Whereas the treble or fifth being made whole-hunts, the first of them can neither be moved down, nor the last up, at the beginning of a peal; therefore one of the twenty four changes must first be made, which is as effectual, as if the treble had moved down, or the 5th up. The Learner may observe, that two of the four and twenty changes are never made together in any sixscore, but as soon as one is made, the whole-hunt moves through the four notes before another can be made. The sixscore changes may be rung one hundred and sixty ways, which are thus demonstrable. There are five times four figures to be produced out of five, and not twice four the same figures: as 1234. 1235. 1245. 1345. 2345. with each four the twenty four changes may be prickt sixteen ways, as before I have shewed on four bells; so that here will be five times sixteen four and twenties, which amount to eighty, and not two alike. Now to each four add the fifth figure which is wanting, as to 1234 add 5, to 1235 add 4, to 1245 add 3, to 1345 add 2, to 2345 add 1, and every fifth figure being hunted through the sixteen four and twenties, which the other four make, as the 5 through the sixteen four and twenties which the 1234 make, and the like of the rest, will produce as many sixscores as there were four and twenties, that is, 80. Then the whole hunt may hunt two ways through each four and twenty, that is, up and down at the beginning, which doubles the former number, and makes 160 in the whole. _Treble up, fifth down._ 12345 │ 12534 │ 15243 │ 21453 │ ————— │ 14325 │ 13524 ————— │ 21534 │ 51243 │ 24153 │ 14253 │_Extre._│ 13254 21345 │ 25134 │ 52143 │ 24513 │ 14523 │ 13425 │ ————— 23145 │ 25314 │ 52413 │ 24531 │ ————— │ ————— │ 13245 23415 │ 25341 │ 52431 │ 24351 │ 15423 │ 13452 │_Extre._ 23451 │ 52341 │ 25431 │ 24315 │_Extre._│ 13542 │ 12345 23541 │ 52314 │ 25413 │ 24135 │ 15432 │ ————— │ 23514 │ 52134 │ 25143 │ 21435 │ ————— │ 15342 │ 23154 │ 51234 │ 21543 │ 12435 │ 14532 │_Extre._│ 21354 │ 15234 │ 12543 │_Extre._│ 14352 │ 15324 │ 12354 │_Extre._│ 12453 │ 14235 │ ————— │ ————— │ _Treble up, fourth down._ 12345 │ 12435 │ 41253 │ 21543 │ 52134 │ ————— │ 14325 ————— │ 14235 │ 14253 │ 12543 │ 51234 │ 15342 │ 13425 21345 │ 41235 │ 12453 │ 12534 │ 15234 │ 15324 │ ————— 23145 │ 42135 │ 21453 │ 21534 │ 15243 │ ————— │ 13245 23415 │ 42315 │ 24153 │ 25134 │ ————— │ 13524 │ 13254 23451 │ 42351 │ 24513 │ 25314 │ 15423 │ 13542 │ ————— 24351 │_Extre._│ 24531 │ 25341 │ 14523 │ ————— │ 12354 24315 │ 42531 │ 25431 │_Extre._│ ————— │ 13452 │ 12345 24135 │ 42513 │ 25413 │ 52341 │ 14532 │ 14352 │ ————— 21435 │ 42153 │ 25143 │ 52314 │ 15432 │ ————— │ _Second down, fourth up._