18 Rev. 0. Fisher on Variations of Gravity and their 



Suppose an elevated plateau of the form of an infinitely 

 long parallelepiped, and that the vertical attraction at a point 

 on its surface, at a distance a from one edge and b from the 

 other, is required. Let a be the angular distance of a sectorial 

 radius from a. Then, dividing the plateau into two portions 

 by a longitudinal plane through the station, and putting u 

 successively = a sec a and =6 sec a, and calling the above 

 expression for the attraction f(a, a) and f(b, a), and intro- 

 ducing the unit-factor ^-, we shall have 



Vertical attraction = 2? 2\ 2 (A a > ")+A b > a )V«- 

 27r Jo 

 A rather tedious integration gives 



(( ^/a 2 sec 2 «+(/i + ^ + 2 - Va 2 sec 2 a + (A + £) 2 )d« 



77 l0g e y 



tan« « + i(l + (^p)*) + \A + (^)*tan« « + tan 4 « 

 + (/ 4 +/;+<) s jn- 1 slna ^-^-t-JJQsin- 1 



xA+fcir,)* ' \/^W 



taken fr 

 / A + & + A 2 



And this, when taken from a =0 to 3 = -, gives 



1+ 



|log«~ 



>H^7 V^fcU 



-(/> + £) sin" 1 - 



From which j 2 (a sec a — */a 2 sec- a + h 2 )da. may be obtained 



by putting A + & = and £ = 7i, and changing the signs. 



I have calculated the vertical attraction, using these ex- 

 pressions ; putting h = 2-915 miles (the height of More) 

 k=25, ^ = 27-925, p=/*=2"68, <r = 2-96,a = 80, & = 400. The 

 result is that the attraction would produce 4*155 swings of the 

 pendulum per diem. 



