44 
PUTNAM. 
added to the above formula, being a correction to the second 
term or to observed gravity on account of such irregularities.* 
This topographical correction will always be positive, as the 
effect of all deviations from the horizontal plain,, whether 
hills or mountains rising above the station or valleys or 
canyons lying below it, will be to diminish the force of 
gravity. It is evident that an elevation of any sort exactly 
neutralizes the vertical attraction of a similar but inverted 
mass below the station level, so that the removal of both 
would not change the force of gravity at the station. This 
correction may be readily computed for any point where 
contour maps of the surrounding country are available by 
describing thereon concentric circles about the station and 
drawing radial lines therefrom at equal angular distances, 
or such a figure may be drawn on tracing paper and used 
on successive maps. The space included between two circles 
may be designated as a zone, and the part of a zone between 
two radii as a compartment. The vertical attraction of a 
cylinder of radius a, height h, and density d on a point at 
one extremity of its axis will be 
2 ~d (a + h — j/a 2 + h 2 ). 
As a zone is the difference between two cylinders, say of 
radii a and a\ its vertical attraction will be 
2 7zd (a — a' — }/a 2 -j- A 2 -f- j/ a' 2 -j- A*). 
The attraction at its surface, of the earth considered as a 
sphere is f n A r, where 4 is the mean density and r the 
radius of the earth. Therefore the effect on gravity of a 
zone is 
which becomes with a sufficient degree of approximation 
when h is small compared with a 
* The method of computing this correction here described is partially 
similar to that given by Professor Helmert, “ Geodasie,” vol. II, p. 169. 
