STATisncAl, Studies on ihk Variation ok Stagbeetles. 



83 



F i.ir. 4 



mode, 29mm, the middle standing class ; that is, it is ye n- near to the normal 



variation curve. The \aliie of the standard deviation y - (-^""■/ ) > whcie / 



n 

 represents the frequency, x the deviation of any class from the mean, and n 



the number of variates, is 2.06. 



The female is, in this respect at least, 

 much more condensed than the other sex 

 and may be taken to be homogenetic, modi- 

 fying itself in the normal way in \\hich 

 Galton's single variation curve is drawn. 



In addition to these facts the mandi- 

 bles of the females are formed always uni- 

 formly like a pair of claws with a fine 

 serrated inner edge ; they arc neither arched 

 antlers, nor severally tined, nor developed 

 in several strengths according to the size 

 of the body, as in the case of the males. 



It follows that the variation in the 

 females is very much narrower in its range 



Fig. 4. Diagram showing frequency of 



body length of female in ClaJo-^nat/tus. than that of the male. 



Figures on axis as previous rigure. 



n. Lucanus maculifemoratus, M&tsch. 



Male. — This species was collected also from our university grounds ; it is 

 in the habit of living close together with the previous species, althogh it is 

 more rare. 



In the male, the big antlers may be said to be uniformlj' built through- 

 out the whole collection ; the most conspicuous feature of this pair of ap- 

 pendages consists in the bifurcation at their terminus. Fig. 5 shows that the 

 antlers are by no means complicated or simplified, according to the body type, 

 i.e. whether the body type is high or low; they are always arched and tined 

 in several ways in the low type {ö) as well as in the high type (a), except 



