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THE AMERICAN NATURALIST [Vol. XLIX 



quencies, and if x 2 = 2(F' — F) 2 /F, then the probability p that 

 in random sampling deviations of equal or greater improba- 

 bility will arise is a function of x 2 which decreases continu- 

 ally as x 2 increases. The best value of the ratio will then be 

 that value which makes p a maximum orx 2 a minimum. The 

 problem taken in the note is to determine this value. Un- 

 fortunately the solution is not a simple one, depending on an 

 equation of the fourth degree. A few cases are, however, taken 

 as illustrations and the question of probable error is discussed. 

 The recognized fact that, especially when the coupling-ratio is 

 high, its value may receive considerable alteration without 

 greatly altering the closeness of agreement between theory and 

 fact, receives additional emphasis from some of the results given 

 and makes it clear that considerable caution must be used before 

 attaching importance to the precise values of high ratios. 



P. L. E and G. U. Y. 



2 Am. Nat., XLVI. 



