ARCHDEACON PRATT ON THE CONSTITUTION 
346 
Table V. (m= 50). 
Punnae. 
Bangalore. 
Damargida. 
Ealianpur. 
Kaliana. 
h 2 = 
00000094 
0-3242313 
0 1341757 
0 1 117431 
00244735 
000003 14 g 
0 0000159 „ 
0 0000053 „ 
0 0000026 „ 
0 0000130 g 
0 0000066 „ 
0 0000022 „ 
00000011 „ 
0 0000007 „ 
0 0000005 „ 
0-00001 20 g 
0 0000055 „ 
0 0000018,, 
0 0000009,, 
0 0000005 „ 
0 0000003 „ 
0 0000002 „ 
00000001 „ 
00000001 „ 
00000001 „ 
0 0000024 g 
0 0000012,, 
0-0000004 „ 
0 0000002 „ 
00000001 „ 
0-0000001 „ 
0-0000001 „ 
Zone 1 
„ 2 
3 . 
’, 4 
5 
6 
„ 7 
8 
’ !) 
,, 10 
,, 11 
12 
„ 13 
14 
Totals, m= 50... 
0 0000552 g 
0-0000241 g 
0 0000215 g 
0-0000045 g 
For m=100 it will be quite near enough to double these; viz. 
Totals, m= 100... 
0-000 11 04 g 
00000482 g 
0 0000430 g 
00000090 g 
16. Suppose on a zone of any width only a comparatively small portion of its whole 
circuit has a mass standing on it. Then, as the distance from the centre of the mass 
increases, the angular width varies nearly as the distance inversely. By paragraph 11 
the Vertical Attraction of the mass on the whole zone, t being its thickness, 
ec\ 
4 c 2c \ 1 uw ) 
From which it is easy to deduce that, for a whole zone, 
Resultant Vertical Attraction = — 
3g w—u ( m + l)/ 2 
4 2c uw 
This varies very nearly inversely as the square of the distance from the centre of the 
mass. Hence, if the mass stands on only a comparatively small portion of the zone 
measured horizontally at the station, the Resultant Vertical Attraction varies nearly 
inversely as the cube of the distance. 
17. I will now consider the case of a zone the height of the mass upon it being such 
that we must not neglect any power of the depth through which the corresponding 
attenuation reaches. 
We must revert to formula (1). The effect of the attenuation below the zone equals 
the difference of the effects of two masses, each 1-mth of the density of rock, running 
down to depths h and h-\-mk below the station-level. Call u and w , as before, the 
bounding chords of the zone. The effect of the attenuation 
= “i w 2 +(/i+m&)” 2 +\/ u?-\-(h+mkf 
+ ~ 2 - U (h mk) — w \J w 2 li'j. 
