390 
PRESTON. 
Since 8 is always less than d, the combined effect of these 
two terms will be essentially negative. The difference be¬ 
tween the effect of the plain and the cone is seen in the last 
term, and the total influence exerted by matter equal in 
volume, and position to that generated by the revolution of 
the trapezoid a P s d around P Q would be 
_ 2 h n 3 d h 
r g 4 J </ 
Since a is always very much greater than h, the expres¬ 
sion 
_ h_ 
V h 2 + a 2 
is a small fraction and the combined effect of the last two 
terms will be of the same sign as the first of them—that is, 
their effect will be essentially positive. This is as it should 
be, and shows that the effect of this matter is to increase 
gravity at P, whereas the effect of the first two terms would 
necessarily be to diminish gravity at the same point, except 
in the extraordinary case where the infinite plain should be 
one-third as heavy again as the average earth matter. A 
uniform density of 7.56 in an infinite plain immediately 
under the station would exactly counterbalance the diminu¬ 
tion of gravity on account of distance. The negative sign 
attributed to the last term must not be interpreted as mean¬ 
ing that the actual effect of this matter is to diminish the 
value of gravity at P. It rather means that the general 
effect of the plain being to increase gravity at P, the influ¬ 
ence of a P s d comes in here as expressing the difference 
between the effect of the plain and cone, and that the plain 
effect must be diminished by 
3 d h 
2 d V h 2 + a 2 
in order to get the cone effect. In fact, the parenthetical 
