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.

[Illustration: [Fleuron]]

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.

┌──┬──┐

│ 1│2 │

├─┬┴┬─┤

│3│4│5│

└─┴─┴─┘

_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. [Illustration: –1–2–3–4–5–] 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.

_Observ. 4._ A Change is to be made betwixt two notes, by moving them

into each others places; wherein ’tis to be observed as a general Rule,

That every change must be made betwixt two notes that strike next to

each other. As if five bells were ringing round in this order, 12345,

the 1 and 2 may make a change, or 2 and 3, or likewise 3 and 4, or 4 and

5, because each two lie next each other; but the 1 and 3 cannot, because

2 strikes between them, much less may 1 and 4, _&c._ The two notes which

make every change, moves into each others places in the making of it;

wherein one note is said to move _up_, and the other _down_. The reason

why one of them is said to move up, is, because he that rings that bell,

in the making of the change must hold it up at the Sett a little longer

than ordinary, to delay its striking, whereby ’tis made to follow the

other note which before it preceded; and because ’tis so held up,

therefore ’tis said to make an _Up-change_, or to move up: and on the

contrary, the reason why the other note is said to move down, is,

because he that rings it, pulls down the bell a little sooner than

ordinary, to make it strike before the note which before it followed;

and because ’tis so pulled down, therefore it is said to make a

_Down-change_, or to move down. I will here give a short though certain

rule to know when an Up-change or a Down-change is to be made:

whensoever any note moves to strike behind the note wherewith it makes a

change, it makes an up-change in doing it; and whensoever it moves to

strike before the note, which ’tis to make a change with, it makes a

down-change in doing it: so that every note which moves fromward the

leading-note, makes an up-change; and when it moves toward the

leading-note, it makes a down-change. I will here shew the manner of

making a change: admitting that a peal of five bells were raised to a

sett-pull, which is the usual compass for ringing of changes; the notes

are first supposed to strike in this order, 12345. Now a change may be

made betwixt any two notes that strike next each other; I will here make

it betwixt the 3d. and 4th. which is to be done by moving them into each

others’ places. Now ’tis observable, that before the making of the

change, the 3d. note lies before the 4th. that is, it strikes next

before the 4th; and the 4th. lies behind the 3d. that is, it strikes

behind it: now in the making of the change, the 3d. must move to strike

behind the 4th: wherein it makes an up-change; and the 4th. note at the

same time must move to strike before the 3d. wherein it makes a

down-change; the change being made, the bells will strike thus, 12435.

All changes whatsoever are made in the aforesaid manner: for as the _3d_

note made an up-change in moving to strike behind the _4th_, and the

_4th_ at the same time a down-change in moving to strike before the

_3d_; so in like manner the two notes that make every change, must in

the making of it move the one up, and the other down, as the _3d_ and

_4th_ here has done. The Learner may take notice, that in ringing termes

’tis not usual to say, that a bell makes an up-change, or a down-change;

but in short, that it _moves up_ or _down_, which implies the former.

When a note makes an up-change, ’tis then said to move _over_ the other

note; and when it makes a down-change, to move _under_ it: as in the

next preceding example, where the _3d_ note is said to move up over the

_4th_, and the _4th_ down under the _3d_, in which manner the terms

_over_ and _under_ are given to the two notes that make every change.

_Observ. 5._ In the time of ringing changes, two things are by the

Practitioners to be well considered. First, to observe and readily to

know, which two bells are always to make the next succeeding change:

Secondly, if he is concern’d therein, to consider what bell he is to

follow in the making of it. Upon a right knowledge of these two things,

depends the Practick part of this Art. To make him expert herein, he

must before hand perfectly understand, and readily remember the course

and method of the changes prickt with figures, wherein he ought to be so

well skill’d, as to be able to prick them down divers ways, that is, to

make any figure a Hunt at pleasure; which when he can readily and

speedily do, without pausing to consider of the course, then ’tis

presumed that he understands the methods throughly. But yet he will not

be capable to put them in practice, untill he understands the manner of

making a change in ringing; neither can he understand that, until he

understands the precedency of the notes; nor the precedency, until he

understands the places; nor the places, until he knows the notes one

from another. Therefore the four preceding observations being first

perfectly understood, and also the methods of the changes as before; the

Practitioner may then successfully proceed in the ringing of changes;

and as a further help therein I will here instruct him. There are three

bells concern’d in the making of every single change, except only when

’tis made behind, and then but two: whensoever the note of his bell is

to make a change with any other note, his ear must then inform him

whether it lies before or behind the other note; if it lies before, then

in making the change it must move up behind it, that is, to follow it;

and consequently, he must draw down his bell next after that which he

makes a change with, which is called an up-change, as I said before. But

if the note of his bell lies behind the other, then in making of the

change it must move down to strike before it, and consequently he must

draw down his bell next after that which the other before followed, this

being a down-change. So that the making of an up-change is very easie,

because he must always follow that bell which he makes a change with;

but a down-change is more difficult, because he cannot so readily

apprehend what bell he is to follow; yet there is a certain rule for it,

which is this: to observe beforehand what note strikes the next but one

before his, which bell he must follow in the making of the change.

Whensoever the two notes, which strike next before his note, are to make

a change; he must consider, that notwithstanding his note is to lie

still in its place, yet he is concern’d therein, because the bell which

he followed before the making of the change, must in the making of it

move away down, and therefore he must follow the bell that comes into

its place.

The changes are to be rung, either by _walking_ them, as the term is; or

else Whole-pulls, or Half-pulls. By _walking_ them, is meant, that the

bells go round four, six, eight times or more in one change; which way

is very proper for young Practitioners, to introduce them into a more

ready way of Practice; for whilst the bells go round divers times in one

change, they have in the mean time leisure to consider which two bells

are to make the next following change, and also what bell each of them

is to follow in the making of it; and so by diligence in practice they

will by degrees acquire a more ready skill to enable them to ring at

whole-pulls. Whole-pulls, is, when the bells go round at the fore-stroke

and back-stroke in a change; and every time they are pull’d down at

Sally, a new change is made. Whole-pulls was the general practice in

former times; and indeed, considering the manner of the hanging of the

bells in those days, they could not well be rung at half-pulls: but

since the improvement of the Art of Bell-hanging, that is, with round

Wheels, trussing them up in the Stock, and placing the Roll at right

Angles with the Sole of the Wheel; the bells go much better, and are

managed with more ease at a Sett-pull than formerly: therefore the

changes are now generally rung at half-pulls, that is, at the

fore-stroke one change, at the back-stroke another, and so throughout.

In ringing half-pulls, some peals of changes will cut compass, wherein

the whole Hunt comes always to lead at the back-stroke; to prevent

which, make the first change of the peal at the back-stroke. In plain

and single changes on six bells, to hunt (that is, whole Hunt) the

Treble, third, or fifth, down at the beginning of a peal cuts compass,

unless prevented as before. Also to hunt the second, fourth, or sixth up

at the beginning of a peal, cuts compass, unless prevented as before.

Which rules, leaving out the Tenor, serves in like manner to prevent

cutting compass on five bells.

’Tis convenient in ringing, to give notice of the extream changes, and

he that rings the slowest Hunt, may best do it. The manner of it is, to

say _Extream_, when the leading bell is pulling down, in order to make

the change next before the extream; by which means there will be one

compleat change betwixt the warning and the extream: longer warning

would be too much, and shorter too little.

The divers kinds of changes on Bells may be comprehended under two

heads, _viz._ Plain Changes, and Cross Peals, which terms are

comparatively given: for as the first are plain and easie only in

comparison to the methods of the second; so consequently the second

cross and intricate in comparison to the methods of the first. I will

first shew in what respect they differ, and then proceed to the methods.

Plain changes (I mean compleat peals) are such as have one universal

method, wherein all the notes except three have a direct hunting course,

moving gradually under each other in one plain and uniform order. But

the methods of cross peals are various, each peal having a course

differing from all others: and although most of them have Hunts, yet the

Hunts have different kinds of motions, and some very intricate. Moreover

plain changes are also term’d Single changes, because in the ringing of

them there is only a single change made in the striking of all the notes

once round either at fore-stroke or back-stroke; whereas in cross

changes ’tis usual to make as many changes as the number of notes will

permit. For example, supposing that a peal of 5 bells were raised, and

rung at a Sett-pull; the notes are supposed to strike round in this

order, 12345: now any two of the notes that strike next together may

make a change, therefore either a single or a double change may be made

at pleasure. The single change is made by changing only two notes; the

double change is made by changing four notes, that is, two to make one

change and two another, yet ’tis called one double change, and not two

changes, in regard ’tis made in the striking of the five notes of the

bells once round: as, admit the treble, second, third, and fourth,

should make a change, ’tis thus to be done, 21435, where the Treble and

Second made one change, and 3, 4 another; which we will imagine to be

made at the fore-stroke of the bells, and therefore ’tis called one

double change, and not two changes, because ’tis entirely made in the

striking of the five notes once round. So that this one double change

has effected that which would have required two single changes to have

done the like. For instance, there can but two notes change their places

at once in a single change, therefore the Treble and Second shall first

change their places thus, 21345; then the third and fourth thus, 21435:

so that here the five notes have gone twice round to effect that, which

in the double change was done in going once round. And this is the

nature of the difference between Plain and Cross changes.

