MILITARY AERONAUTICS SQUIER. 141 



the dirigible balloon have little confidence in the future of the aero- 

 plane, while another class have no energy to devote to the dirigible 

 balloon, and still others prefer to work on the pure helicopter princi- 

 ple. As a matter of fact, each of these types is probably of perma- 

 nent importance, and each particularly adapted to certain needs. 



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 navi- 

 gation. The dynamical properties of water and air are very much 

 alike, and the equations of motion 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 computations 

 for aerial navigation. 



Helmholtz's theorem. — Von Helmholtz, the master physicist of Ger- 

 many, who illuminated everything he touched, has fortunately con- 

 sidered this subject in a paper written in 1873. The title of his 

 paper is " On a theorem relative to movements that are geometrically 

 similar in fluid bodies, together with an application to the problem of 

 steering balloons." 



In this paper Helmholtz affirms that, although the differential 

 equations of hydromechanics 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 integrals 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 

 integrating, however, he applies the hydrodynamic equations to 

 transfer the observations 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 magnitudes. By this 

 means he is able to compute the size, velocity, resistance, power, etc., 

 of aerial craft from given, or observed, values for marine craft. 



He also deduces laws that must inevitably jDlace a limit upon the 

 possible size and velocity of aerial craft without, however, indi- 

 cating 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 working 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 



