How does one get the value of acceleration of gravitation on earth accurately by experiment without electronic device? How does one get the value of acceleration of gravitation on earth accurately to 5 significant digits by experiment without electronic device?
 A: A pendulum of (long) length L will tick with a period of $2\pi\sqrt{L\over g}$, and air resistance can be made negligible for a mm-sized oscillation of a heavy object on a several-meter long rigid arm. You need to determine the location of the center of mass accurately to know the effective value of $L$, but this can be done arbitrarily accurately by balancing the arm and weight on a fulcrum (or by accurately finding the CM of each of the parts and measuring the configuration of the parts accurately). Then you just have to count the number of oscillations over a long enough period of time. This is a practical method that allows the determination of g to 5 significant figures (assuming the error on L is the signifcant one, the lever is 10m, and the position measurements are at the .1mm scale) with no technology.
A: You can make very very sensitive mechanical balances without any electronics.
And with a torsion bar and an optical measurement of the deflection you can probably do a reasonably accurate relative measurement
