;
consent was given. The stranger, when the time came, began a voluntary
which made the people open their ears, and wonder who had got into the
loft: they kept their places to enjoy the treat. When the organist saw
this, he pushed the interloper off the stool, with "You'll never play 'em
out this side Christmas." He then began his own drone, and the congregation
began to move quietly away. "There," said he, "that's the way to play 'em
out!"
I have not scrupled to bear hard on my own university, on the Royal
Society, and on other respectable existences: being very much the friend of
all. I will now clear the Royal Society from a very small and obscure
slander, simply because I know how. This dissertation began with {190} the
work of Mr. Oliver Byrne, the dual arithmetician, etc. This writer
published, in 1849, a method of calculating logarithms.[329] First, a long
list of instances in which, as he alleges, foreign discoverers have been
pillaged by Englishmen, or turned into Englishmen: for example,
O'Neill,[330] so called by Mr. Byrne, the rectifier of the semi-cubical
parabola claimed by the Saxons under the name of _Neal_: the grandfather of
this mathematician was conspicuous enough as _Neal_; he was archbishop of
York. This list, says the writer, might be continued without end; but he
has mercy, and finishes with his own case, as follows:--"About twenty years
ago, I discovered this method of directly calculating logarithms. I could
generally find the logarithm of any number in a minute or two without the
use of books or tables. The importance of the discovery subjected me to all
sorts of prying. Some asserted that I committed a table of logarithms to
memory; others attributed it to a peculiar mental property; and when
Societies and individuals failed to extract my secret, they never failed to
traduce the inventor and the invention. Among the learned Societies, the
Royal Society of London played a very base part. When I have more space and
time at my disposal, I will revert to this subject again."
Such a trumpery story as this remains unnoticed at the time; but when all
are gone, a stray copy from a stall falls into hands which, not knowing
what to make of it, make history of it. It is a very curious distortion.
The reader may take it on my authority, that the Royal Society played no
part, good or bad, nor had the option of playing a part. {191} But I myself
_pars magna fui_:[331] and when the author has "space and time" at his
disposal, he must not take all of them; I shall want a little of both.