Under the gold standard, if Britain became more productive relative to the United States, what would happen

Question:

Under the gold standard, if Britain became more productive relative to the United States, what would happen to the money supply in the two countries? Why would the changes in the money supply help preserve a fixed between the United States and Britain?

Exchange Rate
The value of one currency for the purpose of conversion to another. Exchange Rate means on any day, for purposes of determining the Dollar Equivalent of any currency other than Dollars, the rate at which such currency may be exchanged into Dollars...