# Coulomb's law origin

At the very beginning,how was the Coulomb's law found experimentally? From experiments using two charged balls it can be shown that the force varies with the inverse of square of the distance between them keeping them on different distances times and again but how was the dependence of the force on the product of charges at first found experimentally? i.e

Force is proportional with the product of charges

Because at the very beginning when people didn't actually know about the charges very much it should have been quite difficult to tell about what the charge was. When we can't measure charge we can't simply tell that when force is doubled keeping distance fixed how much times the charge on a particular ball has been increased or decreased. At present we can easily argue that we can send the same current for two different time periods to calculate the charge on the ball but at the time of the discovery of Coulomb's law current was also not precisely known to people. So,what was the trick?

Suppose we have two identical balls, A and B, with conducting surfaces. We charge them and touch them together, ensuring that their charges are equal (Q, say). We measure the force between them at a given separation. We then touch B on to an identical but uncharged ball C. We can assume that B and C now both have charges of $\frac{Q}{2}$. That gives us another two combinations of charges, using A and B (or C) and B and C.