888 Capt. E. M. Boxer on the Effect of the Rotation of the Earth 



tion of the shot may be found by drawing A'C parallel to AB, and 

 B'C will be the difference of length of the two arcs AA' and BB', 

 which will be the deflection of the shot. It will be observed 

 that the two tangents AB, A'C are assumed to be parallel ; but 

 this is not strictly correct ; for the same reason as in the pen- 

 dulum experiment, the apparent revolution of the plane of the 

 pendulum at any place upon the surface of the earth will not be 



OQ.QQA 



. , ^ hours. And the reason of it is this : the path of the 

 sm lat ^ 



point A when projected upon a horizontal plane will be a curve ; 

 therefore in the case of the projectile, the shot only receiving an 

 impulse due to the earth's rotation at the point A from which 

 position it is fired, the two tangents manifestly will not be per- 

 fectly parallel ; but the correction from this cause would be so 

 small as not to be of any moment in an approximation of this 

 sort. In the case of the pendulum, the path of the point of sus- 

 pension when projected upon a horizontal plane being a curve, 

 unless the arc of vibration be infinitely small, the law of inertia 

 will cause the ball to take an elliptical motion, and an apsidal 

 motion will be the result. We will therefore take the two tan- 

 gents to be parallel, or rather AA' to be equal to BC, 



2-8 mUes =2' 48". 



The latitude of the place being 52®, 



51° 57' 12" will be that of B. 



The circumference of the earth being 21,600 geographical 

 miles, the arc 



AA'= 8-513 cos EAl . i,- i -i 



arc BB'=8-513cosEB j"^ geographical miles; 



.-. BC = 8-513(cosEB- cosEA) = 10-914 yards, 



which is the deflection of the shot when fired due south. 



The motion of the earth being from west to east, or from A 

 to A', the ball will fall 10*914 yards to the west, or to the 

 right of its direction. If fired due north from the point A, it is 

 obvious that the shot would fall nearly the same distance to the 

 east of the object, but still to the right of its direction. 



The next point to be considered is, whether if the ball be 

 projected due east or west, or in any other direction, the same 

 amount of effect will be produced. I think there is no doubt 

 that there would be, and perhaps the most intelligible manner 

 of showing this is as follows : — 



The Hue joining the north and south points of any place upon 

 the earth's surface is a tangent to a great circle at that point 

 passing through the two poles ; and the line joining the east 



