M-xsiii upon the Flight of a Projectile, 387 



into account the rotation of the earth : but independently of this 

 consideration, it becomes a very interesting question on account 

 of the amount of eiFect that is produced. 



When I first heard of M. Foucault^s pendulum experiment, I 

 felt perfectly satisfied in my own mind that the principle was 

 correct, by imagining the case of a projectile discharged at an 

 object at some distance in the line of the meridian ; and I com- 

 municated to Professor Barlow a solution of the question, as to 

 the apparent deviation of the plane of the pendulum in different 

 latitudes, by determining the angular velocity of the tangent to 

 the meridian, previously to any similar demonstration appearing 

 in print. Although this may not be the most elegant solution, 

 I think it is more easily comprehended by the majority of per- 

 sons. The investigation of the following problem is according 

 to this method. 



In the experimental practice of 1839, a 56-pounder of 97 cwt. 

 with a charge of 17 lbs. of powder and an elevation of 35°, pro- 

 jected a ball 5600 yards, the time of flight was 34". What effect 

 would the rotation of the earth have in causing the shot to fall 

 to the right or left of the object fired at, assuming the latitude 

 of the place as 52° ? 



Suppose the earth to be a perfect sphere, and a geographical 

 mile equal to 2000 yards, and for the sake of simplicity the gun 

 fired due south. 



Let AEQA' represent 

 aportion of the terrestrial 

 surface between the pa- 

 rallel of latitude AA' and 

 the equator EQ, and let 

 BB' represent another 

 parallel of latitude, di- 

 stant from the former 

 5600 yards, or 2*8 geo- 

 graphical miles the range 

 of the shot. Let a gun 

 be supposed to be placed 

 at A, and fired at an ob- 

 ject at B in the meridian. 



The time of flight of the shot being 34", which is equal to 0^-566, 

 therefore during the time of flight of the shot, the earth will have 

 passed through 8''513 of space. Now suppose at the end of that 

 time the position of the gun to be A', AA' being equal to 8'*513 ; 

 and the object fired at to be at B^, BB' being also equal to 

 8^*513. But the ball participating in the motion of the point A 

 will have arrived only at C, BC being equal to AA'. Consider- 

 ing this small portion of the terrestrial surface as a plane, the posi- 