As the Learner ought to proceed regularly in his practice, beginning

first with the plainest and easiest methods. I will therefore observe

that order, and first shew the course and methods of Plain changes.

_The Changes on two Bells._

Two bells are capable to make only two changes, which is to be done by

changing the notes twice, as in these figures.——

│_1 2_

│ 2 1

│ 1 2

_The Changes on three Bells._

There are six changes on three bells; which are made by this rule: the

two first and two last notes must be changed by turns.

│_123_

First the two first notes, which are 1 2 thus.│ 213

The two last, which are 1 3, thus. │ 231

The two first │ 321

The two last │ 312

The two first │ 132

The two last │ 123

In these six changes ’tis observable, that the two first notes, which

were 1 2, made the first change of the six; but they may as well be rung

by

│_123_

beginning with the two last notes, which are 2, 3 thus——│ 132

Next the two first notes, which are 1 3, thus, │ 312

The two last │ 321

The two first │ 231

The two last │ 213

The two first │ 123

The six changes can be rung no more than these two ways here set down.

The Six changes are sometimes rung by observing a hunt therein, which is

very improper, since every note has a like course. Yet I confess in

demonstrating the methods on twelve, I did there admit a Hunt into the

six changes; but that was only for demonstration sake.

The compleat peals of plain changes, from three to all greater numbers

whatsoever, as the Twenty four changes on four, the Sixscore on five,

the Seven hundred and twenty on six, _&c._ are prickt and rung by one

method; all the notes having a hunting-motion, except only three in each

peal, which three do make the six changes in the same manner as they are

before prickt. So that the Six changes on three may be term’d the

_basis_ or foundation of the compleat peals on all greater numbers.

Every Hunting note in each peal has a certain number of notes assigned,

through which ’tis always to hunt. The term _hunt_ is given to a note in

respect of the manner of its motion, which I will shew in this example.

First, the notes of four bells are supposed to strike round in this

order, 1234. The Treble shall be the Hunt, and the other three assigned

or appointed for it to hunt through. Now whereas the Treble-note leads,

it must move through its assigned number to strike behind them: and

whereas every change must be made betwixt two notes that strike next

each other, as I have shewed before in the _4th Observation_; therefore

the hunting-note is confin’d to move gradually through the rest by

making a change with each note that strikes next to it; and accordingly

it must first move into the _2d_ place, next into the _3d_ place, and

lastly into the _4th_. So that ’tis to make a change with every note

that lies behind it; first with the _2d_ note, next with the _3d_, and

lastly with the _4th_.

│_1234_

The first change is thus│ 2134

The second thus │ 2314

The third thus │ 2341

The hunting note has here moved through its assigned number; for whereas

at first it did lead, now it strikes behind them. Wherein ’tis

observable, that it made up changes all the way; which of necessity it

must do, because every note with which it was to make a change, lay

behind it: and because it made up changes, therefore ’tis said to have

hunted up. The hunting-note shall now move through its assigned number

again, to lead as at first. Therefore first it must move into the _3d_

place, then into the second place, and lastly into the first place,

which is called the Treble’s place; in which motion it must make a

change with each note that strikes next before it: first with the _4th_

note, next with the _3d_, then with the _2d_.

The first change thus│2314

The second thus │2134

The third thus │1234

’Tis observable, that here the Treble made down-changes all the way,

which of necessity it must do, because every note with which it was to

make a change, lay before it: and because it made down-changes,

therefore it is said to have hunted down. This is the manner of the

motion of the hunting notes in all peals of plain changes; for they hunt

up and down through their assigned number, as the 1 here has done. This

example is plain and full to instruct the Learner in the hunting of any

bell, therefore he ought to peruse it diligently, that he may understand

the true scope and meaning of it; and as a help he may apply himself to

practice by taking a Treble, and attempt to hunt it up and down as this

Example directs; which he may the more readily do, if he understand the

_5th Observation_ before set down, which guides him to make a change in

ringing. So that partly by reading and well considering of what I have

here wrote, and partly by practice, he may in a short time become

perfect in the hunting motion of any note; which when he rightly

apprehends, he will then presently be capable of understanding the

following methods; and therefore I shall be the more brief in my

directions to them.

_The Changes on four Bells._

Twenty four changes may be rung upon four bells: but the Learner may

first practice the twelve changes, and the eighteen changes. In the

twelve changes the notes are all to be hunted up after one another,

which may be called the Twelve all over. First the treble-note must be

hunted up, letter (_a_); then the second note must likewise hunt up,

letter (_b_); next the third note must hunt up, letter (_c_); and lastly

the _4th_ note also, letter (_d_).

│_1234_

───┼──────

_a_│ 2134

„ │ 2314

„ │ 2341

───┼──────

_b_│ 3241

„ │ 3421

„ │ 3412

───┼──────

_c_│ 4312

„ │ 4132

„ │ 4123

───┼──────

_d_│ 1423

„ │ 1243

„ │ 1234

The four notes may also hunt down one after another. First, the _4th_

note must hunt down to lead: then the _3d_ note likewise, and so the

_2d_ and Treble one after another, which may be term’d the Twelve all

under.

Courteous Reader, in my directions to the course of each peal, I do

there refer by letters to the examples; which I am forced to do, to

prevent those confused breaks, and unhandsome spaces, which

otherwise would have happen’d both in examples and precepts.

Whatever letter I mention in my directions, refers to the like at

the figures. For instance; in my directions to the twelve changes

next before, I there directed the treble-note to be first hunted up,

letter (_a_); which letter refers to the like letter at the first

three changes of the twelve, where the Treble hunted up, as ’tis

here again represented, and the like of the rest.

_a_│2134

„ │2314

„ │2341

In the Eighteen changes, the Treble is a hunting note, but never hunts

up farther than the _3d_ place; and when it lies there, the two first

notes must make a change; and every time it leads, the two hindmost

notes. First it hunts up into the _3d_ place, letter (_a_); the two

first notes, Which are 2.3, make a change, letter (_b_); the Treble

hunts down (_c_). The two hindmost notes make a change (_d_), the Treble

hunts up (_e_). The two first notes, which are 3.4, make a change (_f_)

the Treble hunts down (_g_); the two last notes, which are 3.2, make a

change (_h_), which method being continued, will bring the bells round

at the end of eighteen changes. The Eighteen changes may also be rung by

hunting the _4th_ note down into the _2d_ place, and then a change to be

made behind: the _4th_ note to be hunted up again into its own place,

and then a change to be made before, which course being continued, will

produce Eighteen changes.

│1234

───┼────

_a_│2134

„ │2314

───┼────

_b_│3214

───┼────

_c_│3124

„ │1324

───┼────

_d_│1342

───┼────

_e_│3142

„ │3412

───┼────

_f_│4312

───┼────

_g_│4132

„ │1432

───┼────

_h_│1423

───┼────

_i_│4123

„ │4213

───┼────

_k_│2413

───┼────

_l_│2143

„ │1243

───┼────

_m_│1234

The Six changes on three are the ground of the Twenty four changes on

four; for one of the four notes hath a constant hunting motion through

the other three, in the same manner as in the preceding Example, _page

50._ and the three notes are to make the six changes in the same manner

as I have before shewed in the changes on three bells; one of the six

changes being always made every time the hunt lies either before or

behind the three bells: therefore if the Learner do but rightly

apprehend the course of the six changes, and also the manner of the

motion of the hunting note, he will presently understand the method of

the twenty four changes. The six changes in the twenty four, according

to the terms of ringing are called Extream changes, and the three bells

which makes them, Extream bells. So that in the twenty four changes,

there is a hunt and three extream bells. Every time the hunt lies either

before or behind the extream bells, an extream change must then be made.

The extream changes may be made two ways, _viz._ either betwixt the two

farthest extream bells from the hunt, or else betwixt the two nearest

extream bells to it. In this Example every extream change shall be made

betwixt the two farthest extream bells from the hunt, and the treble

shall be the hunting note, which must first hunt up (_a_); then the two

farthest notes from the hunt, which are 2.3, must make an extream change

(_b_). The Treble must hunt down (_c_). The two farthest notes from the

hunt, which are 2.4, must make an extream change (_d_). The treble must

hunt up (_e_); the two farthest notes from the hunt, which are 3.4, must

make an extream change (_f_). The treble-note must hunt down (_g_). The

two farthest extream bells from the hunt, which are 3.2, must make an

extream change (_h_). The treble must hunt up (_i_). The two farthest

notes from the hunt, which are 4.2, must make an extream change (_k_).

