OP THE SOLID CRUST OP THE EARTH. 
343 
circles of any zone, drawn around the station on the sphere which represents the sea- 
level. For the zones beyond the central portion t+u is frequently so small that its 
fourth power may be neglected. The case where it is not so small will be considered 
afterwards. Then formula (1) gives for a cap of thickness t below the station-level 
Vertical Attraction t-\- - n - — — ) : 
4c V 1 2c 2 u) 
and therefore for the part of the cap over the zone 
Vertical Attraction - 5 — Y 
4 c 2c \ uw J 
Hence, if h be the height of the station above the sea-level, the Vertical Attraction of a 
mass on the zone, up to the station-level 
4 c 2c \ 1 uw J 
Taking the difference of these, and putting the height of the superficial mass on the zone 
above the sea-level (that is, h—t) =k, 
Vertical Attraction of the mass on the zone at the sea-level 
3 g w—u 
4c 2c 
2 h—k 
c 
If the superficial mass rises above the station-level, we use the formula (2), which gives 
Vertical Attraction = ~ ~ 2 c~(^ — > 
UIV J 
and this, added to the attraction of the mass between the sea-level and the station-level, 
gives, observing that in this case k=h-\-t, 
Vertical Attraction of the mass on the zone at the sea-level 
_3gw-u / 7 . (A a -< a )c \ 
— 4c 2c \ T £ ~r uw J 
3gw—Uj /.. 2 h — k c 2 \ 
4c 2c \ ' c uw) ’ 
precisely the same formula as before. 
The formula is also true when applied to parts covered by the ocean. Let, as be- 
fore, h be the height of the station above the sea-level, but Jc the depth of the ocean 
(supposed uniform under the zone). The ratio of the density of sea-water to that of 
rock, which equals 2*78 (half the mean density of the earth), =0 , 363. Then h-\-Jc and h 
are heights of the station and of the surface of the attracting ocean above the level of 
the ocean-bed ; and therefore, by means of the formula above proved, 
Vertical Attraction of the ocean under the zone on the sea-level 
0-363 k ( 1- 
4c 2c \ 
and therefore the effect of the deficiency of density 
, 2{k + h) — k c 2 \ . 
c ' uw) ’ 
of the ocean below that of rock 
3 g w — u 
4c 2c 
0-637 k 
H 
2A4- k 
3 B 
MDCCCLXXI. 
