1898] CORRESPONDENCE 215 



The tirst premise of Mr \'ernon'.s tlieory (sec Natvral Srinirf, vol. xi. ]>. 40ri) 

 expressed in an algebraic formula is as follows : — 



Small. Medium. Tall. 

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



100 MM ,, l).x d.y. //. x 



100 LL ,, c. X b. X II. X 



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

 a, b, c and d being the percentage numbers of offspring produced ))y 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 as.sumed by Mr Vernon. 



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

 the iutennarriagos of short and medium, and of medium and tall jiarents, "may Itc 

 approxhnately obtained by taking means between the percentages for short and nnulium 

 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 (« + fc).?/ (b + d).// {c + h).y 

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



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



V- 



II.— (ff + 2& + (■).?/ + 2&.,^ I {2b + 2il).y + 2cLz \ {a + 2b + r).y + 2.b.z ; 

 ■ — -^, and z = — ~-, 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.r.; or, as in (I.) a-i-b + 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 of,'-, 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 M under ordinary circumstances. 

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

 than one-uhird 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 M, 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 January number of this review was recently shown me by Mr E. 

 A. Schwarz of the U.S. National Museum. Since seeing this specimen I agree with ]\Ir 

 Gahan's conclusions that DipeUis 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 thinks the smaller specimen figured by me (figs. 4 and 5) may be related with 

 the larva of Lampyi-idae or Dascyllidae. It is more natural to interpret the three 

 anterior large segments of DipeUis as divisions of the thorax of a Lami^yrid larva than 

 that they are parts of the cephalon of an ^^)Ks-like crustacean. 



Charles Schuchert. 

 U.S. National Museum. 



