Part 7

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.

London _Paradox. 1 and 2._

One change is _double_, the next _single_, and so by turns. The motion of the treble is after this manner; in hunting up, first, it makes a dodg in the _2d_ and _3d_ places, then it lies twice in the _4th_ place, and four times behind; in which manner also it hunts down again, and then leads four times. The rest of the bells have a like course and motion with that of the treble, untill the treble leads. Now ’tis observable, that every _single_ change is made in the _2d_ and _3d_ places until the treble leads, and then in the _3d_ and _4th_ places; but when 2 lies next the treble, then an _extream_ behind. The changes at the leadings of the_whole-hunt_ have an absolute dependency upon the course of the _twenty four_ changes, _doubles_ and _singles_ upon four bells; and the _extreams_ to be made as many ways as in that peal, which are here guided by the motion of the _half-hunt_.

_12345_ │_Extre._ 21435 │ 12453 24135 │ ————— 21453 │ 14235 24153 │ 14325 42513 │ 13452 45213 │ 13542 42531 │ ————— 45231 │ 15324 54321 │ 15234 53421 │ 12543 54312 │_Extre._ 53412 │ 12534 35142 │ ————— 31542 │ 15243 35124 │ 15423 31524 │ 14532 13254 │ 14352 13524 │ ————— 15342 │ 13425 15432 │ 13245 ————— │ 12354 14523 │_Extre._ 14253 │ 12345 12435 │

_Phœnix 5 and 4._

One change is _double_, the next _single_, and so by turns. Every bell leads twice, and lies behind four times. Every _single_ is made in the _2d_ and _3d_ places, until the _5th_ comes behind, and then in the _3d_ and _4th_ places; but when the _4th_ leads, (the _5th_ being behind) the _single_ is in the _2d_ and _3d_ places.

_12345_│ 54123 21354 │ 51423 23154 │ 15432 32514 │ 14532 35214 │ 41352 53241 │ 43152 52341 │ 34125 25431 │ 34215 24531 │ 43125 42513 │ 41325 45213 │

London _pleasure. 1 and 2._

This peal in the former printing of it was prickt another way, but I have here transposed that Course, which in my opinion renders it more easie and practical.

_12345_│ 23154 │ 35142 │ 15432 21345 │ 21354 │ 35412 │ ————— 23145 │ 12354 │ 35421 │ 14532 32145 │ 13254 │ 53421 │ 14523 31245 │ 13524 │ 53412 │ 14253 31425 │ 13542 │ 53142 │ 12453 34125 │ 31542 │ 51342 │ ————— 34215 │ 31524 │ 15342 │ 12435 34251 │ 31254 │ 15324 │ 14235 32451 │ 32154 │ 15234 │ 14325 32415 │ 32514 │ 12534 │ 14352 23415 │ 32541 │ ————— │ ————— 23451 │ 35241 │ 12543 │ 13452 23541 │ 35214 │ 15243 │ 13425 23514 │ 35124 │ 15423 │ 13245 │ │ │ 12345

_Mr._ Tendring’_s_ _Peal, call’d_ Grand Paradox. _1 and 5._

One change is _double_, the next _single_, and so by turns. The motion of the _whole-hunt_ is after this manner: first, it moves up into the _2d_ and _3d_ places, lying twice in each; then it moves up and makes a dodg behind, and then lieth still one change in the _5th_ place; then it makes another dodg behind, and so moves down into the _3d_ and _2d_ places lying twice in each as before, and then leads four times. Every other bell hath a like course and motion with that of the treble until the leadings of the treble, and then observe, that every time the treble goeth to lead and leaves leading, the _double_ change is made on the two first and two last bells, except when it goeth to lead if the _half-hunt_ lies next it, and then not. Every bell leads four times, and every _single_ is made behind. The change wherein each bell leaves leading, is always made on the four first bells, except as before.

_12345_│ 45321 │ 21534 │ 43152 │ 13524 │ 14523 21354 │ 45312 │ 25143 │ 43125 │ 13542 │ ————— 21345 │ 54132 │ 25134 │ 41352 │ ————— │ 13254 23154 │ 54123 │ 52314 │ 41325 │ 12453 │ 13245 23145 │ 51432 │ 52341 │ 14352 │ 12435 │ 12354 32415 │ 51423 │ 53214 │ 14325 │ 14253 │ 12345 32451 │ 15243 │ 53241 │ 13452 │ 14235 │ ————— 34215 │ 15234 │ 35421 │ 13425 │ ————— │ 34251 │ 12543 │ 35412 │ ————— │ 15432 │ 43521 │ 12534 │ 34521 │ 15324 │ 15423 │ 43512 │ 21543 │ 34512 │ 15342 │ 14532 │

What you please, _Doubles and Singles._

Every bell leads four times, and lies behind twice, except when the _extream_ is made behind; and twice in the second place, except when the _extream_ is made before: and note, when the treble is before the fourth stroke, the _single_ is in the _2d_ and _3d_, the next time the _single_ is behind; but at other times the _single_ is in the _3d_ and _4th_ places. When any bell leaves leading the _double_ change is on the two first and two last, and the _extreams_ are made by turns, first behind, then before, and so on to the end, for there are six _extreams_.

