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



large in comparison with the height. Any special case — 

 such, for instance, as that of the island of Hawaii — would 

 need to be considered on its own merits, regard being had to 

 the totally different character of its constitution, owing to its 

 not having been accumulated through lateral compression. 



We are now in a position to find an expression for the 

 vertical local attraction arising from a cap -sector and its root. 

 Ci A cap-sector and a zone-sector are corresponding portions 

 of a cap and of a zone, intercepted between two planes passing 

 through the axis, and inclined to each other at the sector- 

 angle,"* a. 



The expression for the attraction of a cap-sector of thickness 

 h, chord-radius u, and density p, is 



neglecting terms in -$ and — . 



To express this local attraction in terms of g, the attraction 



of the sphere, we shall have, putting the mean density at 5 J, 



■p 



Local attraction : g : : p X &c. : -^> 



c 



: : pX &c. : -^ttX -«-' 



: : p x &c. : — (suppose). 



And if c is expressed in miles, we shall find that 



log 7= 5-8384723. 

 Whence, in terms of the attraction of the sphere, 



Local attraction = |— p x &c. 



The negative attraction of the root will be that of a cap- 

 sector of thickness t and of radius w, at a distance h + k, 

 == that of a cap-sector of radius u and thickness h + k + t, 

 — that of a cap-sector of radius u and thickness h + L The 

 radius w therefore does not appear. The chord-radius u may 

 be taken the same for the under as for the upper side of the 

 plateau. 



Hence the negative attraction of the root 



* " Account " &c. p. [151], t Ibid. p. [157]. 



