II 



ON THE MOTION OF PROJECTILES IN THE AIR, TAKING 



INTO CONSIDERATION THE ROTATION OF 



THE EARTH 



BY M. [S. D.] POISSON 1 



In this memoir the projectile will be considered as an isolated 

 and material point, that is to say, as a body whose mass is col- 

 lected at the center of gravity, and the problem will be to ascer- 

 tain the influence of the rotation of the earth on its motion. I 

 shall present shortly another memoir to the Academy, in which 

 we shall take into consideration the form and the dimensions of 

 the moving body, and the object of that will be to determine, 

 principally in what relates to the projectiles used in artillery, the 

 influence that their own rotation can produce on their motion of 

 translation. 



Up to the present time the theory of the resistance which fluids 

 in general, and the air in particular, offer to the motion of the 

 bodies that traverse them, has received only a very imperfect 

 development. We compare this force to a continual succession 

 of shocks of the moving body against the particles of the fluid, 

 which disappear and are annihilated, so to speak, when they have 

 been struck by the body and have carried away small quantities 

 of motion, proportional to their own masses and its velocity. 

 Newton, to whom we owe this theory, had concluded that, ignor- 

 ing the rotation of the moving body, the resistance of the air for 

 a sphere, for example, is equal to the weight of a cylinder of this 

 fluid having for its base the great circle of the sphere and for 

 height the "full-height" due to its velocity. But the experiments 

 made on the fall of bodies in the air soon showed him the inac- 

 curacy of this result, and led him to reduce by one-half this 

 measure of resistance; subsequently.it has been found that this 



1 Memoire sur le mouvement des projectiles dans 1'air en ayant egard 

 la rotations de la terre. By [S. D.] Poisson. Read before the Academy 

 of Sciences, Paris, November, 1837. Published in the Journal de l'Ecole 

 Royale Polytechnique, Vol. XVI, Cahier 26, Paris 1838, pp. 1-68. Trans 

 jated by Profs. Frank Waldo and Cleveland Abbe. 



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