Chapter I: Part 1

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.

]

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._

]

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.

But first, _two_ must be admitted to be varied two ways, thus.——

│12
│21

And then consequently, _three_ will make three times as many Changes as _two_; for there are three times two figures to be produced out of three, and not twice two the same figures, which are to be produced by casting away each of the three figures one after another. First, cast away 3, and 1.2 will, remain; cast away 2, and 1.3 will remain; cast away 1, and 2.3 will remain. So that here are three times two figures produced out of the three, and not twice two the same figures, as 12. 13. 23. each two may be varied two ways, as before: then to the changes which each two makes add the third figure which is wanting; as to the two changes made by 1.2 add the 3, to the changes on 1.3 add the 2, and to the changes on 2.3 add the 1, and the three figures will stand six times together, and not twice alike, as here appeareth.

│123
│213
│———
│132
│312
│———
│231
│321
│———

_Four_ will make four times as many changes as _three_. For there are four times three figures to be had out of four, and not twice three the same figures, which are to be produced by casting away each of the four figures by turns. First cast away 4, and 123 will remain; cast away 3, and 124 will remain; cast away 2, and 134 will remain; and lastly, casting away 1, and 234 will remain; so that here is 123, 124, 134, 234, and not twice three the same figures. Now each three may be varied six ways, according to the preceding Example. Then to the six changes which each three makes, add the fourth figure which is wanting; as to the six changes on 123 add the 4, to the six changes on 124 add the 3, to the six changes on 134 add the 2, and to the six changes on 234 add the 1, which renders the changes compleat; for then the four figures stand twenty four times together, and not twice alike, as here appears.

│1234
│2134
│————
│1324
│3124
│————
│2314
│3214
│————
│1243
│2143
│————
│1423
│4123
│————
│2413
│4213
│————
│1342
│3142
│————
│1432
│4132
│————
│3412
│4312
│————
│2341
│3241
│————
│2431
│4231
│————
│3421
│4321

_Five_ will make five times as many changes as _four_; for there are five times four figures to be had out of five, and not twice four the same figures, which are to be produced as before, by casting away each of the five figures by turns. Cast away 5, and 1234 will remain; cast away way 4, and 1235 will remain; cast away 3, and 1245 will remain; cast away 2, and 1345 will remain; cast away 1, and 2345 will remain. So that here are five times four figures produced, and not twice four the same figures. Now each four may be varied twenty four ways, as in the preceding example; then to the twenty four changes which each four makes, add the fifth figure which is wanting: as to the twenty four changes on 1234, add the 5; to the twenty four changes on 1235, add the 4. to the changes on 1245, add 3. to the changes on 1345, add 2. and to the changes on 2345, add 1. which renders the changes compleat, for then the five figures stand sixscore times together, and not twice alike.

12345│12354│12453│13452│23451
21345│21354│21453│31452│32451
—————│—————│—————│—————│—————
13245│13254│14253│14352│24351
31245│31254│41253│41352│42351
—————│—————│—————│—————│—————
23145│23154│24153│34152│34251
32145│32154│42153│43152│43251
—————│—————│—————│—————│—————
12435│12534│12543│13542│23541
21435│21534│21543│31542│32541
—————│—————│—————│—————│—————
14235│15234│15243│15342│25341
41235│51234│51243│51342│52341
—————│—————│—————│—————│—————
24135│25134│25143│35142│35241
42135│52134│52143│53142│53241
—————│—————│—————│—————│—————
13425│13524│14523│14532│24531
31425│31524│41523│41532│42531
—————│—————│—————│—————│—————
14325│15324│15423│15432│25431
41325│51324│51423│51432│52431
—————│—————│—————│—————│—————
34125│35124│45123│45132│45231
43125│53124│54123│54132│54231
—————│—————│—————│—————│—————
23415│23514│24513│34512│34521
32415│32514│42513│43512│43521
—————│—————│—————│—————│—————
24315│25314│25413│35412│35421
42315│52314│52413│53412│53421
—————│—————│—————│—————│—————
34215│35214│45213│45312│45321
43215│53214│54213│54312│54321
—————│—————│—————│—————│—————

And in this manner the compleat numbers of changes on six, seven, eight, nine, ten, eleven, twelve, _&c._ may also be demonstrated.

