November 28, 1913] 



SCIENCE 



773 



tity. According to this definition every alter- 

 nating group whose degree exceeds 3 is 

 complete, while none of these groups is com- 

 plete according to the definitions of this term 

 given elsewhere. A still more original and 

 more mysterious definition under this term 

 relates to the regular group. It is stated that 

 this is " a transitive group whose order is the 

 same as that of the letter on which it is made." 



It is very difiicult to see how any one can 

 discover any meaning whatever in such a defi- 

 nition. To make a group on a letter is a 

 process which seems to have been foreign to 

 the literature of this subject. A large num- 

 ber of almost equally vague statements occur 

 under other terms. For instance, under the 

 term number it is stated that an irrational 

 number is " a definite number not expressible 

 in a definite number of digits," and a congru- 

 ence group is defined as a group made up of 

 replacements. 



It may probably be assumed that all mathe- 

 maticians who read these few citations will 

 agree that American mathematicians have 

 good reason to protest against such a butchery 

 of their subject in a popular work of refer- 

 ence. Those who desire more evidence can 

 easily obtain it by consulting this dictionary 

 for the definitions of the following terms : 

 analogy, angle — especially angle of elevation 

 and angle of depression, automorphic, frac- 

 tion, matrix, mathematical and variable. 



G. A. Miller 



Univeksity of Illinois 



A REPLY TO DR. HERON's STRICTURES 



The all-too-familiar " blessings " of Pro- 

 fessor Karl Pearson upon " Mendelians " have 

 recently been continued by his understudy, 

 Dr. David Heron, and directed toward Ameri- 

 can work in eugenics in general and that of 

 the undersigned in particular. Like my col- 

 leagues in this country I should have re- 

 mained silent under the attacks, knowing that 

 discriminating men of science in this coun- 

 try as well as in England recognize their 

 true animus and that they lie outside the pale 

 of science. But the notoriety given in a daily 

 paper to the publication of Heron and to a 



" defence " based upon an interview with me 

 by a reporter of the paper lead me to make a 

 brief reply. 



I shall not attempt now to answer all the 

 scores of trivial points of criticism made by 

 Dr. Heron, but shall consider only the paper on 

 heredity of epilepsy by Dr. David F. Weeks 

 and myself, which he singles out for special at- 

 tack. The numerous " errors " to which he 

 calls attention fall for the most part into three 

 categories, based on misunderstanding so gross 

 on the critic's part as to render it difficult to 

 believe that they are not intentional. Pirst, 

 Dr. Heron seems to assume that whenever a 

 symbol in a pedigree chart is not accompanied 

 on the chart by some special description it 

 stands for a person about whom nothing is 

 known. He calls attention to numerous cases 

 where, notwithstanding, the corresponding 

 individual is described in the text. The as- 

 sumption is a gross error. The chart shows 

 mainly the interrelationship of individuals 

 and indicates only certain traits. Second, Dr. 

 Heron catalogues, with infinite pains, " errors " 

 in citing the case number. Here he has fallen 

 into a trap which the authors unconsciously 

 prepared for him. To avoid the possibility that 

 a person who is not authorized should con- 

 nect an individual at the institution with his 

 family history it was decided to apply altera- 

 tions to the case numbers which enable the 

 authors, but not the ordinary reader, to iden- 

 tify the case. None of the " errors " are such 

 as would prevent the use of the numbers by 

 the authors and they could be of no scientific 

 use to others. Dr. Heron used them merely 

 for criticism. Had we anticipated that there 

 was anywhere a man of science with such 

 abundant leisure, we should have published a 

 warning that the reference numbers were for 

 the sake of identification by the authors and 

 not for scientific study. Third, in our tables 

 we analyzed the traits of the " children " into 

 ten columns, but condensed those of the fath- 

 er's sibs, etc., into 5 columns to save space; in 

 some cases father and father's sibs, etc., ap- 

 pear as " children " and the classification is ac- 

 cordingly expanded from 5 to 10 categories. 

 This, of course, is obvious to any intelligent 



