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REV.\ THOMAS BAYES, ETC.
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Before I make my Query let me second the proposal made in p.\ 456,
preceding, that decision should not be announced on subjects which
cannot be discussed. It is not to the credit of our age that abstinence
on this point is necessary for peace : but it cannot he denied that on
all subjects on which men think warmly it is openly avowed, by four
persons out of five at least, that opinions contrary to their own are
\textit{offensive}.  A century and a half ago opinions might be openly
stated, and \textit{opinions} about opinions as openly : we have
rescinded the second permission, and are therefore obliged to rescind
the first. We are a tender and ticklish race. I forget what
\textit{illionth} of an inch Newton found for the thickness---or rather
thinness---of a soapbubble; but the skin of an educated man will beat it
in time, if we go on as now.

Unquestionably no banner of any side in religious or political
controversy has ever been displayed in N.\ \& Q.''  Whether this be
due to the discretion of the contributors or to the suppression of the
editor is among the secrets of the editor's desk; and had better remain
so.  But there is a diminutive of the banner called a \textit{banderol}
or \textit{bannerol}, of which I believe each knight had one  for
himself; and this is sometimes half unfurled; and more frequently of
late than in former years.  In the very admonition which I now second
there is a division of the members of one church into High Churchmen
and Puritans,'' which is very like a banderol; though perhaps all that
is meant is, as in Swift's celebrated case, that the piebald horses of
all degrees of mixture shall by common intendment be included under
black and white horses.

There are many ingenious ways of unfurling the banderol. A person may
contrive to let us know that he thinks \&c.\ is \&c.\ and not \&c.\ by his
mode of informing us that the pages of N. \& Q.' are not the place to
discuss whether \&c.\ be \&c.\ or \&c.''  Again, there are clever modes of
eliminating all but the opinion which is to be insinuated.
Grandmama,'' said the little boy, I wish one of of us three was
hanged; I don't mean pussy and I don't mean myself.'' This little boy,
now grown up, has written several articles in N.\ \& Q.'' and some of
no mean merit: and he writes under more than one signature.

Your journal is a kind of public pic-nic, at which each person is
expected to present his dish quite plain, without any condiment except
salt.  There are difficulties about any other arrangement.  Ah!,''
said an epicure at a public table, Peas!  the first this season!
Capital!''---shaking pepper over them all the time. His opposite
neighbour thereupon scattered the contents of a little  box over the
dish, quietly observing, Sir, you like pepper; I like snuff.''
\textit{Nec lex justior ulla}.

I was led to these reflexions by a Query which I have to make, in which,
by very management I might have shaken the flag of heresy in the faces
of the orthodox of all varieties.  In the last century there were three
Unitarian divines, each of whom has established himself firmly among the
foremost promoters of a branch of science.  Of Dr.\ Price and Dr.\
Priestley, in their connexion with the sciences of life contingencies
and chemistry, there is no occasion to speak: their results are well
known, and their biographies are sufficiently accessible.  The third is
Thomas Bayes, minister at Tunbridge Wells, where he died in 1761.
Whiston belongs to an older period, though he must have been long the
contemporary of Bayes, and so does Humphrey Ditton.  It might be made a
Query which wrote \textit{most}, Whiston or Priestley.  I see
Priestley's writings set down as making seventy octavo volumes, and the
Whiston list was too long for the \textit{Biographica Britannica!}
Could any good reference be given for \textit{complete} lists of the
writings of both.

To return to Bayes.  I want to find out more about him: and therefore
state all I know.  He first turns up, in 1736, as one of the writers in
the celebrated Berkelian controversy about the principles of fluxions:-

{\small An introduction to the Doctrine of Fluxions, and defence of the
mathematicians against the objections of the author of the Analyst, so far
as they, are designed to affect their general methods of reasoning. London:
printed for J.\ Noon . . . . 1786, 8vo.''}

This very acute tract is anonymous but it was always attributed to Bayes
by the contemporaries who \textit{write in} the names of authors; as I
have seen in various copies: and it bears his name in other places.

Whiston, in his Autobiography, (p.\ 426., 2nd ed.), mentions a
conversation he had at Tunbridge Wells with Bayes in 1746. He calls
Bayes the successor of Humphrey Ditton, who it thus appears was also
Unitarian.

But the work on which the fame of Bayes will rest is his paper in the
Philosophical Transactions for 1763, an the supplement in the volume
for 1764. These papers were communicated after Bayes's death    by Mr.\
Richard (afterwards Dr.) Price. They are the mathematical foundation of
that branch of the theory of probabilities in which the probabilities of
the future are matter of calculation from the events of the past.  Bayes
shows a very superior mathematical power: and  Laplace, who makes but
slight mention of him, is very much indebted to him.  More justice has
been done by Dr.\ C.\ Gourand, in his short \textit{Histoire du Calcul
des Probabilit\'es}, Paris, 1848, 8vo.

{\small Bayes, g\'eom\'etre anglais, d'une grande p\'en\'etration
d'espirit, d\'etermina directement la probabilit\'e que les
posibilit\'es indiqu\'ees par les exp\'eriences d\'ej\a faites sont
comprises dans des limites donn\'ees, et fournit ainsi la premi\ere id\'ee
d'une th\'eorie encore inconnue, la th\'eorie de la probabilit\'e des
causes et de leur action future conclue de la simple observation des
\'ev\'enements pass\'ees.}

Bayes gave more than the \textit{premi\'ere id\'ee:} he worked out a
method for solving problems involving large numbers of cases: not so
easily used as Laplace's method \textit{helped by tables}, but far more
easy than could have been expected. Accordingly, Bayes is one of the
chief leaders in the mathematical theory of probabilities. What he did
was of small extent, judged by paper and print, but of fundamental
importance and wide consequence:  he is of the calibre of De Moivre and
Laplace in his power over the subject.  He chose to keep his researches
to himself, and they would probably have been lost but for Dr.\ Price:
of whom I may add that he appears as a far more powerful mathematician
in his explanations upon Bayes than in any part of his own writings on
his own subjects.

I have ascertained that there is no chance of any of Dr.\ Price's papers
being in existence, at least of those which have any reference to the
time at which Bayes was alive.\hfill\textsc{A.\ De Morgan}

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\textit{Notes and Queries} (2) \textbf{9} (1860 January 7), 9--10.

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