628 



SCIENCE 



[N. S. Vol. XXXII. No. 827 



If we take two " breeds " denoted by 



[p^DD) -\-2pq(DR) +q^RR)Y (a) 



and 



{PHDD) + 2PQ(DR} + Q'(RR) }- (6) 



respectively, and cross them at random, it is 

 not difficult to show that the array of the re- 

 sulting hybrid offspring is given by 



[Pp{DD] + {Pp + pQ)(DR) + Qq{RR)}n (c) 



Now, the mean number of recessive ele- 

 ments in these families is 



Thus the mean of (c) is the geometric mean 

 of (a) and (6). 



Since the geometric mean is always less 

 than the arithmetic mean, it follows that the 

 mean number of recessive elements (of the 

 type (BR)) in (c) is less than the collective 

 mean of the families (o) and (i) treated as 

 one population. Moreover, since the recessive 

 elements are fewer, the aggregate elements of 

 the types (DD) and (DR) must be greater. 



If, now, it be assumed that dominance is 

 positively correlated with vigor, we have the 

 final result that the crossing of two pure 

 breeds produces a mean vigor greater than 

 the collective mean vigor of the parent breeds. 



By similar methods it can be shown that 

 the " inbreeding " of a Mendelian population 

 leads to a decrease in the mean number of ele- 

 ments of the types (DD) and (DR). 



I am aware that there is no experimental 

 evidence to justify the assumption that domi- 

 nance is correlated with a " blending " char- 

 acter like vigor; but the hypothesis is not 

 an extravagant one, and may pass until a bet- 

 ter takes the field. 



A. B. Bruce 



The School of Agriculture, 

 Cambridge, England, 

 August 27, 1910 



THE INHERITANCE OF BODY HAIR 



Reading a book on South African stories 

 called " By Veldt and Kopje," by William 

 Charles Scully (London, T. Fisher TJnwin, 

 1907), I was struck by a statement which may 

 be of interest alike to anthropologists and 

 students of " Mendelism," and as the book 

 may not have been seen by either, I will quote 

 the passage. 



In a chapter on " Kaffir Music," written 

 jointly by Mr. Scully and his wife and origi- 

 nally published in the Pall Mall Magazine, 

 incidental mention is made of Madikane, 

 once reigning chief of the Baca tribe of Ban- 

 tus, who was killed in battle on December 19, 

 1824. The Bacas lived on and about the 

 present site of Pietermaritzburg, Natal, until 

 driven into exile by the Zulus or the Amang- 

 wane. 



There is some ground for thinking that Madi- 

 kan&'s mother was an European, possibly a waif 

 from one or other of the vessels which are known 

 to have been wrecked on the east coast of south- 

 ern Africa toward the end of the last century. 



All authorities agree that Madikanft was of 

 great stature, that he was light in color, and that 

 his hair and beard were long. It was his habit 

 to carry his snuff-spoon stuck in the hair of his 

 chest. One of the writers has examined a number 

 of his male descendants, and found about one in 

 every four with traces of hair on the chest. It is, 

 it may be stated, very unusual to find any hair 

 on the body of a Bantu. [The italics are mine.] 



John Burtt-Davy 

 the reformed calendar and a universal 



SABBATH 



To THE Editor of Science: The reform of 

 the calendar is at present so hopelessly aca- 

 demic, that it may not be amiss to add another 

 thought. The Jewish Sabbath, or seventh day 

 of rest, has been adopted by both Christians 

 and Mohammedans^but with changes of the 

 actual week-day in order to emphasize divi- 

 sion. 



In the proposed new calendar the old regu- 

 lar recurrence of named-days would be al- 

 tered by the odd no-day yearly, and the actual 

 Sabbath-succession destroyed, despite the re- 