The treble must hunt down (_l_). The two farthest extream bells, which

are 4.3, must make an extream change (_m_), which concludes the peal.

Now the Learner for his satisfaction may take out the extream changes in

the same order as they were made, as first at (_b_), then (_d_), and so

(_f.h.k.m._) and they will stand as they are here set down; where ’tis

evident, that 2.3.4 have made the six changes according to the method of

the first six changes on three bells, before set down, (_page 48._)

where the first change of that six was 213, and this being 324, is the

same in course though the figures differ, and the rest of the changes in

this six, are likewise the same in course and method with those.

│1234

───┼────

_a_│2134

„ │2314

„ │2341

───┼────

_b_│3241

───┼────

_c_│3214

„ │3124

„ │1324

───┼────

_d_│1342

───┼────

_e_│3142

„ │3412

„ │3421

───┼────

_f_│4321

───┼────

_g_│4312

„ │4132

„ │1432

───┼────

_h_│1423

───┼────

_i_│4123

„ │4213

„ │4231

───┼────

_k_│2431

───┼────

_l_│2413

„ │2143

„ │1243

───┼────

_m_│1234

3241

1342

4321

1423

2431

1234

In the preceding twenty four changes, every extream change was made

betwixt the two furthest extream bells from the hunt. I will therefore

here set down an example, where they shall be made between the two

nearest bells, to it. First, the treble hunts up (_a_). The two next

notes to the hunt, which are 3.4, must make an extream change (_b_). The

Treble must hunt down (_c_). The two nearest notes to the hunt, which

are 2.4, must make an extream change (_d_). The Treble hunts up (_e_).

The two nearest extream bells to the hunt, which are 2.3, must make an

extream change (_f_). The Treble hunts down (_g_). The two next extream

bells to the hunt, which are 4.3, must make a change (_h_). And the like

extream changes being made as at (_k_) and (_m_), concludes the peal.

│1234

───┼────

_a_│2134

„ │2314

„ │2341

───┼────

_b_│2431

───┼────

_c_│2413

„ │2143

„ │1243

───┼────

_d_│1423

───┼────

_e_│4123

„ │4213

„ │4231

───┼────

_f_│4321

───┼────

_g_│4312

„ │4132

„ │1432

───┼────

_h_│1342

───┼────

_i_│3142

„ │3412

„ │3421

───┼────

_k_│3241

───┼────

_l_│3214

„ │3124

„ │1324

───┼────

_m_│1234

The six extream changes, _viz._ (_b.d.f.h.k._ and _m._) being set down

by themselves, will stand in this order, as here you see; where ’tis

plain, that 2 3 4 have made the six changes, according to the method of

the last six changes on three bells, _page 49._ where the first change

of that six is made between the last two notes thus, 1 3 2. So in like

manner is the first here thus, 243, which is the same method with that,

though not the same figures.

2431

1423

4321

1342

3241

1234

So that the making of the extream changes two ways in the twenty four,

proceeds from the two ways of making the six changes on three bells.

This last way of making the extream changes, may, for distinction from

the other way, be called _mediums_; which term is very proper, in regard

that the two middlemost of the four notes do always make the extream

change. The extream changes in one peal must all be made alike, that is,

either betwixt the two farthest notes from the hunt, or else betwixt the

two nearest notes to it; but the most usual way is to make them between

the two farthest.

Any note may be made a hunt at pleasure, and its first motion at the

beginning of the peal may be either up or down. The twenty four changes

may be rung sixteen ways according to the aforesaid method, yet the

changes to each are still one and the same; but by making each note a

hunt, and moving it either up or down at the beginning, and also by

making the extream changes two ways, the course of the changes will be

so altered, that the same changes shall not come all along together in

any two of those sixteen ways. With the hunting of one note it may be

rung four ways; for the note may move either up or down at the beginning

of the peal; then in its motion either way the extream changes maybe

made two ways, as before: so that to make each note a hunt, and with

each hunt to ring it four ways makes sixteen in the whole. Wherein ’tis

observable, that the treble-note cannot be moved down at first, nor the

_4th_ up; therefore an extream change must first be made, which is as

effectual as if either note had moved at first. I have here prickt the

twenty four changes three ways, wherein the extream changes are all made

betwixt the two farthest notes from the hunt.

_2d. │ _3d. │_4th.

down_ │ up_ │ up_

│ │

_1234_│_1234_│_1234_

2134 │ 1243 │ 2134

2143 │ 2143 │ 2143

1243 │ 2134 │ 2413

1423 │ 2314 │ 4213

1432 │ 3214 │ 4231

4132 │ 3241 │ 2431

4123 │ 2341 │ 2341

4213 │ 2431 │ 2314

2413 │ 2413 │ 3214

2431 │ 4213 │ 3241

4231 │ 4231 │ 3421

4321 │ 4321 │ 4321

4312 │ 3421 │ 4312

3412 │ 3412 │ 3412

3421 │ 4312 │ 3142

3241 │ 4132 │ 3124

2341 │ 4123 │ 1324

2314 │ 1423 │ 1342

3214 │ 1432 │ 1432

3124 │ 1342 │ 4132

3142 │ 3142 │ 4123

1342 │ 3124 │ 1423

1324 │ 1324 │ 1243

1234 │ 1234 │ 1234

_The Changes on five Bells._

There are sixscore changes to be rung on five bells; but the Learner may

first practice some shorter peals, as the Ten changes, the twelve, the

Fourteen, the Twenty all over, the Twenty with one hunt, and the Forty

eight.

In the Ten changes the treble must first hunt up (_a_); the 2.3 must

make a change (_b_). The treble must hunt down again (_c_); the 3.2 must

make another change (_d_). The ten changes may also be rung by hunting

down the 5 to lead; then 3.4 to make a change; the 5 to be hunted up

again, and the 4.3 to make another change.

│12345

───┼─────

_a_│21345

„ │23145

„ │23415

„ │23451

───┼─────

_b_│32451

───┼─────

_c_│32415

„ │32145

„ │31245

„ │13245

───┼─────

_d_│12345

In the Twelve changes the treble hunts up into the third place, then the

two first notes make a change; the treble hunts down again, then the two

hindmost notes make a change. First the treble hunts into the _3d_ place

(_a_); the two first notes 2.3 make a change (_b_). The treble hunts

down (_c_); the two last notes make a change (_d_); the treble hunts up

(_e_); the two first notes make a change (_f_); the treble hunts down

(_g_); the two last notes make another change (_h_).

│12345

───┼─────

_a_│21345

„ │23145

───┼─────

_b_│32145

───┼─────

_c_│31245

„ │13245

───┼─────

_d_│13254

───┼─────

_e_│31254

„ │32154

───┼─────

_f_│23154

───┼─────

_g_│21354

„ │12354

───┼─────

_h_│12345

In the Fourteen changes, the treble first hunts up behind; then the 5

hunts down to lead; the treble then hunts down again into its own place;

and the fifth also hunts up into its own place.

The Twenty all over are rung in the same manner as the Twelve all over

upon four bells, to which I refer.

In the Twenty changes with one hunt, the hunting note continually hunts

up and down through the other notes, and every time it lies either

before or behind them, an extream change must be made betwixt the two

farthest notes from it. The treble shall be the hunt, and first hunteth

up (_a_). An extream change is made (_b_); the treble hunts down (_c_);

an extream change is made (_d_); which course must be continued to the

end. The extream changes may also be made betwixt the two next notes to

the hunt. Any note may be made a hunt at pleasure, yet still observing

to make the extreams as before.

│12345

───┼─────

_a_│21345

„ │23145

„ │23415

„ │23451

───┼─────

_b_│32451

───┼─────

_c_│32415

„ │32145

„ │31245

„ │13245

───┼─────

_d_│13254

In the forty eight changes, the _5th_ and _4th_ are both hunts, and 1 2

3 do make the six changes; the 5.4 do hunt down by turns, and when

either of them leads, then one of the six changes is made. First the 5

hunts down (_a_); one of the six changes is made (_b_); the 5 hunts up

into its own place (_c_); the 4 hunts down (_d_); another of the six

changes is made (_e_); then the 4 must hunt up, and the 5 down again,

_&c._ which course must be continued to the end.

