NATCJRE 



201 



THURSDAY, MAY i6, 1918. 



. AERODYNAMICS. 

 Resistance of Air. By Lt.-Col. R. de Villamil. 

 Pp. X+192. (London: E. and F. N. Spon, 

 Ltd., 1917.) Price 75. 6d. net. 



THE phenomenon of the resistance of a fluid 

 to a body moving through it is com- 

 pUcated by the fact that it must depend not 

 only on the density and elasticity of the fluid, but 

 also on its viscous properties and on the nature of 

 the relative motion. Mathematical investigations 

 cannot at present lead to results that can be use- 

 fully applied, say, in aeroplane construction. Re- 

 course must be had to experiment. During the 

 past century many results have been obtained 

 bearing on gunnery and navigation, whilst the 

 great progress in aeronautics has been possible 

 only because of the experiments of pioneers like 

 Lilienthal, Langley, and Eiffel, and the systematic 

 wind-tunnel researches at the National Physical 

 Laboratory and elsewhere. 



One of the most generally accepted conclusions 

 is that fluid resistance is approximately propor- 

 tional to the density, the square of rate of dis- 

 placement, and the square of linear dimension. 

 It is realised that this represents only a rough 

 presentation of the actual state of affairs, and to 

 take account of this fact it has been usual to con- 

 sider the constant of proportionality "K" as a 

 variable constant, depending on the nature of the 

 fluid, the shape of the body, and the circum- 

 stances of the motion. 



Col. de Villamil discusses the question in the 

 light of the available experimental evidence, and 

 in order to prevent the intrusion of irrelevant 

 factors he very wisely restricts himself to a con- 

 sideration of -'the law of the resistance [in air] 

 and the coefficients to be used for jiat, square, or 

 circular plates — with one or two small excep- 

 tions." There are three main questions: (i) Can 

 the elasticity of the air be neglected? (2) Is there 

 a "dimension effect" — i.e. does K vary if the 

 only variable factor is size? (3) How does vis- 

 cosity affect the resistance? 



The author's conclusions can be summed up 

 symbolically in the formula 



'R = Kp{vlf[vlvl-¥c + hvlV), 

 where />, v are the density and kinematic viscosity, 

 V, I are the relative speed and a dimension, V is 

 the "velocity of flow of the fluid into a vacuum 

 at the pressure of the fluid experimented with," 

 h, c are constants, and K is a coefficient of shape. 

 He thus differs from Lanchester, who declares 

 that the elasticity of the air can be neglected, and, 

 though only formally, from Eiffel, and from Bairstow 

 and others at the National Physical Laboratory, 

 who assert the existence of a dimension effect. 



Col. de Villamil bases much of his argument 

 on dynamical similarity, and therefore devotes 

 considerable- — perhaps too much — space to an 

 elucidation of the fundamental units of mechanics. 

 His manner is vigorous and unorthodox, and his 

 NO. 2533, VOL. lOll 



trenchant criticism of the professional mathe- 

 matician is sometimes deserved and always enjoy- 

 able. Yet if the author desires to be read by 

 "young people" he should pay less attention to 

 polemics and more to notation. Not only is it 

 bad pedagogy to present the innocent beginner 

 with long and detailed criticisms of the false views 

 held by others ; but it is also very confusing when, 

 after emerging from this thicket, he is brought 

 up against a peculiar symbohsm that suffers un- 

 expected and unexplained changes. 



With reference to his explanation of dynamical 

 similarity the author says (p. 5) : "I suppose I 

 shall stand to be shot at; and I, equally, suppose 

 I shall deserve it, since I am doing my best to 

 'give the show away.'" His first sentence on 

 the principle as applied to air resistance runs as 

 follows: "We first ask ourselves, Does the re- 

 sistance due to viscosity cause change of momen- 

 tum or not? We know perfectly well that it 

 does : hence it is a ' Force. ' We may conse- 

 (juently equate ju*L"Vy^=Force = MLT-2." Why 

 is this array of symbols used to represent the 

 resistance? Not a word of explanation is given. 

 Why does the author violate his own dictum that 

 symbols of dimension must not be regarded as 

 algebraic symbols? Col. de Villamil need stand 

 in no fear of the consequences of having "given 

 the show away. " S. B. 



MILITARY PSYCHOLOGY. 

 II nostro Soldato. Saggi ,d!i Psicologia Militare. 

 By Fr. Agostino Gemelli. Con prefazione del 

 Padre Giovanni Semeria. Pp. xii + 339. 

 (Milano : FratelU Treves, 1917.) 



THIS work is a study of the psychology of 

 the soldier, and embraces an analysis of 

 the various psychological processes which come 

 into play during the events of the war. The 

 author, who has made the most of his opportuni- 

 ties during the periods of mobilisation, prepara- 

 tion for fighting, and actual warfare, has con- 

 ducted a careful inquiry into the causes predis- 

 posing to cowardice as well as heroism. Every 

 possible condition which influences the soldier's 

 life has received attention at the writer's hands: 

 the combatant's original bias of mind, his ante- 

 cedent social life and habits, his training in camp 

 and in the trenches, and all forms of discipline 

 which teach him to consider himself one of a crowd 

 united by spiritual bonds to each other for a com- 

 mon purpose. 



There is a very interesting chapter on the 

 psychic factors underlying courageous actions. 

 Many soldiers, having passed safely through 

 several dangers, at length develop the conviction 

 that they have acquired an immunity to death. 

 Some become persuaded that their vital parts will 

 escape injury. Others are buoyed up by religious 

 feelings and formulae, while others again are sus- 

 tained by superstition or the war-cries of their 

 regiment. The feeling of danger when shared in 

 common loses in gravity the greater the numbers 

 engaged. 



• M 



