OF THE SOLID CRUST OF THE EARTH. 
345 
increased by the attraction of the addition of matter spread uniformly through the crust 
below the sea-bed according to the hypothesis. 
14. If the Central Portion is distributed through a depth mil below the sea-level, the 
Vertical Attraction of this distributed mass would equal the difference of the attraction 
of two caps running down to depths (m-j-l)A and A, which, by means of the first formula 
in paragraph 11, 
. §£ 
4cm 
111 -f- 1 )ll -j- 
(m-f- 1 )ah (m+ l) 2 /< 2 \ 
'la 
)-(»+£-£)} = 
and when this is subtracted from the same formula, 
Resultant Vertical Attraction of Central Portion = 
icj (m + l)/d 
4c 2 a 
Put a = 2c -^w=49‘45, c=3956, and this 
=0-0000968% or 0-0001917%, 
according to whether m = 50 or 100. 
If the mass on the rth zone is distributed down through a depth mh below the sea- 
level (that is, between the depths h and (m+l)A), the second formula in paragraph 11, 
after substituting for u and w in terms of r, gives for its effect 
^j((l+m)M 
{\+m)Vd 
4 r(r+ 1) 
A*n* \ 
'4 r(r+ 1 )c) 
— 3 9(i . (m + 2)ld n q \ 
4cny ' 4r(r + ]) c) 
Subtracting this from the same formula, h being first put for t, 
Resultant Vertical Attraction for the zone= 
3 gn (m + 1 )/d 
16e 2 r(r+l) 
Put n— 160, c=3956, and this 
=0-0000978-7^ or 0 0001937 
?-(r+l) r(r+l) 
according to whether m=50 or 100. 
15. These formulae I now tabulate for the five stations — observing that the surrounding 
land up to the sea stretches over radii of 0, 3, 5, 9, 14 zones respectively. 
3 b 2 