│12345

───┼─────

_a_│12354

„ │12534

„ │15234

„ │51234

───┼─────

_b_│52134

───┼─────

_c_│25134

„ │21534

„ │21354

„ │21345

───┼─────

_d_│21435

„ │24135

„ │42135

───┼─────

_e_│42315

In the Sixscore changes, four of the notes do make the Twenty four

changes, and the fifth note hunts continually through them: so that the

course and method of the Sixscore is in effect the same with that of the

Four and twenty. For as the Four and twenty comprehended the Six changes

on three; so in like manner the Sixscore comprehend the Four and twenty

changes on four, and the Six changes on three. Therefore in the Sixscore

there must be two hunts and three extream bells; one of the hunts is

term’d the whole-hunt, and the other the half-hunt, The three extream

bells do make the Six changes in the same manner as they were made

before in the Four and twenty changes upon four bells, and are here also

call’d Extream changes: the half-hunt and three extream bells do make

the Four and twenty changes in the same manner as the Four and twenty

changes on four bells were likewise made: and the whole hunt continually

hunts through those four bells, and every time it either leads or lies

behind them, one change must then be made in the twenty four. 1 shall

here be the whole-hunt, 2 the half-hunt, and 345 extream bells: so that

2345 must make the four and twenty changes. Every extream change shall

be made betwixt the two farthest extream bells from the half-hunt.

First, the treble hunts up (_a_). One of the twenty four changes must

now be made; and therefore 2 which is the hunt in the twenty four, must

begin its motion through the extream bells (_b_). The treble hunts down

(_c_); the half-hunt must proceed in its course (_d_); the whole-hunt

hunts up (_e_); The half-hunt proceeds forward (_f_); the whole-hunt

moves down (_g_). The half-hunt should now proceed, but having finished

its course through the extream bells, therefore an extream change must

now be made betwixt the two farthest extream bells from it, which are

3.4 (_h_). The treble must hunt up (_i_); the half-hunt must now begin

its course again through the extream bells (_k_); treble hunts down

(_l_); the half-hunt proceeds in its course down (_m_); treble hunts up

(_n_); the half-hunt proceeds in its course down (_o_); treble hunts

down (_p_); the half-hunt having finished its course, therefore an

extream change must be made betwixt the two farthest extream bells from

it, which are 3.5 (_q_). The treble hunts up (_r_). The half-hunt begins

its motion again through the extream bells, and first it moves up over

_4th_ (_s_). The whole hunt moves down (_t_); the half-hunt must proceed

in its course, and therefore must move over another note (_v_). And this

method being observed, will produce sixscore changes, and then the bells

will in course come round. Now ’tis observable, that the changes at (_b

d f h k m o q s v x_ and _z_), being set down by themselves, that is,

the 1 to be excluded, and the changes on 2345 to be set directly under

one another in the same successive order as they were made, it will

thereby appear, that those four figures have made twelve changes of the

twenty four, according to the method of the first twenty four changes on

four bells before set down. And whereas here are just half the sixscore

changes prickt down, so likewise here are just half the four and twenty

changes made therein: and the remaining part of this sixscore being

likewise prickt, the remaining part of this four and twenty would also

appear therein, which part being added to the former twelve, would make

up the twenty four changes compleat; and the method of them the same in

all respects with the first twenty four changes on four bells, _page._

│12345

───┼─────

_a_│21345

„ │23145

„ │23415

„ │23451

───┼─────

_b_│32451

───┼─────

_c_│32415

„ │32145

„ │31245

„ │13245

───┼─────

_d_│13425

───┼─────

_e_│31425

„ │34125

„ │34215

„ │34251

───┼─────

_f_│34521

───┼─────

_g_│34512

„ │34152

„ │31452

„ │13452

───┼─────

_h_│14352

───┼─────

_i_│41352

„ │43152

„ │43512

„ │43521

───┼─────

_k_│43251

───┼─────

_l_│43215

„ │43125

„ │41325

„ │14325

───┼─────

_m_│14235

───┼─────

_n_│41235

───┼─────

„ │42135

„ │42315

„ │42351

───┼─────

_o_│24351

───┼─────

_p_│24315

„ │24135

„ │21435

„ │12435

───┼─────

_q_│12453

───┼─────

_r_│21453

„ │24153

„ │24513

„ │24531

───┼─────

_s_│42531

───┼─────

_t_│42513

„ │42153

„ │41253

„ │14253

───┼─────

_v_│14523

───┼─────

_w_│41523

„ │45123

„ │45213

„ │45231

───┼─────

_x_│45321

───┼─────

_y_│45312

„ │45132

„ │41532

„ │14532

───┼─────

_z_│15432

Any note may be made a whole hunt at pleasure, and its first motion at

the beginning of the peal may either be up or down. Any note may also be

made a half-hunt, and its first motion likewise up or down at pleasure;

yet still observing that the half-hunt and three extream bells must make

the twenty four changes, as in this last example. So that in the

sixscore changes the Learner may observe, that the three extream bells

are always assigned for the half-hunt to hunt through; and the half-hunt

and three extream bells are also assigned for the whole-hunt to hunt

through: so that the whole-hunt always hunts through four notes, and the

half-hunt through three. The extream changes may be made two ways;

first, betwixt the two farthest extream bells from the half-hunt, as in

this last example; secondly, betwixt the two next extream bells to the

half-hunt, which may be called _mediums_, for distinction from the

former. But the most usual and easiest way, is to make them betwixt the

two farthest notes from the half-hunt.

Whereas the treble or fifth being made whole-hunts, the first of them

can neither be moved down, nor the last up, at the beginning of a peal;

therefore one of the twenty four changes must first be made, which is as

effectual, as if the treble had moved down, or the 5th up.

The Learner may observe, that two of the four and twenty changes are

never made together in any sixscore, but as soon as one is made, the

whole-hunt moves through the four notes before another can be made.

The sixscore changes may be rung one hundred and sixty ways, which are

thus demonstrable. There are five times four figures to be produced out

of five, and not twice four the same figures: as 1234. 1235. 1245. 1345.

2345. with each four the twenty four changes may be prickt sixteen ways,

as before I have shewed on four bells; so that here will be five times

sixteen four and twenties, which amount to eighty, and not two alike.

Now to each four add the fifth figure which is wanting, as to 1234 add

5, to 1235 add 4, to 1245 add 3, to 1345 add 2, to 2345 add 1, and every

fifth figure being hunted through the sixteen four and twenties, which

the other four make, as the 5 through the sixteen four and twenties

which the 1234 make, and the like of the rest, will produce as many

sixscores as there were four and twenties, that is, 80. Then the whole

hunt may hunt two ways through each four and twenty, that is, up and

down at the beginning, which doubles the former number, and makes 160 in

the whole.

_Treble up, fifth down._

12345 │ 12534 │ 15243 │ 21453 │ ————— │ 14325 │ 13524

————— │ 21534 │ 51243 │ 24153 │ 14253 │_Extre._│ 13254

21345 │ 25134 │ 52143 │ 24513 │ 14523 │ 13425 │ —————

23145 │ 25314 │ 52413 │ 24531 │ ————— │ ————— │ 13245

23415 │ 25341 │ 52431 │ 24351 │ 15423 │ 13452 │_Extre._

23451 │ 52341 │ 25431 │ 24315 │_Extre._│ 13542 │ 12345

23541 │ 52314 │ 25413 │ 24135 │ 15432 │ ————— │

23514 │ 52134 │ 25143 │ 21435 │ ————— │ 15342 │

23154 │ 51234 │ 21543 │ 12435 │ 14532 │_Extre._│

21354 │ 15234 │ 12543 │_Extre._│ 14352 │ 15324 │

12354 │_Extre._│ 12453 │ 14235 │ ————— │ ————— │

_Treble up, fourth down._

12345 │ 12435 │ 41253 │ 21543 │ 52134 │ ————— │ 14325

————— │ 14235 │ 14253 │ 12543 │ 51234 │ 15342 │ 13425

21345 │ 41235 │ 12453 │ 12534 │ 15234 │ 15324 │ —————

23145 │ 42135 │ 21453 │ 21534 │ 15243 │ ————— │ 13245

23415 │ 42315 │ 24153 │ 25134 │ ————— │ 13524 │ 13254

23451 │ 42351 │ 24513 │ 25314 │ 15423 │ 13542 │ —————

24351 │_Extre._│ 24531 │ 25341 │ 14523 │ ————— │ 12354

24315 │ 42531 │ 25431 │_Extre._│ ————— │ 13452 │ 12345

24135 │ 42513 │ 25413 │ 52341 │ 14532 │ 14352 │ —————

21435 │ 42153 │ 25143 │ 52314 │ 15432 │ ————— │

_Second down, fourth up._

12345 │ 31524 │ 34125 │ 43512 │ 35412 │_Extre._

————— │ 31254 │ 34215 │ 43521 │ 35421 │ 53142

21345 │ 32154 │ 32415 │ 43251 │ 35241 │ 53124

21354 │ 23154 │ 23415 │ 42351 │ 32541 │ 53214

12354 │ 23145 │ 24315 │ 24351 │ 23541 │ 52314

13254 │ 32145 │ 42315 │ 23451 │ 23514 │ 25314

13524 │ 31245 │ 43215 │ 32415 │ 32514 │ 25341

13542 │ 31425 │ 43125 │ 34251 │ 35214 │ 52341

_Extre._│ 31452 │ 43152 │ 34521 │ 35124 │ 53241

31542 │ 34152 │_Extre._│ 34512 │ 35142 │ _&c._

In ringing terms the hunts are named in short, as in the peals here

prickt. The first which is named is here understood to be the

whole-hunt, and the last the half-hunt. For instance, Treble is the

whole-hunt, and fifth the half-hunt; and treble is the whole-hunt, and

fourth the half-hunt, _&c._

_The Changes on six Bells._

There are seven hundred and twenty changes to be rung of six bells. But

the Learner may first practice some shorter peals.

