44 
ARCHDEACON PRATT ON THE EFFECT OF LOCAL 
The simplicity of this Rule will be seen in the application I propose to make of it 
in the next section. 
It should be mentioned that the only restriction to be attended to in the applica- 
tion of this Rule is, that the ratio of the height of the attracted station above the sea 
to each of the horizontal coordinates of the nearest angle of the attracting mass must 
be small, and so small that its square may be neglected. 
If any part of the attracting mass is nearer to the station than this, the approxi- 
mate formula must for that part of the mass be abandoned, and a direct calculation 
made 
III. Application of the Formula to obtain a rough approximation to the meridian 
defection of the Plumh-line at Burleigh Moor. 
21. In the Plate attached to this paper, an outline sketch is given of the east 
of England, with a view to show how the land lies with reference to Burleigh 
Moor — the station to which I now propose to apply the formula, by way of illustra- 
tion, with the scanty data which I have been able as yet to obtain. By the help of 
accurate survey maps no doubt a very close approximation might be obtained to the 
actual amount of the deflection, not only at Burleigh Moor, but at the other stations. 
The data used in this calculation are taken from the outline map of England in the 
third volume of General Mudge’s Account of the English Survey, published in 1811. 
A number of heights of stations are marked down on the map ; and it is from these, 
as I have no other source of information, that I have inferred the average height of 
the masses into which I divide the land. But as these heights, as I conjecture, 
almost all appertain to elevated points, visible from a distance for the purposes of the 
survey, their average will be much greater than the average height of the country to 
which they appertain. I have taken the height of the masses equal to three-fifths of 
the average height above the sea of the various stations belonging to that mass. The 
result which I arrive at will therefore be only a rough approximation, for want of 
* If XY are the horizontal coordinates to the middle of a vertical prism, of which the height measured from 
the sea-level is H, h being the height of the station, and A the area (in squEire feet) of the horizontal section 
of the prism ; then, if A be small, the horizontal attraction of the prism parallel to x 
_ pAX f h , H- A 1 
X2 + Y2 { v/X2-i-Y2-f/j« ^X‘^-l-Y2-f (H-Ay^J ' 
By the same reasoning as in art. 19, this 
__p AX f h H— A 1 g 
*“5 X^ + Y2 \ //X^+Y^T^'^ J 8764500’ 
D being the mean density of the earth, and A being expressed in square feet, XYHA in feet. 
Or, the angle of deflection, in the vertical plane through the axis of x, caused by this prism 
_p AX f h H-A I 1" 
D X*-f Y'^ 1 4/X2-t- Y2-1-A2 4/X“-f-Y2-t-(H-A)^/ 424-9' 
The value of this must be found for each of the vertical prisms near the station, and their sum taken. 
