Now it must hunt through the other change, which is 2 1, in the same manner as before; that is, first it must lie before, then betwixt the two figures, then behind them, thus, 321, 231, 213. Here it has hunted through again, wherein it made three more variations; which three being set directly under the former, the six variations will then plainly appear, as in these figures: where the three figures stand six times together, and not twice alike.
| 123 | |
| 132 | |
| 312 | |
| 321 | |
| 231 | |
| 213 |
Now the figure 4 being in like manner hunted through each of those six changes, will produce the 24 changes on four. First, therefore it must hunt through the first, which is 123, letter (a), then through the second change of the six, which is 132, letter (b); then through the third, which is 312, letter (c), and so it being hunted through the rest of the changes likewise, will produce the twenty four changes on four.
| (a) | 1234 |
| 1243 | |
| 1423 | |
| 4123 | |
| (b) | 4132 |
| 1432 | |
| 1342 | |
| 1324 | |
| (c) | 3124 |
| 3142 | |
| 3412 | |
| 4312 |
The figure 5 being hunted through each of those twenty four changes, will produce the 120 changes on five, First therefore it must hunt through the first, which is 1234, letter (a); then through the second, which is 1243, letter (b); then also through the third, which is 1423, letter (c). In which manner it being hunted through the rest of the twenty four changes, will produce the 120 on five. And then the figure 6 being hunted through each of those sixscore changes will produce the 720 changes on six. And the figure 7 being hunted through each of those 720 changes, will produce the 5040. In which manner also the eighth, ninth, tenth, eleventh, and twelfth, being successively hunted through each Peal in the aforesaid order, will at length produce the compleat number of changes on twelve. Wherein ’tis observable, that all the figures, except two, have a hunting motion; which two may properly be term’d the Center, about which the rest do circulate. By these methods it is evident, that every hunting figure hath a certain number of figures assigned, through which tis constantly to hunt: as in the aforesaid Example on twelve, where the 1.2 are assigned for the figure 3 to hunt through, as appears in the six changes before. And in like manner, 123 are assigned for the figure 4 to hunt through; 1234 are assigned for the figure 5 to hunt through; 12345 for 6 to hunt through, &c. Now the figure 3 hunts as many times through the 1.2. as those two make changes, that is, two times wherein it makes twice three changes, that is, six, as before appeareth. The figure 4 hunts as many times through the 123, as those three figures make changes, that is, six times; wherein it makes six times four changes, which amounts to twenty four. The figure 5 hunteth as many times through the 1234, as those four figures make changes, that is, twenty four times; wherein it makes twenty four times five changes, which amounts to 120. The figure 6 hunts as many times through the 12345, as those five make changes, that is 120 times, wherein it maketh 120 times six changes, which amounts to 720. And in like manner the figure 7 hunts 720 times through 123456, wherein it maketh 720 times seven changes, which amounts to 5040. The eighth hunteth 5040 times through 1234567, wherein it makes 40320 changes. The 9th hunteth 40320 times through 12345678, wherein it makes 362880 changes. The tenth hunteth 362880 times through 123456789, wherein it makes 3628800. The eleventh hunteth 3628800 times through 1.2.3.4.5.6.7.8.9.10. wherein it makes 39916800. And lastly, the twelfth hunteth 39916800 times through 1.2.3.4.5.6.7.8.9.10.11. wherein it makes 39916800 times twelve changes, which amounts to 479001600, being the compleat number on twelve. By which ’tis evident, that every hunting figure hunts as many times through its assigned number of figures, as those figures are capable of making changes, which in short comprehends the summe and substance of this method, which is universal from two, to all greater numbers whatsoever.