The twenty four changes are thus rung. The treble must continually hunt

through the rest of the notes, and every time it leads or lies behind

them, an extream change must then be made between the two farthest notes

from it. The treble hunts up (_a_). A change is made betwixt the two

farthest notes from it, which are 2.3 (_b_). The treble hunts down

(_c_). An extream change is made betwixt 5.6 (_d_), which method must be

continued to the end. Any note may be made a hunt at pleasure, and the

extream changes may as well be made betwixt the two nearest notes to the

hunt. The Thirty-all-over are rung according to the method of the Twelve

all over upon four bells, to which I refer.

│123456

───┼──────

_a_│213456

„ │231456

„ │234156

„ │234516

„ │234561

───┼──────

_b_│324561

───┼──────

_c_│324516

„ │324156

„ │321456

„ │312456

„ │132456

───┼──────

_d_│132465

The thirty six changes are thus rung. The treble hunts up into the third

place, and then the two first notes make a change. The treble hunts down

again to lead, and then the two notes in the _3d_ and _4th_ places do

make a change, except the 2 lies next the treble, and then the two

hindmost notes. The treble hunts up (_a_). The two first notes make a

change (_b_). The treble hunts down (_c_); the 2.4 make a change (_d_).

In which manner the changes are to be made untill the treble leads, and

the 2 (which may be term’d the half-hunt) lies next it, and then the

extream change is made behind, as in the last change of this example,

there being but two of these changes in the peal.

│123456

───┼──────

_a_│213456

„ │231456

───┼──────

_b_│321456

───┼──────

_c_│312456

„ │132456

───┼──────

_d_│134256

───┼──────

_e_│314256

„ │341256

───┼──────

_f_│431256

───┼──────

_g_│413256

„ │143256

───┼──────

_h_│142356

───┼──────

_i_│412356

„ │421356

───┼──────

_k_│241356

───┼──────

_l_│214356

„ │124356

───┼──────

_m_│124365

│_&c._

In the Twelvescore long-hunts, (otherwise called the _Esquire’s

twelvescore_); the _6th_ and _5th_ are hunts, and 1234 do make the

twenty four changes. The _6th_ and _5th_ do hunt down by turns, and when

either of them leads, one of the twenty four changes must then be made.

The course and method of this is the same with that of the forty eight

changes on five bells, to which I refer the Learner.

In the Sevenscore and four, the treble and tenor are both hunts; and

2345 do make the twenty four changes, 2 being the hunt therein. The

treble and tenor do both hunt at one and the same time, the one up, and

the other down, crossing each others course; and when one of them leads,

the other always lies behind; at which time one of the twenty four

changes must be made. The extream changes in this peal are made in the

same manner as before I have shewed upon four bells. The treble hunts

up, and the tenor down (_a_). One of the twenty four changes is made

(_b_). The treble hunts down, and the tenor up (_c_). Another of the

twenty four changes is made (_d_). The treble hunts up, and the tenor

down (_e_), _&c._ which method must be observed to the end.

│123456

───┼──────

_a_│213465

„ │231645

„ │236145

„ │263415

„ │623451

───┼──────

_b_│632451

───┼──────

_c_│362415

„ │326145

„ │321645

„ │312465

„ │132456

───┼──────

_d_│134256

───┼──────

_e_│314265

„ │341625

„ │346125

„ │364215

„ │634251

───┼──────

_f_│634521

│_&c._

In the sixscore changes there is a whole-hunt, a half-hunt, and four

extream bells. The half-hunt and four extream bells do make the twenty

changes in the same manner as the twenty changes were made upon five

bells with one hunt. _page 61._ The whole hunt hath a continual motion

through the other five notes, and every time it leads and lies behind

them, one of the twenty changes must then be made. In this example,

treble is the whole-hunt, 2 the half-hunt, and 3456 extream bells;

therefore 23456 must make the twenty changes wherein 2 is the hunt, and

every time it lies either before the four extream bells, or behind them,

an extream change must then be made, which here shall be betwixt the two

farthest extream bells from the half-hunt. The treble hunts up (_a_).

One of the twenty changes must now be made, therefore 2 being the hunt

in it, must begin its course through the extream bells (_b_). The treble

hunts down (_c_); The half-hunt proceeds forward (_d_); the treble hunts

up (_e_); the half-hunt proceeds forward in its course (_f_); the treble

hunts down (_g_); the 2 proceeds forward (_h_); the treble hunts up

(_i_); the half-hunt should now proceed forward, but its course through

the extream bells being finished, therefore an extream change must be

made betwixt 3.4, which are the two farthest extream bells from it,

(_k_). The treble must hunt down (_l_); the half-hunt must now go its

course again through the extream bells, and first it moves down under

the _6th_, (_m_) _&c._ which method must be continued to the end. Any

note may be made a whole hunt at pleasure, or a half-hunt also. And the

extream changes may be made betwixt the two nearest extream notes to the

half-hunt; but withall observing to make all the extreams in one peal

alike. There are four extream changes in each peal, and thirty changes

distance from one to another.

│123456

───┼──────

_a_│213456

„ │231456

„ │234156

„ │234516

„ │234561

───┼──────

_b_│324561

───┼──────

_c_│324516

„ │324156

„ │321456

„ │312456

„ │132456

───┼──────

_d_│134256

───┼──────

_e_│314256

„ │341256

„ │342156

„ │342516

„ │342561

───┼──────

_f_│345261

───┼──────

_g_│345216

„ │345126

„ │341526

„ │314526

„ │134526

───┼──────

_h_│134562

───┼──────

_i_│314562

„ │341562

„ │345162

„ │345612

„ │345621

───┼──────

_k_│435621

───┼──────

_l_│435612

„ │435162

„ │431562

„ │413562

„ │143562

───┼──────

_m_│143526

│_&c._

The method of the Seven hundred and twenty, hath an absolute dependency

upon the method of the Sixscore changes on five bells; for five of the

notes are to make the sixscore changes, and the sixth note hunts

continually through them, and every time it leads or lies behind them,

one of the Sixscore changes must then be made. The method of the Seven

hundred and Twenty is in effect the same with that of the Sixscore: for

as the Sixscore comprehended the Twenty four changes on four, and the

Six on three; so likewise the Seven hundred and twenty comprehend the

Sixscore changes on five, the Twenty four changes on four, and the Six

changes on three. Therefore here must be three Hunts, and three Extream

bells: the three Hunts are thus distinguished; one of them is call’d the

_whole-hunt_, another the _half-hunt_, and the other the _quarter-hunt_.

The Half-hunt, Quarter-hunt, and three Extream bells, are to make the

Sixscore changes; the Quarter-hunt and three Extream bells are to make

the Twenty four changes, and the three Extream bells are to make the

_six_ changes, which are here also called _extream_ changes, and made in

the same manner as before I have shewed upon four bells. In this example

here prickt, _treble_ is the _whole-hunt_, _2d_ the _half-hunt_, _3d_

the _quarter-hunt_, and _4 5 6_ _extream_ bells. Now ’tis observable,

that 4 5 6 are to make the six _extream_ changes, which will divide the

_seven hundred and twenty_ into six equal parts; the 3 4 5 6 are to make

the _twenty four_ changes, wherein the _3d_ is the _hunt_, (but in the

_seven hundred and twenty_ ’tis call’d the _quarter-hunt_;) and 2 3 4 5

6 are to make the _sixscore_ changes, wherein the _2d_ is the

_whole-hunt_ (though in the 720 ’tis call’d the _half-hunt_,) by which

’tis evident, that the _treble_ continually hunts through these five 2 3

4 5 6, the _2d_ through the four 3 4 5 6, and the _3d_ through these

three 4 5 6; which are assigned for the respective _hunts_ to hunt

through, from the beginning to the end of the peal. First the _treble_

hunts up (_a_). Now one of the _sixscore_ changes must be made,

therefore the _2d_ being the _hunt_ in the _sixscore_, must begin its

course through the other four notes (_b_). The _treble_ hunts down

(_c_); the _2d_ proceeds in its course (_d_); the _treble_ hunts up

(_e_). The _2d_ proceedeth forward in its course (_f_); the _treble_

hunts down (_g_); the _2d_ proceeds forward (_h_); the _treble_ hunts up

(_i_); the _2d_, which is the _half-hunt_, should now proceed forward,

but having finished its course through the four bells, therefore the

_3d_, which is the _quarter-hunt_, must begin its motion through the

_extream_ bells (_k_). The _treble_ hunts down (_l_). The _half-hunt_

must now begin its course again through the four bells, and first

therefore it moves down under the 6 (_m_). The _treble_ must hunt up

again, and then the _2d_ must move down under another bell, which method

must be observed untill the _2d_ has moved quite down through the four

bells again, and then the _3d_ must proceed forward by moving over

another of the _extream_ bells; which method must be observed in the

motion of the three _hunts_, until the _quarter-hunt_ hath moved up

behind the _extream_ bells, and then the _whole_ and _half-hunts_,

having gone their course again through the bells, an _extream_ change

must be made: after which the _whole_, _half_, and _quarter-hunts_

proceed again in their course as before.

