380 Notices respecting New Books. 



9. The Fluorescence of Gases Excited by Ultra-Schumann 

 Waves. 



10. A Further Study of the Fluorescence produced by Ultra- 



Schumann Rays. 



1 1 . Scattering and Regular Reflexion of Light by an A bsorbing 



Gas. 



12. Separation of Close Spectrum Lines for Monochromatic 



Illumination. 



Unified Mathematics. By L. C. Karpinski, Harry T. Benedict, 

 John W. Calhoun, Professors in the University of Michigan 

 and Texas. D. C. Heald & Co., 1918. 522 pp. 



Perry's ' Practical Mathematics ' would be our equivalent for the 

 scope of this book, intended to show, here and in America, that the 

 old plan is obsolescent of keeping a school-boy marking time for 

 years over arithmetic and algebra, and then rushing him through 

 some Calculus and Coordinate Geometry in his last year. But 

 the essentials of the Cartesian geometry are inculcated here in the 

 use of squared paper, for drawing the simple graphs, and the 

 illustrations follow of the geometrical applications of the Calculus. 



The logarithm is introduced at an earty stage and its use 

 exemplified in multiplication and division in applications of real 

 interest to large numbers and decimals by the aid of a compact 

 four-figure table. But there is no mention of the Slide Rule, 

 equivalent of a three-figure table, and amply accurate for ordinary 

 purposes. Formerly the only table to be found was a seven-figure 

 table, never hardly to be seen. It makes us groan when we have 

 occasion to turn to it, to think how late in life the use of it was 

 introduced to our attention. 



In a first introduction to the logarithm, no base should be 

 mentioned except 10, and then the definition y=10*=al#, 

 .v=\og ?/, with the abbreviation (al) for antilogarithm, as (log) for 

 logarithm. A four-figure table requires the antilogarithm to make 

 both ends of equal accuracy, and with experience the(al) function 

 can be made to serve throughout in place of the (log) function. 

 But the heedless boy will not observe the distinction, so that many 

 a schoolmaster will paste down the antilogarithm table. 



An antilogarithm table is soon calculated, by the ordinary rules 

 of arithmetic; thus y is calculated for #=0-5, 0*25, 0*75, by 

 ordinary square root, for #=02 by Horner's method, and then for 

 a?=0'l, by square root ; and no series is required. 



The historical note on p. 183 seems to show that the Babylonian 

 clay tablet might have a different reading, as the fraction of the 

 illuminated part of the moon's surface is the half versed sine (hav) 

 of the age of the moon. We still employ the Turkish astronomy 

 in speaking of a new moon, and her age. 



The polar coordinates, as exemplified on p. 436, should be laid 

 out .on the Lissajous's system, as they would be in Cartesians for 



