56 JOUENxVL OF THE ROi'AL HORTICULTURAL SOCIETY. 
and by statistical treatment of the mass, that any order or law can he- 
perceived. In the case of a chemical reaction, for instance, by suitable 
means the conditions can be accurately reproduced, so that in every 
individual case we can predict with certainty that the same result will 
occur. But with heredity it is somewhat as it is in the case of the rain- 
fall. No one can say how much rain will fall to-morrow in a given 
place, but we can predict with moderate accuracy how much will fall 
next year, and for a period of years a, prediction can be made which> 
accords very closely with the truth. 
Similar predictions can from statistical data be made as to the dura- 
tion of life and a great variety of events the conditioning causes off 
which are very imperfectly understood. It is predictions of this kind, 
that the study of heredity is beginning to make possible, and in that 
sense laws of heredity can be perceived. 
We are as far as ever from knowing why some characters are trans- 
mitted, while others are not ; nor can anyone yet foretell which individual 
parent will transmit characters to the offspring, and which will not ; 
nevertheless the progress made is distinct. 
As yet investigations of this kind have been made in only a few 
instances, the most notable being those of Galton on human stature, and 
on the transmission of colours in Basset hounds. In each of these cases^ 
he has shown that the expectation of inheritance is such that a simple 
arithmetical rule is approximately followed. The rule thus arrived at 
is that of the whole heritage of the offspring the two parents together on. 
an average contribute one half, the four grandparents one quarter, the 
eight great-grandparents one eighth, and so on, the remainder being, 
contributed by the remoter ancestors. 
Such a law is obviously of practical importance. In any case to 
which it applies we ought thus to be able to predict the degree with 
which the purity of a strain may be increased by selection in each 
successive generation. 
To take a perhaps impossibly crude example, if a seedling show any 
particular character which it is desired to fix, on the assumption that succes- 
sive self-fertilisations are possible, according to Galton's law the expecta- 
tion of purity should be in the first generation of self-fertilisation 1 in 2, 
in the second generation 3 in 4, in the third 7 in 8, and so on. 
But already many cases are known to which the rule in the simple 
form will not apply. Galton points out that it takes no account of 
individual prepotencies. There are, besides, numerous cases in which 
on crossing two varieties the character of one variety is almost always 
transmitted to the first generation. Examples of these will be familiar 
to those who have experience in such matters. The offspring of the 
Polled Angus cow and the Shorthorn bull is almost invariably polled. 
Seedlings raised by crossing Atropa belladonna with the yellow-fruited 
variety have without exception the blackish-purple fruits of the type. In 
several hairy species when a cross with a glabrous variety is made, the 
first cross-bred generation is altogether hairy. 
Still more numerous are examples in which the characters of one 
variety very largely, though not exclusively, predominate in the off^- 
spring. 