│123456

───┼──────

_a_│213456

„ │231456

„ │234156

„ │234516

„ │234561

───┼──────

_b_│324561

───┼──────

_c_│324516

„ │324156

„ │321456

„ │312456

„ │132456

───┼──────

_d_│134256

───┼──────

_e_│314256

„ │341256

„ │342156

„ │342516

„ │342561

───┼──────

_f_│345261

───┼──────

_g_│345216

„ │345126

„ │341526

„ │314526

„ │134526

───┼──────

_h_│134562

───┼──────

_i_│314562

„ │341562

„ │345162

„ │345612

„ │345621

───┼──────

_k_│435621

───┼──────

_l_│435612

„ │435162

„ │431562

„ │413562

„ │143562

───┼──────

_m_│143526

The letter _h_ standing by the figures signifies _half-hunt_, that is,

the motion of the _half-hunt_ in that change; and likewise _q_ the

_quarter-hunt_. Here are the first _sixscore_ changes of a _seven

hundred and twenty_; wherein ’tis observable, that all the changes at

_h_ and _q_ being set down by themselves in the same successive order as

they were made, that is, the 1 to be excluded, and the changes on the

other five figures to be set down directly under one another, and the

_extream_ change at last, it will thereby appear, that the five figures

have made twenty changes of a _sixscore_, according to the method of the

example on five bells, _page 63._ with this only difference, these are

made on 23456, and those were made on 12345; but the five figures of

each have both alike course, the _2d_ and _3d_ going the same course in

this, as the _treble_ and _2d_ did in that. Now whereas the _sixscore_

changes here prickt down are a sixth part of the _seven hundred_ and

_twenty_, so likewise are the _twenty changes_, here made by 23456, a

sixth part of the _sixscore_: and then consequently, the _seven hundred_

and _twenty_ changes being all prickt, the _sixscore_ changes on 23456

would plainly appear therein, in the same manner as twenty of them

appear in this _sixscore_. Therefore more need not be said of the method

of the 720, since the method of the _sixscore_ changes on five bells

being well understood, will be a sure and certain guide to the Learner:

only this one thing farther; in ringing of this peal with any _hunts_,

the second _extream_ change being made between the two bells which made

the first _extream_, will always bring the bells round at the end of the

_twelvescore_. But after _twelvescore_ are made, they cannot in course

be brought round until the end of the 720.

│_123456_│ │ │ │ │ │

│ 213456 │ │ 435612 │ │ 214536 │ │ 456312

│ 231456 │ │ 435162 │ │ 241536 │ │ 456132

│ 234156 │ │ 431562 │ │ 245136 │ │ 451632

│ 234516 │ │ 413562 │ │ 245316 │ │ 415632

│ 234561 │ │ 143562 │ │ 245361 │ │ 145632

_h_│ 324561 │_h_│ 143526 │_h_│ 425361 │_h_│ 145623

│ 324516 │ │ 413526 │ │ 425316 │ │ 415623

│ 324156 │ │ 431526 │ │ 425136 │ │ 451623

│ 321456 │ │ 435126 │ │ 421536 │ │ 456123

│ 312456 │ │ 435216 │ │ 412536 │ │ 456213

│ 132456 │ │ 435261 │ │ 142536 │ │ 456231

_h_│ 134256 │_h_│ 432561 │_h_│ 145236 │_h_│ 452631

│ 314256 │ │ 432516 │ │ 415236 │ │ 452613

│ 341256 │ │ 432156 │ │ 451236 │ │ 452163

│ 342156 │ │ 431256 │ │ 452136 │ │ 451263

│ 342516 │ │ 413256 │ │ 452316 │ │ 415263

│ 342561 │ │ 143256 │ │ 452361 │ │ 145263

_h_│ 345261 │_h_│ 142356 │_h_│ 453261 │_h_│ 142563

│ 345216 │ │ 412356 │ │ 453216 │ │ 412563

│ 345126 │ │ 421356 │ │ 453126 │ │ 421563

│ 341526 │ │ 423156 │ │ 451326 │ │ 425163

│ 314526 │ │ 423516 │ │ 415326 │ │ 425613

│ 134526 │ │ 423561 │ │ 145326 │ │ 425631

_h_│ 134562 │_h_│ 243561 │_h_│ 145362 │_h_│ 245631

│ 314562 │ │ 243516 │ │ 415362 │ │ 245613

│ 341562 │ │ 243156 │ │ 451362 │ │ 245163

│ 345162 │ │ 241356 │ │ 453162 │ │ 241563

│ 345612 │ │ 214356 │ │ 453612 │ │ 214563

│ 345621 │ │ 124356 │ │ 453621 │ │ 124563

_q_│ 435621 │_q_│ 124536 │_q_│ 456321 │ │ Extre.

│ │ │ │ │ │ │ 125463

The 720 changes may be rung one thousand nine hundred and twenty several

ways, which is thus demonstrable. There are six times five figures to be

produced out of six, and not twice five the same: as 12345. 12346.

12356. 12456. 13456. 23456. and with each five the _sixscore_ changes

may be prickt one hundred and sixty ways, as before I have shewed on

five bells. Now to each five add the sixth figure which is wanting, as

to 12345 add 6, to 12346 add 5, to 12456 add 3, to 13456 add 2, and to

23456 add 1. And the sixth figure which is added, being hunted through

all the several _sixscores_ which the other five figures make; for

instance, the 6 through the 160 several _sixscores_ which 12345 make,

and the 5 also through the 160 several _sixscores_, which 12346 make,

and the like of the rest; will produce as many _seven hundred_ and

_twenties_ as there are _sixscores_, that is, six times one hundred and

sixty, which amounts to nine hundred and sixty. Then the note that hunts

through the other five, may hunt two ways through each _sixscore_, that

is, up and down, which will double the former number, and make nineteen

hundred and twenty in the whole.

[Illustration: [Fleuron]]

AN INTRODUCTION

to the Knowledge of

_CROSSE PEALS_.

These Peals are term’d _cross_ in respect of their intricate methods;

wherein several notes moving at one and the same time, do thwart or

_cross_ each other in their course and motion, some moving up, others at

the same time down, gives this Denomination to the Peals. The end of

pricking them is to make the compleat number of changes by a method

differing from that of other Peals. For although five can be varied but

120 ways, and six but 720 _&c._ yet the methods by which they are

varied, are differing, according to the several fancies of the Artist.

And as order and method are the only _basis_ on which this Art is

founded; so the skilful Artists, the better to effect the aforesaid end,

have thought fit in most peals to appoint one note to be as it were a

Helm or Rudder, by which the course of the peal is steered; which note

is term’d a _Hunt_, and hath one constant uniform motion throughout the

peal, differing from that of the other notes. The manner of its motion

is continually through the other notes, that is, from leading to strike

behind, and from thence again to lead, which motion, first up and then

down, is term’d one compleat Course. Some peals upon five bells, as _old

Doubles_, _&c._ consist of single Courses; there being ten changes in

every single Course, and twelve of those Courses in the peal. Other

peals upon five bells, as _London Paradox_, _&c._ consist of double

Courses; there being twenty changes in every double Course, and six of

those Courses in the peal. Upon six bells there are also single and

double Courses, _viz._ twelve changes in every single Course, as in

_Grandsire Bob_ _&c._ and twenty four changes in every double Course, as

in _Colledg Bob_, _&c._ the change wherein the _Hunt_ leaves leading

being the first change of every Course. Now the methods of these peals

being well considered, they will be found more easie than at the first

view they may seem to be; for the first Course of any Cross Peal being

judiciously viewed, the general method of the whole peal will thereby

appear: for all the Courses in a Cross peal do agree in these three

respects. First, in the motion of the _Hunt_; secondly, in the motion of

the rest of the notes; thirdly, in the making of the changes, which will

plainly appear in the following peals, (some few changes in each peal

only excepted, as hereafter I shall shew in my Directions to the several

peals:) for proof of which I will give an instance in the peal of new

Doubles upon five bells, these being the three first Courses of the

peal. Wherein ’tis observable, that the last change of the first Course

which is 13524, I have set down again at the top of the second Course;

and likewise the last change of the second Course which is 15432, I have

also put at the top of the third course; which I have done for the

plainer Demonstration of what I here intend. So that the ten lowermost

changes are the ten changes of each Course.

