CAMPANALOGIA:
_OR THE_
ART
OF
RINGING
Improved.
With plain and easie Rules to guide the Practitioner in the Ringing all
kinds of _Changes_.
TO
Which is added, great variety of
_NEW PEALS_.
_LONDON_,
Printed by _W. Godbid_, for _W.S._ and are to be sold by _Langley
Curtis_ in Goat-Court on _Ludgate_-hill. 1677.
[Illustration: [Fleuron]]
TO
_THE HONOURED_
AND TO
_His much Esteemed_ FRIENDS,
The Members of the Society of
COLLEDG YOUTHS.
_Gentlemen_,
As your Society even _ab origine_ hath deservedly acquired an eminency
in many respects above others of this kind; so more especially for the
pregnancy of its Members in the composing of _Peals_. For when the Art
of _Cross-pricking_ lay enveloped in such obscurity, that it was thought
impossible that double Changes on five bells could be made to extend
farther than _ten_, and triple and double Changes on six farther than
_sixty_; then it was that a worthy and knowing Member of your Society,
to dissipate those mists of Ignorance, and to usher in the bright morn
of Knowledg, prickt those much applauded Peals of _Grandsire_ and
_Grandsire Bob_; which for their excellency have for many years together
continued triumphant in practice amidst all others whatsoever; and which
indeed have been a great light in the production of that great variety
of new Peals herein contained; the greatest part of which being also the
offspring of your Society, I therefore thought fit to usher them into
the world under the wings of your Protection.
_Gentlemen_, as a member I held my self obliged to add my Mite to your
full fraught Treasury of Speculative and Practical Knowledg of this
kind; though I confess your acquisition on this account will be very
mean, since my want of ability sufficient to undertake a thing of this
nature, and also want of opportunity by converse with others to supply
my own defects, have rendred the Book less acceptable than it might have
been done by some more knowing head and acuter Pen. And although I am
conscious that it meriteth not your acceptance; yet I assume the
confidence to believe that you will favour it with a kind entertainment
amongst you; and the rather, for that I know you are too judicious to
sentence it without first casting into the ballance of your indifferent
judgments some Grains of Allowance: The countenance you shew it will
silence Detractors, and be Armour of proof against the fools bolts which
may happen to be soon shot at the Author, who is
_Gentlemen_,
_A constant well-wisher to
the Prosperity (though an
unworthy member)
of your Society_,
F.S.
_ERRATA._
_Courteous Reader_,
_Some few faults have escaped the Press: as page 27 line the 4th, for_
grateful _read_ graceful. _page 31. line the 19th. for_ imitatieg _read_
imitating, _with some others, which you are desired either candidly to
amend, or tasitly to pass over._
[Illustration: [Fleuron]]
OF THE
ART
OF
Changes.
These clear dayes of Knowledge, that have ransackt the dark corners of
most Arts and Sciences, and freed their hidden mysteries from the bonds
of obscurity, have also registred this of _Ringing_, in the Catalogue of
their Improvements; as well the Speculative as the Practick part, which
of late years remain’d in _Embryo_, are now become perfect, and worthy
the knowledge of the most ingenious. Although the Practick part of
_Ringing_ is chiefly the subject of this Discourse, yet first I will
speak something of the Art of _Changes_, its Invention being
Mathematical, and produceth incredible effects, as hereafter will
appear. But first, I will premise a word or two, to shew what the nature
of those _Changes_ are. Some certain number of things are presupposed to
be changed or varied; as 2.3.4.5.6. or any greater number whatsoever;
then the number of things to be so varied must have the like number of
fixed places assigned them. As if five men were sitting upon five stools
in a row; the stools are supposed to be fixed places for the five men,
but the men by consent may move or change to each others places at
pleasure, yet still sitting in a row as at first: now this Art directs
how, and in what order those five men may change places with each other,
whereby they may sit sixscore times in a row, and not twice alike. And
likewise a _Peal_ of five Bells, being raised up to a fit compass for
ringing of _Changes_, are there supposed to have five fixed places,
which time assigns to their notes or strokes; yet the notes of the Bells
may change into each others places at pleasure: now this Art also
directs the manner and method of changing the five notes in such sort,
that they may strike sixscore times round, and not twice alike.
The numbers of _Changes_ are thus to be discovered. _Two_ must first be
admitted to be varied two wayes; then to find out the Changes in
_three_, the Changes on two must be multiplied by three, and the product
will be six, which are the compleat number of Changes on three.
Those six Changes being multiplied by four, will produce 24, which are
the compleat number of Changes on four. The 24 Changes on four, being
multiplied by five, will produce 120, which are the compleat number of
Changes on five. And in like manner the 120, being multiplied by six,
will produce 720, which are the compleat number on six. The 720, being
multiplied, by seven, will produce 5040, which are the number of Changes
on seven. The 5040, being multiplied by eight, will produce 40320, which
are the number of Changes on eight. Those Changes on eight, being
multiplied by nine, will produce 362880, which are the number of Changes
on nine. Those Changes on nine, being multiplied by ten, will produce
3628800, which are the number on ten. Those on ten, being multiplied by
eleven, will produce 39916800, which are the number on eleven. Those
also being multiplied by twelve, will produce 479001600, which are the
compleat number of Changes on twelve. And if twelve men should attempt
to ring all those Changes on twelve Bells, they could not effect it in
less than seventy five years, twelve Lunar Months, one week, and three
days, notwithstanding they ring without intermission, and after the
proportion of 720 Changes every hour. Or if one man should attempt to
prick them down upon Paper, he could not effect it in less than the
aforesaid space. And 1440 being prickt in a sheet, they would take up
six hundred sixty five Reams of Paper, and upwards, reckoning five
hundred Sheets to a Ream; which Paper at five shillings the Ream, would
cost one hundred sixty six Pounds five Shillings,
The reason of the aforesaid Multiplication, by which the numbers of
Changes are discovered, and also that those Products are the true
numbers of Changes, will plainly and manifestly appear in these
following Demonstrations.