;3« 



NATURE 



[November 25, 1915 



This leads to very heavy work which could have 

 been avoided by takingf 



U^. = A + B(-t--r?) + C(.i--^/)(.r-/^)+ . . . 

 where a, h, . . . are the values of x for which 

 the function is ^iven. This is actually given in 

 a later chapter, but its use in this connection is 

 not mentioned. The section on Two-Variable 

 Interpolation seems out of place, in view of the 

 introduction of a chapter dealing- entirely with 

 this branch of the subject. The short chapter on 

 Central Differences, which is practically a repro- 

 duction of the obsolete, cumbersome, and im- 

 perfect demonstration given in the Institute of 

 Actuaries' Text-book, part ii., might well have 

 been dropped, as the work is redone by a better 

 method in the chapter on Stirling's Formula. As 

 is shown in the latter chapter, the formulae follow 

 at once from assumptions of the form 



U^ = A + B.r+Ci-(.r->) + DCr+T)..(.r-i)+ . . . 

 The authors, however, make their demonstrations 

 unduly long by obtaining Uq, AUq, A^U-j, ... by 

 detailed expression of Uq, Uj, U- j, ... in terms 

 of A, B, . . . If Uj had been written in the form 

 A + Bx+C.-VDCv+.r:^ 

 2: 3! • 



the difference of U^^ for all values of x could have 

 been written down without the tedious arithmetic 

 which is employed. Two pages are devoted to 

 the CD. expansions of V^ in which the leading 

 terms are Uj and U_i respectively. All this is 

 quite unnecessary, as the formulae can be deduced 

 from those already obtained by writing 

 U, = UHr.-i, or U_.^f,^j,. 

 It is to be regretted that the opportunity was 

 not taken to revise the chapter on Summation. 

 The function is frequently written before the 

 operator, and we have such surprising state- 

 ments as 



l'„ + , = U„(i+/\)^ 



u„+u„,,+ . . . +u„,„_,=u„{«+''''^7^)a+ . . .} 



and the operators are spoken of as the coefficients 

 of Ua. The introduction of the alternative so- 

 called demonstration for Lubbock's formula is un- 

 fortunate, as the symbolical method employed is 

 quite unsound, and may be mistaken by students 

 for a proof. The chapter on Interpolation of In- 

 verse Functions, consisting mainly of two examples, 

 is unnecessary, and the examples might have been 

 incorporated with those on Legrange's formula. 



Three-quarters of the book (parts ii. to iv.) are 

 taken up with solutions of questions set in the 

 first examination of the Institute of Actuaries be- 

 tween the years 1887 and 1902. The questions 

 include Permutations and Combinations, Binomial 

 Theorem, Probabilities, and Elementary Finite 

 NO. 2404, VOL. 96] 



Differences. The solutions are instructive, but 

 those on Finite Differences follow too closely the 

 methods of algebra text-books instead of the 

 neater methods of Finite Differences. The in- 

 correct solution to problem 212 given in the first 

 edition is repeated, and the solution to problem 

 202, giving the expression of Uo+ UjA; + V^x^ + . . . 

 in terms of differences of Uq, should have been 

 incorporated in the chapter on Summation. It 

 would have been more useful to the students for 

 whom the book is intended if solutions of ques- 

 tions from recent examination papers of the 

 Institute of Actuaries had been given, as the 

 syllabus now includes the elements of Differential 

 and Integral Calculus. 



PRACriCAT. AND APPLIED CHEMISTRY. 

 (i) Practical Physical Chemistry. By Dr. A. 

 Findlay. Third edition. Pp. xvi + 327. (Lon- 

 don: Longmans, Green and Co., 1914.) Price 

 4.V. 6d. net. 



(2) Practical Physical Chemistry . By J. B. Firth. 

 Pp. xii + 178. (London: Methuen and Co., 

 Ltd., 1915.) Price 2s. 6d. 



(3) Volumetric Analysis. By A. J. Berry. Pp. 

 137. (Cambridge : At the University Press, 

 191 5.) Price bs. 6d. net. 



(4) .4 First ('nurse in Practical Chemistry for 

 Rural Secondary Schools. By W. Aldridge. 

 Pp. xii+ 122. (London : G. Bell and Sons, Ltd., 

 1915.) Price IS. 6d. 



(5) Dyestuffs and Coal-Tar Products: their Chem- 

 istry, Manufacture, and Application. By T. 

 Beacall, Dr. F. Challenger, Dr. G. Martin, and 

 Dr. H. J. S. Sand. Pp. vii + 156. (London: 

 Crosby Lockwood and Son, 191 5.) Price 

 75. 6d. net. 



(i) and (2) ^-pHE third edition of Prof. Find- 

 X lay's " Practical Physical Chem- 

 istry " contains a description of several new 

 experimental methods, especially in connection 

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 surface-tension by the drop method, molecular- 

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 decomposition and of ionic-discharge potentials. 

 The new edition retains all the merits which have 

 long been recognised in its predecessors. 



Mr. Firth's book is of a similar type to Prof. 

 Findlay 's, and seems to indicate th^t a standard 

 course of physical chemistry has now been de- 

 veloped, and is being followed with very little 

 modification in a number of different centres. The 

 coincidence in this case extends not merely to 

 identical illustrations of standard apparatus, but 

 even to the inclusion in each volume of a picture 



