An introduction to the mathematical theory of attraction ...

4 Resultant Force.
CHAPTER II.
RESULTANT FORCE.
7. Force at a Point.-If f denote the mutual force between
unit masses when concentrated at points at the unit distance
from.i each other, - expresses the force between two particles whose masses are m and m', and whose distance apart
is r. The resultant force at a point P due to any system of
acting masses may be defined as the resultant of the forces
which would be exerted by these masses on the unit mass if
concentrated at P. Let x, y, z be the coordinates of P;
4,,, 4 those of a point Q at which the acting mass is in, and r
the distance of P from Q, then the force at P due to m is
f2 or, according as the forces under consideration are
r r2
electric or gravitational. In order to find the total force at P
we must resolve each elementary force into its components
parallel to the axes, and find the sum of these for each axis.
If X, Y, Z be the components of the resultant at P, we have,
then,
z: +; [f z -r
z A/ S - i
These expressions may be simplified by taking as the unit
of force the repulsion or attraction between unit masses at
the unit distance apart, in which case f becomes unity. If
we select any other unit of force we must introduce the corresponding value off.
Not only for the reason mentioned in Art. 2, but also