Professor Johannsen's Experiments in Heredity. 241 
less. Such low coefficients must mean a relatively very high effect 
of circumstance, and in such a case the initial correlation 
betiveen the daughters and grand-daughters of one mother must be 
exceedingly small and the approach towards the ultimate value 
extremely slow. I have calculated the figures given below as a rough 
illustration of the sort of thing to be expected ; the figures were 
obtained on the assumption of asexual propagation, which is not 
quite the same (on the continuous-variation hypothesis) as self- 
fertilization. The slowness of increase in the coefficient of 
correlation is possibly greater than that to he expected in Professor 
Johannsen’s cases, as the ultimate coefficient (*117) is a little lower, 
but one cannot say for certain, not knowing the grand parental 
coefficient. 
Table illustrating the gradual increase in the intensity of heredity 
between the successive generations of a pure line on the assumption 
of continuity^of variation in the germ-plasm'. The ancestor is 
reckoned as generation 0, and ;q. 2 , r 2 . 3 , etc, are the coefficients 
of correlation between individuals of generation 1 and individuals 
of generation 2, between the latter and individuals of generation 
3 and so on. s lt s 2 , s 3 , etc. are the relative standard deviations of 
the successive generations. 
r ,. 2 
•0072 
$1 
1000 
'*ll-'2 
•0656 
5 n 
1032 
'* 2 3 
0143 
s 2 
1004 
'* 1 2 • 1 3 
•0698 
5 12 
1034 
4 
•0211 
S 3 
1007 
'*13-14 
•0738 
S|3 
1037 
n-s 
•0276 
S 4 
1010 
'*1415 
•0774 
S,4 
1039 
'Vo 
•0340 
S 5 
1014 
'*1516 
•0809 
5 15 
1041 
r 6 - 7 
•0400 
So 
1017 
' 10-17 
•0840 
SlG 
1043 
'Vs 
•0457 
S- 
1020 
'*1718 
•0869 
S17 
1045 
'Vo 
•0511 
1024 
'*18-19 
•0896 
^18 
1046 
'V10 
•0563 
s o 
1026 
'*19-20 
•0920 
5 19 
1048 
■'Vo-11 
•0611 
Sio 
1029 
'*20-21 
•0943 
S 2 o 
1049 
ultimate value of r *1172 
ultimate value of s 1064 
Now the probable error of any correlation coefficient less than 
0*2 or so is T ’021 for a thousand observations, and the coefficient only 
reaches this value between the third and fourth generations. 
That is to say, if a thousand individuals (single beans) were gathered 
at each generation the correlation would only begin to be fairly well 
marked when the fourth generation of the “ pure line ” had been har¬ 
vested. In many of Professor Johannsen’s “ pure lines’’there were only 
two or three hundred seeds weighed ; seven or eight generations 
might be grown before such numbers gave a clear result. The large 
effect of definite circumstances on plants (producing fluctuations not 
of the nature of errors of sampling at all) would further tend to 
obscure the results. The increase in variation, it should be noted 
would also be difficult to attest. The whole increase in twenty 
