188 



SCIENCE 



[N. S. Vol. XXXIII. No. 840 



ever, shows that the results of oxygen absorp- 

 tion and carbondioxide elimination as deter- 

 mined by the Benedict calorimeter and the 

 Zuntz apparatus are identical. There is there- 

 fore no doubt that the preeminent feature of 

 the apparatus used by Benedict is the calori- 

 metric determinations. 



The authors find that the average heat pro- 

 duction for fifty-five subjects during waking 

 hours is 9Y.1 total calories, 1.52 per kilogram 

 of body weight, and 49.2 per square meter of 

 body surface, per hour. These records are 

 35 per cent, above the requirements in sleep. 

 Further experiments showed an average re- 

 quirement of 1Y.8 additional calories when 

 a subject undressed, weighed himself and 

 dressed again. An important generalization 

 is that the pulse rate is more or less parallel 

 to the total metabolism. 



This book suffers very greatly from a fault 

 that has pervaded the publications of the Nu- 

 trition Laboratory, both at Boston and at 

 Middletown, and that is that the new discov- 

 eries are not sharply defined as separate from 

 well-known facts. This fault occurs in Bene- 

 dict's splendid monograph on " Inanition " 

 where the one new fact, the quantitative de- 

 termination of the amount of glycogen 

 oxidized on the first and second days of fasting 

 is passed over without emphasis. 



The authors make the following statement: 

 " A striking series of experiments has demon- 

 strated very clearly that a change from a diet 

 poor in carbohydrates to one rich in carbo- 

 hydrates is accompanied by a considerable re- 

 tention of water by the tissues of the body." 

 This however is not an original observation, 

 having been noted by Bischoff and Voit, fifty 

 years ago. 



The world owes a great debt to the work of 

 the Carnegie Nutrition Laboratory and its 

 forerunner in Middletown, which no one can 

 gainsay. Criticism is offered in the spirit of 

 Pfliiger who held it to be the mainspring of 

 every advance and the Altmeister adds, " des- 

 halb iibe ich es." Graham Lusk 



The Elements of the Theory of Algehraic 

 Numbers. By L. B. Eeid. New York, 



The Macmillan Company. 1910. Pp. 



xix + 454. 



The title of this book is misleading, as it 

 treats of no algebraic numbers other than 

 quadratic; it can not he said to present even 

 the elements of the theory of algebraic num- 

 bers. The author devotes 150 pages to the 

 elementary congruencial properties of rational 

 numbers and 300 pages to quadratic numbers. 

 In view of the intimate relations between 

 quadratic forms and the numbers and ideals 

 of a quadratic field, the omission of an ac- 

 count of quadratic forms is certainly a serious 

 defect in a book having the aims of the pres- 

 ent one. 



In a review of a book of the character of 

 the present text, one has only to discuss ques- 

 tions of pedagogy. The author desires to 

 bring out a closer relation between rational 

 numbers and quadratic numbers. This he 

 accomplishes by complicating the elements of 

 rational numbers with the unnecessary ma- 

 chinery of quadratic numbers ! We find on 

 page 91 Wilson's theorem stated in the form 



r^n ... rj;-|- 1 =0 (mod p), & = 0(p), 



where r^, • ■ •, rj^ form a complete set of resi- 

 dues modulo p, a prime. A similar unneces- 

 sary complication is met on page 105. Posi- 

 tive and negative primes p are used, so that 

 one must face <^(p) = | P | — 1. 



On page 24Y the " introduction of the 

 ideal " should read introduction of ideals. 

 After stating formally theorem A and de- 

 voting fifteen lines to its proof, the author 

 informs us that the " theorem therefore fails." 

 Similarly, on pages 250-251, theorems are 

 formally stated and later shown " not to hold 

 in general." This peculiar style of pedagogy 

 is decidedly a novelty to the reviewer. It may 

 at least serve to put the reader on his guard 

 as to the fallibility of " what is written in the 

 book." In the present instance the reader 

 may be prepared for the actual error in the 

 theory as presented on page 316, where the 

 author makes a general theorem depend upon 

 an equation which he has earlier proved only 

 for a few special cases. His single reference 

 is to the case of Gauss's field of complex 



