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Campanalogia

Chapter 63: The Experiment.
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About This Book

A practical and mathematical manual on the art of change-ringing, presenting clear rules for composing and performing sequences of bell changes, mathematical demonstrations of how changes multiply to form complete sets, and numerous example peals and methods for practitioners. It balances speculative discussion of permutation principles with detailed practical guidance for ringing technique, notation, and composition, and includes newly devised peals and corrective notes addressing errors in earlier printings.

Colledge Bob the First.
123456 435216
214365 &c.
124356 163542
213465 bob.
231456 165324
324165
321456 123564
234165 bob.
243615 125346
426351
462315 143526
643251 134562
634521
365412 165432
356421 156423
534612
543162 124653
451326 142635
453162
541326 136245
514362 bob.
153426 132654
513462
154326 156234
145362 bob.
413526 152643
143562
415326 146253
451362 164235
543126
541362 132465
453126 123456
Colledge Bob the Second.
123456 543216
214365 &c.
124356 153624
213465 bob
231645 135642
326154
231654 153462
326145 bob
362415 135426
634251
364215 153246
632451 152364
623541
265314 125634
625341 126543
263514
236154 162453
321645 164235
236145
321654 146325
312564 bob
135246 164352
315264
132546 146532
135264 bob
312546 164523
132564
315246 146253
351426 142635
534162
351462 124365
534126 123456
Colledge Bob the Third.
123456 462513
214365 &c.
123465 165432
214356 bob
241365 156423
423156
241356 143526
423165 bob
243615 134562
426351
423615 152364
246351 153246
423651
246315 126543
243651 125634
426315
246135 164235
421653 162453
246153
421635 143652
412653 bob
146235 134625
412635
146253 165324
142635 bob
416253 156342
142653
416235 132546
461253 135264
642135
461235 124365
642153 123456
Colledge Bob the Fourth.
123456 462513
214365 &c.
124356 165432
213465 bob
231456 156423
324165
321456 143526
234165 bob
243615 134562
426351
246315 152364
423651 153246
246351
423615 126543
243651 125634
426315
462135 164235
641253 162453
642135
461253 143652
416235 bob
142653 134625
412635
146253 165324
142635 bob
416253 156342
146235
412653 132546
421635 135264
246153
241635 124365
426153 123456

Colledge Bob the fourth. When the Treble leaves the two hind bells, they dodg until it comes there again; and then the two first bells dodg until the Treble gives way for the two hind bells to dodg again, and then the two first bells cease dodging.

Colledge Bob the Fifth.
123456 632514
214365 &c.
124356 163542
213465 bob
231456 136524
324165
321456 163425
234165 bob
324615 136452
236451
234615 163254
326451 162345
234651
326415 126543
324651 125634
236415
326145 152436
231654 154263
236145
321654 145362
312645 bob
136254 154326
316245
132654 145623
136245 bob
312654 154632
132645
316254 145236
361245 142563
632154
631245 124365
362154 123456

Colledge Bob the fifth. When the Treble leaves the two hind bells, they dodg until it comes there again. And when it leaves the two first bells they lie still one change, dodg the next, and so by turns until it comes down there again; during which time the bells in the third and fourth places dodg except when the Treble hindereth them.

By these methods each of them will go 120 changes, and by making of bobs they will go 240, 360, or 720. In the first of them the bell in the second place lieth still at the bob-changes, and in the other four the bell in the fourth place always lieth still.

To ring 240. Every time the half-hunt dodgeth behind a bob must then be made, as in these peals here prickt; where, in the first peal the 4 is the half-hunt, and in the other four peals the 2 is the half-hunt.

To ring 360. Every time the half and quarter-hunts dodg together behind, a bob must then be made.

To ring 720. Every time the half-hunt dodgeth behind a bob must then be made, except when the quarter-hunt dodgeth there with it, and then not.

In the 360 or 720 of each peal the 2 may be the half-hunt, and 4 the quarter-hunt or others at pleasure.

The Experiment.

