Segar. — A Note on Drawing for Competitions. 501 



we shall understand, I hope, that the fact will not necessarily 

 constitute an impeachment of free-trade principles. England 

 is necessarily becoming relatively smaller in respect to her 

 resources as compared with the developed resources of the 

 whole world, and the position her industries and commerce 

 occupy must change correspondingly. This cannot be pre- 

 vented. All that can be done is to maintain and provide 

 education and an enlightened commercial oolicy, and, with 

 a spirit of enterprise, to take advantage of every opening, 

 every improvement, and every means of economy, and so 

 increase the return to labour and capital expended. This 

 will insure the best possible result under circumstances other- 

 wise beyond control. How the result is then distributed over 

 home trade or foreign trade is a mere matter of detail. Of 

 one thing we may be sure — namely, that, whatever tendencies 

 may have existed of late in England to lag behind in such 

 matters, such tendencies must have been aggravated if there 

 had been in existence any scheme of protection. That in 

 spite of such tendencies the United Kingdom, which is in 

 area only a shade bigger than New Zealand, only one-half 

 the size of France or Germany, and about one-thirtieth of 

 the United States, should support the population she does, 

 in the standard of comfort it enjoys, and occupy in the world 

 to-day still the first place in respect to industry, commerce, 

 and power are facts which constitute the most eloquent 

 justification of her commercial policy it is possible to bring 

 forward. The best advice that can be given to other nations 

 that would emulate her success is " Go, thou, and do like- 

 wise." 



Art. XLIX. — A Note on Dratving for Competitions. 



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

 sity College, Auckland. 

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

 The question was recently put to me, in connection with a 

 local association of clubs, whether it were possible for seven 

 •competing clubs to arrange their fixtures, in which each was 

 to play every other, so that each club should play its matches 

 at home and away alternatively througliout, thus removing 

 the objectionable feature of a succession of matches played 

 ■either all at home or all away. 



The problem was a somewhat interesting one in arrange- 

 inents, and the result came out in a form that was obviously 