The numbers of changes will also plainly appear by the methods, whereby they are commonly prickt and rung. Now the nature of these methods is such, that the changes on one number comprehends the changes on all lesser numbers, and that so regularly, that the compleat number of changes on each lesser number are made in a most exact method within the greater; insomuch that a compleat Peal of changes on one number seemeth to be formed by uniting of the compleat Peals on all lesser numbers into one entire body; which will manifestly appear in the 479001600 changes on twelve: for that Peal comprehends the 39916800 changes on eleven; these likewise comprehend the 3628800 changes on ten, these changes on ten comprehend the 362880 on nine, these on nine comprehend the 40320 on eight, these on eight comprehend the 5040 on seven, these likewise the 720 on six, the 720 also comprehend the 120 on five, the 120 comprehend the 24 changes on four, these also comprehend the six changes on three, and the six comprehend the two changes on two. Each of these Peals (_viz._) on eleven, ten, nine, eight, seven, six, five, four, three, and two, being made in a most exact method within the changes on twelve. For Example, _two_ are first admitted to be varied two ways, thus——

│12
│21

Now the figure 3 being hunted through each of those two changes, will produce the six changes on three. The term _Hunt_, is given to a Bell to express its motion in Ringing, which in figures is after this manner. It must lie behind, betwixt, and before the two figures: first behind them thus, 1 2 3; then betwixt them, thus, 1 3 2; now before them, thus, 3 1 2: this is called a _hunting_ motion, and here it has hunted through the first change of the two, wherein it made three variations, as appears in the figures, standing thus in order.——

│123
│132
│312

Now it must hunt through the other change, which is 2 1, in the same manner as before; that is, first it must lie before, then betwixt the two figures, then behind them, thus, 321, 231, 213. Here it has hunted through again, wherein it made three more variations; which three being set directly under the former, the six variations will then plainly appear, as in these figures: where the three figures stand six times together, and not twice alike.

│123
│132
│312
│321
│231
│213

Now the figure 4 being in like manner hunted through each of those six changes, will produce the 24 changes on four. First, therefore it must hunt through the first, which is 123, letter (_a_), then through the second change of the six, which is 132, letter (_b_); then through the third, which is 312, letter (_c_), and so it being hunted through the rest of the changes likewise, will produce the twenty four changes on four.

(_a_)│1234
„ │1243
„ │1423
„ │4123
│
(_b_)│4132
„ │1432
„ │1342
„ │1324
│
(_c_)│3124
„ │3142
„ │3412
„ │4312

The figure 5 being hunted through each of those twenty four changes, will produce the 120 changes on five, First therefore it must hunt through the first, which is 1234, letter (_a_); then through the second, which is 1243, letter (_b_); then also through the third, which is 1423, letter (_c_). In which manner it being hunted through the rest of the twenty four changes, will produce the 120 on five. And then the figure 6 being hunted through each of those sixscore changes will produce the 720 changes on six. And the figure 7 being hunted through each of those 720 changes, will produce the 5040. In which manner also the eighth, ninth, tenth, eleventh, and twelfth, being successively hunted through each Peal in the aforesaid order, will at length produce the compleat number of changes on twelve. Wherein ’tis observable, that all the figures, except two, have a hunting motion; which two may properly be term’d the Center, about which the rest do circulate. By these methods it is evident, that every hunting figure hath a certain number of figures assigned, through which tis constantly to hunt: as in the aforesaid Example on twelve, where the 1.2 are assigned for the figure 3 to hunt through, as appears in the six changes before. And in like manner, 123 are assigned for the figure 4 to hunt through; 1234 are assigned for the figure 5 to hunt through; 12345 for 6 to hunt through, _&c._ Now the figure 3 hunts as many times through the 1.2. as those two make changes, that is, two times wherein it makes twice three changes, that is, six, as before appeareth. The figure 4 hunts as many times through the 123, as those three figures make changes, that is, six times; wherein it makes six times four changes, which amounts to twenty four. The figure 5 hunteth as many times through the 1234, as those four figures make changes, that is, twenty four times; wherein it makes twenty four times five changes, which amounts to 120. The figure 6 hunts as many times through the 12345, as those five make changes, that is 120 times, wherein it maketh 120 times six changes, which amounts to 720. And in like manner the figure 7 hunts 720 times through 123456, wherein it maketh 720 times seven changes, which amounts to 5040. The eighth hunteth 5040 times through 1234567, wherein it makes 40320 changes. The 9^{th} hunteth 40320 times through 12345678, wherein it makes 362880 changes. The tenth hunteth 362880 times through 123456789, wherein it makes 3628800. The eleventh hunteth 3628800 times through 1.2.3.4.5.6.7.8.9.10. wherein it makes 39916800. And lastly, the twelfth hunteth 39916800 times through 1.2.3.4.5.6.7.8.9.10.11. wherein it makes 39916800 times twelve changes, which amounts to 479001600, being the compleat number on twelve. By which ’tis evident, that every hunting figure hunts as many times through its assigned number of figures, as those figures are capable of making changes, which in short comprehends the summe and substance of this method, which is universal from two, to all greater numbers whatsoever.

