366 



NA TURE 



[September 23, 1909 



what bird it is to the voice of which he is listening, for 

 in the process, even if it be a long one, he will learn 

 a good deal about the bird and its habits. But some 

 learners are less gifted than others with a capacity for 

 listening carefully, and have little or no musical ear, 

 and a book like this may be of good service to these. 

 Dr. Voigt's method is a very sensible one ; he makes 

 no great use of musical notation, but has invented a 

 notation of his own which is likely to be much more 

 useful to the ordinary observer. B)' a series of dots 

 and dashes, inclining or curving up or down if neces- 

 sary, he contrives to give a very fair idea of the char- 

 acter of the notes he wishes to represent, and also of 

 their tendency to rise and fall. In some cases, e.g. 

 in that of the swallow, he does not make use of either 

 kind of notation, simply because neither would be any 

 real help. His descriptions of the songs seem remark- 

 ably accurate. We have tested them in the case of 

 many of the small warblers, which are among the 

 most difficult to describe, and have invariably found 

 them excellent, and the tendency of particular indi- 

 viduals of a species to vary the utterance is also duly 

 noted. Thus of the marsh warbler {Acroccphahts 

 pahistris). Dr. Voigt says that it has troubled him 

 more in the way of variation than any other species. 

 In writing of this species he seems to have omitted 

 the peculiar alarm-note uttered when an intruder is 

 near the nest, but as a rule something is said of alarm- 

 and call-notes. On the \\hole, we consider this book 

 the most useful practical manual we have met. 



\\\ W. F. 



The Force of the Wind. By Prof. Herbert Chatley. 



Pp. viii + Sj; illustrated. (London: C. Griffin and 



Co., Ltd., 1909.) Price 3s. net. 

 Prof. Chatley has evidently devoted himself to a 

 study of hydrodynamics and of its literature. He has 

 attempted to boil down into an inordinately small 

 compass, so as to be useful to engineers, an exposi- 

 tion of one of the most difficult and elusive subjects 

 with which either the engineer or the mathematician 

 has to deal. Explanation of principles which might 

 be useful to a novice is replaced by a multiplicitv of 

 formulas, which are flung at the reader with but little 

 regard to dimensions or units. Numerical examples 

 which, even in the case of clear exposition, always 

 assist the student who wishes to apply a formula to 

 any case in which he is interested are entirely absent. 



Much information is collected, and numerous 

 authorities are cited, but the result can hardly be 

 considered satisfactory. 



LETTERS TO THE EDITOR. 



[TIic Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neither can he undertake 

 to return, or to correspond with th& writers of, rejected 

 manuscripts intended for this or any other part o/Naturk. 

 A^p notice is taken of anonynwus communications.] 



Stability of Aeroplanes. 



I HAVE recently been occupied with a comparative study 

 of the theories of stability of aeroplanes deduced by Prof. 

 Bryan, Captain Ferber, and Mr. F. W. Lanchester, and 

 have just noticed a parallelism between the formulae of 

 Ferber and Lanchester which is strongly corroborative of 

 the practical application of both. 



In Ferber's " Les Progr^s de rAviation par le vol 

 Plane " {Revue d'.irtillerie, November, 1905) he deduces 

 from an extension of Prof. Bryan's analysis a formula for 

 ihe conditions of longitudinal stability 



Vi „ 



where P is the total mass of the machine, B is the 

 moment of inertia about a transverse axis through the 

 NO. 2082, VOL. 81] 



eg, S is the area of the supporting surfaces, 6 is the 

 distance of the centre of pressure from the centre of area 

 of the supporting surfaces, and K is an aerodynamic 

 constant (0-7) kilometre-second system. 



Lanchester 's equation for longitudinal stability is 



\K tCpa^J 



where 1 is the distance from the centre of pressure on a 

 tail plane to the C^, H„ is the kinetic head of the machine 

 corresponding to its ndimal velocity, y is the normal 

 gliding angle, I is the moment of inertia about a trans- 



weight 



verse axis through the Ct', K = ; ; ; — r--r,, and trie 



° * (normal velocity) 



denominator of the second term in the expression within 

 brackets is the lift on the tail plane (ft. -lbs. -sec. -units) 

 divided by the square of the velocity. 



Now the mass varies as the lifting force, which again ' 

 varies as the square of the velocity, so that P" cc H,,-. 



The torque which restores the machine to equilibrium 

 depends in the case of a machine without a tail plane on 

 b, and with a tail plane on /, so that if Lanchester's 

 form is to refer to a machine without a tail plane b must 

 be substituted for /. 



B and I are identical in kind. 



K varies as the lift -;- square of the normal velocity, 

 and since the lift varies as the product of the area and 

 the square of the velocity, K cc S. 



The term relating to the tail plane is peculiar to that 

 type studied by Lanchester, so that it can be omitted from 

 our comparison. 



Tan 7 is a constant for any one type of surface. 



Hence it will be seen that the two formulre are exactly 

 of the same form, and it only remains exactly to deter- 

 mine the appropriate constants to discover if the two ex- 

 pressions can be made identical. 



As has been pointed out by Prof. Bryan, everything 

 (except for a machine with a tail) depends on b, and unless 

 db/da, where a is the angle of attack, is negative, the 

 torque will not produce equilibrium. The Government's 

 committee is, I believe, giving this attention. 



I would further point out that the variations in velocity 

 leading to Lanchester's " phugoid oscillations," and the 

 oscillations due to the variation of b with a, will serve to 

 explain the two types of oscillation, respectively of long 

 and short periods, observed by Prof. Bryan and Mr. W. E. 

 Williams, and shown by the former to be deducible from 

 the equations of motion. Herbert Chatley. 



Imperial Railways of North China, Engineering 

 and Mining College, August 24. 



It is dangerous to draw conclusions from half- 

 finished investigations, and anything 1 may now say must 

 be subject to confirmation or modification when I have 

 completely disposed of the mathematical theory of stability, 

 both longitudinal and lateral, as I hope to do in a very 

 few months unless any further pressure of professorial 

 duties necessitates again hanging the matter up indefinitely. 

 But results which I have recently obtained seem rather 

 to corroborate instead of contradicting Lanchester's equa- 

 tion as holding good, subject to suitable assumptions and 

 for the types of machine to which such a formula is applic- 

 able. I may state tliat 1 have alreadv obtained expressions 

 for the conditions that the quick or slow small motions 

 may be subsident or oscillatory, and for their coefficients 

 of subsidence in the first case and their periods and moduli 

 of decay in the second. This applies to longitudinal 

 stability, and a similar investigation is in progress regard- 

 ing lateral stability. 



It will, I believe, be easy to explain also why 

 Lanchester's method, which to a mathematician certainly 

 appears wanting in rigour, may lead to a correct result. 

 But the matter will, I hope, be cleared up very shortly. 



In the meanwhile, Prof. Chatley's comparative studies 

 appear to indicate that we are within measurable distance 

 of obtaining consistent results from widely differing 

 methods. 



G. II. Bryan. 



