406 Notices respecting New Books. 



found by bim for tbe otber elements (where b on an average 

 = 7*4). The results also do not admit of any doubt as to 

 the place of the different elements. 



A calculation of the whole L ai -group hitherto known shows 

 besides, that the formula (1), theoretically set up bjr Moseley, 

 does not give the best representation of the experimental 

 values. If (1) is written in the form 



v /?=a[N-6], (2) 



the calculation for b gives the value 7'12 (a = 122*8 instead 

 123'4 by Moseley). A divergence from the linear relation 

 given in (2) between \/v and N does not seem to take 

 place within the examined domain of 52 elements. 



For the present may be noticed, that fhe second line of the 

 doublet (a 2 ), for instance, of thallium has a wave-length of 

 X oa == 1-220 (X ai =l'209). 



Physical Laboratory, 



University of Lund, 

 Dec. 1915. 



XLVIII. Notices respecting New Books. 



The Tutorial Algebra {Advanced Course). Based on the Algebra of 

 RadhaTcrihlinan. By William Briggs, LL.D., M.A., B.Sc, 

 F.R.A.S., and G. H. Bryan, Se.D., F.B.S. London: W. B. 

 Clive. University Tutorial Press. 1913. 

 r PEXT-BOOKS on Algebra are, in these days, as plentiful as 

 -*- blackberries, and it must be no easy matter discriminating 

 among them. Each doubtless has its peculiar virtues ; but all of the 

 same standard must cover much the same ground, discuss the 

 same methods in much the same way, and append to each chapter 

 appropriate examples for the student to sharpen his wits on. The 

 authors of the Tutorial Algebra, now in its fourth edition, have 

 certainly satisfied all the requirements of a sound treatise, and 

 have placed in the hands of the intermediate student a book, the 

 careful study of which will bring him up to the threshold of 

 higher mathematics. The book assumes a knowledge of elementary 

 algebra up to the solution of quadratic equations ; and the scope 

 of the treatment may be inferred from the enumeration of a few 

 of the headings of the later chapters, such as progressions and 

 series, logarithms, permutations, combinations, complex quantities, 

 determinants, continued fractions, and so on. The historic foot- 

 note on page 219, dealing with the discovery of logarithms, hardly 

 brings out the facts of the case as recorded by Briggs himself. 

 See Professor G. A. Gibson's article on " Napier's Logarithms and 

 the Change to Briggs's Logarithms," recently published in the 

 ' Napier Tercentenary Memorial Volume.' 