(_a_)│12345
„ │12354
„ │12534
„ │15234
„ │51234
│
(_b_)│51243
„ │15243
„ │12543
„ │12453
„ │12435
│
(_c_)│14235
„ │14253
„ │14523
„ │15423
„ │51423

If we consider the multitude of different words, wherewith we express our selves in Speech, it may be thought almost impossible that such numbers should arise out of twenty four Letters; yet this Art of variation will produce much more incredible effects. To give an instance thereof, I will shew the numbers of every quantity of Letters from two to twelve, that may be produced out of the Alphabet. The generality of Words consisting of these quantities, (_viz._) two letters, three letters, four, five, six, seven, eight, nine, ten, eleven, and twelve letters. There are 10626 times four letters to be produced out of the twenty four letters of the Alphabet, and not twice four all the same Letters. There are likewise 42504 times five letters, 134596 times six letters, 346104 times seven, 735471 times eight, 1307504 times nine, 1961256 times ten, 2496144 times eleven, and 2704156 times twelve. Now each quantity being varied by the rules of this Art, will produce incredible numbers. First the 10626 times four letters, being multiplied by 24, which are the number of ways to vary each four letters, will produce 255024 that is to say, four letters may be produced out of the Alphabet to stand together after this manner (_a b c d_) two hundred fifty five thousand and twenty four times, and not twice alike. And in like manner, the 42504 times five Letters, being multiplied by 120, which are the number of ways to vary each five, will produce 5100480. The 134596 times six letters, being also multiplied by 720, will produce 96909120. The 346104, being multiplied by 5040, will produce 1744364160. The 735471, being multiplied by 40320, will produce 29654190720. The 1307504, being multiplied by 362880, will produce 474467051520. The 1961256, being multiplied by 3628800, will produce 7117005772800. The 2496144, being multiplied by 39916800, will produce 99638080819200. And lastly, the 2704156 time twelve letters, being multiplied by 479001600, will produce 1295295050649600, which products being all added together, as also 12696 which are the numbers consisting of two and three letters, the whole will amount to 1402556105125320, wherein there are not two alike, nor two letters of one sort in any one of them; which being written or printed on large Paper in _folio_, allowing 5000 to a sheet, they would take up 561022442 Reams of Paper and upwards, reckoning 500 sheets to a Ream: which Paper all the Houses in the City and Liberties of _London_ would not contain; and in quantity doubtless infinitely exceeds all the Books that ever were printed in the world, reckoning only one of each Impression. And at the rate of five shillings the Ream, the Paper would cost 140255610.5 Pounds sterling; which is above four times as much as the yearly Rent of all the Lands and Houses in _England_ amounts to. And all the people both young and old in the City and Suburbs of _London_ (admitting they are five hundred thousand) could not speak the like numbers of words under forty years and upwards, each of them speaking 15000 every hour, and twelve hours every day. These prodigious numbers are the more to be admired, considering that the greatest number of letters in any of them, exceeds not twelve, neither are two letters of one sort in any one of them: but by producing and varying all the greater quantities, and placing two or more letters of one sort, or two of one sort and two of another, with all variety of the like nature that commonly happens in words, the numbers arising thereby would infinitely exceed the former; And if all the numbers of every quantity of letters from one to twenty four, together with all the variety as aforesaid, were methodically drawn out and varied according to the rules of this Art; which might easily be performed in respect of the plain and practical method of doing it; but the infinite numbers of them would not permit a Million of men to effect it in some thousands of years: it would be evident, that there is no word or syllable in any language or speech in the world, which can be exprest with the character of our _Alphabet_, but might be found _literatim_ and entire therein; and more by many thousands of Millions than can be pronounced, or that ever were yet made use of in any language.

