42 
ARCHDEACON PRATT ON THE EFFECT OF LOCAL 
Hence, since 0*43429 is the modulus of common logarithms, 
attraction=Q:^^|log tan + log tan ^45°+^ 
- log tan (^45°+^ — log tan (^45°+^ 
17 . A similar formula is true for the attraction parallel to the axis of 3 / ; and may 
be obtained from the above by interchanging X and Y, x and 3 /. 
‘18. As a kind of test of the truth of the formula deduced in the last article but 
two, let X=a:-j-dx and In this case the tabular mass becomes an 
elementary vertical prism of height H and base dx.dy \ and by expanding in powers 
of dx and dv the expression comes out, as it should, attraction i= 
19. The attraction of the earth on a point at its surface, that is, gravity 
47r 
(^)=— D.a, where D is the mean density of the earth, and a the radius, 
D = 
At: a 
and the coefficient of the last formula in art. 16 
3 q 9 
^ TT 
~-434 47r(-434) D a 
Let the density of the attracting mass be taken to be that of granite*, that is, about 
* Should the density dilFer from this in any particular case of application of the formula, especially for parts 
in the immediate neighbourhood of the plumb-line, then the coefficient must be altered in proportion. 
Judging from the following Table, which is taken from Colonel’s Sabine’s volume on the Pendulum, p. 338^ 
it would appear that pendulum experiments afford a good means of measuring the relative density of the parts 
of the earth’s crust near the place of observation. He gives this as the result of his calculations on the subject : — 
Stations. 
Excess or defect 
of vilirations. 
Scale of density 
[of the strata beneath]. 
St. Thomas 
+ 5-58 
100 
Ascension 
-f 5-04 
94 
Spitzbergen 
+ 3-50 
79 
Jamaica 
-1-0-28 
45 
New York 
-f 0-00 
43 
Greenland 
-0-08 
43 
Sierra Leone 
— 0-12 
42 
London 
-0-28 
41 
Hammerfest 
-0-52 
37 
Bahia 
— 1-80 
26 
Drontheim 
—3-10 
12 
Trinidad 
— 4-12 
2 
Maranham 
— 4-34 
1 
Thus pendulum experiments seem well calculated to test the existence of local attraction, at any rate the 
vertical part of it. But they can be of no service in determining the part of local attraction which is effective 
in deflecting the plumb-line, except in determining the density of the attracting mass ; for the part which is 
effective in one case is entirely inoperative in the other. If G be the force of local attraction, and this be 
resolved into two forces, V vertical and H horizontal, then H is the only part which has any sensible effect in 
