Fbbetjaet 19, 1909] 



SCIENCE 



287 



Fortunately for the development of each 

 type, the experiments made with one class 

 are of value to the other classes, and these 

 in turn bear close analogy to the types of 

 boats used in marine navigation. The 

 dynamical properties of water and air are 

 very much alike, and the equations of mo- 

 tion are similar for the two fluids, so that 

 the data obtained from experiments in 

 water, which are very extensive, may, with 

 slight modification, be applied to computa- 

 tions for aerial navigation. 



Eelmholtz's Theorem. — Von Helmholtz, 

 the master physicist of Germany, who illu- 

 minated everything he touched, has fortu- 

 nately considered this subject, in a paper 

 written in 1873. The title of his paper is 

 "On a Theorem Eelative to Movements 

 that are Geometrically Similar in Fluid 

 Bodies, together with an Application to the 

 Problem of Steering Balloons." 



In this paper Helmholtz afSrms that, al- 

 though the differential equations of hydro- 

 mechanics may be an exact expression of 

 the laws controlling the motions of fluids, 

 still it is only for relatively few and simple 

 experimental cases that we can obtain in- 

 tegrals appropriate to the given conditions, 

 particularly if the cases involve viscosity 

 and surfaces of discontinuity. 



Hence, in dealing practically with the 

 motion of fluids, we must depend upon 

 experiment almost entirely, often being able 

 to predict very little from theory, and that 

 usually with uncertainty. Without inte- 

 grating, however, he applies the hydrody- 

 namic equations to transfer the observa- 

 tions made on any one fluid with given 

 models and speeds, over to a geometrically 

 similar mass of another fluid involving 

 other speeds, and models of different mag- 

 nitudes. By this means he is able to com- 

 pute the size, velocity, resistance, power, 

 etc., of aerial craft from given, or observed, 

 values for marine craft. 



He also deduces laws that must inevitably 



place a limit upon the possible size and 

 velocity of aerial craft without, however, 

 indicating what that limit may be with 

 artificial power. Applying this mode of 

 reasoning to large birds, he concludes by 

 saying that, "It therefore appears probable 

 that in the model of the great vulture, 

 nature has already reached the limit that 

 can be attained with the muscles as work- 

 ing organs, and under the most favorable 

 conditions of subsistence, for the magnitude 

 of a creature that shall raise itself by its 

 wings and remain a long time in the air." 



In comparing the behavior of models in 

 water and air, he takes account of the 

 density and viscosity of the media, as these 

 were well known at the date of his writing, 

 1873 ; but he could not take account of the 

 sliding, or skin-friction, because in his day 

 neither the magnitude of such friction for 

 air, nor the law of its variation with ve- 

 locity had been determined. 



Even as late as Langley's experiments, 

 skin-friction in air was regarded as a negli- 

 gible quantity, but, due to the work of Dr. 

 Zahm, who was the first to make any really 

 extensive and reliable experiments on skin- 

 friction in air, we now can estimate the 

 magnitude of this quantity. As a result of 

 his research he has given in his paper on 

 atmospheric friction the following equa- 

 tion: 



/ = 0.00000778 i-'-'X'ci'-^' ...(v = it. sec), 

 / = 0.0000158 Z-^-^t)^"'... (« = mi. hr.), 



in which / is the average skin-friction per 

 square foot, and I the length of surface. 



Eelative Dynamic and Buoyant Support. 

 — Peter Cooper-Hewitt has given careful 

 study to the relative behavior of ships in 

 air and in water. He has made a special 

 study of hydroplanes, and has prepared 

 graphic representations of his results which 

 furnish a valuable forecast of the problem 

 of flight. 



Without knowing of Helmholtz 's the- 