Triples and Doubles. The Treble is the whole-hunt, but never hunteth up farther than the fourth place, for the four first bells go Doubles and Singles; and every time the Treble leads an extream is made in the third and fourth places, according to the common course of doubles and singles upon, four bells; which course of doubles and singles must be continued, the two hind bells in the mean time dodging, until the making of the first Parting change, which will separate the two hind bells; and then the four first bells go the same course of doubles and singles again, the two hind bells dodging as before, until the making of the second Parting change, and so successively. The Parting change is a double change on the four middle bells, and made at the leading of the Treble. The first Parting change may be made either at the first second or third leading of the Treble, observing, that whatsoever bell in the first Parting change moves down to the Treble, when the Treble leads and that bell lieth next it again, the second Parting change must then be made. And whatsoever bell in the second Parting change moves down to the Treble when the Treble leads, and that bell lieth next it again, the third Parting change must then be made, and so successively. There being five Parting changes in the Peal, and as many half-hunts, each of the bells (the Treble excepted) taking that place one after another; and consequently, the five persons that ring them must call the Parting changes one after another as their turn comes, according to the aforesaid rule.

Changes upon Seven Bells.

The methods upon five may be prickt upon seven, observing but the true difference of proportion in the changes; that is, doubles upon five bells must be triples upon seven; doubles and singles upon five must be triples and doubles upon seven, &c.

Plain Triples.

All the bells have a direct hunting course. All peals upon six bells wherein half the changes are triples, will go upon seven according to this method here prickt; two of the changes upon six being always made at the leadings of the Treble, the six hindmost bells making them: the first is a triple change brought in by the course of the bells, and the next must either be double or single according to the method of the changes upon six.

1234567
2143657
2416375
4261735
4627153
6472513
6745231
7654321
7563412
5736142
5371624
3517264
3152746
1325476

Dodging Triples.

Triples and Doubles upon six may also go upon seven, according to this method here prickt, but in the same manner as the former.

1234567
2143576
2415367
4251376
4523167
5432617
4523671
5432761
4523716
5432176
5341267
3514276
3152467
1325476
1352746

Colledge Bob Triples.

1234567 6745312
2135476 7654132
2314567 7561423
3241657 5716243
3426175 5172634
4362715 1527364
4637251 1253746
6473521  

Every time the Treble leaves leading, the bell in the third place lieth still, whilst the four hind bells dodg; but otherwise all the bells have a direct hunting course as Plain Triples. By this method it will go seventy changes, and by making of bobs it will go 350. The rule for the bobs is this; when the Treble goeth to lead, if the half-hunt lying before gives it place, then a bob must be made at that change, wherein the bell in the third place lieth still, and the four hind bells dodg; so that at every bob the four hind bells make two dodges before they part. By making of two extreams it will go 700, and with four extreams it will go 1400. But by making of intervening bobs it will go 700 compleat triples without any extream; 1400 with two extreams, and 2800 with four extreams. Any bell may be made a half-hunt.

Colledge Bob, Triples: the second way.

1234567 4536271 7162534 7326145
2135476 5463721 1726354 3762415
2314567 5647312 1273645 3674251
3241576 6574132 2176354  
3425167 6751423 2713645  
4352617 7615243 7231654  

When the Treble leaves leading, the two hind bells dodg until Treble parts them; but in all other respects ’tis the same with the former, and the bobs made in the same manner, and by the same rule as in that peal, and it will go as many changes also as that.

Colledge Triples, dodging behind.

1234567 5346271 7165324 3675124
2143576 3564721 1756342 6357214
2415367 3657412 1753624 6532741
4251376 6375142 7135642  
4523167 6731524 7316524  
5432617 7613542 3761542  

Colledge Triples, dodging before and behind.

1234567 2436571 4126753 4726153
2143576 4263751 1462735 7462513
2415367 2467315 1467253 4765231
4251376 4276135 4176235  
2453167 2471653 4712653  
4235617 4217635 7421635  

Each of these two peals by the method here prickt will go Eighty four changes; and then when the Treble leads, and the half-hunt lieth next it, a Parting change being then made, they will go 420. And by making of bobs they will go 5040. 2 may be the half-hunt, or any other at pleasure. The Parting change is a double on the four middlemost of the six hind bells.

’Tis plainly demonstrable, that the Principle upon five may go 420 triples upon seven, which is a twelfth part; 840, which is a sixth part; or 1260, which is a fourth part of the whole, and the utmost period of triple changes. And then by making of four extreams it may go 5040, the compleat peal.