| (a) | 12345 |
| 12354 | |
| 12534 | |
| 15234 | |
| 51234 | |
| (b) | 51243 |
| 15243 | |
| 12543 | |
| 12453 | |
| 12435 | |
| (c) | 14235 |
| 14253 | |
| 14523 | |
| 15423 | |
| 51423 |
If we consider the multitude of different words, wherewith we express our selves in Speech, it may be thought almost impossible that such numbers should arise out of twenty four Letters; yet this Art of variation will produce much more incredible effects. To give an instance thereof, I will shew the numbers of every quantity of Letters from two to twelve, that may be produced out of the Alphabet. The generality of Words consisting of these quantities, (viz.) two letters, three letters, four, five, six, seven, eight, nine, ten, eleven, and twelve letters. There are 10626 times four letters to be produced out of the twenty four letters of the Alphabet, and not twice four all the same Letters. There are likewise 42504 times five letters, 134596 times six letters, 346104 times seven, 735471 times eight, 1307504 times nine, 1961256 times ten, 2496144 times eleven, and 2704156 times twelve. Now each quantity being varied by the rules of this Art, will produce incredible numbers. First the 10626 times four letters, being multiplied by 24, which are the number of ways to vary each four letters, will produce 255024 that is to say, four letters may be produced out of the Alphabet to stand together after this manner (a b c d) two hundred fifty five thousand and twenty four times, and not twice alike. And in like manner, the 42504 times five Letters, being multiplied by 120, which are the number of ways to vary each five, will produce 5100480. The 134596 times six letters, being also multiplied by 720, will produce 96909120. The 346104, being multiplied by 5040, will produce 1744364160. The 735471, being multiplied by 40320, will produce 29654190720. The 1307504, being multiplied by 362880, will produce 474467051520. The 1961256, being multiplied by 3628800, will produce 7117005772800. The 2496144, being multiplied by 39916800, will produce 99638080819200. And lastly, the 2704156 time twelve letters, being multiplied by 479001600, will produce 1295295050649600, which products being all added together, as also 12696 which are the numbers consisting of two and three letters, the whole will amount to 1402556105125320, wherein there are not two alike, nor two letters of one sort in any one of them; which being written or printed on large Paper in folio, allowing 5000 to a sheet, they would take up 561022442 Reams of Paper and upwards, reckoning 500 sheets to a Ream: which Paper all the Houses in the City and Liberties of London would not contain; and in quantity doubtless infinitely exceeds all the Books that ever were printed in the world, reckoning only one of each Impression. And at the rate of five shillings the Ream, the Paper would cost 140255610.5 Pounds sterling; which is above four times as much as the yearly Rent of all the Lands and Houses in England amounts to. And all the people both young and old in the City and Suburbs of London (admitting they are five hundred thousand) could not speak the like numbers of words under forty years and upwards, each of them speaking 15000 every hour, and twelve hours every day. These prodigious numbers are the more to be admired, considering that the greatest number of letters in any of them, exceeds not twelve, neither are two letters of one sort in any one of them: but by producing and varying all the greater quantities, and placing two or more letters of one sort, or two of one sort and two of another, with all variety of the like nature that commonly happens in words, the numbers arising thereby would infinitely exceed the former; And if all the numbers of every quantity of letters from one to twenty four, together with all the variety as aforesaid, were methodically drawn out and varied according to the rules of this Art; which might easily be performed in respect of the plain and practical method of doing it; but the infinite numbers of them would not permit a Million of men to effect it in some thousands of years: it would be evident, that there is no word or syllable in any language or speech in the world, which can be exprest with the character of our Alphabet, but might be found literatim and entire therein; and more by many thousands of Millions than can be pronounced, or that ever were yet made use of in any language.
I will here give one instance of another kind, shewing the admirable effects of this Art, and so conclude. A man having twenty Horses, contracts with a Brick-maker to give him one hundred pound Sterling; conditionally that the Brick-maker will deliver him as many Loads of Bricks, as there are several Teams of six Horses to be produced out of the aforesaid twenty to fetch them, and not one Team or Sett of six Horses to fetch two Loads. The Brick-maker might be thought to have made a very advantageous bargain, but the contrary will appear. For there are thirty eight thousand seven hundred and sixty several Teams of six Horses, to be produced out of twenty, and not twice six the same Horses; then the Brick-maker must deliver as many Loads as there are Teams, and each Load consisting of five hundred Bricks, the whole would amount to 19380000, which being bought for one hundred pounds as aforesaid, would not cost above five Farthings a thousand; and at the rate of thirteen shillings and four pence the thousand, they amount to twelve thousand nine hundred and twenty pounds Sterling. But should a contract be made with the Brick-maker to deliver as many Loads of Bricks, as there are Teams of six Horses in each, to be produced out of the aforesaid twenty, which shall stand in the Cart in a differing manner; that is to say, although there may be the same Horses in several Teams, yet their places shall be so changed, that they shall not stand twice alike in any two Teams. On this account the Brick-maker must deliver seven hundred and twenty times as many as before; for there are 38760 several Teams as before I have shewed: then each Team may be placed 720 ways in the Cart, and not twice alike, which is to be done according to the methods whereby the 720 changes on six Bells are rung. So that 38760, which are the number of Teams, multiplied by 720, which are the number of ways to vary the six Horses in each Team, the product will be 27907200, which are the compleat number of Teams; and every Team carrying one Load, consisting of five hundred Bricks, the Whole will amount to 13953600000 Bricks. And after the proportion of a hundred and fifty thousand of Bricks to a House, they would build ninety three thousand and twenty four Houses; which are above six times as many as the late dreadful fire in London consumed. And at the rate of thirteen shillings and four pence the thousand, they are worth 6976800 pounds Sterling, which is at least four hundred Waggon-loads of money, as much as five Horses can ordinarily draw.
