August 25, 1910] 



NATURE 



231 



probably have to be explained elsewhere at greater 

 length than is possible in this review ; for this reason it 

 is useful to have a name for the result, and I call 

 it the Principle of Independence of Height. It is, of 

 course, liable to modification in consequence of skin 

 friction and other causes. In the meantime, it is an 

 error, into which it is easy to fall, to imagine that 

 because the weight has a moment about the centre of 

 pressure, the aerodrome will swing about that point. 

 It will acquire angular momentum about that point by 

 slipping sideways without rotating. To examine the 

 tendency to rotation, moments must be taken about 

 the centre of gravity. 



The mistake was indeed a very excusable one, but 

 the wording of such statements as 



"The force G,E and the angle ^ produce a com- 

 ponent 0,D." '"Which is the best way to obtain a 

 low centre of gravity ? The oldest method was to 

 arrange the planes so that they formed an obtuse 

 dihedral angle," 



hardly tends to make matters clearer. 



The book contains much descriptive matter regard- 

 ing motors, the fuselage, and methods of starting and 

 landing, but the author would have been more con- 

 vincing if he had been less dogmatic in the chapter 

 on "The Future" in his attacks on the ornithopter 

 and helicopter, and his claims for the monoplane as 

 against the biplane. 



We hope the criticisms contained in this review will 

 not deter Messrs. Hubbard and Ledeboer from mak- 

 ing further contributions to our aeronautical literature. 

 So many books have recently appeared in France of 

 about the same size and character as " How to Build 

 an Aeroplane" that English translations are at pre- 

 i«ent particularly useful in giving some insight into 

 the state of progress on the other side of the Channel. 



Theoretical considerations of all kinds have been 

 carefully avoided in .Mr. Morgan's little book (3), 

 which deals purely with the details of construction 

 of a biplane glider. Now that public attention has 

 been centred on record-breaking flights, it is pecu- 

 liarly important that the initial requirements for 

 "learning to fly" should be brought before our notice, 

 and the author strongly emphasises in his preface the 

 fact that all our most successful flyers have com- 

 menced with gliders before taking to motor-driven 

 machines, the W'right brothers having spent no fewer 

 than three years in gliding flights. The author shows 

 how anyone can build a glider of the type developed 

 by Octave Chanute at a cost for the materials of 

 about 2I. or 3Z., and it is much to be hoped that the 

 book will induce would-be aviators to start in the 

 right way. 



M. Paul Raybaud's pamphlet (4) of twentv-four 

 pages is intended to advance certain views regarding 

 air resistance, such as, for example, that the air 

 resistance on a moving surface does not act normally 

 to the surface, but in a direction determined by the 

 law of equality of action and reaction, that the centre 

 of pressure of a plane area is fixed relative to the 

 plane, that if any area is projected on a plane per- 

 pendicular to the line ofr relative motion, the projec- 

 tion of the centre of pressure is the centre of pressure 

 NO. 2130, VOL. 84] 



of the projection (p. 9), and so forth. The arguments 

 are of a superficial character, such as " it is evident " 

 (p. 9), and when it comes to explaining the behaviour 

 of a plane let fall obliquely (p. 13), he is compelled to 

 introduce a force Q, which is statically equivalent to 

 admitting a shifting of the centre of pressure, con- 

 trary to the previous statements. 



Histories of balloons have been published in France 

 at various times, some of them illustrated by grotesque 

 figures of flving machines imagined or proposed. M. 

 G. Besan^"on has now given us, in a small pocket- 

 book (5), a pretty complete history of the actual de- 

 velopment of aerial navigation from Galileo's experi- 

 ments on the density of the atmosphere and Mont- 

 golfier's discovery of the balloon down to Bleriot's 

 cross-Channel flight. The first section, which deals 

 with balloons, contains a brief account of the con- 

 struction of their envelopes, of motors and propellers, 

 and a reference to the advantages and disadvantages 

 of various gases for the purpose of inflation. 



Profs. Painlev^ and Borel (6), on the other hand, 

 condense their historical introduction into the first 

 twenty pages, where they divide the history into four 

 periods, namely, the legendary period, the heroic 

 period, the .scientific period, and the industrial period. 

 They discuss the laws of air resistance, and briefly 

 refer to the well-known controversy on the sine law 

 versus the sine squared law, and the discussion em- 

 braces not only aeroplanes, but also bird-flight, 

 ornithopters, and helicopters. Stability is referred to, 

 but not at great length ; the property which we have 

 described as the principle of independence of height is, 

 however, mentioned. In an appendix of more than 

 eighty pages, ' certain elementary applications of 

 mechanical principles are discussed at greater length 

 than would be possible in the text. 



The term " aerial navigation" is now used in so 

 wide a sense that it is necessary to explain that Prof. 

 .•\dolf Marcusc's article, "Navigation in der Luft " (7), 

 deals with navigation proper, or the steering of a 

 dirigible by means of charts and geodetic and astro- 

 nomical observations. It is a general summary of 

 progress made up until the autumn of 1909, in a 

 subject which is much studied in Germany, but is 

 altogether neglected in England. The author distin- 

 guishes three methods of place-determination, giving 

 rise to terrestrial, astronomical, and magnetic naviga- 

 tion ; of these the first three will be readily under- 

 stood, while the third embraces not only steering by 

 the compasses, but the determination of position by 

 observation of the magnetic elements and the use of 

 magnetic charts. 



We now come to two papers which represent sub- 

 stantial progress in developing mathematical theories 

 of equilibrium and stability. Prof. Marcel Brillouin's 

 paper on metacentric curves and surfaces (8) is an 

 important contribution to the theory of statical 

 equilibrium and stability. When an aeroplane is mov- 

 ing uniformly and the lines of action of the resultant 

 thrust are plotted relative to the aeroplane for different 

 inclinations of the relative wind these lines will envelop 

 a curve whch the author calls the metacentric curve. 

 Diagram^ are given of these curves for different 

 arrangements of two planes, showing that they are 



