After stone was abandoned as the material for the manufacture of weights in favour of base metals such as lead or bronze, specimens of ancient weights which have survived are too corroded to be of value for the determination of standards. We are dependent upon the weights of gold or silver coins for such knowledge as we possess. These coins have been in circulation and therefore subject to wear, whilst silver coins during their long burial in the earth have been in addition exposed to corrosion. They have lost weight. The method of fixing the standard of weight has in consequence been to select such coins as appear to have suffered little loss and draw conclusions from them. The weights of such coins, however, are variable, and no principle can be laid down to determine the particular coin which represents the true standard. For stone weights a sufficiency of specimens of which we know fairly accurately the original weight is often available to enable the problem to be solved statistically, but unworn coins are rare. In this paper an endeavour is made to draw conclusions as to the average loss of weight of worn coins from observed data so that statistical methods can be applied. This is done by means of an hypothesis for which an experimental verification is adduced from modern English coinage. From the hypothesis a formula is obtained connecting the original standard weight of a given series of coins with the mode derived from a statistical investigation.