OCTOBEB 30, 1908] 



SCIENCE 



611 



eral plan, the scholar is much more apt to 

 acquaint himself with advances outside of his 

 particular field, and thus such an arrangement 

 tends, at least in a slight degree, towards 

 maintaining that community of interest and 

 sympathy which is so helpful in the harmoni- 

 ous development of science. As Darhoux 

 pointed out in his recent address before the 

 International Congress of Mathematicians at 

 Home, there is danger of estrangement even in 

 a single science, and this danger is still more 

 real as regards the various sciences which 

 should be mutually helpful. 



In arranging the material of the present 

 volume we are told that it frequently became 

 necessary for a specialist to examine the 

 articles in some detail, as the headings were 

 often too vague to give a definite idea in 

 regard to the results which were reached in 

 the articles. This is especially true of those 

 which appeared between 1884 and 1900, while 

 most of the earlier papers were classified ac- 

 cording to their headings. Although great 

 care seems to have been exercised, it is not 

 difficult to find instances where the classifier 

 did riot exhibit sufficient knowledge of the 

 subject. For example, it is difficult to see 

 why a note on " Test of a simple group " 

 should be classed under general group theory 

 while such a general article as that of Dyck 

 on " Groups of discrete operations " is classed 

 among -the more special articles on discrete 

 groups of finite order. An instance where the 

 classification according to the headings of 

 articles is entirely misleading is furnished by 

 the papers by Cockle which appeared in vol- 

 umes VI., VII. and VIII. of the Gamhridge 

 and Dublin Mathematical Journal, under the 

 title of " Method of vanishing groups," al- 

 though they relate to a species of indeter- 

 minate analysis and have nothing in common 

 with what is now regarded as group theory. 

 In the present volume they appear, however, 

 under this general heading. 



An instance where the classifier seems to 

 have misunderstood the meaning of a tech- 

 nical mathematical term is furnished by the 

 note on permutants, published by Bilenki in 

 Nouvelles Annales de Mathematiques (1900). 

 As the heading implies, this note relates to the 



theory of matrices, but it is classified with 

 substitutions and permutations in the present 

 volume. It may be of interest to observe that 

 the term permutants does not appear in 

 Miiller's " Mathematisches Vocabularium," al- 

 though this valuable work contains more than 

 ten thousand technical terms with their 

 French equivalents. 



These instances suffice to make it clear that 

 the scholar can not regard the present index 

 as final authority, either as regards complete- 

 ness or as regards reliability. On the other 

 hand, extensive historical research among the 

 literature of the historical century will still 

 be richly rewarded. The present volume will, 

 however, be of great assistance in making 

 such research on the part of the mathema- 

 tician more effective, and it is to be hoped 

 that later editions will be free from many 

 imperfections which could scarcely have been 

 avoided in the first edition of such a very 

 extensive work. The undertaking is a highly 

 laudable one and bespeaks in clear terms a 

 willingness to render an important service, 

 which offers little reward beyond the pleasure 

 in rendering such a service. From this view- 

 point the bibliographical activity of the pres- 

 ent time exhibits a most inspiring picture of 

 the trend of thought actuating scientific men. 

 G. A. Miller 



UNrVEBSITT OF ILLINOIS 



NOTES ON ENTOMOLOGY 

 The Germans have always been considered 

 the authorities on forest entomology, and 

 their text-books the standards. Now a most 

 excellent work has been issued in English by 

 A. T. Gillanders.' Mr. Gillanders is manager 

 of the forests of the Duke of Northumberland, 

 and so has had much practical experience. 

 The insects are considered under the order to 

 which they belong; there being tables to 

 families, and often to the genera. After each 

 group there is a short bibliography. Many 

 of the illustrations are photographs of injured 

 parts of the tree, and of the insect upon it. 

 The last chapter contains a list of trees with 

 their injurious insects. Perhaps the weakest 

 ' " Forest Entomology," pp. 422, figures 351. 

 W. Blackwood and Sons, London, 1908. 