Great variety of peals may be prickt upon seven: as Triples, Triples and Doubles, Triples Doubles and Singles; Doubles, Doubles and Singles, &c. But changes upon seven being seldom practised, I will therefore forbear to wast more paper in pricking down examples, and proceed to the changes on eight.

Changes upon Eight Bells.

Sixscores upon five bells are commonly rung upon eight, three bells lying behind. The most musical to lie behind are 218, 418, 148, 248, 348, 468, 648, 548, 864, 241, 321, and 135 to be laid behind, and then 1 and 3 to dodg throughout the peal. And also 184 to be laid behind, and to go the six changes thus, 814. 841. 481. 418. 148. 184. 814. &c. and so on to the end of the sixscore. They may go the sixes either at whole or half-pulls. Peals upon six, as Triples and Doubles, &c. make exceeding good musick upon Eight, 48. 68. 41. or 18. lying behind. Or else Triples and doubles upon the six middle bells, the Treble leading, and the Tenor lying behind. And also Triples upon seven, the Tenor lying behind. But for such as have not yet attain’d the skill to ring these compleat peals, Sett-changes are very proper for them, being easie and rung with little difficulty.

Colledge Grounds.

The grounds of these sett-changes are of two kinds. First, placing of the bells Fifths, or secondly Thirds. To place them fifths; the 4 must hunt up behind the 7, the 3 behind the 6, and the 2 behind the 5. Or else the 5 may hunt down under the 2, the 6 under 3, and the 7 under 4. Or otherwise, first a single, then a double, and then a triple change to be made on the middlemost bells, all which are to one effect; for then the bells will lie fifths thus, 15. 26. 37. 48. Here are four Concords to be chiefly regarded in the peal. The first is 15. the second 26. the third 37. and the fourth is 48. These four Concords may go the methods of any changes upon four bells; 1.5 being taken for the Treble, 2.6 for the Second, 3.7 for the Third, and 4.8 for the Fourth; and the Concords to change places with each other at pleasure. Wherein ’tis observable, that the two notes of every Concord must constantly attend each other in their motion; that is, whensoever one of the two notes moves, the other must follow it. For example: admit they were to go the twenty four changes, and that 1.5 were to hunt up over 2.6, 3.7, and 4.8. first therefore it must move up over 2.6, wherein it makes four changes: for first, the 5 moves up over the 2 thus, 12563748, the 1 must follow it thus, 2156.37.48. Then the 5 moves up over 6. 2165.37.48. the 1 follows it again 26.15.37.48; here the two Concords have made a change. In which manner also 1.5 must move up over 3.7. and 4.8. And in this manner are the Concords to move and change places with each other throughout the peal. Or secondly, to place the bells thirds, the 64 and 2 must hunt up, or else the 357 down; or otherwise a triple, a double, and a single change to be made on the middlemost bells; all which are to one and the same effect, for then the bells will lie thirds thus, 13.57.24.68. Here are also four Concords principally to be regarded in the peal: the first is 1.3, the second 5.7, the third 2.4, and the fourth 6.8. These four Concords may also go the methods of any changes upon four bells, 1.3 being taken for the treble, 5.7 for second, 2.4 for the third, and 6.8 for the fourth, and they must move in the same manner as before I have shewed. By these Grounds great variety of excellent and Musical changes are to be rung. If they go the twenty four, then the peal will consist of four times that number, that is, ninety six changes. But they may go only the first eight changes of the twenty four, and then the peal will consist of thirty two. Or else the first eight changes of a twenty four doubles and Singles, which will consist of forty eight if the double changes of the twenty four are singled, otherwise but thirty two as before. Any Concord may be made a hunt and to move either up or down at the beginning: so that these Grounds afford great diversity. In the ringing of these Sett-changes the notes will lie sometimes fifths, sometimes thirds, and sometimes thirds and fifths, and then ’tis pleasant Musick to Clam them, that is, the two notes of each Concord to strike together; and if they are clam’d true, the eight bells will strike as if they were but four, but with far greater harmony. They may Clam two or three bouts, and then strike open as many, and so alternately; or else they may Clam one pull, open the next, and so on. To reduce the notes of the fifths to their right places again at the conclusion of the peal, either 234 must hunt down, or else 765 up; or otherwise a Triple double and single change to be made on the middlemost bells, all which are to one effect, and will bring the bells round. To reduce the thirds either move down 246 into their places, or else move up 753 into theirs; or otherwise make single, double, and triple change on the middlemost bells; all which are to one effect, and will bring the bells again round.

