MENSURATION. XXxiii 



For the entire sphere 



F= ^ TT r^ = 4.1888 r^ approximately. 

 (For IT and log ir see c above.) 



For a spherical segment of height /i 



V=7r/r (r—'s/i). 



For a zone, or difference in volume of two segments whose altitudes are ^i and 

 /lo respectively 



r= TT r (//I — /if) — J TT (/il — /i^) 

 == 1 TT A /. (3 rn + 3 ^ + A /^^), 



where ri and r^ are the radii of the bases of the zone and ^ h-=. h^ — h^. 



f. Volume of ellipsoid. 



a, b, c =:^ semi axes, V^ volume. 



F= ^ t: a b c. 



For an ellipsoid of revolution about 



the «-axis, F= ^ ir a b\ 

 the i^-axis, V z= ^ tt a^ b. 