First │ 2d │ 3d

Course│Course│Course

│ │

12345 │13524 │15432

──────┼──────┼──────

21354 │31542 │51423

23145 │35124 │54132

32415 │53214 │45312

23451 │35241 │54321

32541 │53421 │45231

23514 │35412 │54213

32154 │53142 │45123

31245 │51324 │41532

13254 │15342 │14523

13524 │15432 │14253

First therefore, as to the motion of the _hunt_, the 1 which is the

_hunt_ moves directly up behind, where it lieth twice, and then down

again to lead, where it lieth also twice; as appears in each of these

three Courses, and the like also throughout the peal.

Secondly, as the _2d_, _3d_, _4th_, and _5th_ bells move through the

first Course, so the bells that lie in the _2d_, _3d_, _4th_, and _5th_

places in the last change of every course, moves in the same manner also

through the next following course. For instance; first, for the bell in

the _2d_ place: in the first course the _2d_ bell moves down to lead,

where it lieth twice, and then dodges untill the _treble_ comes down to

it. So likewise in the second course, the _3d_ bell lying in the _2d_

place moves down to lead, where it lies twice, and then dodges until

_treble_ comes down to it; and also in the third course, the _5th_ bell

lying in the _2d_ place, moves down to lead where it lieth twice, and

dodgeth until the _treble_ moves down to it. Secondly, for the bell in

the _3d_ place. In the first course the _3d_ bell moves down to lead,

and there dodgeth untill the _treble_ comes down to it: so likewise in

the second course the _5th_ bell lying in the _3d_ place moves down to

lead, and there dodgeth untill the _treble_ comes down to it: and also

in the _3d_ course the _4th_ bell lying in the _3d_ place moves down to

lead, and there dodgeth until the _treble_ comes down to it. Thirdly,

for the bell in the fourth place: In the first course, the fourth bell

moves up behind, then down into the _3d_ place where it lieth twice,

then up again behind; so likewise in the second course, the _2d_ bell

lying in the _4th_ place moves up behind, then down into the _3d_ place

where it lieth twice, then up again behind; and also in the third course

the _3d_ bell lying in the _4th_ place, moves therefore up behind, then

down into the _3d_ place where it lieth twice, then up again behind. And

such uniform motion also hath the bell in the _5th_ place through every

course.

Thirdly, that the changes in all the courses of the peal are made alike,

will here also plainly appear in the three courses. For the first change

of every course is made on the two first and two last bells; the second

change of every course is made on the four last; the third is made on

the four first; the fourth on the two first and two last; the fifth on

the four first; the sixth on the two first and two last; the seventh on

the four first; the eighth on the four last; the ninth on the two first

and two last; and the tenth single.

And thus in every Cross-peal the Courses do all agree, first in the

motion of the Hunt, secondly in the motion of the rest of the notes, and

thirdly in the making of the changes, as before I have showed. So that

these three things being well observed, will be very helpful both in

pricking and ringing them; the first and third being most proper to

direct the pricking of them, and the first and second the ringing of

them. Therefore if the Practitioner do but observe how the changes are

made in the first course of a peal, wherein he must have particular

regard to the motion of the Hunt, (with a little further help from the

following directions to each peal, as to the making of _Extreams_ and

Bob-changes) he may easily prick down all the following Courses of the

same peals and therefore in the following peals I have onely prickt down

two or three of the first courses for an example, and then have abridged

the rest of the peal by setting down only the changes that are made at

the leadings of the Hunt. But note, there are some few _Cambridg_-peals

upon five bells, wherein all the courses of each peal do not agree in

the aforesaid three respects: For although as to the motion of the

_whole-hunt_ they do, yet in the motion of the rest of the notes, and

consequently in the making of the changes they do not.

It being very difficult to begin the following peals with cross _hunts_,

that is, to make the _2d_, _3d_, _4th_ _&c._ whole-hunts, I will

therefore set down a general rule for making the first changes at the

beginning of each Peal, wherein consists the great difficulty. In any

Cross-peal the _whole-hunt_ may move either up or down at the beginning;

and the motion of the _whole-hunt_ in the first course of each of the

following peals will direct the first motion of any cross _hunt_, and

consequently of making the first changes in that peal. For Example,

admit the _4th_ were made the _whole-hunt_ in the peal called _Old

doubles and singles_ upon five bells, and to _hunt_ up at first: now to

know how to make the first changes, observe how the change is made

wherein the treble (which is there the _whole-hunt_) moves up out of the

_4th_ place, and in the same manner must the change be made wherein the

_4th_ bell also moves up out of that place: therefore as the change

wherein the treble moves up out of the _4th_ place is a _single_ behind;

so likewise must the change wherein the _4th_ bell moves up out of that

place, be also a _single_ behind thus, 12354: and then as the next

change wherein the treble lieth still behind is double of the four first

bells; so likewise the next change wherein the _4th_ bell lieth still

behind, must also be made on the four first, thus, 21534, _&c._ Or admit

the _4th_ were to hunt down at the beginning, then observe how the

change is made wherein the treble hunts down out of the _4th_ place, and

so in like manner must the change be made wherein the _4th_ hunts also

down out of that place: therefore as the change wherein the treble hunts

down out of the _4th_ place, is double of the four first bells; so

likewise must the change wherein the _4th_ bell hunts down out of that

place, be also double of the four first thus, 21435; then as the

_treble_ makes a _single_ when it moves down out of the _3d_ place, so

likewise must the _4th_ next make a single change in moving down out of

the _3d_ place thus 24135, _&c._ which observations will guide the

making of the first changes in any cross peal with any Hunts; but

observe whensoever the first change of any peal happens to be single, it

must be made at the back-stroke to prevent cutting compass; and the like

when a double change happens first in a peal of Triples and Doubles. And

moreover by the way observe, that all the following peals are so prickt,

that in ringing them at half-pulls, if the first change of each peal is

made at the fore-stroke, the single changes in each peal will always be

made at the back-stroke; and also the double changes in Triples and

Doubles, excepting some few Single in two or three peals. But when it

happens that the first change of a peal is made at the back-stroke, then

consequently the bells at the end of the peal will come round at a

fore-stroke change.

In such peals on five bells where _singles_ are made in the _3d_ and

_4th_ places at the leadings of the _whole-hunt_, the _extreams_ may

there be made three ways in each peal; _viz._ every time the _half-hunt_

lieth next to the _whole-hunt_; secondly, every time it lieth behind;

thirdly, every time the _half-hunt_ lieth next the _whole-hunt_, and

also behind: in this last way there are six _extreams_ in each peal, but

in other ways only three in each; the _extreams_ being always made when

the _whole-hunt_ leads, and betwixt the two farthest _extream_ bells

from the _half-hunt_.

In such peals upon five bells wherein there are three _extreams_, and

made in the _3d_ and _4th_ places at the leadings of the _whole-hunt_;

the rest of the _singles_ at the leadings of the _whole-hunt_ may be

made two ways in each peal, _viz._ either in the _2d_ and _3d_, or the

_4th_ and _5th_ places; if they are made in the _2d_ and _3d_, then the

_extreams_ must be made when the _half-hunt_ lyeth behind; but if the

_singles_ are made behind, then the _extreams_ must be made when the

_half-hunt_ lieth next the _whole-hunt_, the _extreams_ being always

made between the two next _extream_ bells to the _half-hunt_.

In all the following peals the figures standing by themselves at the

title of the peal, are the _hunts_ in the peal there prickt: for

instance, in the first _cross-peal_ upon five bells call’d _Old doubles

and singles_, the two figures standing thus _1 and 2_, are the _hunts_

in that peal; 1 is the _whole-hunt_, 2 the _half-hunt_, and the like of

the rest.

