> (7.) 



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

 ing one of equations (4.), our equations of motion become 



</>=-(KH-N)^-f-N/" 



r?,«;?=-(K + N)-+N»^ 



Now suppose the oscillations very small. Then a:, y, z, and N 

 will be small quantities whose squares and products may be 

 neglected. Therefore equation (1.) becomes 



/a7 + 7wy + 7i2r=0 (8.) 



Equations (7.) become (calling — ^a^) 



^/2^=-fl2y + Nm > (9.) 



But equations (3.), (8.), and (9.) are precisely the equations 

 of motion of the former problem ; and the two problems are 

 therefore identical. 



LVIII. On the Effect of the Rotation of the Earth upon the Flight 

 of a Projectile. By Captain E. M. Boxer, R.A."^ 



To the Editors of the Philosophical Magazine and Journal, 



Mill Hill, Woolwich, 

 Gentlemen, June 10, 1851. 



HAVING lately been investigating a curious question with 

 regard to the rotation of the earth, viz. the amount of its 

 effect upon a projectile in causing it, during its flight, to deflect 

 from the object to which it was directed, or more correctly speak- 

 ing, the object to alter its position with regard to the path of 

 the shot, the data, so far as the range and time of flight are 

 concerned, not being assumed, but taken from actual practice, 

 I have been surprised at the result. Although I do not con- 

 sider it to be of any practical importance in the present state of 

 gunneiy, yet perhaps at some future time such perfection may 

 be obtained in the machine from which the shot is propelled, as 

 well as in the projectile itself, as to make it worth while taking 



* It is due to the author to state, that this paper was received by us on 

 the 17th of June last; its pubUcation has been delayed owing to great presi 

 of matter.— Edits. 



