Geology and Natural History. 159 



As Dr. Wilson explains in his preface, the book is divided 

 roughly into three distinct parts. In the first are treated the 

 addition and products of vectors ; in the second, the application 

 of the differential and integral calculus ; in the third, the theory 

 of the linear vector function and a few special applications. 

 There are seven chapters, each of which is concluded by an excel- 

 lent summary and a few selected exercises. 



The scope of the work may best be indicated by a resume of 

 the table of contents. Chapter i discusses scalars and A r ectors, 

 addition and subtraction, the three unit vectors i,j, Jc, centers of 

 gravity, representation of areas ; chapter u, scalar and vector 

 multiplication, reciprocal systems, kinematics and dynamics of a 

 rigid body ; chapter in, kinematics of a particle, the vector and 

 scalar differentiating operator, divergence, curl, and combinations 

 of these operators ; chapter iv, the theorems of Gauss, Stokes 

 and Green, and the integrating operators, " potential," " new- 

 tonian," " laplacian " and " maxwellian "; chapter v, the theory of 

 linear vector functions and the application of various theorems in 

 regard to dyadics ; chapter vi, the description and discussion of 

 rotations and strains by dyadics ; chapter vn, applications of 

 vector analysis to quadric surfaces and the theory of light. 



From the first page to the last, the logical development is 

 clear and forcible. Special attention is paid at every point to 

 render the book efficient for use in a class ; and anyone having 

 an opportunity to instruct a class in Vector Analysis would cer- 

 tainly be most grateful to Dr. Wilson. 



The book is to be recommended to every student of physics 

 and mathematics, and the thanks of every reader are due the 

 publisher for the excellence of the type and paper. No important 

 typographical errors have been noted ; but the absence of an 

 index is unpardonable. j. s. a. 



II. Geology and Natural History. 



1. Catalogue of the Types and figured Specimens in the Palmon- 

 tological collection of the Geological Department, American 

 Museum of Natural History • by R. P. Whitfield, assisted by 

 E. O. Hovet (vol. xi, Bull. Am. Mus. Nat. Hist.) ; pp. 1-500. 

 1898-1901. — The completion of this catalogue of one of the most 

 important series of Paleozoic fossils in the United States, repre- 

 senting as it does a large proportion of the types upon which 

 American Paleozoic paleontology is founded, calls for special 

 notice. From the preface of the completed work written by the 

 able author, the following quotation is made, viz : 



" This Hall collection may well be considered the standard refer- 

 ence collection for all workers in North American Palaeozoic 

 palaeontology. Most of the ' figured specimens ' in the series are 

 those which were identified, redescribed, illustrated and pub- 

 lished by Prof. Hall in the .early volumes of the Palaeontology of 



