8589357125

t6

Rope-Stght.

therefore {from 2 1 4 3), only che twe middle bells; the next row will then read 2413. It is no w again possible to change the position of all four bells (in fact, if you again only changed the two middle bells the previous row would be the result). Change, therefore, all four bells ar.d you have 4 231. No w changc only the two middle beks, you have 432 1. Then all four, and you have 3412; then only two, which gives 3 142; then four, which gives 1324; and then the two middle ones. which will produce 1 2 3 4 and bring the bells into the position from which they started, namely, rounds.

On three, five, six, or any number of bells, the changes may be pricked in the same way. On three bells, two helis only can be changed each time, but on hve bells, four i.an be changed each time ; on six bells you first change all the six, and next time change only the middle four. The following changes are those produced in thls rnanner on three, four, five, and six bells. The brackets show which wouid be the liaud and back-strokes were these changes rang.

223    1234    12345    1 2 3 4 5

J 2    t    3    I2143    0:435    ( 2 1 4 3 6 5

I231    124^3    1²4*53    <241635

( 3 ^{2 1}    1 + 231    (42513    f    4    2    6 t    5    3

I 3 ^{1 2}    '4 3 2 1    145231    1462513

,132    (3 452    15 4 3 ² *    i'    6    4    5 2    3    ¹

'123    13542    ^ł 5 3 4 ¹ 2    )    6    5    4 3    ^2    1

P 3 ² 4    13514 2    I    5    fi    3 4    i    ²

P 2 3 4    131524    1536142

P 3 ² 5 4    i 3 5 ³ fi ² 4

I ^{1 2} 3 4 5    1315264

J 1 3 2 5 4 6 P 2 3 4 5 ⁶

1 f the path in which each beli moves, in stepping from one row of changes to the next, be exammed_t it wdl] be seen that a beli movesone place at a time, until it arrives in tbe first place