194 



NATURE 



[June 30, 1904 



(5) Mr. Dale's tables have been compiled with the 

 view of meeting the requirements of workers in phy- 

 sical science and applied mathematics, and exclude 

 such functions as are of use only in navigation. They 

 comprise tables of common and hyperbolic logarithms, 

 of reciprocals, squares, cubes, square roots, and cube 

 roots; natural and logarithmic functions of angles; 

 elliptic, Bessel, gamma, exponential, and hyperbolic 

 functions: zonal surface harmonics and some other 

 tables. 



The table of logarithms of numbers is modelled on 

 the ordinary four-figure log tables now so largely 

 employed. It has the same number of rows of figures, 

 the mean differences for each row being given, and it 

 occupies only three pages. From it the five-figure 

 log. of any three-figure number can be read directly. 

 For a four-figure number the tabulated difference 

 would require to be added, and for a five-figure number 

 an additional difference for the last figure must be 

 added. In the early part of the table the mean differ- 

 ences vary so quickly as to be of no use for five-figure 

 accuracy, and, indeed, here the fourth figure is scarcely 

 trustworthy. In such cases the author ingeniously 

 recommends the use of the table of anti-logs, in which 

 at the corresponding- region the differences vary slowly. 



The tables of trigonometrical functions each take up 

 four pages. Five-figure values are given for intervals 

 cf 3' or o°.o5, and the mean differences for each row 

 are given for i' and 2'. 



Probably these five-figure tables of logarithms and 

 functions of angles are not quite so convenient in use 

 as the more lengthy five-figure tables provided with a 

 thumb index. But occupying as they do only about 

 <ine-tenth the space, the author has been able to in- 

 clude in a handy volume, at a moderate cost, tables 

 of many transcendental functions which hitherto have 

 not been very readily accessible, and they will be 

 welcomed by the class of people for whom they are 

 intended. 



(6) Mr. Pickworth states that the object of his little 

 book is to give a more detailed and practical explana- 

 tion of the use of logarithm.s than is to be found in 

 the text-books of algebra and trigonometry. The 

 ordinary two-page tables of four-figure logarithms and 

 anti-logarithms of numbers are given, and the detailed 

 explanations are accompanied by exercises for practice, 

 the answers to which are collected at the end. There 

 is also a short table of the logarithms of some 

 numbers which are of frequent occurrence in numerical 

 work. 



Students who are being taught practical mathe- 

 matics at the present time, and who use a suitable 

 modern text-book, will find in the latter all the infor- 

 mation they need on the subject, without having 

 recourse to a book like Mr. Pickworth's. The work 

 seems specially adapted to meet the case of those who 

 received their mathematical training at a time when 

 logarithms were neglected or relegated to the higher 

 branches, and who wish to be able to use this method 

 of computation. 



(7) In the preface the author of these tables expresses 

 the opinion that the ordinary aids to arithmetical 

 calculation, such as slide rules, tables of logarithms, 



NO. 1809, VOL. 70] 



&c., are not adapted for general use. Thus he states 

 that logarithms are only understood by very few, that 

 they involve considerable trouble in searching the 

 pages, and that they are seldom employed except for 

 trigonometrical work. However true this may be of 

 Germany, it is scarcely applicable to this country at 

 the present time, where, thanks largely to the influ- 

 ence of South Kensington, logarithms are being 

 taught to large numbers of youths in the classes for 

 practical mathematics, and four figure log tables are 

 in very general use throughout the kingdom. 



The author's plan of meeting the common want of 

 the computator is to supply a large multiplication 

 table, which covers 200 pages and goes up to 100 

 times 1000. That is, the product of any two numbers 

 one of which contains not more than three digits, and 

 the other not more than two, can be taken directly 

 from the table. Running along the bottom of the 

 pages is a table giving, for three-figure numbers 

 ranging from o. i to 999, the square and square root, 

 cube and cube root, reciprocal, logarithm, and the 

 products T)i/2 and ttii'I^. On the last two pages are 

 several useful subsidiary tables. In the introductory 

 pages the uses of the tables are fully explained and 

 illustrated with examples, worked out. It is shown 

 how to deal with numbers of more than three digits, 

 and how to perform division, square and cube root, 

 &c. One advantage in the use of these tables is that 

 the calculations are readily adapted to anv degree of 

 accuracy that may best suit the particular case under 

 consideration, and contracted methods of working are 

 explained by means of which all superfluous figures 

 may be omitted. 



The book should prove very useful for many pur- 

 poses, such as in mercantile calculations, the evalu- 

 ation of convergent series, the compilation of tables, 

 &c. Every care has been taken by both author and 

 printer to make the tables thoroughly trustworthy, and 

 to facilitate reference. They are printed in clear bold 

 type, and the general arrangement is very attractive. 



RECENT ENTOMOLOGICAL WORKS. 

 Monograph of the Coccidae of the British Isles. Vol. 

 ii. By Robert Newstead. Pp. 270; pis. F., xxxv.- 

 Ixxv. (London : Ray Society, 1903.) 

 The Coccidae of Ceylon. By E. Ernest Green, F.E.S. 

 Parts i.-iii. Pp. xliii-l-249; pis. i.-xciii. (London: 

 Dulau and Co., 1896, 1899, 1904.) 

 New Zealand Neuroptera; a Popular Introduction to 

 the Life-histories and Habits of May-Flies, Dragon- 

 Flies, Caddis-Flies, and Allied Insects inhabiting 

 New Zealand, including Notes on their Relation to 

 .Angling. By G. V. Hudson, F.E.S. Pp. ix+102; 

 with eleven coloured plates. (London : West, New- 

 man and Co., 1904.) Price los. 6d. 



ENGLISH entomologists and horticulturists are to 

 be congratulated on the completion of Mr. 

 Newstead's important work, which furnishes us, for 

 the first time, with a satisfactory account of the British 

 species of one of the most destructive families of in- 

 sects, the Coccidee or scale insects. They are 

 peculiarly destructive to trees and greenhouse plants. 



