546 SCIENCE PROGRESS 



it is proved that the " terminal " motion is in the nature of a 

 fluctuation about a straight line inclined to the vertical (see 

 also Science Progress, Oct. 191 8, p. 185). 



The motion of the balloon forms the subject of an elaborate 

 investigation by F. Jentzsch-Grafe : " Zur Mechanik des 

 Freiballons " (Phys. Zeit. 1919, 20, 320-8). After quoting the 

 ordinary theory of a body moving under a constant force—the 

 lifting power — and the air resistance, which is taken to vary 

 as the square of the speed, the author discusses the steady 

 motion upwards, the greatest height attainable b}^ a given 

 balloon, and the time taken to reach this height. The tem- 

 perature effect is also taken into account. The interesting 

 remark is added that the results were worked out in 191 5 

 and used in the German Army. 



Corresponding work on aeroplane motion is contained in 

 a series of short papers by A. Rateau (Comptes Rendus, 1919, 

 168, 1 142-7, 1246-51, 1 295-1 30 1 ; 169, 156-61). The theory 

 of steady horizontal flight at various altitudes is followed by 

 the determination of the greatest height at which such flight 

 is possible with a given machine. Then comes an investigation 

 of rectilineal climbing and the maximum vertical rate of climb, 

 with an application of the theory in a numerical example. 



Bairstow's Wilbur Wright Lecture, already quoted above, 

 is well described by its title : " Progress of Aviation in the 

 War Period : Some Items of Scientific and Technical Interest." 

 In addition to the question of model and full-scale experiments, 

 the author discusses the control of aeroplanes and the oscilla- 

 tions of stable and unstable aeroplanes when left to themselves. 

 The reader should also refer to the Technical Report of the 

 Advisory Committee for Aeronautics for the year 191 3— 14, which 

 has been recently released for publication, and which contains 

 valuable information on theoretical and practical aerodynamics, 

 aeroplane control and stability, and other matters of interest 

 in the mechanics of the airship and aeroplane. 



The problem of struts in aeroplane construction has already 

 been referred to in a -former article (Science Progress, July 

 1919, p. 15). A marked advance in the mathematical methods 

 available for the study of the flexure of beams, the torsion of 

 cylinders (as well as the motion of a fluid round a cylinder), 

 is represented "by the paper by L. Bairstow and A. Berry : 

 " Two-Dimensional Solutions of Poisson's and Laplace's Equa- 

 tions " (Proc. Roy. Soc, 1919, 95, A, 457-75). The method of 

 the paper depends on the well-known Irydrodynamical theorem 

 that " any irrotational acyclic motion can be reproduced by 

 an appropriate choice of simple sources round the fixed boun- 

 daries." This is essentially a theorem in pure mathematics, 

 which can be interpreted in terms of elasticity as well as of 



