MOTION OF PROJECTILES POISSON 13 



found very nearly six seconds for the duration of the fall. 

 By means of this latter datum I have been able to calculate with- 

 out any hypothesis the coefficient of resistance of the air which 

 the moving body must have experienced, and the formula gives 

 27.5 mm for the deviation; which 'differs from the experiments 

 by less than a millimeter. In a vacuum this deviation would 

 not have exceeded by a tenth of a millimeter that which 

 occurred in the air; so that in this case the resistance of the air 

 has had only an inappreciable influence. 



When the projectile starts from the surface of the earth and is 

 thrown vertically from below upwards with a given velocity, we 

 conceive that during the time of its ascent it must be departing 

 from the vertical toward the west, or in a direction contrary to 

 the rotation of the earth. It would seem that afterwards during 

 its fall it should approach this line and return again very nearly 

 to its point of departure, but this is in fact not the case. When 

 it has arrived at the highest point of its trajectory and has lost all 

 its vertical velocity, the projectile by deviating towards the west 

 has also acquired a horizontal velocity in the same direction, by 

 virtue of which it continues to deviate in this direction, at least 

 during part of its fall. The analytical difficulty which this second 

 case presents is to reconcile, so to speak, the two successive motions, 

 ascending and descending, of the projectile, which are expressed 

 by very different formulae when we take account of the resistance 

 of the air. In order to apply to an example the formula expressing 

 the total deviation of the moving body when it has fallen back to 

 the earth, I have assumed that this body is a spherical ball fired 

 vertically from an infantry gun, with a velocity of about 400 

 meters per second. The amount of this deviation varies much 

 with the resistance of the air; by giving successively to the coeffi- 

 cient of this resistance different values which have to each other 

 the ratio of four to three, we find deviation toward the west in 

 both cases but of about one and three decimeters respectively. 

 In a vacuum this deviation would be about fifty-five meters, so 

 that by the greater of these two resistances it is reduced to the 

 fifteenth part of this value. 



I have also examined in particular the case where the initial 

 velocity of the projectile is nearly horizontal, which corresponds 

 to firing at a target. In my present memoir will be found the for- 

 mulas that relate to this and which express all the rircumstances 

 according as the firing is directed toward any given point of the 

 horizon. Here I shall only stop to say that the initial velocity 



