January 6, 192 1] 



NATURE 



593 



developed a theory in which half the final momen- 

 tum of the slip stream was added in front of the 

 propeller disc. Lanchester applied the idea to 

 aerial screws, but, with his sense of the physical 

 incompleteness of the theory, he did not accept 

 "half" as anything more than an approximation! 

 The Fage-CoUins theory referred to on p. 19 is 

 merely a theory which suppwses that wing 

 elements modified by the assumption of an inflow 

 velocity can be made to agree with an experi- 

 mental check by the choice of a certain constant 

 closely related to Froude's half. 



It is known that a second approximation so 

 made is important, but it is also realised that 

 every unknown quantity, such as the effect of the 

 ends of the blades, their shape, and the changes 

 in type of flow due to centrifugal action, are at- 

 tributed to inflow. Wood and Glauert devised a 

 scheme for the experimental determination of "in- 

 flow " without the above complications, and de- 

 scribed their tests in the report referred to by Mr. 

 Fage. It was pointed out that a logical exten- 

 sion of the aerofoil theory would be obtained by 

 placing a succession of aerofoils behind each other 

 in a wind channel so that some of them were 

 working in the disturbed air of blades further 

 into the wind. The relative positions of the blades 

 to correspond with an airscrew were not found 

 to be inconvenient for experiment, and, finally, 

 after tests in a wind channel, a further approxi- 

 mation was made which brought theory nearer to 

 the truth. The differences from the Fage-CoUins 

 theory are too great to be dismissed as unimport- 

 iiii, ind show that there still remain further 

 factors to be investigated. 



This fundamental step in analysis of airscrew 

 performance is the one dismissed by Mr. Fage in 

 less than twopagesof his book, and his closing re- 

 marks indicate the rather illogical contention that 

 because other points still remain to be explained, 

 the new experiments are of little use. This should 

 surely not be the attitude of research workers at 

 the National Physical Laboratory. It is to be 

 hoped that it does not rcpre.sent the views of the 

 bite Advisory Committee for Aeronautics, to which 

 most of the items of work at the National Physical 

 Laboratory were presented before publication. 



This example has l)een taken at some length 

 a>» typical of the b<x)k, which, on the theoretical 

 side, is sketchy throughout. Perhaps one is 

 irmpted to be too critical of a work which largely 

 records war activity. On the other hand, where 

 are we to look for the progressive development of 

 knowledge in aeronautics if such places as the 

 National Physical laboratory fail us? Is the new 

 Aeronautical Research Committee still accumulat- 

 NO. 2671, VOL. 106] 



ing a great mass of undigested material, of which 

 Mr. Page's contribution is a part, or is it keep- 

 ing its activities for advice on the general lines 

 of experiment and research? One is not too hope- 

 ful that the incubus of the war is being thrown off 

 any more completely by his employers than by 

 the author of the book under notice. 



Nomography. 



A First Course in Xoniographv. By Dr. S. 

 Brodetsky. (Bell's Mathematical Series. 

 Advanced Section.) Pp. xii+135. (London: 

 G. Bell and Sons, Ltd., 1920.) Price 105. net. 



THE subject of nomography may be shortly 

 described as dealing with the graphic repre- 

 sentation of formulae. As developed by M. 

 d'Ocagne, there has been an increasing interest 

 taken in recent years in the application of its 

 methods to facilitating calculation in engineering 

 and scientific work generally. 



In this "First Course," nomography is arbi- 

 trarily restricted to graphic representation in 

 parallel co-ordinates, the resulting diagram being 

 read by the collineation of points. It is true that 

 there is a growing tendency to use the word 

 " nomogram " for such a representation only ; but, 

 apart from nomenclature, there are grave disad- 

 vantages in this isolated treatment. 



For a clear and intelligent appreciation of the 

 subject it is a matter of great importance to keep 

 in the forefront the principle of duality, the con- 

 nection between graphic representation in Cartes- 

 ian co-ordinates (the intersection diagram) and 

 that in parallel co-ordinates (the alignment 

 diagram), and the transformation of the one into 

 the other. 



Throughout the book the explanations are clear 

 and the diagrams excellent, but the former appear 

 occasionally to be unnecessarily diffuse. Nearly fifty 

 pages out of a total of fewer than one hundred 

 and fifty are mainly occupied with a minute de- 

 scription of nomograms for performing simple 

 addition and .subtraction, a purpose for which they 

 are seldom practically used. Some introductory 

 reference to them is certainly advisable, but all 

 that is necessary might quite well have been given 

 in a few pages and a couple of illustrations. 



Some of the space so saved could with advan- 

 tage have been devoted to a description of the 

 direct-reading four-variable nomogram, which is 

 a combination of two parallel scales and a net- 

 work. To this no reference is made, but it is of 

 great importance in practical work. 



Diversity of notations is a continual source of 

 irritation in such subjects, but, of course, is .ii 



