Ill 10 INTERNAL WORK OF THE WIND. 85 



Let us now suppose that the wind erases when the aeroplane readies the point 

 D' (Fig. 7). The aeroplane will then find itself in a calm atmosphere and possessed 

 of a vertical velocity equal to : Y„ ; sin p = 20.9311 x sin (55° 1') = 17.1493 m. 



If the aeroplane is now oriented in a vertical direction so as to eliminate air 



resistance, this velocity of 17.1493 m. will enable it to cover in its ascent a space 



DD' = 14.9916 in. We have, therefore, for the different vertical distances 



traversed: 



Descent Ascent 



From A to A' 5.007465 m. From C to D' 35.504 m. 



From A to C 82.0908 m. From D to D 14.0916 in. 



Total 27.188265 m. Total 50.5856 m. 



Thus the finishing point D is found to be about 23.40 meters above the start- 

 ing point A; furthermore, although we have not calculated x, it is certain that the 

 aeroplane has made progress against the wind, since the point D' is to the left of 

 C which is itself to the left of the starting point A. In reality, from C to E the 

 horizontal component of the velocity is greater thau the velocity of the wind; the 

 aeroplane therefore gains the distance from C to D' with reference to the earth 

 since, as we have seen, the velocity of the aeroplane relative to the earth is equal 

 to the velocity relative to the air minus the velocity of the wind. 



Finally, since its velocity at D is zero, the aeroplane is again in the same posi- 

 tion as at the start; it can therefore repeat the same maneuvers and proceed 

 indefinitely by a series of bounds, provided of course, that the puffs of wind 

 succeed each other in regular order. 



