710 



THE POPULAR SCIENCE MONTHLY. 



of which Mr. David T. Day, Chief of Di- 

 vision of Mining Statistics and Technology, 

 is the editor, is to record annually the most 

 important facts concerning the development 

 of the minerals found in the country. The 

 present, the sixth volume, is for the year 

 1888. The method of treatment pursued in 

 the previous volumes is continued in this. 

 The report opens with a summary statement 

 as to the condition of each mineral industry 

 at the close of the period under review the 

 calendar year. At the end of this summary 

 is a table in which the values of the various 

 products are added, so as to furnish an esti- 

 mate of the relative importance of the min- 

 ing industry as a whole. Following the 

 summary each important mineral industry 

 is discussed in a separate chapter. The sta- 

 tistical tables given in former reports are 

 extended to include 1888, but otherwise the 

 material in each chapter is intended to show 

 the developments in 1S88 only and not in 

 previous years. To facilitate the consulta- 

 tion of all the volumes of the scries, an 

 index to the six is in preparation. (Gov- 

 ernment Printing-Office, Washington ) 



Volume XXIV of the Annals of the Har- 

 vard Observatory is devoted to Results, of 

 Observations with the Meridian Photometer, 

 from 1882 to 1688, by Edward C. Pickering 

 and Oliver 0. Wendell. The measurements 

 are of stars having magnitudes brighter 

 than 9 - l of the Durchmustcrung. The ob- 

 jects observed number 20,9S2. Four photo- 

 metric settings were made upon each ob- 

 ject, and these were repeated on the average 

 between three and four times. The total 

 number of settings is 207,092. 



The Elements of the Differential and In- 

 tegral Calculus of Prof. Arthur Sherburne 

 Hardy (Ginn & Co.) is based on the system 

 of rates which, in the author's experience, 

 has proved most satisfactory in a first pres- 

 entation of the object and scope of the sci- 

 ence. The object of the Differential Calcu- 

 lus is the measurement and comparison of 

 rates of change when the change is not uni- 

 form. The rate at any instant is determined 

 by ascertaining what the change of a quan- 

 tity would have been in a unit of time had 

 its rate remained what it was at the instant 

 in question. This change the Calculus en- 

 ables us to determine, however complicated 

 the law of variation may be. 



The Bureau of Education has issued, 

 among its Circulars of Information for 1890, 

 a book of some four hundred pages on The 

 Teaching and History of Mathematics in the 

 United States, by Prof. Florian Cajori. The 

 first chapter, dealing with elementary schools, 

 the colleges then existing, and self-taught 

 mathematicians in colonial times, describes 

 persons and ways of teaching, many of which 

 seem very quaint to modern eyes. The 

 next two periods treated cover respectively, 

 the influx of English mathematics and the 

 influx of French mathematics. The list of 

 colleges grows longer in these two chapters, 

 and among the other topics which now enter 

 into the history are the surveying of Govern- 

 ment lands, mathematical journals, and the 

 United States Coast and Geodetic Survey. 

 A chapter on mathematical teaching at the 

 present time contains the answers obtained 

 by sending a list of questions to several hun- 

 dred colleges, normal schools, academics, 

 etc. This is followed by several historical 

 essays on mathematical subjects, and a bib- 

 liography of fluxions and the calculus. 



The Laboratory Manual of Chemistry, 

 Medical and Pharmaceutical, by Oldbcrg and 

 Long, which we noticed in July, 18S8, has 

 come out in a revised and enlarged edition 

 (Keener, $3.50). The preface states that 

 the greater part of this edition is an exact 

 reprint of the first, but that the chapter on 

 the chemical analysis of urine has been en- 

 tirely rewritten, and a new chapter has been 

 added on the microscopic examination of the 

 sediment. 



Mr. Wcstcl W. Willoughby, in his mono- 

 graph on the Supreme Court of the United 

 States (Baltimore, Johns Hopkins Press), 

 holds up that tribunal as an illustration of 

 the maxim that in America, as elsewhere, 

 institutions are the result of an evolution, 

 and not an invention ; and that constitu- 

 tions, whether written or unwritten, are but 

 the results of the gradual recognition of 

 those laws and methods which are the best 

 suited for the government of a politically 

 organized people. The history of the Su- 

 preme Court begins with accounts of the 

 judiciaries in the colonies and under the 

 Confederation, and is carried on through 

 the Convention, the State Conventions, the 

 establishment and jurisdiction of the Fed- 



