April <^, 1877] 



NATURE 



493 



It has, I believe, become more generally known than 

 formerly, that although the characteristics of height, 

 weight, strength, and fleetness are different things, and 

 though different species of plants and animals exhibit 

 every kind of diversity, yet the differences in height, 

 weight, and every other characteristic, are universally 

 distributed in fair conformity with a single law. 



The phenomena with which it deals are like those per- 

 spectives spoken of by Shakespeare which, when viewed 

 awry, show nothing but confusion. 



Our ordinary way of looking at individual differences 

 is awry ; thus we naturally butl wrongly judge of differences 

 in stature by differences in heights, measured from the 

 ground, whereas on changing our point of view to that 

 whence the law of deviation regards them, by taking the 

 average height of the race, and not the ground, as the 

 point of reference, all confusion disappears, and unifor- 

 mity prevails. 



It was to Quetelet that we were first indebted for a 

 knowledge of ihe fact that the amount and frequency of 

 deviation from the average among members of the same 

 race, in respect to each and every characteristic, tends to 

 conform to the mathematical law of deviation. 



The diagram contains extracts from some of the tables, 



in them refer to the heights of Americans, French, and Bel- 

 gians respecdvely, and the fourth to s-trength, to that of 

 Belgians. In each series there are two parallel columns, 

 one entitled " observed," and the other " calculated," and 

 the close conformity between each of the pairs is very 

 striking. 



These Tables serve another pwirpose ; they enable those 

 who have not had experience of such statistics to appre- 

 ciate the beautiful balance of the processes of heredity in 

 ensuring the repetition of such finely graduated propor- 

 tions as those they record. 



The outline of my problem of this evening is, that since 

 the characteristics of all plants and animals tend to con- 

 form to the law of deviation, let us suppose a typical case, 

 in which the conformity shall be exact, and which shall 

 admit of discussion as a mathematical problem, and find 

 what the laws of heredity must then be to enable succes- 

 sive generations to maintain statistical identity. 



by vhichhe corroborates his assertion. Three of the series 



Fig. I. 



I shall have to speak so much about the law ot devia- 

 tion, that it is absolutely necessary to tax your attention 

 for a few minutes to explain the principle on which it is 

 based, what it is that it professes to show, and what the 

 two rmmbers are which enable long series to be calculated 

 like those in the tables just referred to. The simplest way 

 of explaining the law is to begin by showing it in action. 

 For this purpose I will use an apparatus that I employed 

 three years ago in this very theatre, to illustrate other 

 points connected with the law of deviation. An extension 

 of its performance will prove of great service to us to- 

 night, but I will begin by working the instrument as I did 

 on the previous occasion. The portion of it that then 

 existed and to which I desire now to confine your atten- 

 tion, is shown in the lower part of Fig. i, where I 

 wish you to notice the stream issuing from either of 

 the divisions just above the dots, its dispersion among 