I will here give one instance of another kind, shewing the admirable effects of this Art, and so conclude. A man having twenty Horses, contracts with a Brick-maker to give him one hundred pound Sterling; conditionally that the Brick-maker will deliver him as many Loads of Bricks, as there are several Teams of six Horses to be produced out of the aforesaid twenty to fetch them, and not one Team or Sett of six Horses to fetch two Loads. The Brick-maker might be thought to have made a very advantageous bargain, but the contrary will appear. For there are thirty eight thousand seven hundred and sixty several Teams of six Horses, to be produced out of twenty, and not twice six the same Horses; then the Brick-maker must deliver as many Loads as there are Teams, and each Load consisting of five hundred Bricks, the whole would amount to 19380000, which being bought for one hundred pounds as aforesaid, would not cost above five Farthings a thousand; and at the rate of thirteen shillings and four pence the thousand, they amount to twelve thousand nine hundred and twenty pounds Sterling. But should a contract be made with the Brick-maker to deliver as many Loads of Bricks, as there are Teams of six Horses in each, to be produced out of the aforesaid twenty, which shall stand in the Cart in a differing manner; that is to say, although there may be the same Horses in several Teams, yet their places shall be so changed, that they shall not stand twice alike in any two Teams. On this account the Brick-maker must deliver seven hundred and twenty times as many as before; for there are 38760 several Teams as before I have shewed: then each Team may be placed 720 ways in the Cart, and not twice alike, which is to be done according to the methods whereby the 720 changes on six Bells are rung. So that 38760, which are the number of Teams, multiplied by 720, which are the number of ways to vary the six Horses in each Team, the product will be 27907200, which are the compleat number of Teams; and every Team carrying one Load, consisting of five hundred Bricks, the Whole will amount to 13953600000 Bricks. And after the proportion of a hundred and fifty thousand of Bricks to a House, they would build ninety three thousand and twenty four Houses; which are above six times as many as the late dreadful fire in _London_ consumed. And at the rate of thirteen shillings and four pence the thousand, they are worth 6976800 pounds Sterling, which is at least four hundred Waggon-loads of money, as much as five Horses can ordinarily draw.

]

AN
INTRODUCTION
To the Practice of
RINGING

As the original design of casting Peals of Bells was in order to make pleasant Musick thereon; so the Notes in every Peal are formed apt for that end and purpose, every Peal of Bells being tun’d according to the principles of Musick; for in a Peal of six Bells are the six plain Song-Notes, whereupon all Musick consists, namely, _la sol fa mi re ut_. But in regard that in ringing of them the Notes cannot be had at command, as the Notes of other Instruments may; therefore, as the Practitioners in ancient time found some necessity to cause all the Notes to strike successively after one another, so likewise they thought fit in ringing them to place the Notes in this following order. The least note to lead or strike first, then the Note which is the next degree deeper or flatter, and so the rest of the notes to strike after each other according to their degrees, the flattest striking last; in which order the notes were successively reiterated both at fore-stroke and back-stroke, from the beginning to the end of each Peal. And at this day the same order is also observed in raising, ceasing, and ringing them at a low compass; wherein each note being confin’d to strike in a certain place, therefore had they their terms of First, Second, Third, Fourth, Fifth, _&c._ given them, to denote their order and places of striking; from whence also the Bells derive those terms of distinction by which they are now known. Although the ringing of a Peal of Bells in the aforesaid order, (which is commonly term’d _Round-ringing_) is in it self Musical; yet the Notes may be so placed in ringing, that their Musick may be rendred much more pleasant: for in Musick there are Concords, which indeed may be term’d the very life and soul of it, that renders all Musick exceeding pleasant: the principal are Thirds, Fifths, and Eights; Thirds are 1 3. 2 4. and such like: Fifths are 1 5. 2 6. _&c._ Eights are 1 8. 2 9. 3 10. _&c._ each Concord consisting of two notes. They may well be termed Concords, in respect of their agreement and harmony; for the two notes (as if it were by mutual consent) being struck together at one instant, or else immediately after one another, affords delightful melody to the ear; in which respect, a peal of five Bells are capable of making better Musick than a peal of four; six better than five; and more especially will ten or twelve make more excellent Musick than any lesser numbers can possibly do, there being greater variety of Concords therein, and especially of Eights. For this Musical end were changes on Bells first practised, _changes_ being nothing else but a moving and placing of the Notes in ringing, whereby variety of pleasant Musick is made; and as the manner of moving the notes, is, for two notes to change places with each other, therefore are they called _Changes_. The methods of changes being somewhat intricate, I have therefore penn’d the following Treatise as a Clue to guide the Practitioner through the Labirinth of them, wherein I have made use of figures to represent the notes of Bells, the manner thus. In a peal of five Bells there are five several notes, which with figures are thus exprest, 1 2 3 4 5: the figure 1 represents the least or sharpest note, which is term’d the First, because its place in round ringing is to lead; this note is most commonly called the _Treble_. The figure 2 represents the note which is the next degree deeper or flatter, and is term’d the Second, because it strikes in the second place. And in like manner 3 represents the note of the third Bell, 4 the note of the fourth Bell, and 5 the note of the Fifth or Tennor. In which manner, the figures in all the following methods do likewise represent the notes of Bells.

