RECENT ADVANCES IN SCIENCE 15 



senting the resistance forces and couples in aeroplane flight 

 render it doubly improbable that general integrals are obtain- 

 able. Two methods suggest themselves. One is an extension 

 of that used in the discussion of stability, and consists in assum- 

 ing that the disturbed motion differs only slightly from the 

 steady flight. The other is based on the method of initial 

 motions, and attempts to solve the problem by means of ex- 

 panding all the variable quantities in ascending powers of the 

 time as measured from the instant when the steady flight is 

 disturbed, and then equating coefficients of powers of the time 

 in the equations of motion. 



Both methods have their advantages and disadvantages. 

 The former needs very much arithmetic, and is, after all, only 

 applicable to a very restricted domain of divergence from the 

 steady flight. The latter has the advantage that with suffi- 

 cient labour it will yield results for any divergence from steady 

 flight, yet it has the disadvantage that the algebra is very 

 involved, and that no beautiful symmetrical results are pos- 

 sible in terms of determinants. Both methods have already 

 been used — the former by E. B. Wilson in America, the latter 

 by the writer of these notes. In an account of a " Symposium 

 on Aeronautics" (Proc. Amer. Phil. Soc. lvi. 191 7, 161-257), 

 Wilson discusses the question in some detail. Other informa- 

 tion of value in aeronautics is to be found in the symposium. 



The construction of aeroplane wings and other frameworks 

 liable to great stresses has given rise to much work on the 

 behaviour of beams under loads. The following are some 

 recent investigations : 



W. L. Cowley and H. Levy, Critical Loading of Struts and Structures, Proc. 



Roy. Soc. 94, A, 1917, 405-21. 

 W. H. Barley, and H. A. Webb, Design of Aeroplane Struts, Aer. Journ. xxii. 



1918, 313-29. 

 H. A. Webb, and J. R. Airey, The Practical Importance of Confluent Hypergeo- 



metric Functions, Phil. Mag. vi, 35, 191 8, 129-41. 



In this paper it is shown that the use of the functions there 

 tabulated renders possible the solution of many problems, 

 such as that of the vibration of a circular disc, or the whirling 

 speed of a shaft, and many aeronautical problems : 



H. H. Jeffcott, The Periods of Lateral Vibrations of Loaded Shafts, Proc. Roy. 



Soc. 95, A, 1918, 106-15. 

 J. J. Guest, Curved Beams, Proc. Roy. Soc. 95, A, 19 18, 1-2 1. 

 J. Prescott, The Buckling of Deep Beams, Phil. Mag. vi, 35, 1918, 297-314. 



