504 



Transactions. — Miscellaneous. 



each match in such a way that each club plays either two 

 matches at home or two away in succession, but this occurs 

 not more than once for any club in the whole competition. 



Table III., indicating the result for eight clubs, and 

 Table IV., indicating the general result, the number of clubs 

 being 2n, will help to make this clear. 



Table III. 

 Scheme of Matches between Eight Competitors. 



Table IV. 

 Scheme of Matches between 2n Competitors. 



Art. L. — A Gomjmrison of the Age-distribution of the Popu- 

 lations of the Four Chief Provincial Districts of Netv 

 Zealand. 



By H. W. Segar, M.A., Professor of Mathematics, Auck- 

 land University College. 



[^Read before the Auckland Institute, 6th July, 1903.] 

 Plates XLII.-XLIV. 

 The census returns of New Zealand give the distribution of 

 tlie populations of the several provincial districts into the 

 usual quinquennial age-periods. But the numbers only in 

 each age-period are given. For the purpose of comparing the 

 age-distributions of the populations of the provincial districts 

 these numbers are directly of little service. It is first neces- 