_12345_ │ 34521 │ 21435 │ 45231 │ 14352 │ 14235 21354 │ 34251 │ 21345 │ 54213 │ 14532 │ 14325 21534 │ 43215 │ 23154 │ 54123 │ 15423 │ 13452 25143 │ 43125 │ 23514 │ 51432 │_extre._│_extre._ 25413 │ 41352 │ 32541 │ 51342 │ 15432 │ 13425 52431 │ 41532 │ 32451 │ 15324 │ ————— │ ————— 52341 │ 14523 │ 34215 │ 15234 │ 13254 │ 12534 53214 │ 14253 │ 34125 │ 12543 │ 13524 │ 12354 53124 │ 12435 │ 43152 │_extre._│ 15342 │ 13245 35142 │_extre._│ 43512 │ 15243 │_extre._│_extre._ 35412 │ 12453 │ 45321 │ ————— │ 13542 │ 12345 │ │ │ │ ————— │

_Old Doubles. 1 and 2._

The changes are all _double_, except one _single_ every time the treble leads. The treble hath a perfect hunting course as in plain changes, and every other bell hath a like hunting course with that of the treble until the treble leads, and then a _single_ is made in the _3d_ and _4th_ places; but when the 2 lies next the treble, the _single_ is behind which is call’d _extream_.

_12345_ │ 13254 │ 51432 │ 12453 │ 15234 │ 14532 21435 │ 13524 │ 15342 │ ————— │ ————— │ 14352 24153 │ 31254 │ 15432 │ 14235 │ 12543 │ ————— 42513 │ 32145 │ ————— │ 14325 │_extre._│ 13425 45231 │ 23415 │ 14523 │ ————— │ 12534 │ 13245 54321 │ 24351 │ 14253 │ 13452 │ ————— │ ————— 53412 │ 42531 │ ————— │ 13542 │ 15243 │ 12354 35142 │ 45213 │ 12435 │ ————— │ 15423 │_extre._ 31524 │ 54123 │_extre._│ 15324 │ ————— │ 12345

_New Doubles. 1 and 2._

The changes are all _double_, except one _single_ at every leading of the treble. The treble hath a perfect hunting course as in plain changes; and when it moves up from leading, the two first bells dodg untill it comes down again and displaceth them. Every bell that comes into the _3d_ place lies there twice, and then moves up behind; but the bell which lies there when the treble leaves leading, moves down. Every bell lies twice behind, except at the changes wherein the treble goeth to lead and leaves leading. Every time the treble leads, a _single_ change is then made in the _3d_ and _4th_ places; but when the 2 lies next the treble, an _extream_ behind.

_12345_ │ 13254 │ 51324 │ 12453 │ ————— │ 14352 21354 │ 13524 │ 15342 │ ————— │ 12543 │ ————— 23145 │ 31542 │ 15432 │ 14235 │_extre._│ 13425 32415 │ 35124 │ ————— │ 14325 │ 12534 │ 13245 23451 │ 53214 │ 14523 │ ————— │ ————— │ ————— 32541 │ 35241 │ 14253 │ 13452 │ 15243 │ 12354 23514 │ 53421 │ ————— │ 13542 │ 15423 │_extre._ 32154 │ 35412 │ 12435 │ ————— │ ————— │ 12345 31245 │ 53142 │_extre._│ 15324 │ 14532 │ │ │ │ 15234 │ │

_Reding Doubles. 1 and 2._

The treble hath a direct hunting course as in plain changes, and when it moves up from leading the two first bells dodg until it comes down again and displaceth them; and whilst they dodg before, every bell that comes down into the _3d_ place lies there twice, and then moves up again behind. But after the dodging all the bells go a direct hunting course up and down, until the dodging again hindreth them as before. Every bell lies twice behind, except when the treble leaves leading if the _2d_ lies next it, and then the _double_ is made on the two first and two last bells; by which means the two hind-bells then make a dodg, which happens in course once in twenty changes, that is, every second time the treble leaves leading. By this method it will go sixty changes, and then an _extream_ must be made. The _extreams_ in this peal may be made according to the preceding general rule set down in the _Introduction_. Here the first _extream_ is made at the end of sixty changes, the bells lying 1 3 2; and when they come to lie so again, the second _extream_ must be made; the _extream_ is made behind, two of the _extream_ bells lying there, and the _single_ is made in the _2d_ and _3d_ place at both the _extreams_.

_12345_ │ 12534 │ 12354 21354 │ 21543 │ ————— 23145 │ 25134 │ 13524 32415 │ 52314 │ 15342 23451 │ 25341 │ ————— 32541 │ 52431 │ 14253 23514 │ 25413 │ 12435 32154 │ 52143 │ ————— 31245 │ 51234 │ 14325 13425 │ 15324 │ 13452 14352 │ 13542 │ ————— 41532 │ ————— │ 15234 45123 │ 14235 │ 12543 54213 │ 12453 │ ————— 45231 │ ————— │ 15423 54321 │ 14523 │ 14532 45312 │ 15432 │ ————— 54132 │ ————— │ 13245 51423 │ 13254 │_extre._ 15243 │_extre._│ 12345

_Grandsire. 1 and 5._