472 THE GRAMMAR OF SCIENCE 



both parents, i.e. the mid-parent, and the variability 

 = 0-3^1 — R"^ = .90550-3. Select one parent only and the 

 variability of the offspring = 0-3^ i — r^ = .95390-3. Thus 

 selecting one parent we reduce the variability of the race 

 about 5 per cent, selecting both about 10 per cent. We 

 shall see later that this is almost the limit of the reduction 

 possible, even if the whole back ancestry be selected. 

 The variation, of course, is from the new type, not the 

 unselected type, but continuous selection does not in- 

 definitely modify variability, however much it shifts type. 

 Now we have examined the relation of race variability 

 to the variability which follows a bi-sexual union, let us 

 stay for a little to consider two further points before 

 summing up our results for bi-sexual inheritance. My 

 first point is this : the individual is not immensely less 

 variable than the race. Consider, for example, the stig- 

 matic bands on the capsules of Shirley poppies. The 

 racial variability = 1.885 bands, the individual variability, 

 based on a consideration of 300 plants, is .8518 x 1.885, 

 or a reduction of i 5 per cent. Take, again, the number 

 of leaflets on the compound leaf of the ash. The racial 

 variability, based on an examination of 200 trees, is 

 1.976, the individual variability is .9181 X 1.976, or is 

 only about 8 per cent less than the racial variability. 

 These are not theoretical conclusions, but only two results 

 selected from a great variety of data at my disposal. The 

 individual is not indefinitely less variable than the race ; 

 its most marked difference is not in variability but in 

 type. My second point concerns asexual reproduction. 

 What happens if instead of two parents we have one ? 

 As we have seen on p. 471, with self- fertilisation we might 

 expect the relation of the offspring to the single parent to 

 reduce to that of his relation to a single parent in bi-sexual 

 union, for we are probably dealing with a case of perfect 

 assortative mating. But what happens in a purely asexual 

 case, such as the parthenogenetic reproduction of daphnia? 

 This important question has been answered for us by 

 Dr. E. Warren.^ The variability of the parthenogenetic 



1 Royal Society Proceedings, vol. Ixv. p. 154 et seq. 



