No. 1, July, 1920] GENETICS 93 



l'3X* + 4X + 2) (2X + 1) 

 probable error of X = 0.477 (X + 1) "U . _i_ ox 4- Dn 



. / X + 7/0 

 approximately 0.6745 (X + 1) "W > 



I (2Y 2 + 4Y + 3) Y(Y + 2) 

 probable error of Y = 0.477 (Y + 1) "W ~ 



approximately 0.07 •!•"» 



(Y 2 + 2Y + 3)n 



( Y + D a 



Vn ' 



These results are employed to show that F 2 is almost as accurate a means of measuring link- 

 age as are the offspring from FiX double recessive; it is also slightly more sensitive as a means 

 for the detection of linkage. — John W. Gowen. 



591. Haldane, J. B. S. The combination of linkage values, and the calculation of distances 

 between the loci of linked factors. Jour. Genetics 8: 299-309. 1 fig. Sept., 1919.— Using the 

 data contained in "Sex-linked inheritance in Drosophila" by Morgan and Bridges a curve is 

 derived of the equation 



x = 7y--Log. e (l-2y), 



where x = distance, y = crossover value in 100 times the unit in ordinary use ("Morgan"), 

 to describe the relation of observed crossover value for two factors in comparison with the 

 actual distance were all crossovers. — From this equation it is shown that if A, B, and C are 

 three factors lying in a chromosome in that order, and if m is the crossover value for A and B, 

 n that for B and C, then the value for A and C lies between m+n and m+n— 2mn, being nearer 

 the former when m+n is small, to the latter when it is large. — To explain these results the hy- 

 pothesis of a partly rigid chromosome is urged. — The relation between crossover value and 

 distance permits the calculation of one of the crossover values for three factors from the other 

 two with a probable error of less than 2 per cent. — The results above cited are used to show 

 the incompatibility of Trow's form of the reduplication theory. — John W. Gowen. 



592. Haraldson, C. Report of the Fruit Breeding Farm, Zumbra Heights. Minnesota 

 Sta. Rept. 1918: 94-98. 1918.— A report of progress in fruit breeding. Promising varieties of 

 strawberry, plum and apple, have been numbered and recommended for trial. Selections 

 are made only from the most hardy sorts. Additional crosses have been made in plum, rasp- 

 berry, strawberry, apple, blackberry and dewberry. — M. J. Dorsey. 



593. Harlan, H. V., and H. K. Hayes. Breeding small grains in Minnesota. II. Barley 

 investigations. Univ. Minnesota Agric. Exp. Sta. Bull. 182: 45-56. Fig. 11-14- Mar., 1919. 

 — Minnesota ranks second as a producer of barley. Prior to 1915 there were two barley breed- 

 ing nurseries at the Minnesota Experiment Station Farm, one operated by the Office of Cereal 

 Investigations, Bureau of Plant Industry, the other operated by the Minnesota Experiment 

 Station. In 1915 the work of the two sets of barley investigations was combined. The aver- 

 ages of oats for 68 selections and crosses are given in tabulated form, together with botanical 

 types and agronomic characters. Three superior barleys survive a large number of field 

 selections. These are Featherston, Lake City and Excelsior. The Manchuria selections 

 showed some to be superior to others. One of the highest breeders from these selections was 

 propagated for field growing. As wide variations in yielding-ability was found in the Manchu- 

 ria variety as are ordinarily obtained when comparing different varieties. As the result of 

 crosses, superior smooth-awned barleys have been produced. The smooth awn character 

 was obtained from Lion, a smooth-awned black parent, and Manchuria, a standard variety. 

 The smooth-awned types produced are illustrated by cut showing variations in types as the 



