Ringing the Changes is a phrase often used by the general public in every-day life, and especially by some who wish to appear witty or clever, but to whom, as a rule, if a question be put as to its meaning, or proper application, it is seen in a moment that such knowledge is either too great or too small for them—in fact, that they know nothing at all about it. The lack of this special knowledge is easily traced to its origin; for how many schoolboys ever have a sum or exercise in the rule of permutation? Many, if not most, boys on leaving their studies and school would, it is believed (or as has been tested to some extent), be found utterly ignorant both of its use or practice. They may have learnt that it is the changing or varying the order of things; and that to multiply all the given terms or numbers the one into the other the last product will be the number of changes required—as 1, 2, 3, 4, 5, 6:—

1
2
2
3
6
4
24
5
120
6
720

Note.—Any changes of a complete number or course through a series of permutations is called a “Peal.”

Thus 2 bells (they may learn) produce 2 changes, 3=6, 4=24, 5=120, 6=720, and so on. They may have had the old tale told, and the old and often single, as well as singular, question put to them in this rule:—A young scholar, coming into town for the convenience of a good library, demands of a gentleman with whom he lodged what his diet would cost for a year, who told him £10; but the scholar, not being certain what time he should stay, asked him what he must give him for so long as he should place his family (consisting of six persons beside himself) in different positions every day at dinner? The gentleman, thinking it would not be long, told him £5, to which the scholar agreed. What time did the scholar stay with the gentleman? Which, as a matter of simple multiplication, is very easy to answer—5,040 days. And even the other, and most likely last question, may have been put, viz.:—How many changes may be rung upon 12 bells, and in what time would they be rung once over, supposing 10 changes may be rung in a minute, and the year to contain 365 days 6 hours?—Answer: 479,001,600 changes in 47,900,160 minutes, or 91 years 3 weeks 5 days 6 hours.

Either of these examples may be very easy so far, but as to the practical part of working them out in any performance in every-day life is quite another matter, and it is left for the schoolboy to wait or to forget all about both the rule and the figures, unless he comes to see its workings in the steeple or the fireside, upon the church or the musical hand bells, he would, perhaps, never see it necessary to prove by practice, attention, thought, and care that which is multiplied and multiplied, and left on the slate with astonishment, without any good or lasting effect either upon the mind or the senses. The Rev. Mr. Wigram very well shows a supposed case of persons changing positions upon steps, ascending and descending in method or order, as an example of permutation. But the positions or places may be made or taken, and the rule worked out for amusement and practice at the breakfast or dinner table, where there may be several persons meeting repeatedly. And in this it is not more astonishing than it is amusing to see the zest and interest given and taken by a boy of only eight years of age in its practice, when once fairly explained and started, cultivating both memory, thought, and interest in a fixed plan until it is accomplished, by no means an unimportant trait in character (for how many begin a task with zest, and falter or never finish, is abundantly seen). Such, in a higher sense, is the effect of change ringing on bells, where, beyond the changing places at a table, the sense of hearing and the practice of time or order are added to those of sight and touch.

Three questions naturally suggest themselves to the student at the very outset of the art of change ringing upon church bells, viz.:—

1st. How many changes can be rung on various rings of bells of various numbers numbers from 2 to 12?

2nd. How long would it take to ring them?