304 THE AMERICAN NATURALIST [Vol. XLVI 



this bean possesses much economic significance in Maine. It is 

 esteemed above all other sorts for baking purposes, and if a 

 strain could be developed which would possess (a) high yielding 

 qualities, (b) reasonable disease resistance and (c) earliness 

 and uniformity of maturing it would be of great value to the 

 bean growers of the state. In connection with the purely bio- 

 logical studies an attempt is being made to see whether a pure 

 line possessing these desirable qualities may not be found. 



In this specific breeding problem we obviously have the con- 

 ditions which demand the aid of selection index numbers. Sev- 

 eral characters (not one only) must be concurrently selected. 

 An estimate must be formed in each case of the net worth of an 

 individual plant (or of a biotype), taking into account at least 

 all of the three factors named. In order to do this impartially 

 and accurately a selection index number has been devised. 



In deriving this bean selection index a general equation of a 

 slightly different type than that discussed in our former paper 

 has been employed. In that paper (loc. ext., p. 389) the general 

 formula suggested is 



ax±by±cz± ...±uv 

 1 a'p±b'q±LC'r±i ... ±«'{' 

 In the case of beans (and very likely this may prove true for 

 other plants and animals as well) it has seemed desirable to form 

 an index number on the plan of the following type of equation : 



j. axy ± bwz =fc • • • ± nvv 

 = a'pq±b'r8± . . . ± »V 



In this equation, as before, a, b, c, . . . n, and a', b', c' . . . 

 n' are constants, given arbitrary values in accordance with the 

 scheme of weighing adopted, and x, y, z, w, u, v, are variables 

 which measure characters increasing in desirability (from the 

 breeders' standpoint) as their absolute magnitudes increase, 

 while p, q, r, s and t are variables measuring characters which 

 decrease in desirability as their absolute magnitudes increase. 

 The variables specifically taken account of in the bean selection 



Y = Absolute yield. The weight in grams of dried shelled 

 beans per plant. 



