March 17, 1910] 



NATURE 



69 



reason is not far to seek. The air motion known as 

 wind is not even approximately steady and uniform until 

 at least a height of looo feet is reached, and on some 

 days there is no uniformity about it until much greater 

 heights are attained. The supposition made, therefore, 

 that the motion is uniform is incorrect, and if this assump- 

 tion has been made by Prof. Bryan it limits the use of 

 his equations to times of perfect calm. 



He has probably also assumed that the flying machine, 

 or at least the separate parts of it, may be treated as a 

 rigid body. The small gliders made of thin mica, and 

 described by Mr. Lanchester, may, no doubt, be treated 

 as rigid, but cloth or canvas forms an important part of 

 an aeroplane, and however tightly it may be stretched it 

 certainly is not equivalent to a rigid sheet, but must yield 

 under varying pressure. 



My practical experience on this subject is with kites, 

 and although there are fundamental differences between a 

 kite and a flying machine, there are many points of 

 resemblance, and it is probable that if the question of the 

 stability of a kite could be completely elucidated, that of 

 the stability of an aefoplane would follow. Almost any 

 kite will fly in a steady wind of moderate velocitj-, but, so 

 far as I know, there is no kite that will remain stable 

 when the wind increases beyond a certain value. The 

 limit with the kites used here is about forty-five to fifty 

 miles an hour at a height of 1500 feet. The question is. 

 Why do they become unstable? There are, perhaps, three 

 reasons. The flying of a kite depends on gravity, for a 

 weightless kite could not fly, as there would be no directive 

 force. As the wind pressures increase, the necessary 

 relationship between the magnitudes of the pressures and 

 the weight is lost, and the kite becomes unstable. A 

 cure, perhaps, lies in increasing the dead weight. 

 Secondly, the stresses produced by the strong wind very 

 likely deform the kite. It is not possible to meet this 

 by increased strength, for increased strength means 

 stronger, and therefore heavier, materials, and hence, un- 

 like a dead weight at the centre of gravity, a greater 

 moment of inertia, which, as I have long known from 

 practical experience, and Mr. Lanchester has shown from 

 the theoretical side, is inimical to stability. Thirdly, it 

 may be that there is a certain critical velocity, like that 

 of water in a pipe, beyond which the motion over the 

 edges of the sails becomes turbulent, and the form of the 

 stream lines suddenly changes. 



These points can best be cleared up by extensive experi- 

 mental work, and I much regret that no such work is 

 being done. W. H. Dines. 



Pyrton Hill. 



It was difficult to prevent my article from running to 

 ten times its present length, and a similar difficulty occurs 

 in this letter. I can only state that the more I have 

 examined the problem of stability the more I have been 

 brought to conclusions exactly the opposite to those ex- 

 pressed in Mr. Dines 's letter. My original view was to 

 limit the mathematical investigation to the formation of 

 the biquadratics and their discriminants, leaving their 

 coefficients to be determined by experiment. In several 

 popular articles I have advocated such experiments. 

 Further experience has shown that there was little prospect 

 of any conclusions of a pract cal character being obtained 

 without a considerable further development of the problem 

 from the mathematical side. 



Moreover, experience has led me to believe that the 

 English practical man is sometimes right when he says 

 that if you cannot get a complete solution of a problem 

 you ought to try to obtain the nearest approach to it that 

 you can, and, further, that an admittedly approximate 

 solution is often more useful than a more complicated 

 exact one. In the present case the methods are perfectly 

 general, and while it would have been futile to start, in 

 Sie first instance, by making the problem too complicated, 

 there is little difficulty in introducing any necessary 

 modifications subsequently. 



In regard to the assumption of uniform relative velocity, 

 surely Mr. Dines is confusing the issues between stability 

 and something else. The very notion of stability implies 

 the existence of a state of equilibrium or of steady motion. 

