More about this epigram
One of Burns favoured styles of verse was the epigram, which he often inscribed on the windows of taverns with a diamond he possessed purely for this purpose. This one is dated from October 1786 by Scott Douglas who names the said roads as those between Kilmarnock and Stewarton.
However many think it more likely that this is from the later Highland Tour that Burns embarked on from Edinburgh with William Nicol and that the rough roads referred to are those the two had to negotiate as they travelled through the country.
Alistair Braidwood