316 



SCIENCE 



[N. S. Vol. XLIV. No. 1131 



Theory of Errors and Least Squares. A Text- 

 hook for College Students and Research 

 Workers. By LeEoy D. "Weld, M.S. New 

 York, The Macmillan Company, 1916. 8vo. 

 Pp. xii + 190. 



The two pages of " Preface " of this book 

 made a very unfavorable impression on the 

 reviewer. It would take too much space to 

 point out the expressions that seemed catchy 

 but meaningless or non-committal. It gave 

 the impression that possibly the author had 

 not caught the fundamental purpose and na- 

 ture of the method of computation discussed 

 in the volume. The idea of having the theory 

 for its amateurish " satisfaction " and of 

 getting it " in an evening or so and then put 

 it into immediate practise " did not at all har- 

 monize with the reviewer's knowledge that only 

 a fairly experienced observer has much real 

 use for the method of least squares in his 

 computations. 



As a text-book for " undergraduates," unless 

 they are classed with the " casual readers," it 

 presupposes a half-year at least of training in 

 the calculus. Compare pages 54, 57, 60, 67, 71, 

 90 and others. Any student of the desirable 

 amount of inquisitiveness would like to know 

 under what conditions and to what extent he 

 may play such tricks of the calculus as he sees, 

 e. g., following equation (h) on page 181 ; and 

 it would take considerable advanced calculus 

 to make it all clear to him. 



As a book for " handy reference " it would be 

 vastly more useful by having a carefully pre- 

 pared, detailed index. This need is partially 

 met by " Appendix P. Collection of Impor- 

 tant Definitions, Theorems, Pules and Por- 

 naulas for Convenient Reference," pp. 185 sq. 

 Throughout, references are made to Article, 

 Equation (number), or even to Chapter, with- 

 out adding the page, which would facilitate the 

 use of the book, since only page numbers ap- 

 pear on the tops of the pages. It would help 

 much to have the number of the page on which 

 each formula originally appears given as well 

 as the number of the formula on pp. 188-190, 

 and elsewhere. 



Happily, the " Preface " is the poorest part 

 of the whole book and that may be omitted by 

 the reader. On pages 17 and 28 the author 



states clearly the " special office of the method 

 of least squares," yet he nowhere emphasizes 

 the fact that he is dealing with a method of 

 computation. He does not make use of the 

 splendid opportunity of forcing and fixing 

 upon the attention of the reader the facts that 

 the method does not improve the quality of 

 poor or careless observations, and that only 

 the beginning student carries readings as of 

 grams out to six or seven decimal places (see 

 any reference to grams, e. g., p. 155). It fur- 

 ther would not be difficult and much worth 

 while to point out that in the formula 

 y = ce- % "^ (24), p. 56, the exponent must be 

 an abstract number so that 1/h and x must be 

 measures in the same unit. The types of 

 readers for whom the book is intended are the 

 very ones that should have these matters in- 

 delibly impressed upon them. Although it is 

 sometimes stated that illustrations are from 

 students' work, it is passing strange that the 

 author should have let such matters escape his 

 notice. 



Barring two cases of questionable English, 

 pp. 65, 170, that only a purist might notice, the 

 book is quite free of errors of speech and of 

 typography. The treatment is remarkably 

 clear and well-ordered. The topics are nicely 

 correlated. Especial attention should be 

 called to Chapters IV. and VIII., and to Art. 27 

 of the former chapter in particular. Lucid is 

 not too strong to describe some portions of the 

 book. On the whole, readers who want only a 

 general idea of what the theory is about can 

 scarcely find a more concise and clear presenta- 

 tion for that purpose. The numerous, excel- 

 lent, well-chosen exercises at the end of each 

 chapter will, if solved, greatly enhance the 

 permanent value of the book. 



The adverse criticism is herein placed first 

 so that the reader may finish the review with 

 the desire to get and read the book, and find it 

 as interesting and profitable as the reviewer 

 has found it. Chakles C. Grove 



ARISTOTLE'S ECHENEIS NOT A 

 SUCKING-FISH 



In the course of a rather extensive series of 

 researches on the shark-sucker, it has been 



