64 
ARCHDEACON PRATT ON THE ATTRACTION OF THE 
Hence in the whole lime we may fairly consider that no appreciable error will be 
incurred. 
19. I now proceed to select the Law of Dissection, that is, the relation of the 
lengths of the respective compartments to their distances from A. Upon this depends 
the simplicity and the success of the method of calculation now proposed. 
Let the relation between a and (p be always such, that 
<P COS' 
a numerical constant = c. 
To fix the value of this constant I shall make <p=YQa when (p and a are indefinitely 
small. Hence, expanding in powers of p and a, 
9 
1 
4 
T 1 i“2r 
-«+-? 5 +- 
and the Law of Dissection of the earth’s crust is expressed by the equation 
(3.) 
This reduces the formula (2.) to the following : — Attraction of mass standing on 
any compartment 
4 .1 
(4. 
4 • 1 q A 
— 91 ^ 
which depends simply upon the average height (A) of the surface of the mass 
above the surface through A, and not at all upon the distance of the compartment 
from A. 
20. It is in this that the remarkable simplicity of the method consists. We have 
but to calculate the angles from the Law of Dissection (3.), and lay down the circles 
and the lines diverging from A upon a good map on which the elevations and de- 
pressions are marked, and the attractions of the several masses standing on the 
compartments thus marked out will be given by the formula (4.) at once, when we 
determine upon their average elevations. 
21. Let D be the mean density of the earth, which has been finally fixed at 5*66 of 
distilled water by the recent experiments of the late Mr. Baily ; r the radius of the 
earth = 4000 miles ; g the measure of gravity ; then 
4 • ^ ^ 
— D.r 
r 
