42 GENETICS [BoT. Absts., Vol. IX, 



2C3. Oppenheim, J. D. De erfelijkheid van het vrueg of laat bloeien bij erwten. [In- 

 heritance of early and late flowering in peas. Mededeel. Ver. Bevord. Wetenschap. Teelt 10. 

 5 p. 1921. — The node at which individuals of a certain pure line start flowering is strikingly 

 constant, though often fluctuating within 3 nodes. Other pure lines produce their first flower 

 always at a certain node. Early-flowering varieties, such as Extra Early Pilot-pea, start 

 at the Sth node, Sutton's Emerald Gem at 9th to 10th, Senator 10th to 11th. The later-flow- 

 ering varieties such as Pois Ture, begin at the 17th to 19th and the Blue-flowering pea at the 

 18th to 19th node. — In crosses, the F2 splits to early and late, the late being dominant in Fi. 

 — /. C. Th. Uphof. 



2G4. Papanicolaou, Geokge N. Developmental competition in its relationship to the 

 sex ratio. [Abstract.] Anat. Pec. 21: 76. 1921.^ — The average sex ratio in a stock of 3472 

 guinea-pigs is 10G.54 when the individuals born in all litters are considered. On comparing 

 the ratios from different-sized litters great discrepancies are found. In litters of 1 the sex 

 ratio is 112.58; in litters of 2, 112.07; in litters of 3, 97.95; in litters of 4, 108.73; and in litters 

 of 5, 141.02. These variations may be explained on the following principles derived from a 

 careful analysis of the developmental conditions in guinea-pigs: 1. There is a competition 

 between developing germ-cells and embryos in the ovary and the uterus. 2. In the compe- 

 tition males have some advantage over the females. 3. Competition is higher in the larger 

 litters (by a litter is meant the number of co-developing germ-cells and embryos). 4. In 

 litters consisting of embrj^os of the same sex competition is higher than in mixed litters. 

 5. The competition is stronger among females than among males. — In agreement with these 

 statements there is a higher percentage of complete elimination of large litters consisting 

 chiefly of females than of any other large litters. This elimination produces the high sex 

 ratio for the litters of 4 and 5. The originally large litters in which the subsequent elimina- 

 tion is partial result in births of 1 and 2. Elimination being more severe on the female mem- 

 bers causes the production of a higher sex ratio than occurs among individuals produced in 

 litters of 3. Litters of 3 have the lowest sex ratio and approach nearest an expected condition, 

 having suffered little or no prenatal mortality. This explanation is supported by a study 

 of more than 100 litters with early partial absorptions which gave the high sex ratio of 123.37. — 

 George N. Papanicolaou. 



2G5. Pearson, Karl. On the probable errors of frequency constants. Biometrika 13: 

 113-132. 1920.^ — This editorial treats of the probable errors of constants supposed to be de- 

 termined by a knowledge of the ranges in which certain proportions of the frequency lie. For- 

 mulae are derived for the standard deviations and correlations of the errors in any lengths 

 measured along the a;-axis as determined by the frequency of the corresponding ranges. Cor- 

 relations of errors are calculated for various combinations of median, quartile, and decile when 

 determined from grades and from moments. These are compared to show the relative errors 

 of each method. The best method to determine the median and quartile divisions from ranks 

 is indicated. Similar formulae are presented for the cases where the data are grouped into 

 broad categories.^ — John W. Gowen. 



26G. Pearson, Karl. The fundamental problem of practical statistics, Biometrika 

 13: 1-lC. 2 diagrams. 1920. — The fundamental problem of statistics is, "An 'event' has oc- 

 curred p times out ol p -\- q = n trials, where we have no a priori knowledge of the frequency 

 of the event in the total population of occurrences. What is the probability of its occurring 

 r times in a further r + s = m trials." — Prefacing his remarks with the interesting historical 

 background, the author shows that it is sufficient to assume any continuous distribution 

 in order to reach Bates's theorem, the fundamental basis of statistics. — He then proceeds to 

 expand and develop Bayes's theorem showing that the Gaussian is applicable only under the 

 special condition that n, p, q, and ?« are large. Under other conditions the skew frequency 

 curves of types I or III give better results. Attention is called to the problem: Can the 

 incomplete /3 function be expressed even approximately in terms of a limited number of 

 incomplete T functions? John W. Gowen. 