Since the ringing of changes requires the peal of Bells, on which the changes are to be rung, to be first raised up to a set Pull, which compass is most proper for the ringing of them; therefore the Learners first practice must be to raise a Bell true in peal, to ring it at a low compass, and also to cease it true in peal, wherein consists the chief grounds of this Art, which depends on the Ear, and therefore much judgment is required therein. And to speak the truth, most practitioners are in these days somewhat deficient herein; the ringing of changes having generally diverted the Learners fancy from the practice of _raising_, _round-ringing_, and _ceasing_, by which means we have in a manner lost one Excellency in the pursuit of another. Therefore I could wish that the Practitioners of this Art would set a greater esteem on true Ringing in general, since the only excellency as well in the ringing of Changes as Rounds, depends thereon: the keeping of time being as essential to render all kinds of ringing pleasant to the ear, as ’tis to render any other kind of Musick; therefore the practitioner ought to have a Musical eare, and to have some judgment in beating time, without which he can never ring his Bell true in its place. A prospect of true ringing at any certain compass under the Sett, may thus be taken; for Instance, in ringing a peal of 5 Bells; from the fore-stroke of every note to the next fore-stroke of the same note, there ought to be eleven _punctums_ or Beats of time, which are all supposed to stand at Æquidistances: now in ten of these _punctums_, the five notes ought exactly to strike at the fore-stroke and back-stroke, and the eleventh stands as a Cypher to guide the Treble-note at fore-stroke to a double proportion of time from the Tennor-note at back-stroke: which blank _punctum_ must also be beaten in the same place by every note, to render its fore-stroke answerable to that of the Treble. For example; the third note having struck at fore-stroke, it must beat eleven _punctums_ of equidistance unto its striking there again. The first _punctum_ is that of the 4^{th} note, the second 5, the third 1, the fourth 2, the fifth 3, the sixth 4, the seventh 5, the eighth 0, the ninth 1, the tenth 2, the eleventh its own place of striking again at fore-stroke. These _punctums_ or Beats of time, must be proportioned either wider or closer, according to the compass of the Treble: therefore first the Treble must fix its compass certain and true at fore-stroke, which ought to be proportionate to what the number of the notes, and compass of the peal of Bells, may according to judgment permit; and then from one fore-stroke of it to the next, if there are five notes; there ought to be eleven _punctums_ of equidistance assigned, wherein the notes should exactly strike (except the blank) as before. From hence ’tis, that the most judicious Ringer ought to be put to the Treble; for that bell cannot possibly be rung true by any other means than by beating of its own time; and although the exactness of true ringing requires the like in every note, when once the compass is fixed, yet the leading note being rung true, may be a guide to the rest of the notes, which may tolerably take their measures of time from the Treble-note: but for every note to take its measure of time solely from the next preceding note, must needs be very erronious; for thereby they implicitely lead one another out of the way. Or else in the ringing of five bells, from the fore-stroke of every note to the next fore-stroke of the same note, there may be one and twenty _punctums_ or beats of time assigned, to stand at equidistances; and the five notes, as they follow one another, at the fore-stroke and back-stroke to strike in every second _punctum_, except the Treble-note at fore-stroke, which must strike in the third _punctum_ from the Tenor at back-stroke; so that then there will be two of those spaces betwixt every note, and three betwixt the note of the Tenor at back-stroke and the note of the Treble at fore-stroke, which possibly by some may be held a better compass than the former: but _quot homines tot sententiæ_. Every Practitioner, that has judgment to beat his own time, has the advantage of ringing his bell true, whilst the rest of the notes commit faults; for the compass being once fixed, as many bells as do either rise or fall from thence commit errors.

