Chemistry and Physics. 501 



New York, 1922 (D. Van Nostrand. Company). — It is to be 

 expected that a mathematician trying to teach physics would 

 write a very different book from that of a physicist teaching 

 mathematics. The present work may fairly be said to come 

 within the former category. The author being primarily inter- 

 ested in the field of associative algebra is disposed to view the 

 method of quaternions as preferable to other systems of vector 

 analysis, but for those who are contrary-minded he has been to 

 considerable pains to explain the characteristics of a variety of 

 systems and the notations employed in them. 



The introductory chapter sketches the history and character 

 of vector analysis. The second and third chapters are intended 

 to be explanatory of scalar and vector fields, but as expositions of 

 the meaning of physical quantities they are occasionally sadly 

 lacking. For example, on p. 14 we read : 



"Action. This quantity is much used in physics the principle 

 of least action being one of the most important fundamental 

 bases of modern physics. The dimensions of action are [®<£]," 

 (i. e. the unit of electricity times the unit of magnetism) "and 

 the unit might be a quantum but for practical purposes a joule- 

 second is used." Now waiving the question whether there is 

 any occasion for bringing dimensional equations unto a vector 

 calculus, the obvious meaning of the expression quoted is that 

 the unit of action is the product of the unit charge by the unit 

 pole. But there is no known action of a magnetic charge on 

 an electric charge, which reduces the whole statement to an 

 absurdity. 



Chapters IV, V, and VI explain the rules of the game for 

 that particular complex of hypernumbers called a quaternion, 

 after which the author proceeds to the main purpose of the 

 book which is to familiarize the student by easy gradations with 

 the profundities of mathematical physics. Chapter VIII is 

 devoted to derivative and integral theorems and their physical 

 applications. Chapter IX is given to the linear vector function; 

 Chapter X to homogeneous strains and Chapter XI to hydro- 

 dynamics. 



As a discussion of physical subjects from the vectorial stand- 

 point the book will be found perhaps the greatest mine of 

 examples and illustrations since Tait's Quaternions. Issue 

 mast be taken with the author's statement that Gibbs considered 

 scalar and vector multiplications as functions of the dyadic 

 rather than as multiplications (v. Scientific Papers Vol. II, 

 p. 20), and that he considered the dyadic as a quantity. 



In dissent from the author's view that, in comparison to other 

 vector methods, the use of quaternions is by far the simplest in 

 theory and practice, one has only to run his eye over the equa- 

 tions in the physical applications to see how readily intelligible 

 they would be to one understanding the function Sa/3 and Va/? 



