27(3 



SCIENCE 



[N. S. Vol. XXXII. No. 817 



by him are synonyms and 44 per cent, are 

 wrongly placed as regards genera. Finally, in 

 the whole treatment of the family, covering 

 but seven and a half pages, I am able to count 

 offhand as many as 49 misleading errors, and 

 to offset these not a single feature which in 

 any sense can be called progressive. Hence 

 the obvious conclusion is that we find our- 

 selves no farther advanced, as far as this fam- 

 ily is concerned, than formerly. And as a 

 corollary that which is not progi-essive and 

 helpful in regard to taxonomy is worthless. 



It is not fair, however, to condemn the 

 whole work on such restrictive criticism with- 

 out examining other parts of it, but space of 

 course will not allow more than a few general 

 remarks. Suffice it to say that in all of the 

 other groups we find the same state of affairs 

 as in the Trichogrammidse and especially a 

 lack of up-to-dateness in regard to new genera 

 and species. Thus even as a bare list of de- 

 scribed genera and species the volume would 

 be seriously incomplete and as a contribution 

 to the taxonomy of the superfamily absurd 

 and ludicrous. As a catalogue it would take 

 lower rank than that of de Dalla Torre (1898), 

 which is notorious for its looseness, errors and 

 lack of critical ability, but which, notwith- 

 standing these, possesses much worth as a 

 bibliography of the genera and species. But 

 Schmiedeknecht lacks even in this respect — 

 mainly because of incompleteness. 



Of the 83 figures given but 18 of them are 

 colored, in spite of the statement in regard to 

 the 8 colored plates. Many of these figures 

 are copied directly from Ashmead, Howard 

 and Masi, and I find serious differences be- 

 tween these and the originals, but will not 

 particularize here. They may finally take rank 

 with the famous concoctions of Snellen van 

 Vollenhoven ; at any rate, it should be pointed 

 out that they are none too trustworthy and by 

 reason of that both obstructive and mislead- 

 ing. Moreover, many are given as original 

 drawings without reference to sources, if such 

 exist, and at least some of these are grotesque 

 and bizarre in the extreme — to wit, the one of 

 Tricli ogramma. 



It is a serious thing to have to condemn in 



its entirety the result of such a prodigious 

 amount of labor, yet it is no more than just 

 and right that others should be warned to 

 keep out of the path of this tasonomic dere- 

 lict that they, ourselves and the whole future 

 be not imperilled. Truly this volume is both 

 a tragedy and a comedy of errors. 



A. Arsene Girault 

 Uebana, III., 

 August 2, 1910 



THE POPULATION OF THE UNITED STATES 



To THE Editor of Science: In the Popular 

 Science Monthly for last April, and also in its 

 issue for November, 1900, a formula was given 

 for calculating the population of the United 

 States corresponding to any time between 

 1790 and 1900. 



As the results of each formula agree only 

 approximately with those of the census, I 

 thought it might be of some interest to present 

 a formula that should agree exactly. Such 

 a formula is the following: 



P = A + at + bt-+ ct^ + dt* -f et^ -\- ft', 



in which P denotes the population, in mil- 

 lions, t the time expressed in decades and 

 estimated from 1790; while 



A = 4-3.9, 0.= -I- 0.523333, 6 = -)- 1.603889, 



c = — 1.020833, d = -I- 0.343056, 

 e = — 0.0525, /= -I- 0.00305555. 



The formula holds good from 1790 to 1850, but 

 from 1850 to 1910 the coefficients have the 

 following values: 

 A = -1-23.2, o=-l- 18.303333, 6 =— 19.481111, 



c= -I- 12.470833, d = — 3.544444, 

 e = -1- 0.475834, / = — 0.0244444, 



and the origin of t is at 1850. 



Any series of observations which depend on 

 a single variable may be represented by a 

 formula of this kind, and a table has been 

 prepared by means of which the values of the 

 coefficients, a, h, c, etc., can be easily and ex- 

 peditiously calculated. By the aid of this 

 table a formula could be developed which 

 would give the exact results of the census from 

 1790 to 1910, and without any change in the 

 values of the coefficients. 



