MOTION OF PROJECTILES POISSON I 5 



a deviation in a distance of 1200 meters corresponds to an angle 

 of about three minutes of arc, it follows that in order to be more 

 sure of hitting the mark it will be necessary to aim in a vertical 

 plane to the left of the given plane, and making with that an angle 

 of three minutes. The consideration of this result may influence 

 the accuracy of the aim and the chance of striking the target in 

 exercises where the gunner must seek great precision. The hori- 

 zontal deviation Avill be a little less and will be toward the east 

 when we fire toward the north; it will be a little more and to ward 

 the west when we fire toward the south. In the firing of a shell 

 at long range, for example, at a distance of about 4,000 meters 

 from the mark, which supposes an initial velocity of a little more 

 than one-third of 800 meters, at the elevation angle of 45 , and 

 for a projectile weighing 90 kilograms and a third of a meter 

 in diameter, the limits of deviation, firing either to the east or to 

 the west, will be very nearly 5 meters and 10 meters, respectively. 

 Estimating then its average amount at 7 or 8 meters, we see that 

 in sieges some buildings and persons have been reached because of 

 the deviation of a shell by the motion of the earth and others 

 have not been from the same reason. 



These numbers, and those that we have before given, relate to 

 a mean latitude; they vary with the latitude of the place of the 

 experiment. At the equator when the firing takes place in its 

 plane, the horizontal deviation vanishes while the increase in the 

 duration of the trajectory and in the length of the range attain 

 their maximum values. In high latitudes, on the contrary, it is 

 the deviation which approaches its maximum and the increase 

 of duration which diminishes. At the pole, the horizontal devi- 

 ation, which is the same at this point for all vertical planes of 

 firing, would exceed by very nearly one-half that which takes 

 place in our latitude. Everywhere the increments of the range 

 and of the time are nothing when the initial velocity is directed 

 111 the plane of the meridian. 



[The preceding text is followed by a detailed mathematical 

 analysis that need not be reproduced here]. 



