I realize this is four years after the original question, but this is an interesting problem. Use an AC source to generate a voltage across the piece of silver. Two Arduino outputs from a counter can be used as an H bridge to generate the source voltage. Then use an AC amplifier as a sense amplifier and connect it's output to an A/D input and use synchronous detection to recover the signal. Note that the A/D input needs to be biased to half the supply voltage using a resistive voltage divider.
Synchronous detection consists of simply synchronizing the A/D with the counter so that it reads once when one side is high and the other low and again when one side is low and the other high. The readings are differenced and then averaged. By using a high gain, low noise AC amplifier and long averaging times it's possible to measure in the sub microvolt range. This is how a cheap AM radio can pick out microvolt signal levels clearly.
Amplifier DC offsets are no longer a problem since the signal is capacitively coupled. Four wire Kelvin connections are required and thermal offsets may be problem so some thermal insulation and draft protection may be required.
If there is excessive phase shift through the AC amplifier, this can be compensated for by using sine and cosine detection. This requires four measurements over one cycle spaced 90 degrees apart. The averaged "cosine" or in phase value and the averaged "sine" or 90 degree displaced reading are then squared, added and the square root calculated to get the final reading independent of any phase error.
This is an old school technique which is rarely used now because op-amps have such awesome DC offset specifications, but they won't get you into the microvolt region without very careful DC design. Vacuum tube meters were able to measure in the microvolt region, but they used special choppers and AC amplifiers with feedback.