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.