Discrete From The Start

Why would you ever multiple two mass values or charge values?

Four force lines joins the right singular point mass or charge to the four on the left in the top picture.  When the two groups of points are far a part and very small, these force lines are parallel and are just summed to given the total force on the single point.  What if we have two other points on the right?  This group will experience a total 3 x 4 force lines.  If fact given two groups of mass/charges numbered at M and N, the total force lines between them is MxN.

Given a configuration of charges in two or more groups, MxN the total number of force lines between them are fixed.  Let's define a forces line per unit area term,  $\Phi$  over the area of a sphere around one of the group

${\Phi_1}.{4\pi r^2_1}={\Phi_2}.{4\pi r^2_2}=M.N$

and we have,

$\Phi_1=\cfrac{{\Phi_2}.{4\pi r^2_2}}{4\pi r^2_1}=\cfrac{M.N}{4\pi r^2_1}$

In general,

$\Phi=\cfrac{M.N}{4\pi r^2}$

${\Phi}$ =  number of force line per unit area = flux,

What is this force lines per unit area over a sphere?  Image a force being divided over small points covering a sphere.  Each of these points joins the center of the sphere along a radius.  The force at each of these points is a force along the radial line of the sphere.

Compare this with,

$F_c=\cfrac{q_M.q_N}{4\pi {\varepsilon_o} r^2}=\cfrac{Me.Ne}{{\varepsilon_o}}\cfrac{1}{4\pi  r^2}=\cfrac{e^2}{{\varepsilon_o}}\cfrac{M.N}{4\pi  r^2}=\cfrac{e^2}{{\varepsilon_o}}\Phi$

We found that the  $\cfrac{1}{r^2}$ dependence is the result of the total flux being conserved and that the source of this total flux is,

$F_{co}=\cfrac{e^2}{{\varepsilon_o}}$    and so,

$F_c=F_{co}\Phi=\cfrac{e^2}{{\varepsilon_o}}\Phi$

In a similar way,

$F_m=\cfrac{Gm_Mm_N}{r^2}=4\pi G\cfrac{Mm_s.Nm_s}{4\pi r^2}=4\pi Gm^2_s\cfrac{MN}{4\pi r^2}$

$F_m=4\pi Gm^2_s\Phi$

where $m_s$ is an elemental mass,  $G$ is the gravitational constant.  Let

$F_{mo}=4\pi Gm^2_s$    and so,

$F_m=F_{mo}\Phi=4\pi Gm^2_s\Phi$

The point is the basic number counting in such formula.  They assume that charges or mass are made up of countable elemental point quantities and there are distinct countable force lines.  In the first place, discrete.  And that the formulation can be separated into a source part and a flux part (flux are just lines).

If such formula are experimental and valid, then an elemental mass  $m_s$  exists already, thanks to Newton.