One camp firmly believed that the only way to acheive a truly balanced rotor was to ensure that the two blades weigh exactly the same and the the two blades' centers of gravity at exactly the same difference from the rotor head (or from the mounting bolt, really). It was impossible to balance the rotor system otherwise, they claimed.

The other camp was equally firm in their belief that the centers of gravity and weights need not be identical, but must only result in the same moment when balanced in see-saw fashion.

When the dust settled, some of the first camp were convinced that, surprisingly enough, it is possible for a rotor system to be balanced without using blades whose masses and CG's were truly identical, or even remotely close!

The forces that act on a seesaw are 'moments.' Moment is equal to the product of mass and distance (radius) from the center of rotation:

moment = M x R

The forces that act on a rotating rotor head are centrifugal forces. (some prefer to use the term centripetal, which is a bit more to the point but boils down to effectively same thing). This force is equal to the product of the mass and the square of velocity, divided by the radius of the center of mass:

centri{fugal|petal} force: M x V x V / R

Velocity is distance over time, and in this case distance is the product of two, pi, and radius.

velocity = 2 x pi x R / T

The question then is - can the equation for centrixxxx force be reduced to the equation for moment? The answer is yes. I'm now kicking myself for throwing away the proof, but I do have a counterexample below. Consider a 10 gram blade with a CG 1 centimeter from the root, and a 1 gram blade with a CG 10 centimeters from the root. It's trivial to prove that their moments are the same: 10 x 1 is equal to 1 x 10. But will they exert the same centrifugal force on the rotor head?

F = M x V x V / R

F = M x (D/T) x (D/T) / R

F = M x (2 x pi x R / T) x (2 x pi x R / T) / R

so now we substitute real numbers into each equation...
T has been set to 1 for simplicity.

blade 1: m = 10 grams, r = 1 centimeter,   v = 2 x pi x 1
blade 2: m = 1 gram,   r = 10 centimeters, v = 2 x pi x 10

F1 = 10g x (2 x pi x 1)  x (2 x pi x 1)  / 1
F2 = 1g  x (2 x pi x 10) x (2 x pi x 10) / 10

divide by (2 x pi) x (2 x pi) to get:

F1 = 10g x 1  x 1  / 1
F2 = 1g  x 10 x 10 / 10

multiply to get:

F1 = 10g x 1  / 1cm
F2 = 1g x 100 / 10cm 

divide to get:

F1 = 10g / 1cm    (note that this looks a lot like the equation for moment)
F2 = 100g / 10cm     (that is definitely not a coincidence, I assure you!)

reduce the fraction in the second equation to get:

F1 = 10g / 1cm
F2 = 10g / 1cm

and note that:

F1 = F2