MEAN DENSITY OF THE EARTH. 
389 
the above term, depending on the attraction of the plain, 
must receive the correction : 
3 h 
+ 4 A i/V'+tf’ 
where a is the radius of the base. This expression reduces 
to zero for an infinite value of a in which we have the 
previous case of an infinite plain. For a value of a equal 
to zero the entire effect of the intervening matter disappears, 
as it should do, from the formula. The expression for the 
differential of gravity at the summit of a conical mountain 
would therefore be: 
3 d - 3 £ 
4J+4 ~A C ° SP 
(16) 
where /3 is the semi-vertical angle of the mountain. When 
a is very large compared with h the correction for a para¬ 
boloid is two-thirds and that for a sphere is one-half that 
given above.* 
We have a greater value of gravity in the case of the 
cylinder than for the paraboloid and a greater one for the 
paraboloid than for the cone. In Fig. 17, gravity at Q 
would be diminished by passing to P, if no intervening 
matter existed, by 
— g = correction for distance (negative). 
If we interpose the infinite plain abed gravity will be 
increased by 
~r~ ^ T ^ == correc ti ori f° r plain (positive). 
*Helmert (Dr. F. R.) Die math, und phys. theorieen der hoheren 
geodasie. 8°. Leipzig, 1884. Part 2, p. 172. 
