THE 



PHILOSOPHICAL MAGAZINE 



AND 



ANNALS OF PHILOSOPHY. 



[NEW SERIES.] 



NOVEMBER 1829. 



LI. On the Deviation of a Falling Body from the Vertical to 

 the Earth's Surface. By William Galbuaith, Esq^. 



To the Editors of the Philosophical Magazine and Annals. 



Gentlemen, 



nPHE problem of determining the deviation of a body from 

 -*• the vertical to the earth's surface at a given point when 

 let fall from another given point above it, has exercised the 

 talents of the greatest mathematicians. Emerson in this 

 country, and Laplace in France, have successively considered 

 it, and given solutions ; — the former in his Algebra, problem 

 198; the latter in the Bulleti?i des Sciences, No. 15. 



The solutions are obtained on the supposition of the earth 

 being a sphere, which may be considered sufficiently accurate ; 

 since the difference for the spheroidal figure would in this case 

 be quite insensible. Indeed, the difference of the effect arising 

 from the centrifugal force being derived from the ordinate to the 

 polar axis of a splieroid of small eccentricity, such as the earth, 

 instead of the cosine of the latitude to radius unity, must be 

 very slight. The ratio of the centrifugal to gravity at the 



equator is expressed by y~ — —fy (I'hil. Mag. Old Series, 



vol. Ixiv, p. 1G3). Now if r be the radius of the e(]uator, it 

 will be (Phil. Mag. vol. ii. New Series, p. 5\:) 20921178 feet. 

 But if r be the radius of the inscribed sphere;, it will be 

 20H5318't feet: and taking p, the length of the pendulum, at 

 3-2511 feet, we should have/= 0-003't5.5 in the one case, 

 and 'f = 0-0034"t4 in the other, or 



•'^°"^ mi ^"^ iW ^■espectively. 



N.S.Vo\.6. No. 35. A^oT. 1829. 2T Hence 



