September 20, 19 17] 



NATURE 



43 



!>. 50) to contracted methods, leaves the door 

 pen for the perpetration of unmathematical in- 

 accuracies in the evaluation of results from 

 approximate data. Thus, in the example on 



p. 50:— 



1670 

 275 



8350 

 1 1 690 

 3340 



4593-50 



the final '50 are wrong, because o and two blanks 

 do not make o, nor do 5 and o and one blank 

 make 5. We do not know what these blanks 

 are, and there is no justification for writing- down 

 •50 as the result of addition of these incomplete 

 columns. If we remember that 2-75 really may 

 mean anything between 2745 and 27549 it will 

 readily be seen that the inaccuracies go further. 

 Of course, if all the data are given and results 

 required to three significant figures, the rule given 

 on p. 50 is applicable, but a lot of superfluous 

 figures will be written down and incorrectly 

 added. Again, on p. 55 (Ex. 46: Divide 231-4 by 

 I "938) the author puts a lot of zeros at the end 

 ,; of the dividend and also carries down a lot of 



I^its, although there are blank spaces requiring 

 ing above them. 

 The rest of the book deals with logarithms, 

 5nsuration, the slide rule, and graphs. This is 

 useful and practical work, which may very 

 well hv taught to students other than engineers, 

 perhaps with some reduction of the number of 

 examples in mensuration. The majority of the 

 "graphs" considered connect magnitudes of dif- 

 ferent kinds. Where this is not the case (as in 

 equations of straight lines) we are glad to see that 

 the author does represent the variables in their 

 correct relative proportions, instead of perpetrat- 

 ing the distorted figures in which straight lines 

 do not cut at the correct angle. 



(3) For those who want the sort of thing that 

 is contained in Part ii. of Messrs. Usherwood and 

 Trimble's "Practical Mathematics," that book 

 undoubtedly provides just the sort of thing they 

 want. It is not the kind of book one altogether 

 likes, and we could not recommend it to students 

 of the academic type, except an occasional candi- 

 date reading for the B.Sc. degree in physics with- 

 out taking mathematics as well. Undoubtedly 

 vector analysis, advanced calculus and differential 

 equations, Fourier's series, and inverted delta (v) 

 are required by engineering students, and if they 

 can get all this and a little thermodynamics in a 

 book of this size, they will not quarrel about 

 rigorous demonstrations. The result is, how- 

 ever, a formidable mass of symbols and formulae. 

 Individually, we consider that the binomial, ex- 

 ponential, and hyperbolic functions should not be 

 taught until after the elements of the calculus 

 have been mastered ; however, it is quite easy to 

 begin at chap. vi. and take some of the earlier 

 parts afterwards. The attempt to prove the dif- 

 ferentiation formula for the sine savours too 

 NO. 2499, VOL. 100] 



much of the "we see" or "we may put" of the 

 typical narrow-minded mathematician. On the 

 other hand, in dealing with symbolical notation, 

 the authors make some effort to keep out of the 

 pitfall into which Edwards plunged when he ap- 

 plied to inverse operations formulae which he had 

 proved only for direct ones. The introduction 

 of thermodynamics in §51 enables the authors to 

 teach some very important theorems in partial 

 differentiation which the average academical 

 student overlooks in his rush and hurry to satisfy 

 the demands of the external examiner. 



The examples are distinctly good, and this 

 feature will undoubtedly appeal to teachers of 

 pure as well as applied science. 



At the end there is the usual collection of tables, 

 with the usual superfluous duplication of log- 

 arithms and antilogarithms, squares and square 

 roots, sines and cosines, and the usual short- 

 comings in the absence of tables of logarithms of 

 reciprocals, and in the fact that the tables of 

 squares do not give correct results when applied 

 to the squares of integers. G. H. B. 



OUR BOOKSHELF. 



Steam Turbines. By J. A. Moyer. Third edition, 

 revised and enlarged. Pp. xi + 4(38. (New 

 York : J. Wiley and Sons, Inc. ; London : 

 Chapman and Hall, Ltd., 1917.) Price 165. 6d. 

 net. 



This book was first published in 1908; the addi- 

 tions made in the present edition have been mainly 

 in the line of new applications. The book opens 

 with some historical descriptions, followed by a 

 brief section dealing with the elementary theory pf 

 heat, including explanations of entropy diagrams. 

 The following chapters take up the design of 

 nozzles and blades, and descriptions of commer- 

 cial types of turbines. 



The treatment of low-pressure, mixed pressure, 

 bleeder, and marine turbines occupies separate 

 chapters. Of these, the section dealing with the 

 marine turbine is least satisfactory; the author's 

 bias towards certain types is apparent here and 

 elsewhere in the volume. Thus no mention is 

 made of the Ljungstrom turbine, despite its 

 importance, and in the marine section justice is 

 not done to types of reduction gear other than 

 the Westinghouse floating-frame type. Hydrau- 

 lic transmission is not mentioned, and electrical 

 transmission is dismissed in a few inadequate 

 lines. There is a chapter on steam turbine 

 economics giving information on cost of plant, 

 maintenance and running; this information is of 

 interest and is frequently omitted in I>iilisli uxt- 

 books. Other chapters deal w ith stiesseN in i ings, 

 drums, etc., and include a few words on the 

 critical speeds of loaded shafts. In describing 

 testing arrangements, power is to be measured by 

 Prony or water brake, or by electrical appliances ; 

 shaft-horse-power of marine turbines and its 

 measurement by torsion-meter are not treated. 

 Another chapter gives some information regarding 

 the gas turbine, and might well have been omitted. 



