Why is it that the resistance scales on the display of the analog multimeter is in unequal graduation?
Because the meter measures the current through the resistance with a fixed voltage applied. I = E/R, there is an inverse relation between the current, the meter deflection, and the resistance, and that cause the non-linear scale. Digital multimeters apply a constant current to the resistor and measure the voltage, so the relationship is E = IR, in this case the voltage is directly proportional to the resistance. The reason analog meters do not use the second method is that they were built before ICs were available, and a constant current requires opamps to generate and control the constant current supply. Plus, you need a very high impedance voltmeter to avoid loading the unknown resistor, and that also requires ICs. .
