18 INTRODUCTORY REMARKS. Chai\ I 



that in the seven kinds of plants, whose measurements I have 

 examined, the ratio between the heights of the crossed and of 

 the self-fertilised ranges in five cases within very narrow limits. 

 In Zea mays it is as 100 to 84, and in the others it ranges 

 between 100 to 76 and 100 to 86." 



" The determination of the variability (measured by what is 

 technically called the ' probable error ') is a problem of more 

 delicacy than that of determining the means, and I doubt, after 

 making many trials, whether it is possible to derive useful 

 conclusions from these few observations. We ought to have 

 measurements of at least fifty plants in each case, in order to 

 be in a position to deduce fair results. One fact, however, 

 bearing on variability, is very evident in most cases, though not 

 in Zea mays, viz., that the self-fertilised plants include the 

 larger number of exceptionally small specimens, while the 

 crossed are more generally full grown." 



"Those groups of cases in which measurements have been 

 made of a few of the tallest plants that grew in rows, each of 

 which contained a multitude of plants, show very clearly that 

 the crossed plants exceed the self-fertilised in height, but they 

 do not tell by inference anything about their respective mean 

 values. If it should happen that a series is known to follow 

 the law of error or any other law, and if the number of indi- 

 viduals in the series is known, it would be always possible to 

 reconstruct the whole series when a fragment of it has been 

 "iven. But I find no such method to be applicable in the 

 present case. The doubt as to the number of plants in each row 

 is of minor importance ; the real difficulty lies in our ignorance 

 of the precise law followed by the series. The experience of 

 the plants in pots does not help us to determine that law, 

 because the observations of such plants are too few to enable 

 us to lay down more than the middle terms of the series to 

 which they belong with any sort of accuracy, whereas the cases 

 wo are now considering refer to one of its extremities. There 

 are other special difficulties which need not be gone into, as the 

 one already mentioned is a complete bar." 



Mr. Galton sent me at the same time graphical 

 representations which he had made of the measure- 

 ments, and they evidently form fairly regular curves. 

 He appends the words " very good " to those of Zea aud 



