14 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



being always about 400 meters and the distance of the target, 

 placed point blank, being equal to 200 meters, then the horizontal 

 and vertical deviations of the ball, due to the motion of the earth, 

 would amount to scarcely half a centimeter, that is to say, they 

 have no sensible influence on the precision of this shooting and 

 it is unnecessary to consider them in practice. These deviations 

 are equally unimportant in firing a cannon, and in all motions 

 which take place in a nearly horizontal direction. 



In general the effects that the motion of the earth produces on 

 the motion of a projectile are: first, to increase, either positively 

 or negatively, the interval of time that the moving body takes to 

 go from its point of departure to the point where it falls on the 

 earth; second, to increase the distance of this latter point from the 

 former, which we call the horizontal range. The signs of these 

 increments depend on the direction of the vertical plane in which 

 the projectile is thrown; there is augmentation in one direction 

 and diminution in another; their values are expressed by double 

 integrals, whose numerical calculation would be very laborious. 



In addition to this the diurnal motion causes the moving body 

 to leave the vertical plane in which it was initially projected. 

 This gives place to a horizontal deviation, whose value is composed 

 of two distinct parts, expressed also by double integrals. One 

 of these partial deviations is independent of the direction of the 

 vertical plane; it is always toward the right of an observer stationed 

 at the point of departure and facing the trajectory. In our lati- 

 tude we can consider it as being the principal effect of the rotation 

 of the globe, and happily we can obtain for it limiting values that 

 are easier to calculate than its own value, and which may, if we 

 wish, be deduced numerically by means of the length of the range 

 and the duration of the movement as given by observation, with 

 an accuracy sufficient to appreciate the amount of the deviation. 

 Applying, for example, these limits to such firing of shells as 

 takes place in actual artillery practice, that is to say, at an angle 

 of elevation of 45 , with an initial velocity of 120 meters per second, 

 which gives a range of about 1200 meters, for a projectile of 27 

 centimeters in diameter, and 51 kilograms in weight (the shell 

 of 10 inches and 104 pounds old French measure); we find that 

 the deviation of the point of impact will be between 90 and 120 

 centimeters when we aim in a vertical plane, tangent to the parallel 

 of latitude at the point of departure. The deviation will be toward 

 the south if we fire toward the east, and toward the north if we 

 fire toward the west. Calling it a meter and observing that such 



