November 14, 1912] 



NATURE 



503 



than Bow's notation, in which the spaces between 

 the members of a structure are designated by a 

 letter or numeral. The concluding third of the 

 book contains a short dissertation on reinforced 

 concrete (in which the ratio of the moduli of 

 elasticity of steel to concrete is taken at the low 

 value of 10), and this is followed by tables usually 

 found, in engineers' handbooks on the geometrical 

 properties of structural shapes, such as moments 

 of inertia. There are many blemishes due to im- 

 perfect translation, and we find such expressions 

 as " lo-fold security" for "factor of safety of 

 ten." The translation does not extend to weights 

 and measures, which are in the metric system. 



(2) The preface to this volume is, for the most 

 part, a reprint of remarks made by M. Maurice 

 d'Ocagne, Ingenieur en chef des Fonts et 

 Chaussees, at the Fourth International Congress of 

 Mathematicians, in Rome, 1908. In this paper 

 he defines the word "nomogramme," which is 

 probably new to most English mathematicians, 

 the nearest English equivalent being an abacus, 

 known as an instrument for performing calcula- 

 tions by balls sliding on wires, which are still 

 employed in Russia, China, and Japan. M. 

 d'Ocagne has brought forward this system of 

 graphical calculation by published researches 

 extending over twenty-five years, and the 

 author of this work employs the method for 

 solving problems in military engineering, though 

 many of the examples are of wider applica- 

 tion, and are of extended use in the solution of 

 equations of three or four (or more) variables. 

 The interest in the work would therefore lie chiefly 

 in the method as such, the particular applications 

 of the method to the solution of equations used by 

 the military engineer being of secondary import- 

 ance, though, as a handbook for rapid calculation 

 within the limits of the chosen field of utility, it 

 would certainly serve a useful purpose to many. 

 The reader will doubtless find himself constructing 

 nomogrammes to suit particular problems of his 

 own, and thus the work before us is extremely 

 suggestive, and a fruitful stimulus to the use of a 

 graphical method of varied application. 



There are eighty-five nomogrammes in the work, 

 each on a separate sheet and consisting for the 

 most part of straight lines upon which divisions 

 arc marked. A loose celluloid sheet marked off 

 in rectangular coordinates is provided for laying 

 upon the nomogramme, and upon placing it in 

 such a position that the known values of the 

 variables in the equation are cut by the lines, the 

 value of the unknown variable may be ascertained 

 by intersection upon the scale provided for that 

 variable. Thus, for example, the solution of plane 

 triangles may be taken as being a problem of 

 XO. 2246, VOL. 90] 



general application. Given the two sides and in- 

 cluded angle, the opposite side [a] may be found 

 directly by the application of the rectangular co- 

 ordinates to the nomogramme ; in other words, 

 the equation 0^ = b^ + c- — 2ab cos 4 may be solved 

 for all values of h, c and A. Besides the usual 

 problems in mensuration, the safe loads on 

 columns for given values of the ratio of length 

 to least radius of gyration for various materials, 

 the bending of beams, stresses in roof trusses and 

 bridges and numerous other problems may be 

 solved without calculation. The printing of the 

 scales on the nomogrammes leaves much to be 

 desired, but the work as a whole is a most interest- 

 ing contribution to graphical methods of solution. 



(3) This little book is made up of twenty-five 

 single perforated sheets bearing upon each a con- 

 cise description of a simple laboratory experiment 

 in applied mechanics with an illustration of the 

 apparatus. The experiments are of the usual kind 

 for the elementary mechanical laboratory and com- 

 prise statics, efficiency of lifting machines and 

 friction, forces in braced structures, moduli of 

 elasticity, spring vibrations, pendulum, and others. 

 Prof. Morley states that they are selected from in- 

 struction sheets used in his laboratory, and may 

 be usefully employed in conjunction with his text- 

 books on elementary applied mechanics. However 

 opinions may differ concerning the expediency of 

 giving a student cut-and-dried directions concern- 

 ing his laboratory work and leaving little to his 

 own judgment and talent, those who favour this 

 plan of instruction will find all that they desire 

 in these well-arranged experiments. It saves much 

 time and needless explanation on the part of the 

 demonstrator to have the experiments written out, 

 and as these are selected by experienced teachers 

 they should prove useful in the elementary 

 laboratory. 



(4) This work contains a mass of constructional 

 detail on the gas engine which should find favour 

 with engineers and draughtsmen engaged in the 

 design of such motors. It represents the results 

 of much practical experience, and on the part of 

 both the author and translator it shows a very care- 

 ful scrutiny of the best engineering practice. The 

 thermodynamics of the subject is somewhat 

 neglected, but this omission is counterbalanced by 

 the exhaustive treatment of the forces developed 

 by the engine when running. The effect of the 

 inertia of the reciprocating parts, turning moment 

 diagrams for calculating fly-wheel masses, and 

 balancing, are discussed with the view of assisting 

 the draughtsman in his design, and the effects of 

 various combinations of cylinders receive more 

 attention than usual in works of this kind. Minute 

 details are set forth with painstaking care, and 



