14 SCIENCE PROGRESS 



The question of notation in aeronautics is now also one of 

 pedagogical interest, for the great developments that all 

 interested in aviation are expecting in the near future are also 

 mirrored in our academic life. In several colleges and univer- 

 sities provision has been or is being made for aeronautical 

 teaching. In at least two universities courses of lectures have 

 been delivered on the rigid dynamics and the stability of the 

 aeroplane, and the effect will no doubt take the form of in- 

 creased theoretical and practical activity in aeronautical re- 

 search. 



A notable advance in the study of aerodynamics by mathe- 

 matical analysis is indicated in a brief note by Bryan (Aer. 

 Journ. xxii. 191 8, 255-7) containing the equations of motion 

 for a compressible fluid. A differential equation is deduced 

 for the velocity potential — an extension of the well-known 

 Laplacian form when the fluid is incompressible. If mathe- 

 matical analysis is capable of attacking the problem of the 

 compressible fluid in practical applications, then we have 

 another line of research that should yield results of great value. 



Mathematicians in general are paying more attention to 

 the mechanics of the aeroplane, and an interesting sign of the 

 times is the paper by W. Burnside (Proc. Lond. Math. Soc. 

 xvii. 191 8, 42-53), entitled : " On the Efficiency of a Surface 

 of Pressure Discontinuity regarded as a Propeller." 



A paper of considerable interest at the present juncture in 

 aeroplane development is one by W. F. Durand {Aer. Journ. 

 xxii. 191 8, 183-201) on " Some Outstanding Problems in 

 Aeronautics. " Whereas the problem of stability has been studied 

 theoretically and practically with success, not much has yet 

 been done on the control of aeroplanes. 



The problem of aeroplane control is, of course, intimately 

 bound up with that of the behaviour of an aeroplane when its 

 steady flight is disturbed, either by a change -in the state of 

 the engine, or by a change in the machine, or by a change in the 

 air conditions produced by a sudden squall or a modification 

 of the velocity and direction of the wind. We can say, a priori, 

 that any attempt at a complete solution of this problem, applic- 

 able to considerable changes in the condition of flight, must end 

 in failure. Not much success has yet been attained in even 

 the simple problems of three-dimensional rigid dynamics, and 

 the complication imported by the involved functions repre- 



