296 



NA TURE 



[March 9, 1922 



invention made in the course of his work in order to 

 exploit it commercially, he is rarely in a position 

 adequately to carry this through, either from want of 

 time on account of his normal duties, or from want of 

 business ability. The inventor had the alternative 

 in the event of a process proving an important one 

 either to leave the Government Service and devote 

 himself to his patent, or to remain in the Service and 

 see the success of his invention jeopardised in its civil 

 applications. The exploitation of Government-owned 

 inventions by business men who have had experience 

 in work of this kind is the only other way out of the 

 difficulty that can readily be seen, and it is to be hoped 

 that the confidence of the Committee will be justified 

 by suitable public-spirited men coming forward to take 

 up the work. 



The Report bears internal evidence of much thought 

 and consideration of diverse opinions, and thanks are 

 due to members of the Committee for their hopeful 

 effort to suggest an organisation which, by settling 

 claims and disputes definitely and rapidly, will thereby 

 remove an impediment to progress in investigation 

 and at the same time afford the worker the opportunity 

 of stating his case. 



Principles and Problems of Aeronautics. 



The Mechanical Principles of the Aeroplane. By 

 Dr. S. Brodetsky. Pp. vii + 272. (London: J. 

 and A. Churchill, 192 1.) 21s. net. 



THE entry of Dr. Brodetsky into the ranks of 

 workers on aeronautical topics marks an 

 important development in the higher study of aerial 

 navigation. Why the achievements of modern aviation 

 have not from the outset been built up on a sub- 

 structure of purely abstract mathematical theory 

 such as has arisen concomitantly with other branches 

 of physics and engineering is difficult to understand. 

 The behaviour of laminae and other bodies moving 

 through a medium under assumed laws of resistance, 

 whether artificially propelled or otherwise, opens up 

 a vast collection of problems which might well have 

 occupied the attention of mathematicians and been 

 illustrated by experiments with models long before 

 the evolution of the full-sized aeroplane. Instead of 

 this being done, flying machines have been built, 

 flown, wrecked, and their pilots killed, by designers 

 who have not even fully appreciated such elementary 

 facts as that when an aeroplane is moving with uniform 

 velocity the forces acting on it must be in equilibrium, 

 that three forces in equilibrium must meet in a point, 

 that an aeroplane has six degrees of freedom, that 

 stability and equilibrium are not the same thing, and 

 so forth. Whether the Tarrant triplane could have 

 NO. 2732, VOL. 109] 



been saved by a full appreciation on the part of its 

 pilots oi the validity of the equation of initial angular 

 acceleration, W2^/^/2 ^ ]yi^ qi- numerous aviators saved 

 from death by a better knowledge of the forces and 

 couples on which longitudinal and lateral stability 

 depend, are debatable questions. Meanwhile mathe- 

 maticians of repute have attacked the writer of this 

 review for intimating that a fuller theoretical study 

 of the problem should be undertaken. 



The National Physical Laboratory and the Royal 

 Aircraft Establishment have absorbed many of the 

 most enlightened of our university graduates who 

 are competent to study aeronautical problems, afid 

 they are doing excellent work there. But, unfortun- 

 ately, the amount of constructional work that had 

 been going on while the mathematicians of our univer- 

 sities were making and marking examination questions, 

 with their eyes shut to the outside world, has thrust 

 on our Government institutions vast arrears of ques- 

 tions arising out of the engineering and physical 

 difficulties associated with aviation. It is therefore 

 not surprising that scarcely any one previous to Dr. 

 Brodetsky has started at the opposite end and tried 

 to fathom the capabilities of pure mathematical reason- 

 ing as distinct from experiment in throwing light on 

 the study of aeronautical problems. 



A notable exception is afforded by Mr. Lanchester, 

 whose two volumes certainly represent a genuine 

 attempt to investigate the behaviour of aeroplanes 

 as deduced from a priori reasoning. But the subject 

 was bristling with mathematical difficulties of a cut- 

 and-dried character quite outside the scope of Lan- 

 chester's resources, and no mathematician would take 

 up the challenges so oft repeated in Nature until 

 Dr. Brodetsky came on the scene. Contrast this 

 state of affairs with the past history of electrical engin- 

 eering, in which subject mathematical tripos candi- 

 dates were being worried with solutions of Laplace's 

 equations for infinitely long charged cylinders and condi- 

 tions for solenoidal and lamellar magnets long before 

 Lord Kelvin presented Peterhouse with its electric light. 



In recent years nearly every publisher has decided 

 that there is a demand for an up-to-date book on 

 aeronautics, and has got some one to write one. In 

 all these books the effects of the policy of " putting 

 the cart before the horse" is painfully evident. The 

 mathematics is usually of a very elementary and 

 insufficient character until we are confronted with 

 the invariable chapter headed " Stabihty, Mathe- 

 matical Theory." This is usually nothing more or less 

 than a mutilated copy of part of the " Science Mono- 

 graph " on " Stability in Aviation " by the present 

 writer, accompanied by a misuse of signs and symbols 

 and a total disregard for all the accepted doctrines 



