536 



SCIENCE 



[N. S. Vol. XXVII. No. 692 



listed in ttis country. On tlie contrary. Pro- 

 fessor Bocher's book bears closer resemblance 

 to Weber's " Lebrbueb der Algebra " or 

 Serret's " Cours d'algebre superieure " even if 

 it is mucb less compreliensive than these 

 classic works. It exhibits the same masterly 

 grasp and improvements in the presentation 

 of fundamental matters. For instance, the 

 theory of linear dependence is treated here in 

 a more complete and satisfactory manner than 

 in any other text-book. Another special 

 feature of this work is the thorough treat- 

 ment of quadratic forms, culminating in the 

 important but not easily accessible theory of 

 elementary divisors. 



The book is intended "for students who 

 have had two or three years' training in the 

 elements of higher mathematics, particularly 

 in analytic geometry and the calculus," and 

 is based upon the courses of the author's lec- 

 tures delivered at Harvard IJniversity. The 

 mode of treatment is in accord with the 

 modern tendency not to be satisfied with re- 

 sults which are true " in general " ; that is, 

 which are true except in some isolated cases. 

 In using such results it is always necessary 

 first to inquire whether the case to which we 

 desire to apply them is not really one of the 

 exceptional ones, and hence they are very 

 much less desirable than the theorems which 

 have no exceptions. This mode of treatment 

 is a consequence of the effort to actually 

 prove things instead of being content with 

 some more or less plausible intuitions which 

 so often pass for proofs. The scope and con- 

 tents of the work may be inferred from the 

 following list of the headings of its twenty- 

 two chapters; Polynomials and their most 

 fundamental properties, a few properties of 

 determinants, the theory of linear dependence, 

 linear equations, some theorems concerning 

 the rank of a matrix, linear transformations 

 and the combination of matrices, first prin- 

 ciples and illustrations of invariants, bi- 

 linear forms, geometric introduction to quad- 

 ratic forms, quadratic forms, real quadratic 

 forms, the system of a quadratic form and one 

 or more linear forms, pairs of quadratic forms, 

 some properties of polynomials ^n general. 



factors and common factors of polynomials 

 in one variable and of binary forms, factors 

 of polynomials in two or more variables, gen- 

 eral theorems on integral rational invariants, 

 symmetric polynomials, polynomials sym- 

 metric in pairs of variables, elementary di- 

 visors and the equivalence of A-matriees, the 

 equivalence and classification of pairs of 

 bilinear forms and of coUineations, the equiva- 

 lence and classification of pairs of quadratic 

 forms. 



G. A. Miller 

 University of Illinois 



SCIENTIFIC JOURNALS AND ARTICLES 

 The Journal of Experimental Zoology, Vol. 

 v., No. 2 (December, 1907), contains the fol- 

 lowing papers : " Regeneration of Compound 

 Eyes in Crustacea," by Mary Isabella Steele. 

 The small hermit crab {Eupagurus longi- 

 carpus), the shrimp {Palwmonetes vulgaris) 

 and the sand shrimp (Crangon vulgaris) were 

 used for experiment material. Each indi- 

 vidual had either a part or the whole of one 

 or both eyes removed. Results obtained after 

 removing part of the eye show: that hermit 

 crabs may regenerate a perfect eye even after 

 the destruction of as much as half the optic 

 ganglion ; that Palcemonetes does not regenerate 

 an eye if the optic ganglion has been at all 

 injured; and that Crangon regenerates an eye 

 much more slowly than either of the other 

 species, and only after little or no injury to 

 the optic ganglion. After removal of the eye 

 so that the entire optic ganglion is destroyed, 

 the hermit crabs and Crangon may regenerate 

 an antenna-like organ in place of the excised 

 eye. Palcemonetes does not show any sort of 

 true regeneration unless the optic ganglion 

 has been left intact. The results of the whole 

 series of experiments tend to show that the 

 regeneration which takes place from any level 

 is largely influenced by the presence or ab- 

 sence of the whole or a part of the optic 

 ganglion. " On Some Phenomena of Coales- 

 cence and Regeneration in Sponges," by H. V. 

 Wilson. Cells of siliceous sponges (Micro- 

 ciona) when separated by pressure from the 

 skeleton are able to recombine, forming a 

 plasmodial mass which differentiates anew 



