extensible to the case of any odd number of clubs. The arrangement cannot be completely carried out for the case of an even number of clubs, but a very close approximation to it can be made.

I have never heard of any rule or system being used in the arranging of inter-club fixtures. On the other hand, the common circumstances of the home and away fixtures being somewhat irregularly distributed, and of a few straggling fixtures generally remaining at the end of a season, for which apparently no places could be found on the dates when the main body of fixtures were played off, indicate the want of a rule which would enable a better arrangement to be carried out. It has appeared to me, therefore, advisable to give publicity to the result referred to above. It is as follows:—

Let the number of clubs be odd, and represent them by consecutive integers beginning from unity. Write down these integers in succession in a column, beginning with unity, until we have written down the middle integer; then write the next integer on the right of it and begin to ascend, writing down the remaining integers on the right of those previously written down. The last integer will be written down in the second row. the first integer remaining alone in the first row. Then begin a parallel column with the integer 2, and proceed in a similar way, writing down the integers in succession down the column until the last row is reached, and then write the next integer on the right and begin to ascend. The last integer will be written in the third row, but in the vacant place in the second row write unity. Then begin another parallel column with the integer 3, then another with 4, and so on until columns have been written down beginning with each of the integers used to represent the clubs. When the last integer has been used, continue in each case with the consecutive integers, beginning with unity, but never write a second integer in the first row.

The columns now represent the consecutive rounds, the numbers written together representing the competing clubs. Any club will play every other once. The clubs indicated in the first row have byes in the respective rounds. By subscribing “h” and “a,” indicating “at home” and “away” respectively, alternately to the numbers in each column in the order in which they were written down, but beginning with the second in each case, we have the home club indicated for each match, so that no club shall play two matches in succession either at home or away.

Table I., following, indicates the result in the case of seven clubs, and Table II. the general result for (2n + 1) clubs.

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Thus, e.g., in the first round 1 has a bye, 2 (at home) plays 7 (away), 3 (away) plays 6 (at home), and 4 (at home) plays 5 (away).

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If this rule were adopted the only drawing necessary would be for the numbers to represent the several clubs, everything else would then follow.

It has already been mentioned that it is impossible to completely achieve this arrangement in the case of the number of clubs being even. The nearest approach that is possible appears to be as follows:—

Write down columns as in the case above of an odd number of clubs, taking the odd number which is one less than the actual number of clubs. Then take the even number representing the number of clubs and write it at the side of each of the solitary numbers in the first row, but alternately on the right and on the left of them consecutively. The several columns then represent, as before, the competing clubs for the successive rounds, each club playing every other once. There are, of course, no byes.

If, further, we subscribe “h” and “a,” with the same meanings as before, to the numbers in each column alternately, descending with the numbers on the left and rising with those on the right, we get the home club indicated for