The truest way of raising a peal of bells according to the best of modern practice, is, as quick as may be; every Ringer taking assistance to raise his bell, according as the going of it requires. In raising of them, the lesser bells as the Treble _&c._ ought at the first pull to be swayed very deep, and held down in the sway by strength of armes as much as may be, to delay the time of their first striking, by which means the bigger bells, which carry a large compass, may have space to come in; and the raising of the smaller bells to be continued with a strong pull, giving them scope over head (for the aforesaid reason) untill they come up Frame-high, or thereabouts, and then the pull to be slacken’d, and the bells leisurely to be raised to the intended height or pitch. The bigger bells of the peal, as the Tenor _&c._ must in their first raising be checkt or pinch’d over head, by which means the notes of all the bells may be made to strike round in their due place and order from the beginning; and observe, that at the first pull all the bells must follow one another as close as may be. A peal of bells may thus be ceased: the falling of the bells from a Sett-pull must gradually be done, by checking them only at Sally, until the low compass renders the Sally useless; and when they are ceased so low, that they scarce strike at back-stroke for want of compass: then he that rings the Treble, may give notice (by stamping on the ground) that the next time the bells come to strike at the fore-stroke, they may be checkt down so low as to cease their striking at the back-stroke, yet their striking round at the fore-stroke may be continued, until they are brought into a chime, which is a graceful conclusion of a peal.

In raising of a peal of bells, all the notes ought to strike round at one pull: but mistake me not, I do not mean at the first pull; for at small bells ’tis usual to sway them all round at the first pull without striking; at the second pull to strike them at the fore-stroke, and at the third pull at back-stroke. In raising of a peal of more weighty bells, ’tis usual to strike them double at the fourth pull, because the extraordinary weight and large compass of the hind-bells permits it not to be done sooner. In the first raising of a peal of bells, one bell ought not to strike before the rest, or to miss striking when the rest go round: neither ought any bell in ceasing to strike after the rest, or to leave striking before the rest; all which, according to the strictness of true ringing, are accounted great faults.

The peal of bells on which the changes are to be rung, must first be raised up to a Sett-pull, which compass is most proper for the ringing of changes; for then the notes of the bells may be had at command. Therefore before the young Practitioner can be capable of ringing changes, he must be extraordinary well skill’d in the managing of a bell at a Sett-pull, which is absolutely requisite, for this reason: In the ringing of changes, his mind will be so busied and wholly taken up with the consideration of the course and method of them, and his eye continually wandring about to direct his pull in the following of the other bells; that unless he has extraordinary skill in the managing of his own bell, and can set it in a manner hood-winkt, he will be apt either to drop or overturn it; or else on the other hand, for want of skill, his eye and mind will be so fixed on his own rope and bell to guide the managing of it, that he cannot at the same time mind the course of the changes, and then no wonder if he is in a wood, which consequently follows; and indeed hence partly ’tis, that the Learners in their first practice do oftentimes toil and moil themselves to so little purpose. Therefore ’tis not enough that the young Practitioner can set a bell it may be half a score times together, when ’tis an even wager that he either drops or overturns it in those ten-pulls: but he must be so perfectly skill’d, as that he might adventure to lay ten to one, that he can set it thirty or forty times together, both fore-stroke and back-stroke, without dropping or overturning it, and without looking directly either on his hands or rope whilst he sets it. Therefore in his practice of setting a bell, he may cast his eye about on the other bell-ropes whilst he manageth his bell, whereby he may accustom himself to manage it as the ringing of changes requires.

