502 Transactions. — Miscellaneous. 



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, 

 unti^ 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 be- 

 ginning 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 sub- 

 scribing " h " and " a," indicating " at home" and "away" 

 respectively, alternately to the numbers m 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 suc- 

 cession eitlier at home or away. 



Table I., following, indicates the result in the case of seven 

 clubs, and Table II. the general result for (2w + 1) clubs. 



