396 
Proceedings of the Boyal Society of Edinburgh. [Sess. 
XXVIII. — Point Binomials and Multinomials in relation to 
Mendelian Distributions. By John Brownlee, M.D., D.Sc. 
(Read November 20, 1911. MS. received February 16, 1912.) 
The subject of this paper is a consideration of the mathematics of some of 
the problems given by present-day developments of Mendelism. Breeding 
formula are becoming more and more complex, and it seems probable that 
many others are yet more complex. Without a suitable mathematical 
analysis it will be nearly impossible to analyse some of these by direct 
experiment, while a suitable analysis must always render the method of 
experimental attack much less obscure. Some of the formulae in the present 
paper were calculated when I read my last paper * on this subject to this 
Society, but most of the developments seemed too remote from actual 
experimental work to render their publication useful. However, a paper 
published in the last number of the Journal of Genetics, by H. M. Leake, 
concerning the hybridisation of the cotton plant suggests that the time has 
come when they may prove of practical value. 
Before approaching the mathematics, however, I think that some 
remarks on the notation of Mendelism may be profitably made. This 
notation seems to me specially cumbrous. When the elements are indicated 
by letters they are regularly written in sequence. Thus an organism 
containing three pairs of elements is denoted by (aa bb cc). If this mate 
with another of similar constitution but different properties, (AA BB CC), 
all the possible combinations of these appear in the second generation, and 
it becomes very fatiguing to the eye and brain to read the notation. I think 
that it would be preferable if the different elements which can combine 
were written in parallel rows. We have then the two arrangements above 
described denoted by 
aa 
AA 
bb 
BB 
cc 
CC 
and when we come to consider such combinations as 
ak. 
BB , 
cC 
* “ The Inheritance of Complex Growth Forms on Mendel’s Theory,” Proc. Roy. Soc. 
Edin ., vol. xxxi. p. 251. 
