The Oxford English Dictionary has potass from potash:
An alkaline substance obtained originally by lixiviating or leaching the ashes of terrestrial vegetables and evaporating the solution in large iron pans or pots (whence the name). Chemically, this is a crude form of potassium carbonate (more or less mixed with sulphate, chloride, and empyreumatic substances), but was long thought to be (when freed from impurities) a simple substance.
And further defines it as:
Used also to include the impure carbonate of soda, barilla. [Obscure]
barilla is defined as:
An impure alkali produced by burning the dried [maritime plant barilla (Salsola Soda) which grows extensively in Spain, Sicily, and the Canary Islands] and allied species; formerly imported in large quantities, and used in the manufacture of soda [...]
So it's basically an old-time crude form of soda.
So he's having a (probably, by modern standards, quite disgusting and strong) whisky and soda.
The point the author might be making is it's not a lady's drink. But something a real man would drink to "refresh" himself. Perhaps with some intended irony.