APPENDIX.* 



SOLUTION OF A SPECIAL CASE OF THE GENERAL PROBLEM. 



By Rene de Saussure. 



In this solution which has been selected from a number, independently ob- 

 tained, and relating to special cases, integration has been carried out between the 

 vertical tangent at the right of Figure 3 and the poiut D, as this interval bears 

 on the most important feature of the demonstration, that is : the proof that the 

 aeroplane can lift itself without expending a perceptible amount of energy while 

 making progress against the wind. 



PROBLEM. 



An aeroplane of mass m is projected into tlie air with an initial velocity V , at 

 an angle b with the horizontal. Find the velocity of the aeroplane at a given instant 

 and the equation of the trajectory described by its center of gravity. 



(It is to be noted that as the velocity V is the velocity of the aeroplane 

 irrespective of the velocity of the wind, the problem is the same whether the 

 atmosphere is in motion or not, providing the coordinate axes move with the air 

 currents.) 



The proposed solution does not lead to an equation for the trajectory in x and 

 y, but it gives the value of y in terms of the angle ft, the angle which the tangent 

 to the trajectory makes with the x axis, and permits it to be demonstrated that 

 within the limits between which that angle is supposed to vary, the aeroplane can, 

 under certain conditions, make progress against the wind. To prove this is the 

 aim of this paper. 



The exact value of x in terms of ft is not given here, although it is possible 

 to obtain it by a long series of calculations. It is simpler to use an approximate 



* Translated from " Le Travail Interieur <lu Vent," par M. S. 1'. Langley, Jievue de V 

 nautique Theoriqut et Appliqude, pp. 58-68, Paris, 1893. 



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