46 



Mr. F. Galton. 



[Jan. 21, 



will be identical with one another. Every other rectangular file 

 "being similarly represented, a complete squadron Z of the kinsmen 

 is produced. It is obvious, then, that the squadrons A and Z are 

 identical, and as the ranks of Z have proceeded from the files of A, 

 the result is that the two squadrons will stand at right angles to one 

 another. The upper surface of A was curved in rank, but was 

 horizontal in file ; that of Z is curved in file, but is horizontal in 

 rank. 



Kinsmen in near degrees are represented by squadrons of inter- 

 mediate form. These will not have lost the whole of the curvature 

 in rank of A, nor will they have acquired the whole of the curvature 

 in file of Z. Consequently they will be curved moderately in both 

 ways.* Also it will be found that the intersection of their surfaces by 

 the horizontal plane of median height forms in each case an approxi- 

 mately straight line that assumes different and increasing inclinations, 

 in the successive squadrons of intermediate shape between A and Z. 

 These lines are indicated by straight lines on the squares below the 

 squadrons in fig. 4, which represent the square bases upon which the 

 squadrons stand. 



I shall now show how these curves in rank and file should be 

 treated. But before doing so, it is necessary to remark that female 

 adult stature (I speak throughout of adults) may be safely trans- 

 muted to its male equivalent by multiplying it by a constant constant, 

 which as regards my data is 1*08. After this has been done, the 

 transmuted female statures may be treated on equal terms with the 

 male statures, and the word " men " or other masculine term will 

 include both sexes, unless otherwise stated distinctly. This procedure 

 is adopted in the present memoir. 



It is now generally recognised that the statures in every ordinary 

 population are distributed in approximate conformity with what 

 might have been inferred, if it were known that their variations were 

 governed by such conditions as those upon which the exponential law 

 of frequency of error is based. Therefore the upper boundary of the 

 stature-scheme is approximately a curve (I call it an " ogive ") that 

 admits of mathematical expression. The abscissae of the normal ogive 



1 f 



(fig. 3) are values of the probability integral —j=\ e~ fi dt t and the 



ordinates are the corresponding values of t. These are given in 

 column A of Table I. Column B contains the same values divided 

 by 0*477, by which means they are expressed in units of the probable 

 error. I find it convenient to call the ordinates to an ogive (drawn 



* A plaster model of one of these intermediate forms was exhibited at the 

 meeting by Mr. J. D. H. Dickson, who stated that his recent mathematical investi- 

 gation of the properties of their surfaces, had shown that no strictly straight line 

 could be drawn upon them. — F. Gr. 



