Sex-limited iuheritance in Lychnis dioica L. 271 



been recorded for all the males, both broad -leafed and narrow -leafed. 

 In Figure 2 the length of bristles in all of the 788 narrow-leafed males 

 that bloomed, and those in a like number of broad-leafed males, taken 

 without selection, from the same families, are presented in the form of 

 variation-curves for comparison, the curves being drawn in such manner 

 as to correct for the changing basis of comparison, so that the difference 

 in variability as well as in the actual and average lengths of the "bristle" 

 appear to the eye with little distortion^). It is seen that the curves 

 overlap slightly, because a few of the narrow-leafed plants have bristles 

 shorter than the longest bristles which occur in the broad-leafed plants. 

 When the lengths of the bristles iu the nan'ow-leafed plants of each 

 family are averaged and compared with the average lengths of those in 

 the broad -leafed plants of the same family, the difference between the 

 two groups is always striking. The ranges of these averages for the 

 33 families in wliich narrow-leafed males appeared, are indicated by the 

 braces at the base of the two curves in Figure 2. Numerically these 

 averages for the narrow-leafed plants are .5*0 — 6' 6 mm and for the 

 broad-leafed plants only 1'5 — 2'5 mm. It is clear, therefore, that the 

 factor B, which increases the width of the leaf, also definitely decreases 

 the length of the rudimentary ovary of the male. Perhaps this increase 

 in the size of the rudimentary ovary in the angustifolia male represents 

 a variation in the direction of hermaphroditism, but there was no other 

 evidence to support such an inference. Of the two hermaphrodite mu- 

 tants found in these families, one was included among about 800 narrow- 

 leafed males, wliile the other occurred among a little more than 1,000 

 broad-leafed males. 



^) The reader may be interested in the method of construction of this diagram. 



The theoretical values of maximum frequency, Yq = — , were calculated for both 



o V 2 ic 

 curves referred to the mean value of the right-hand curve. Vertical lines representing 

 these two maximum frequencies were erected on the base-line at a convenient distance 

 apart, and their summits connected by a line extended to the left until it intersected 

 the base-line. Through the point of intersection radiating lines were drawn, dividing 

 the vertical lines into equal segments. The remaining vertical lines were then erected, 

 dividing the sectors thus formed into equal areas of such magnitude that the distance 

 between the originally erected vertical lines included the number of classes required by 

 the actual calculated difference between the means of the two curves. Had these two 

 curves been drawn in the usual manner on ordinary coordinate paper, the left-hand 

 curve would have been tall and narrow, apparently indicating relatively slight variability, 

 but actual calculation shows the left-liand curve to have a coefficient of variability 

 more than 50 per cent greater than the right-hand curve. I gratefully acknowledge the 

 assistance of my brother, S. P. Shull, in solving the mathematical problems involved 

 in the method of plotting here used. 



