Correlation and Application of Statistics to Problems of Heredity 15 



predict the probable value of any third variate from a knowledge of two 

 others*. The working of the Forecaster is almost obvious on examination of 

 the diagram, but for the benefit of those who come for the first time to the 

 subject of regression I give Galton's own words: 



"The weights M and F have to be set opposite to the heights of the mother and father on 

 their respective scales; then the weight sd will show the most probable heights of a son and 

 daughter on the corresponding scales. In every one of these cases it is the fiducial mark in the 

 middle of each weight by which the reading is to be made. But, in addition to this, the length of 

 the weight sd is so arranged that it is an equal chance (an even bet) that the height of each son or 

 each daughter will lie within the range defined by the upper and lower edges of the weight on 

 their respective scales. The length of sd is 3 inches = 2/t ; that is, 2 x 1 -50 inch. 



"A, B and C are three thin wheels with grooves round their edges. They are screwed together 

 so as to form a single piece that turns easily on its axis. The weights M and F are attached to 

 either end of a thread that passes over the movable pulley D. The pulley itself hangs from a 

 thread which is wrapped two or three times round the grove of B and is then secured to the 

 wheel. The weight sd hangs from a thread that is wrapped in the same direction two or three 

 times round the groove of A, and is then secured to the wheel. The diameter of A is to that of 

 B as 2 to 3. Lastly, a thread wrapped in the opposite direction round the wheel C, which may 

 have any convenient diameter, is attached to a counterpoise. 



"It is obvious that raising M will cause F to fall, and vice versd, without affecting the wheels 

 A, B, and therefore without affecting sd; that is to say, the parental differences may be varied 

 indefinitely without affecting the stature of the children, so long as the mid-parental height is 

 unchanged. But if the mid-parental height is changed, then that of sd will be changed to §- of 

 the amount. 



"The scale of female heights differs from that of the males, each female height being laid 

 down in the position which would be occupied by its male equivalent. Thus 56 is written in the 

 position of 60 - 48 inches, which is equal to 56 x 1*08. Similarly, 60 is written in the position of 

 64-80, which is equal to 60 x 1-08 J." 



The last words indicate what is, I think, an important point: Galton 

 obtains the female from the male stature by multiplying by the constant factor 

 1'08. This he obtained as the ratio of the male to the female mean value, 

 and he practically assumes this ratio to be the same for all other statures. 



In a certain sense I think this is, at least theoretically, a retrograde step 

 from his suggestion of 1877. He then took the transmuted female mean to be 

 the male mean plus the female deviation increased in the ratio of male to 

 female variability. This appears to be theoretically a better process of trans- 

 mutation. Practically the two methods will only agree, if the ratio of the 

 two variabilities is equal to the ratio of the two means, i.e. if the so-called 

 coefficients of variability of the two sexes are equal. This is approximately 

 but not absolutely true for a number of human characters. 



There are of course several other conditions which must be fulfilled to 

 make Galton's definition of midparent valid, and some of these he discusses. 

 In the first place the parents must mate at random with regard to the 

 character dealt with, i.e. there must be no sexual selection in the form of 

 assortative mating with regard to stature, tall must not tend to marry tall, 



* It would only be needful to adopt scales in accordance with the constants of the bivariate 

 regression formula. 



t In this paper Galton uses the symbol /for the quartile deviate. 

 j Journ. Anthrop. Institute, Vol. xv, p. 262. 



