DAVENPORT AND BULLARD. — CORRELATED VARIATION. 91 



1. Average number of glands in (^ R . . . . 3.547 



2. " " " ^ L . . . . 3.540 



3. " " " 9 R . . . . 3.501 



4. " " " 9 L . . . . 3.521 



Comparing the average of (1) and (2) with the average of (3) and (4) 

 it appears that the average number of glands in the males (3.544) is 

 tolerably close to that in the females (3.511) but that a real dilfereuce 

 exists between the two. llie (jhtiids are slif/htly less abundant in the 

 female than in the male in the ratio, 100 : 100.94. The average number 

 of glands on the right side of the body is so close to tliat on the left side 

 (3.524:3.531) that we may conclude: The average numbers of the 

 glands on the right leg and on the left leg taken without regard to sex are 

 about equal. 



2. Variability correlated with the Sex and with the Side of the Body. 



In seeking to determine whether, in this matter of glands, male or 

 female swine are the more variable, it is necessary to employ a method 

 of stating variability quantitatively. Quetelet, Stieda, and Galton * 

 have employed such a method, based upon the fact that the organs of 

 an animal vary about their mean dimensions to an extent and with a 

 frequency indicated by the probability-of-error equation,! 



y = k.e-^'-''"-. 



Two of the principal features involved in such a distribution are that 

 deviations of a given size are equally apt to occur above and below the 

 mean, and that small deviations are more apt to occur than large ones. 

 These and other characters of the '•' probability " curve are indicated in 

 that shown in dotted line in the accompanying diagram. The diagram 

 also shows the curve of distribution of the various numbers of glands oc- 

 curring on a leg, from 1 to 10. This curve is drawn from the right female 

 leg only ; the curve for the other legs would be very similar. We shall 

 speak in a moment of the method of construction of these curves ; but we 

 want now to call attention to the fairly close similarity of the two curves, 

 — that gained by observation and the theoretical one, — a similarity so 

 close that we are justified in concluding that the law of distribution of the 

 variants in the lesr glands of swine is the same as that of accidental errors. 



* Quetelet, Lettres sur la theorie des probabilites, Bruxelles, 1840. Stieda, 

 in Archiv fiir Anthropologie, Bd. XIV. pp. 167-182. Galton, Natural Inheritance, 

 New York and London, 1889. 



t See any text-book on " Least Squares." 