The ringing of changes is performed, partly by the ear, and partly by the eye; the ear informs when to make a change, the eye directs the pull in the making of it, but then again the ear guides the striking of the note true in its place according to time. So that the ear and eye have each of them its proper object in the ringing of changes, and therefore ought at the same time to be absolutely free from all others whatsoever, the notes of the bells being the object of the ear, and the bell-ropes the object of the eye. Now these two Senses in the time of ringing do each of them thus perform its office. First, the ear, as a Sentinel, discovers the near approaching change, and also the place wherein his note lies, that is, whether before or behind the note wherewith ’tis to make a change, and gives present information to the eye, to perform its part accordingly in the making of it; but then again the eye refers it to the ear, to place the note true in striking. But questionless (by the bie) the truest ringing of changes is to be performed only by the ear; but then the Practitioners must be capable to judg of time, and to beat it true, which must be the only direction to guide their pull; and then it must be performed at a peal of bells that may be managed with ease: and being so fitted in all respects, the changes may doubtless be rung more true, with greater pleasure to the Practitioners, and much more free from mistakes and forgets, only by the ear, than by making use of the eye to direct their pull. But in regard that either the ill going of the bells, or want of fit accomplishments in the practitioners, may render it unfit for common practice; therefore the surest way is to ring both by the eye and ear, as I said before. Now to render the eye and ear rightly useful in the ringing of changes, five things ought by the young Practitioner to be well understood. First, he must be able to distinguish the notes of a peal of bells, and to know one from another in the time of ringing. Secondly, he must apprehend the places of the notes. Thirdly, the precedency of notes. Fourthly, the manner of making a change in ringing. Fifthly, a general prospect of the manner of putting the four preceding notions into practice.

_Observation 1._ The Learner must be able to distinguish the notes of a peal of bells one from another, and to know them asunder; as the Treble-note from the Second, the Second from the Third, _&c._ which, tis true, may readily be done in round ringing, because each note may be known by the place wherein it constantly strikes; but in ringing of changes it is more difficult. For admitting that six bells should strike in this order, 5.3.6.1.4.2. it might puzzle an unskilful ear to judg which is the Treble, or which the Second note, especially whilst any other note strikes betwixt them: and the like difficulty might happen in distinguishing the rest of the notes, as the _2d_ from the _3d_, _&c._ To remove this difficulty, he must endeavour to acquire some skill in tuning the notes of a peal of bells, with his voice, which he may do by imitating the notes of the bells when he hears them ring: or else any person that has skill in singing, will presently direct him therein, and also how to take the true pitch of any notes with his voice, which will be the only means to distinguish them asunder.

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│ 1│2 │
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│3│4│5│
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_Observ. 2d._ The Learner must rightly apprehend the places of the notes, which I think cannot better be done than by this means. Considering that the notes of a peal of bells do all strike one after another at the fore-stroke, and the like at back-stroke; it might be requisite for him to imagine, that the notes in their striking do lie in a direct line, that is, in a row at the fore-stroke, and the like again at back-stroke; for then the places of the notes will much resemble the places of the figures wherewith the changes are prickt: for as the figures of every change do all stand in a row; so likewise the notes of the bells, being imagined to strike in the like row, he may the more readily apprehend the places of the notes, and consequently of changing them. For the practick part of this Art, is performed by means of imaginary, not real notions; which will thus manifestly appear. This is the platform of a Frame, wherein five bells may be supposed to hang in a Steeple, the figures therein representing the places wherein the five bells hang. Now in the sixscore changes on five bells, we will suppose the Treble to be the whole Hunt, and to hunt up first over the Second, then over the Third, _&c._ Now the Treble cannot really move out of the place wherein it hangs; but by delaying its striking untill the Second Bell has struck, it may by that means strike next after it; and again, by delaying its striking until the Third has struck; it may also strike next after that, this being the true manner of the changes; by which ’tis evident, that the bells have neither really such places nor motion as is pretended, but is meerly imaginary, and was at first feigned only as a Guide to direct the Practitioner’s apprehension in the ringing of them. So that although the art of changes is in it self a real thing, yet the notions by which they are reduced to practice on bells, are not so. For which reason, the several practitioners of this Art, before they can become expert, are fain to form in their minds imaginary notions to guide them; some after one manner, some perhaps after another, according to their several fancies, yet all tending, to render the methods of changes practicable on bells; and having once form’d in their minds such imaginary helps, they become expert in short time: and then no sooner do they understand the methods of changes prickt with figures, which they commonly discover at first view; but they are presently capable of ringing them readily on bells, which experience daily testifies. And hence it is, that oftentimes the Learners, although they perfectly understand the methods of changes prickt, and also can perfectly manage a Bell; yet for want of a right apprehension of the nature of changing the notes, which of themselves it may be they cannot soon attain, are therefore much puzzled in their first practice of ringing changes. Therefore as a guide, the Learner must first form in his mind a fit representation of the places of the notes; which I think cannot better be done, than by imagining each note to be a figure; as the Treble-note to be the figure 1, the second note the figure 2, the third note the figure 3, and the like of the rest. Then whensoever he hears a peal of bells ring, let him by strength of imagination conceit, that each note bears the shape of a figure; that is, at the same instant of time that the note strikes, he may imagine that it leaves the impression of the figure behind it, and that with the eye of his imagination he perfectly sees it: and likewise as the notes of the bells do all strike after one another at the fore-stroke, so he may imagine that they lie in a row in the shape of figures; and the like again at back-stroke. For instance: suppose that five Muskets were charged with five bullets, and that each bullet bears the shape of a figure; one Gun to be charged with the figure 1, another with the figure 2, and the other three Guns with these three figures, 3. 4. 5. Then supposing a straight line were drawn upon the wall, thus —————————— and that the five Muskets were by five men levell’d against the line, which is to be the mark for them to shoot at; the figure 1 to be first shot off, then the figure 2, and so the rest in order immediately after one another: now at the same instant of time that the Guns are heard to go off, the five figures would appear in a row upon the wall, thus. So in like manner when he hears a peal of five bells strike after one another at the fore-stroke, and again at back-stroke, he may imagine that at the very instant of their striking their notes appear to his apprehension in the shape of the five figures, and that they strike in a row, thus, 1 2 3 4 5, as if each Bell were a Gun, and had shot out its note in the shape of a figure. There being necessity that the young Practitioner must either imagine each note to be a real figure, or else a representative: for as the ear is to be his guide to direct when to make each change; so a right apprehension of the motion and places of the notes, must be a means to guide his ear. Now in regard that the changes are first prickt with figures, from whence the notes of the bells derive their course, therefore if in ringing he imagine each note to be a real figure, then the same knowledge that guides the pricking, guides also as readily the ringing of them, for then the note of his bell is supposed to have the same course with that of a real figure. But if he imagines that each note is not a real, but a representative of a figure; then consequently it must only have the like, and not the same course: by which means, whilst he is ringing of changes, his mind must have frequent recourse to his Pocket, that is, to the changes there prickt; from whence he must continually fetch instructions to direct the course of his Bell, which is oftentimes the case of the Learner: his thoughts in the time of ringing being commonly upon the figures that are prickt, either upon paper, or else upon the Steeple-wall, whilst it should be wholly intent upon the notes. Therefore in a word, the Practitioner whilst he is ringing of changes, must fix his mind fully and wholly upon the notes of the bells, and not permit it in the least to wander from thence; for the notes are to be the sole object of the thoughts in the time of ringing.