 The behaviour of an aeroplane or kite in a turbulent 



NO. 2107, VOL. 83] 



atmosphere is a problem, not of stability, but of forced 

 oscillations. The effect of these oscillations is to modify 

 the motion of the kite ; but it is necessary in the theory 

 of forced oscillations to assume as a standard of com- 

 parison the state of equilibrium or steady motion which 

 would exist if the disturbing forces were absent, and the 

 character of the forced oscillations will depend vital'y 

 upon whether this state of equilibrium is stable or unstable. 

 The first thing is to investigate the free oscillations, but 

 there is nothing to prevent the investigation extending to 

 forced oscillations as well. It is only a question of time 

 and opportunit)'. Meanwhile, aviators are performing 

 record flights on aeroplanes which do not satisfy the con- 

 ditions of stability, and Mr. Dines 's turbulent air currents 

 are getting blamed for much that is not their fault. No 

 solution of the problem can be final which does not com- 

 pletely separate the effects of free and forced oscillations. 

 I do not see how this can be done by purely experimental 

 methods of investigation, and surely the questions which 

 Mr. Dines raises in connection with the behaviour of kites 

 refer to this very point. He has, in fact, stated another 

 problem for the mathematician. 



Again, like Mr. Dines, I was at first of opinion that 

 it might be possible to establish a simple connection 

 between the stability of an aeroplane and that of a kite, 

 and I suggested this problem to Mr. Harper. The in- 

 vestigation turned out to be more complicated and less 

 likely to lead to any practical conclusions than was origin- 

 ally anticipated. With so many other problems on hand, 

 it appeared desirable to give this one up for the present. 

 I do not think Mr. Dines will find it possible to obtain 

 an experimental solution. If he can, a great deal of 

 trouble will be saved ; but so many variables enter into 

 the problem that it appears to me necessary to start with 

 some idea as to what the connection is likely to be, i.e. 

 with some kind of a mathematical theory as a starting 

 point. 



When Newton published his " Principia " it would have 

 been an easy matter for a forerunner of Mr. Dines to raise 

 objections to this attempt to solve problems relating to 

 moving bodies by applications of the laws of motion on 

 the ground that the motions must largely depend on air 

 resistance, friction, the earth's rotation, and other causes, 

 and that a solution which did not take all these effects 

 simultaneously into account could be of no practical value. 

 Similarly, it might have been objected that the solution 

 of the problem of stability of ships could not be approached 

 by means of the theory of the metacentre on the ground 

 that it failed ^o take account of wave motion, the velocity 

 of the ship, the effects of the wind, and such resistances 

 as viscosity. I venture to suggest that if the above 

 problems had been attacked by purely experimental methods 

 alone, we might still have been in the dark as to their 

 solutions. 



In my article I alluded to difficulties caused by " want 

 of opportunity," but out of fairness reference ought to 

 have been made to the similar difficulties referred to in 

 Mr. Lanchester 's book. Had his investigations been pub- 

 lished when they were made, a large amount of work 

 might now have been accomplished which is still undone. 



It is only fair also to add that since the appearance of 

 the note I have had some correspondence with the editor 

 of the Aeronautical Journal, and I hope he will succeed in 

 maintaining the same high standard in its published papers 

 of a mathematical character as in its illustrated articles 

 on general aeronautics. G. H. Bryan. 



Colour- Blindness. 



In the issue of N.ature of January 27 there is a dis- 

 cussion of colour-blindness, with particular reference to 

 the case of Mr. John Trattles, whose colour-vision seems 

 to have been difficult to determine. It is not my purpose 

 to discuss the peculiarities of this case, or the methods 

 of examination used by the Board of Trade. As a worker 

 in this branch of science, however, I may be permitted to 

 say that in any case of supposed defective colour-vision 

 there need be no appeal from the opinion of Sir William 

 Abney, who is so justly celebrated on both sides of the 

 .\tlantic for his researches on the perception of colour. 



Since, however, in the case of Mr. Trattles, and possibly 

 in others as well, the evideiKe was not regarded as con- 