The methods of all peals upon six bells may be prickt upon eight, observing but proportion in the changes, according to the difference in the number of bells, viz. Triples and doubles upon six must be quadruples and triples upon eight. Doubles upon six must be Triples upon eight, &c.

Bob-Major.

12345678
21436587
24163857
42618375
46281735
64827153
68472513
86745231
87654321
78563412
75836142
57381624
53718264
35172846
31527486
13254768
13527486

Plain Quadruples and Triples. All the bells have a direct hunting course until the Treble leads, and then the six hindmost bells dodg. By this method it will go 112. And by making of bobs it will go 224, 336, or 672. The bob is a triple change at the leading of the Treble, wherein the bell in the 4th place lieth still.

To ring 224. Every time the half-hunt dodgeth behind, a bob must then be made.

To ring 336. Every time the half and quarter-hunts dodg together behind, a bob must then be made.

To ring 672. Every time the half-hunt dodgeth behind, a bob must then be made, except when the quarter-hunt dodgeth there with it, and then not. The 2 may be the half-hunt, and 4 the quarter-hunt, or others at pleasure.

By making of two extreams it will go 1344, and with four extreams it will go 2688.

All peals upon six bells wherein half the changes are triples, will go upon eight according to the method before prickt, but after this manner. If it is a peal upon six, which consists of 360 or 720 changes, then in the ringing of it upon eight there must be five hunts. The Treble may be the first hunt; 2 the second &c. Now the method of the peal must go on according to that before prickt until the Treble leads, and the 2 lie next it, and then two of the changes upon six are always made, the six hind bells making them: the first is always a triple change brought in by the course of the bells thus, 12436587, and the second either double or single according to the method upon six; and the third fourth and fifth Hunts in eight, are the whole half and quarter-hunts in the changes upon six. By this method it will go 40320 compleat, but then every 112th change will be a double, and sometimes single in some peals. The bells may be brought round at 672 in some peals, but in others not till 1344.

Colledge Bob-Major.

The first. The second. The third. The fourth.
       
12345678 12345678 12345678 12345678
21436587 21436587 21436587 21436587
24163578 24163578 24135678 24135678
42615387 42615387 42316587 42316587
46251378 24651378 43261578 24361578
64523187 42563187 34625187 42635187
65432817 24536817 36452817 24365817
56348271 42358671 63548271 42638571
53684721 24385761 65384721 24368751
35867412 42837516 56837412 42637815
38576142 24873156 58673142 24367185
83751624 42781365 85761324 42631758
87315642 24718356 87516342 24613785
78136524 42173865 78153624 42167358
71863542 41237856 71856342 41263785
17685324 14328765 17583624 14627358
16758342 13482756 15786342 16423785

Quadruples and Triples. The first hath single dodging behind; the second single dodging before and behind; the third double dodging behind; and the fourth double dodging before and behind. It may also be prickt a fifth way, viz. with single dodging before, and double dodging behind. And likewise a sixth way, viz. with doubled dodging before, and single dodging behind. The dodging is without intermission except when Treble hindreth, and also betwixt two bells until Treble parts them. By this method each of them will go 112, and by making of bobs they will go 224, 336, or 672. The bobs are triple changes at the leadings of the Treble; in the first second and sixth the bell in the 4th place lieth still at the bobs, and in the third fourth and fifth the bell in the 2d place lieth still. The warning for the bobs is the same with that in Bob-major next before. And the extreams made as in that peal, 2 may be the half and 4 the quarter-hunt in the four first, or others at pleasure.

Colledge Triples, dodging before and behind.

12345678 42587613
21435687 24578163
24153678 42571836
42513687 24517863
24531678 42157836
42536187 41275863
24563817 14725836
42568371 17452863
24586731  

By this method it will go 112, and by making of bobs it will go 224, 336, or 672. The bob is a triple-change at the leadings of the Treble, wherein the bell in the 4th place lieth still. The warning for the bobs is the same with that in Bob-major, and the extreams also the same as in that peal. The 2 may be the half-hunt, and 4 the quarter-hunt, or others at pleasure.

The Wild-Goose Chase.

