1898] COBjR.E^PONDENCE 2ir. 



The first premise of ilr Vernon's theory (see Kntural Science, vol. xi. p. 405) 

 expressed in an algebraic formula is as follows : — 



Small. Medium. Tall. 



Parents : 100 SS give offspring a. x b.x c. x 



100 MM ,, b.x cl.x b.x 



100 LL ,, c. X b. X a. x 



I.—{a + b + c). X =(2b + d). x ={a + b + c). x ; 



a, b, c and d being the percentage numbers of offspring produced by the intermarriages 



between S with S, M with M, and L with L under normal conditions ; x = — 



being the measure of fertility under those new conditions as assumed liy Mr Vernon. 



The second premise of the theory (I.e.) is that the numbers of offspring produced by 

 the intermarriages of short and medium, and of medium and tall parents, "may be 

 approximately obtained by taking means between the percentages for short and medium 

 parents on the one hand, and for medium and tall ones on the other." Hence we 

 have : — 



Small. Medium. Tall. 



Parents : 100 SM + 100 MS give offspring {a + b).y (b + d).y {c + b).y 



lOOML + lOOLM ,, {b + c).i/ (d + b).y (b + a).y 



lOOSL + lOOLS ,, 2b.z 2d.z 2b.'. 



ll.—{a + 2b + c).7j + 2b.z \ (2b + 2d).y + 2d.~. | {a + 2b + c).y + 2.b.-: ; 



y=z and z = — TTTTT-, being the measure of fertility of the intermarriages between 



different parents. 



The number of medium offspring will be smaller or larger than that of small and 

 tall ones, or equal to this number, if we have — 



> 

 (2b + 2d).y + 2d.z={a + 2b + c).y + 2b.z; or, as in (I.) a + h + c^2b + d, 

 < 



d=b', 

 < 



that means, the answer to the question whether there are more medium than small 

 individuals under II. is entirely independent oi x, y, z, or of the degree of fertility 

 resp. sterility, but depends solely on the percentage number of small (b), medium (a), 

 and tall (b) offspring produced by M intermarrying with jVI under ordinary circumstances. 

 JSIr Vernon must so alter his premise I., that of the offspring of M marrying M less 

 than one-third are medium individuals (d<b) ! This, however, cannot be a premise 

 of " Reproductive Divergence," as it would mean putting the cart before the horse. 



If this simple mathematical demonstration should not be intelligible enough, Mr 

 Vernon will perhaps see the fallacy in his theory, if he takes that degree of sterility 

 between different parents, which should be the most favourable one for the theory, 

 namely, absolute sterility not only between the extremes S and L, but also between S 

 and !^l, and between M and L. In this case we have to do only with the outcome of 

 the marriages of S with S, M with M, and L with L ; i.e., only with the numbers under 

 I., which are equal, as Mr Vernon says himself (I.e.). Karl Jordan. 



Zoological Museum, Tring, 

 February 12, 1898. 



dipeltis an insect larva 



I am much obliged to Mr C. J. Gahan for directing attention to the fact that Dipeltis 

 bears close relationship with certain coleopterous larvae. A larva almost identical with 

 the one figured in the Jaimary number of this review was recently shown me by Air E. 

 A. Schwaiz of the U.S. National Museum. Since seeing this specimen I agree with Mr 

 Gahan's conclusions that Dipeltis is the larva of some insect, and not one of the 

 Apodidae. The "two small shallow pits, which are interpreted as ocelli," and the 

 " two faintly preserved eye spots," need be no longer explained as ocelli and eyes, since 

 in the above-mentioned larva very similar modes and depressions are present, Mr 

 Schwarz tliinks the smaller specimen figured by me (figs. 4 and 5) may be related with 

 the larva of Lampyridae or Dascyllidae. It is more natural to interpret the three 

 anterior large segments of DrpcUis as divisions of the thorax of a Lamjjyrid larva than 

 that tliey are parts of the cephalon of an y/^ws-like crustacean. 



Charlks Schuchert. 

 U.S. National Museum, 



