How accurately can you measure the volume of a bar (or coin)?
Using equipment that I could make from stuff around the house I could do it to one part in a thousand, and with stuff a hired chemist could carry in a suitcase we could measure volume to one in 10,000.
I'd do it by displacement, dunk it in water and weigh the water that spills over. Same method Archimedes used to measure gold purity for the government thousands of years ago --except I would run down the street naked screaming 'eureka' like he did.