12345678
21536784
25163748
52613784
56231748
65327184
63572814
36752841
37625481
73265418
72356148
27531684
25713648
52173684
51237648
15327684
13572648
31752684
37125648
73215684
72351648

Triples. The fourth bell must first hunt up into the 7th place and then the 4 and 8 continually dodg behind throughout the peal, except when the Treble hindreth them. The bell that moves up into the 6th place when the Treble moves down from thence, lieth still there until the Treble displaceth it; during which time the two hind bells dodg, and the five first go a perfect hunting course. And also when the Treble moves up out of the 5th place, the five first bells go a hunting course until it comes down there again. By this method it will go eighty changes, and by making of bobs it will go 160, 240, or 480. The bob is a triple change at the leading of the Treble, wherein the bell in the 4th place lieth still.

To ring 160. Every time the half-hunt maketh a change in the 2d and 3d places, a bob must at the same time be made.

To ring 240. Every time the half and quarter-hunts make a change together in the second and third places, a bob must then be made.

To ring 480. Every time the half-hunt maketh a change in the second and third places, a bob must then be made, except when the quarter-hunt makes a change there with it, and then not. The 2 may be the half-hunt, and 6 the quarter-hunt, or others at pleasure.

Colledge Triples, dodging behind.

12345678 62345178
21435687 26431587
24153678 24613578
42513687 42163587
45231678 41236578
54326187 14326587
53462817 13462857
35642871 31642875
36524781 36124857
63254718 63214875

The method of ringing this peal is the same in all respects with that next before, with this only difference. Every time the whole-hunt leads, the triple change is here made on the six middle bells, which parts the two hind-bells, and so introduceth them by degrees into the body of the peal. By this method it will go 112, and by making of bobs it will go 224, 336, or 672. The bob is a triple change at the leading of the Treble, wherein the bell in the 6th place lieth still. The warning for the bobs in the 224 is the same with that in the 160 next before. In the 336 ’tis the same with that in the 240 next before. And in the 672 ’tis the same with that in the 480 next before. 2 may be the half-hunt and 5 the quarter-hunt, or others at pleasure.

The Grand Experiment.

Quadruples and Triples. The Treble is the whole-hunt, but never hunteth up farther than the sixth place; for the six first bells go triples and doubles, it matters not of what sort, provided that the double changes at the leadings of the Treble are always made on the four hindmost of the six bells; which course of triples and doubles must be continued, the two hindmost of the eight bells in the mean time dodging until the first Parting change is made, which will separate the two hindmost bells; and then the six first bells go the same course of triples and doubles again, the two hindmost bells in the mean time dodging as before, until the second Parting change is made, and so successively. The Parting change is a triple change on the six middle bells, and made at the leadings of the whole-hunt. The first Parting change may be made either at the first second third fourth or fifth leading of the Treble; observing, that whatsoever bell in the first Parting change moves down to the Treble, when the Treble leads and that bell lieth next it again, the second Parting change must then be made. And again, whatsoever bell in the second Parting change moves down to the Treble, when the Treble leads and that bell lieth next it again, the third Parting change must then be made, and so successively; there being seven Parting changes in the peal, and as many half-hunts, each of the seven bells taking that place one after another. So that the seven persons that ring the 2d, 3d, 4th, 5th, 6th, and 7th bells, must call the Parting changes one after another, according as the aforesaid rule directs them: or else he that rings the Treble may do it, but not so well as the rest. To ring it with such peals upon six bells which consist of single courses, it will go 420; with double courses 840. This peal may also be rung triples, that is, the six first bells to go doubles, the two hind bells in the mean time dodging, and the Parting changes to be made as before. But in ringing it with such Peals of Triples and Doubles, or else Doubles upon six bells, where the double change at every leading of the Treble is made in the 2d 3d 5th and 6th places, there, whatsoever two bells lie next the Treble at the first Parting change, the same two bells will lie next it at every Parting change, which will be a rule for calling them, there being only five Parting changes in it, which are triples as before. The first Parting change may also here be made either the first second third fourth or fifth time the Treble leads. If it is rung with peals upon six bells, consisting of single Courses, it will then go 300, with double Courses 600. This peal may also be rung by Concatenating of divers kinds of methods. For as the peal consists of several parts, viz. from one Parting change to the next, being accounted a compleat part; so each part may be rung by a different method from the rest. For any peals upon six bells, whether doubles, or triples and doubles, consisting either of single or double Courses, may indifferently be rung together in this peal, succeeding each other in the several parts of it, and at every Parting change a new method to begin. Or else any two of them to succeed each other alternately throughout the parts of the peal, or more or less at pleasure. But still observing, that all that are rung together in one peal must be such, where the doubles at the leadings of the Treble are made on the four hindmost of the six bells; or else all of them such, where the doubles at the leadings of the Treble are made in the second and third, and the fifth and sixth places. If they are of the first kind, then there will be seven Parting changes in the peal, and as many half-hunts; and the half-hunts must successively call the Parting changes as before I have shewed: if of the later kind, then but five Parting changes, which must be call’d by the same rule as before I have shewed in ringing it with one peal of this kind. And also observing, if the first Parting change is made at the first second third or fourth leading of the Treble, then whatsoever method it goes at first, it must also go the same again after the last Parting change is made. But in ringing it with peals of the first kind, the second being made the first half-hunt, and to call the first Parting change; and with peals of the later, the 3d likewise: then the last Parting change in either of them will conclude the peal.

