90 



SCIENCE 



[N. S. Vol. XXXVIII. No. 



Jepson's " Silva of California," ' the same to 

 be reprinted under the above name in Univer- 

 sity of California Publications, Agricultural 

 Science Series, Vol. II., No. 1 (now in press). 



The chief reason for describing this form 

 as a variety rather than a species is that U 

 does not hreed true. Several tests of seeds 

 from different trees of this form have been 

 made by the writer and in all but one test a 

 number of the seedlings (never the same pro- 

 portion) are typical J. californica in leaf 

 characters. Obviously this is sufficient proof 

 of a relationship which it is highly desirable 

 to indicate by the name employed. 



The reason for rejecting the name querci- 

 folia is that the leaves are not oak-like. They 

 resemble leaves of certain species of Rhus 

 more than oaks. For this reason the writer 

 had considered anacardifolia as a name, but 

 the leaves are very unlike those of some spe- 

 cies of the Anacardiacese. On the other hand, 

 in general appearance of the trees this walnut 

 does resemble a small-leaved oak. This is 

 largely due to the habit of growth, the small 

 size of the leaves and the dark green color of 

 the foliage. Hence the name quercina is 

 deemed proper, especially when used in va- 

 rietal rank. 



E. B. Babcock 



SCIENTIFIC BOOKS 



Principia Mathematica. By Alfred North 

 Whitehead, Sc.D., F.E.S., Fellow and late 

 Lecturer of Trinity College, Cambridge, 

 and Beetrand Eussell, M.A., F.E.S., Lec- 

 turer and late Fellow of Trinity College, 

 Cambridge. Cambridge University Press. 

 1912. Vol. II. Pp. xviii -f 112. 



Differential and Integral Calculus. An Intro- 

 ductory Course for Colleges and Engineer- 

 ing Schools. By Lorrain S. Hulburt, Col- 

 legiate Professor of Mathematics in the 

 Johns Hopkins University. New York, 

 Longmans, Green and Co. 1912. Pp. 

 xviii -f 481. 



An Elementary Treatise on Calculus. A Text- 

 book for Colleges and Technical Schools. 

 By William S. Franklin, Barry MacNutt 



' Ibid. 



and EoLLiN L. Charles, of Lehigh Univer- 

 sity. Published by the authors. South 

 Bethlehem, Pa. 1913. Pp. vi + 292. 

 The Calculus. By Ellery W. Davis, Professor 

 of Mathematics, the University of Nebraska, 

 assisted by Willlvm 0. Brenke, Associate 

 Professor of Mathematics, the University of 

 Nebraska. Edited by E.'.rl Eaymond Hed- 

 RiOK. New York, The Macmillan Company. 

 1912. Pp. XX + 446. 



Eeaders who desire to gain with a minimum 

 of effort a fair knowledge of the nature, mag- 

 nitude, method and spirit of Messrs. White- 

 head and Eussell's great undertaking and 

 achievement may be referred to the Bulletin 

 of the American Mathematical Society, Vol. 

 XVIII., and to Science for January 19, 1912, 

 where will be found somewhat extensive re- 

 views of Vol. I. of the " Principia." The im- 

 mensity of Vol. II., together with its exceed- 

 ingly technical content and method, make it 

 undesirable to review this volume minutely in 

 this journal, and the purpose of this notice is 

 merely to signalize the appearance of the work 

 and to indicate roughly the character and scope 

 of its content. 



Owing to the vast number, the great variety 

 and the mechanical delicacy of the symbols 

 employed, errors of type are not entirely avoid- 

 able and the volume opens with a rather long 

 list of " errata to Volume I." The volume in 

 hand is composed of three grand divisions: 

 Part III., which deals with cardinal arith- 

 metic; Part IV., which is devoted to what i3 

 called relation-arithmetic; and Part V., which 

 treats of series. The theory of types, which is 

 presented in Vol. I., is very important in the 

 arithmetic of cardinals, especially in the mat- 

 ter of existence-theorems, and for the con- 

 venience of the reader Part LEI. is prefaced 

 with explanations of how this theory applies 

 to the matter in hand. In the initial section 

 of this part we find the definition and logical 

 properties of cardinal numbers, the definition 

 of cardinal number being the one that is due 

 to Frege, namely, the cardinal number of a 

 class C is the class of all classes similar to 0, 

 where by " similar " is meant that two classes 

 are similar when and only when the elements 