The notes being imagined to strike in a row as aforesaid, their places will then soon be understood. The notes do take their places according to their successive order of striking both at fore-stroke and back-stroke; each succeeding note taking its place next to that which preceds it: for whatsoever bell leads either at fore-stroke or at back-stroke, its note lieth in the first place of the supposed row of notes; and that which strikes next after the leading note, its note lieth in the second place of the supposed row of notes, and so the rest in the like order. As if five bells should strike thus after one another either of fore-stroke or back-stroke, 5 4 1 2 3. here the _5th_ lieth in the first place, because it was first struck; the _4th_ in the second place, because it was second struck; the Treble in the third place, because it was third struck; the _2d_ in the fourth place, because it was fourth struck; and the _3d_ in the last place, because it was last struck; and the like of the notes in every change.

_Observ. 3._ The next thing to be understood by the Learner, is the precedency of the notes. Now whereas in the ringing of changes, the notes do all strike after one another at the fore-stroke, and again at the back-stroke, therefore are they said to lie before or behind each other, according to their places of striking. As if five men were standing in a row, as these five figures represent, 1 2 3 4 5, the first man to stand at the fig. 1, the second man at the figure 2, _&c._ and that they stand with their faces all one way, that is, the first man ready to lead, and the rest to follow him one behind another. Now the first man stands before the rest, and the fifth man behind the rest; the second man stands behind the first man, but before the third; the third man stands behind the second, but before the fourth; and the fourth stands behind the third, but before the fifth. In which manner the notes being supposed to strike in the like row, may also be laid to lie before or behind each other as the men did. For whatsoever note leads either at fore-stroke or back-stroke, is said to lie before the rest; and that which strikes last, to strike behind the rest. The note which lieth in the second place, as on the one hand it lieth behind the leading note, so on the other hand it lieth before the note in the third place. As the note in the third place lieth behind the note in the second place, so it lieth before the note in the fourth place. And in like manner, every note is said to lie behind those that strike before it, and before those that strike after it.