THE INTERNAL WORK OF THE WIND. 31 



For the sake of greater simplicity, and to work under the same conditions that 

 prevailed in Figure 4, let us assume that the air is alternately at rest and in 

 motion, each for a definite period of time, the velocity of the air while in motion 

 being constant. In other words, instead of assuming that the velocity of the air 

 varies continuously in obedience to a certain law we suppose that it jumps ab- 

 ruptly from zero to a finite value (to 12 meters per second for example), sustains 

 this speed for a certain period, and drops again abruptly to zero, the calm prevail- 

 ing for some seconds only to give place to a new puff, and so on. 



If we suppose an aeroplane to be set free in a perfectly calm atmosphere, it 

 may happen that after having fallen a certain distance the aeroplane can reascend 

 on account of the increase of the resistance of the air with its velocity, but even 

 under the most favorable conditions, if its initial velocity is zero, it can never 

 regain the level from which it started. 



In order to understand better the effect of successive puffs of wind on the 

 ascension of the aeroplane, it would be well to find out first to just what level the 

 aeroplane would ascend in a calm atmosphere. 



Given quantities (see the text referring to Fig. 3): 



Surface of the aeroplane : A = 1 square meter 

 Weight of the aeroplane : rag = 2 kilograms 

 Density of the air : <5 = 1.293 



These quantities are chosen to correspond to those of the example previously 

 mentioned in this memoir, and not because they give the best results. 



The angle a should remain small, so we will assign as its limits and 7°. 



From the data of previous experiments on this subject, 1 we find that the con- 

 stant h should be taken as 3.322 to represent conveniently the function/ («) be- 

 tween and 7°. We have then, between these limits/ (a) = 3.322 a. 



In the equation a = ^-, the constant c should be selected so that the angle a 

 never exceeds 7°. We see that this condition is fulfilled if <fis taken as 7.808. 



We can now calculate out the expression K =z- !--, and find that K = 16.769. 



The initial velocity of the aeroplane is zero ; therefore, since a = ~ the angle 

 a is infinite at the point of departure, although we have seen that the formulae do 

 not apply when a is greater than 7°. 



To remove this difficulty, however, it is only necessary to assume that the 

 aeroplane, remaiuing in a vertical position, falls by reason of its weight until it 



1 Experiment* in Alrodynamics. S. P. Langley. "Smithsonian Contributions to Know- 

 ledge," vol. xxvii , L891. We have chosen here the curve which represents the function ,/'(<i) 

 derived for an aeroplane whose breadth is six times its length, and whose motion is in 

 the direction of its short dimension. 