All peals of _doubles_ upon five bells, which go sixty changes compleat

without any _single_, by making of two _extreams_ they will go 120. And

also all peals of _doubles_ upon six bells, and _triples_ and _doubles_

upon six, which go 360 changes without any _single_ or _extreme_, by

making of two _extreams_ they will go 720. The _extreams_ in all these

compleat peals proceeding from one and the same cause, are therefore to

be made after one manner, according to this general and infallible rule:

Wheresoever any two of the _extream_ bells are in course to make a

change, those two bells by lying still will effectually make the

_extream_. So that the making of the _extream_ in _doubles_ upon five

bells, necessitates the making of a _single change_ at the same time, by

reason that the two _extream_ bells which should contribute to the

making of the _double_ change, do lie still; so that the _single_ change

is accidental, and very improperly called the _extream_. When the

_extreams_ in _triples_ and _doubles_ upon six bells are made at

_double_ changes, then there happens two _singles_ in the peal; but when

they are made at _triple_ changes, then those two changes will become

_double_, and consequently the 720 will then go compleat without any

_single_. Upon five bells the first _extream_ must be made within sixty

changes from the beginning, and the second _extream_ just sixty changes

from the first. Upon six bells the first _extream_ must be made within

360 changes from the beginning, and the second _extream_ just 360

changes from the first. The easiest way in practice, is to make the

_extremes_ at the leadings of the _whole-hunt_; wherein it may be

observed as a general rule, That in all peals upon six bells, where the

_half-hunt_ dodgeth behind at the _bobs_, there the first _extream_ may

be made either the first, second, or third time: the _half_ and

_quarter-hunts_ dodg together behind, and then the second _extream_ must

be made the third time those two bells dodg again together behind, after

the first _extream_ is made. And also in all such peals upon six bells,

where the _doubles_ at the leadings of the _whole-hunt_ are made on the

four middle bells, there the first _extream_ may be made either the

first, second, or third time the _half_ and _quarter-hunts_ do make a

change in the _2d_ and _3d_ places, and then the _2d_ _extream_ must be

made the third time those two bells come there again to make a change

after the first _extream_ is made. The _singles_ at all these _extreams_

must be made by the _half_ and _quarter-hunt_. The first _extream_ in

any peal may also be made at any place, where two of the _extream_ bells

are in course to made a change according to the preceding general rule;

and then the making of the second _extream_ may be guided by

observations taken from the changes at the leadings of the _whole-hunt_:

for at the leadings of the _whole-hunt_ the _half_ and _quarter-hunts_

always come together to make a change in one place, just at 120 changes

distance from one another throughout each peal. Now as the second

_extream_ must be made just 360 changes from the first, so the making of

it may thus be guided: Look how many changes, or else how many leadings

of the _whole-hunt_ the first _extream_ is made after the _half_ and

_quarter-hunts_ have made a change together, so many changes or leadings

of the _whole-hunt_ must the second _extream_ be made, after the third

following time that those two bells do made a change in the same place

again. And likewise in all peals, where there are single and double

_bobs_, the same observations will also hold good, in making the

_extreams_ either after the single or double _bobs_ as before; there

being likewise 120 changes distance between the single _bobs_ and also

between the double _bobs_: so that if the first _extream_ is made at a

single _bob_, the second must then be made at the third following single

_bob_, and the like also at double _bobs_. And such kind of

observations, according to the nature of the peal, will guide the making

of the second _extream_ in any peal, either upon five or six bells.

Wherein ’tis observable, that the second _extream_ must always be made

by the same two bells, and in the same place where the first was made,

which two bells will in course lie apt for that purpose; and the rest of

the bells will also in course lie in the same places at the second

_extream_ where they lay at the first. After the making of the first

_extream_, the method of the peal goeth on as if no _extream_ had been

made; and also after the making of the second _extream_ if any

remaineth, it also goes on, until in course the bells come round.

In all compleat peals of _doubles_ upon six bells there may also

moveable _extreams_ be made, which are made according to this rule;

wheresoever any two of the _extream_ bells are together, and in course

to lie still, those two bells by making a change will thereby make the

_extream_, which is as effectual as the fixed _extream_, the reason and

ground of both being one and the same. There are also two of these

_extreams_ in the peal, and the second always made 360 changes from the

first, and the making of it guided by such kind of observations as

before. When moveable _extreams_ are made, then there will be two triple

changes in the 720; but when fixed _extreams_ are made, then two

_singles_.

The art of _cross-pricking_ may receive a being from this consideration.

As every compleat peal of plain changes upon one number comprehends the

compleat peals on all lesser numbers; so likewise every compleat

_cross-peal_ must of necessity do the like, although their cross course

permits it not to be done so regularly and demonstrably as the former.

From whence may be inferr’d, that every note in a _cross-peal_ must of

necessity lie as many times in one place, as the rest of the notes are

capable of making changes; and also that two or more of the notes must

jointly lie in the same places as many times, as the remaining number

are also capable of making changes: this being a certain touchstone to

prove all _cross-peals_ after they are prickt, and must be held as a

principle on which to ground such methods of pricking, that the course

of all the notes may demonstrably tend to produce those effects. And

from hence it is, that the whole _hunt_ immediately derives the manner

of its uniform motion through the courses of each peal. And the changes

in every course are as so many guides to conduct the rest of the notes

in such sort, that they may be prepared to lie at the last change of the

course in apt places for each succeeding course to receive them, and to

perform the like. Now as the changes in all the courses of a peal are

made alike, except as before; so in the composing of _cross-peals_, by

pricking of one course may soon be discovered, whether or no a compleat

Peal will from thence arise.

* * * * *

_Cross Peals._

_The Twenty four, Doubles and Singles on four Bells._

This peal consists equally of _double_ and _single_ changes; one change

is _double_, the next _single_, and so throughout. 1 is here the _hunt_,

and 2.3.4 _extream_ bells. Every _double_ change is made on the two

first and two last bells, and every _single_ on the two middle bells,

except when the 1 leads, and then behind which is call’d _extream_. All

the bells have a direct Hunting course up and down until 1 leads, and

then the bell in the second place lyeth still, whilst the two hind-bells

make a dodg; which being made, all the bells proceed again in their

Hunting course. The three changes of (_a.b.c_) are the three _extream_

changes.

_1234_

2143

2413

4231

4321

3412

3142

1324

_a_ 1342

3124

3214

2341

2431

4213

4123

1432

_b_ 1423

4132

4312

3421

3241

2314

2134

1243

_c_ 1234

There are three ways to make the _extream_ changes. First, every time

the _hunt_ leads, as in the peal here prickt; secondly, every time it

lies behind; thirdly, every time it leads and lies behind: in this last

way there are six _extream_ changes in the peal, but in the other two

ways, only three _extreams_; the _extream_ changes must always be made

betwixt the two farthest bells from the _hunt_. Any bell may _hunt_ at

pleasure, and it may move either up or down at the beginning of the

peal. If the _1st_ or _3d_ do _hunt_ down, or the _2d_ or _4th_ up at

the beginning, the first change must be _single_, and made of the

back-stroke (if ’tis rung at half-pulls) to prevent cutting compass; but

if either of those bells do _hunt_ the contrary way, then the first

change must be double.

_Old Doubles and Singles. 1 and 2._

One change is _double_, the next _single_, and so by turns. The treble

hath a direct hunting course, as in plain changes. Every _double_ change

is on the four first bells, and the treble is one of the two bells that

makes every _single_ change, except when it leads, and then the _single_

is in the _3d_ and _4th_ places; but when 2 lies next the treble, then

the _single_ is behind, which is call’d _extream_. Every time the treble

leaves leading, the two first bells continue slow dodging, until the

treble comes down and displaceth them. And when the treble moves down

out of the _5th_ place, the bell that comes into it lies still there,

untill the treble comes thither again, except when the _extream_ change

is made behind. Every bell lies twice together in the _3d_ and _4th_

places, except when the treble leads, and also when it hinders them in

hunting.

_12345_ │ 51432 │ —————

21435 │ 15342 │ 12543

24135 │ 15432 │_Extre._

42315 │ ————— │ 12534

42351 │ 13254 │ —————

24531 │ 13524 │ 13425

24513 │ ————— │ 13245

42153 │ 12435 │ —————

41253 │_Extre._│ 14532

14523 │ 12453 │ 14352

14253 │ ————— │ —————

41523 │ 15324 │ 15243

45123 │ 15234 │ 15423

54213 │ ————— │ —————

54231 │ 13452 │ 12354

45321 │ 13542 │_Extre._

45312 │ 14235 │ 12345

54132 │ 14325 │

This old peal may be rung by a new course, which differs from the former

only in the _single_ changes that are made every time the _whole-hunt_

leads, _viz._ every _single_ may be made either in the _2d_ and _3d_, or

_4th_ and _5th_ places. If they are made in the _2d_ and _3d_, then the

_extreams_ must be made when the _half-hunt_ lies behind; but if they

are made in the _4th_ and _5th_ places, then the _extreams_ must be made

when the _half-hunt_ lies next the _whole-hunt_, the _extreams_ being

always made in the _3d_ and _4th_ places.