AVIATION IN FRANCE JOURDAIN. 149 



P=Rj cos i=KSV- sin i cos i or h KSV- sin 2i. 



KS sin 2i 

 f=Rj sin i=KSV^ sin^ i. 



P2 

 •^-KSV^ cos2 —^ ^^^ '• 

 T=/V=KSV3 gin2 1^ 



KSX4P2sin-i 



VK^S^ sin^ 2t 

 Whence: 



By eliminating V we have- 



T= 



KSV cos2 i 



ens 7, V 1 



p 



tan I 



cos i V KS 



7n case of the aeroplane. 



F= total force of movement. 



/■'= force required to overcome resistance to advancement. 



K'=coefficient of resistance of the air to advancement. 



S^=ideal surface corresponding to framework, with motor, rigging, aviator and 



equipment. 

 /^=K^S^V2. 



'^^--^ — ^-^K'S^V^ 

 KSV cos^ I 



To secure the minimum value of 'i§ tlie derivatives may be used with the following 

 result: 



— = -^Qv^f ^.+3K^S'V2=0. 



^V KSV^ cos^ t 



Whence: f=^f- 



Propulsion creates and accompanies sustenance. 



In this connection I wish to make clear one frequently disputed 

 point in regard to aerial navigation — that is, as to the impor- 

 tance of the part played by the wind. As far as the aeroplane is 

 concerned this is reduced to a minimum. As a matter of fact, the 

 governing feature of an aeroplane is the speed of the machine itself 

 against the air. If the air produces a pressure that is negative, or 

 of no effect at all, it will influence only the horizontal displacement 

 of the machine ; the vertical displacement will depend always on the 

 speed of the aeroplane itself. If the speed of the wind blowing 

 against the machine is equal to the machine's own speed, the aeroplane 

 will rise but will not advance; it will fly and yet be stationary in 

 the air. If there is no opposing wind, the machine will move hori- 

 zontally at a rate equal to its own speed; if the wind blows in the 

 direction the machine is going, the rate of advance of the aeroplane 

 will be the sum of its own speed and of the speed of the wind. 



