The Variety of Changes on Any Number of Bells
The changes on bells do multiply infinitely. On two bells there are two changes. On three bells are three times as many changes as there are on two; that is—three times two changes, which makes six. On four bells there are four times as many changes as on three; that is—four times six changes, which makes Twenty-four. On five bells there are five times as many changes as there are on four bells; that is—five times Twenty-four changes, which makes Six-score. On six bells are six times as many changes as there are on five; that is—six times Six-score changes, which makes Seven-hundred and twenty: And in the same manner, by increasing the number of bells, they multiply innumerably, as in the Table of Figures next following; where each of the Figures in the Column of the left hand, standing directly under one another (which are 1.2.3.4.5.6.7.8.9.10.11.12.) do represent the number of bells; and the Figures going along towards the right hand, directly from each of those twelve Figures, are the number of changes to be rung on that number of bells which the Figure represents: For Example, the uppermost Figure on the left hand is 2, which stands for two bells; and the Figure next to it on the right hand is also 2, which stands for two changes; that is to say, on two bells there are two changes. The next Figure below in the left Column is 3, which stands for three Bells; and the Figure next to it on the right hand is 6, which stands for six changes; that is—on three bells are six changes, and so of the rest as follows.
| bells | changes |
|---|---|
| 2 | 2 |
| 3 | 6 |
| 4 | 24 |
| 5 | 120 |
| 6 | 720 |
| 7 | 5040 |
| 8 | 40320 |
| 9 | 362880 |
| 10 | 3628800 |
| 11 | 39916800 |
| 12 | 479001600 |
The lowest of these figures are 479001600, that is, Four hundred seventy nine Millions, one thousand six hundred, which are all the changes that can be made on twelve bells: And supposing that twelve men should take 12 bells with intent to ring the changes on them, they would be Seventy five Years, ten Months, one Week and three Dayes in ringing them, according to the proportion of ringing 720 changes in an hour; reckoning 24 hours to the day, and 365 dayes in the Year.
Having given Directions for all sorts of plain and single Changes, I will now proceed to Cross-peals, and first to Doubles and Singles on four Bells.