This peal may go the method of the Experiment upon six bells, page 162, that is, the four first bells to go the Twenty four Doubles and Singles as in that peal; and the four hindmost bells in the mean time to dodg double. The Parting changes are triples on the middle bells, and the same rules observed in making and calling them, as in that peal: but here are seven of them in this, and 168 changes.

The Experiment upon six may also be rung Comprehensively herein. The six first bells to go that compleat peal, the two hindmost of the eight bells in the mean time dodging; and every time the 3d bell comes to call the Parting change on six, then instead of it a Grand change must be made, that is, a triple on the six middle bells: and then the six first bells to go the compleat peal again, the two hindmost bells in the mean time dodging as before, untill the third bell calls another Grand change, and so successively; there being three of them in the peal, and 360 changes. If the bells are placed 23567148 at the beginning, the 4.8 will dodg behind the first sixscore of it, 4.1 the second, and 1.8 the third, and then the 5th may call the Grand changes in the place of the 3d; or any other three bells may be laid behind at first, for the sake of Musical dodging. The first Grand change may be made either at the first second third fourth or fifth Parting change, observing, that whatsoever bell at the first Grand change should then in course have call’d a Parting change, every time that bell comes to call a Parting change, it must call a Grand change in the place of it: or else any one of the six first bells (the whole-hunt excepted) may be appointed beforehand to attend the calling of the Grand changes, observing, that every time that bell comes to call a Parting change, a Grand change must be call’d in the place of it.

Imperial Bob.

Quadruples and Triples. The Treble hath a dodging course. The two first and two last bells always dodg until the Treble hindreth them, and in the mean time the two next bells to those dodging bells do lie still one change, dodg the next, and so by turns until the Treble also hindreth them. And the two bells in the fifth and sixth places whilst the Treble is behind, and those in the 3d and 4th places when ’tis before dodg, until Treble likewise hindreth them. By this method it will go 224, and by making of bobs it will go 448, 672, or 1344. The bob is a triple change at the leading of the Treble, wherein the bell in the fourth place lieth still.

12345678 42361875 16847253 14283675
21436587 24368157 16482735
12346578 42631875
18645273
21435687 24613857 18765432 18462537
24136578 42168375 bob
42315687 24618357 17864523 16587432
24135678 42163875
bob
42316587 41268357 16573824 15684723
24361578 14623875 bob
42635187 41263857 15678342 18753624
24631578 14628375
bob
42365187 14263857 17352648 17856342
24635817 41628375 17536284
42368571 14268357
15372846
24365817 41623875 13274586 15738264
42638571 46128357 13725468
24365871 64213875
13254768
42638517 46123857 12438765 13527486
24635871 64218375 12347856
42368517 46281357
12436587
24638157 &c. 14826357 12345678

To ring 448. Every time the half-hunt dodgeth behind a bob must then be made, as in this here prickt, where 2 is the half-hunt.

To ring 672. Every time the half and quarter-hunts dodg together behind, a bob must then be made.

To ring 1344. Every time the half-hunt dodgeth behind a bob must then be made, except when the quarter-hunt dodgeth there with it, and then not. The 2 and 4 may be the half and quarter-hunts, others at pleasure.