GRAVITY MEASUREMENTS. 
45 
This approximate formula may be readily computed with 
a table of squares and reciprocals if convenient numbers are 
taken for a' and a , and will be sufficiently accurate except 
when the topography is very uneven near the station, in 
which case the preceding formula must be used, h is to be 
taken for each compartment as the difference in elevation, re¬ 
gardless of sign, between the station and the average surface 
of the compartment. As this will vary for different portions 
of a zone, the parts of the formula involving h must be com¬ 
puted separately for each compartment therein and the 
mean applied in the formula for the zone. When these 
zones have been carried to such a distance from a station 
that their effect becomes small, the vertical attraction for 
the remaining region may be computed by the formula 
dg = (Va? + K — a), 
where a is the outer radius of the last zone, this being the 
formula for the difference between an infinite plain of thick¬ 
ness h and a cylinder of height h and radius a. The area 
immediately about the station within the first circle may 
often be neglected as approximately level, or otherwise the 
effect of its irregularity may be computed by taking the 
difference between a cylinder and a cone, the formula be¬ 
coming 
, 3 q d ( ^ a 2 ; \ 
dg 2 r d\ i/a 2 + li‘) ’ 
where a is the radius and h the difference of elevation at 
distance a from the station taken for each compartment 
separately, keeping in mind always that we are computing 
only the correction to the vertical attraction of an infinite 
horizontal plain through the station and therefore only need 
take account of deviations therefrom. The total correction 
for a station will of course be the sum of the corrections for 
the separate zones. Where the station is at the summit of 
a small hill rising out of a comparatively level country, it 
will generally suffice to treat the hill as a cone, without 
