THE GENUS PISSODES. 29 



no matter what differences there may be in the length ol' the body 

 of the individuals, we get a mathematical expression, or index, of 

 the difference in tlieir relative })ro[)ortions. 



The following examples will serve to illustrate the application of 

 the method : "■ 



Example 1. 



Female individual of Pissodes strobi. 

 a, Length of beak, 29 micrometer divisions. 

 6, Length of prothorax, 31 micrometer divisions. . 

 c, Length of elytra, 73 micrometer divisions. 



a-^fe=.935. 



a-^c=. 397, + .935=1.332, -^ 2=.666 =Index of relative proportions of an individual. 

 Now, if 50 male individuals of this species show a range in the individual index of 

 61 to 64, with an average or mode of 63, and 50 females show a range of 65 to 69, 

 with a mode of 68, the relative proportions for each sex and for the species are 

 expressed by the formula, $ 63-9 68. 



Example 2. 



Female individual of Pissodes fraseri (fig. 9). 



a, Length of beak, 45 micrometer divisions. 



b, Length of prothorax, 33 micrometer divisions. 



c, Length of elytra, 85 micrometer divisions. 



a^6=1.366. 



a-HC=. 529, +1.366=1.895,-1-2=. 947+. If 50 male individuals show an index range 



of 72 to 73 and a mode of 72, and 50 females show a range of 91 to 111, with a 



mode of .100, the formula would be $ 72-9100. 



P. strobi, formula ^ 63-968. 

 P. fraseri, formula J" 72 -9 100. 



According to other characters, these two species fall in the same division of the 

 genus, but in different subdivisions. The formulas for the species of the first division 

 range from $ 57-9^2 to (J 72— 9 100, Those of the first subdivision range from 

 ^ 57 — 9 62 to ^74—9 79, while those of the second subdivision range from ^ 64 — 9 70 

 to ^72-9100. 



Thus the formulas for P. strohi and P. fraseri, together with the 

 characters wliich refer them to their respective primary and minor 

 divisions, indicate the natural position and rank they should occupy 

 in the classification. (See Plate II.) 



It is interesting to note that the Hylobiinae, which are plainly less 

 mothfied in respect to the length of the beak than the Pissodinae, 

 show their relative lower position in the determined formulas for 

 representatives of the 4 principal genera (Paraplinthus, J 47, 9 58; 

 Hilipus, J 35, 9 68; Evdocmius, J 38, 9 49; Ilylobius, J 48, 9 56). 

 It will be noted that the females of only two of the genera fall within 

 the range of the Pissodinse, while Ilylobius, which has some affinities 



a Measurements up to 10 mm. may be made by means of a microscope with a mi- 

 crometer eyepiece and a 2-inch objective, the tube adjusted so that each division in 

 the micrometer scale equals five one-hundredths of a millimeter. 



