In the book, The Wealth of Nations, what does it mean to "receive money by tale"?

Solution 1:

I think it refers to the archaic meaning of tale:

• enumeration; count.

(Dictionary.com)

• Money were accepted by weight (he probably refers to coins of gold and silver, not paper money ) in the same manner as ingots of gold and silver are at present.

The old meaning that refers to enumeration was probably the original one in Germanic:

Tale:

• Old English talu "series, calculation," also "story,....."to recount, count." The secondary Modern English sense of "number, numerical reckoning" (c. 1200) probably was the primary one in Germanic;

• The ground sense of the Modern English word in its main meaning, then, might have been "an account of things in their due order."

(Etymonline)

Solution 2:

As indicated by @Josh61, "tale" means "count".

There were many different coins, each one having different designs, weights, inscriptions, and the purity of the metals (gold, silver, copper) varied greatly. The value of a coin primarily depended on its weight and composition.

Even if the weight and composition of each coin was standardized, Antique coins were subject to clipping and the most effective way to combat clipping was to have coins weighted rather than counted in transactions.