114 NATURAL INHERITANCE. [chap. 



the general Population, we arrive at a general equation 

 that is true for all degrees of Kinship ; namely — 



r 2 +f 2 =p 2 (1) 



but r, the curvature in rank, is a regressed value of p, 

 and may be written icp, w being the value of the 

 Kegression. Therefore the above equation may be put 

 in the form of 



w P + J— P ( 2 ) 



in which f is the Q of the Co-kinsmen in the given 

 degree. 



It will be found that the intersection of the surfaces 

 of the Squadrons by a horizontal plane, whose height is 

 equal to P, forms in each case a line, whose general in- 

 clination to the ranks of A increases as the Kinship 

 becomes more remote, until it becomes a right angle in 

 Z. The progressive change of inclination is shown in 

 the small squares drawn at the base of Fig. 13, in which 

 the lines are the projections of contours drawn on the 

 upper surfaces of the Squadrons, to correspond with the 

 multiples there stated of values of p. 



It will be understood from the front views of the 

 four different Squadrons, which form the upper part of 

 Fig. 13, how the Mid-Statures of the Kinsmen to the 

 Men in each of the files of A, gradually become more 

 mediocre in the successive stages of kinship until they 

 all reach absolute mediocrity in Z. This figure affords 

 an excellent diagramatic representation, true to scale, 

 of the action of the law of Kegression in Descent. I 

 should like to have given in addition, a perspective 

 view of the Squadrons, but failed to draw them 



