RECENT ADVANCES IN SCIENCE 545 



Wimperis (Aer. Journ. 1919, xxiii. 445-68), and teachers of 

 dynamics should not fail to use the practical problems discussed 

 here in order to give additional force and reality to their lessons 

 on vectors. Two papers of similar interest have been published 

 by L. Dunoyer (Comptes Rendus, 1919, 168, 726-9, 1 102-5). 



If the student finds it difficult to grasp the theory of rota- 

 tional dynamics, he finds it equally difficult to understand the 

 theory of units and dimensions. The elementary treatment of 

 mechanics does not admit of the inclusion of an adequate 

 theory of dimensions, and the result is that many of our 

 students cannot think in any but certain stock units. Thus, 

 e.g., accelerations are almost invariably given in ft./sec. 2 or 

 cm./sec. 2 An acceleration like ten miles an hour each minute 

 would be understood by the better class of student after some 

 little thought — but not instinctively. The mental effort be- 

 comes positively painful when he is asked to apply the idea 

 of units to, say, electricity and magnetism, or to the a priori 

 discussion of fluid resistance. Many attempts have been made 

 recently to render the theory of dimensions clearly and simply — • 

 with varying success. The subject is discussed by H. Levy 

 in his lecture : " From Model to Full Scale in Aeronautics " 

 {Aer. Journ. 1919, xxiii. 326-45, 352-6), in which are treated 

 also the problems of fluid resistance and of vortex motion in a 

 viscous fluid. The theory of dimensions and the value of model 

 experiments in aeronautics are also dealt with by L. Bairstow 

 in his Wilbur Wright Lecture (Aer. Journ. xxiii., supplement 

 to July issue, 19 19), whilst in the same journal W. S. Farren 

 gives an account of full-scale experiments on aeroplanes 

 (xxiii. 34-72, 1 9 19). The theory of screw propellers based on 

 the theory of dimensions and of dynamical similitude is dis- 

 cussed by Amans (Comptes Rendus, 19 19, 168, 822-5). 



Several papers dealing with motion in a resisting medium 

 have been published during the past few months. The approxi- 

 mate path of a bomb dropped by an aeroplane in horizontal 

 flight, valid when the length of the trajectory is about 1,000 

 or 2,000 feet, is deduced by E. B. Wilson : " Note on Bomb 

 Trajectories " (Phys. Rev. (2), 1919, xiii. 305-6), who gives a 

 corrective term to be added to the usual parabolic equation 

 of the path. Another approximate construction for a resisted 

 trajectory consists in combining a parabola for the initial part 

 and the highest portion of the path, with a hyperbola for the 

 remainder, which, as is well known, is asymptotic to a vertical 

 straight line. See M. Risser : " Sur les formules representatives 

 des trajectories " (Comptes Rendus, 1919, 168, 390-2). The 

 rigid dynamics of resisted motion is worked out for the " Two- 

 Dimensional Motion of a Plane Lamina in a Resisting Medium," 

 by S. Brodetsky (Proc. Roy. Soc, 1919, 95, A, 516-32), where 



