Words of true wisdom from Will!
Looks like Spider mites to me, which thrive in hot, dry environments. Horticultural oil can smother them, but must be done 3 times at 7-10 day intervals, with particular attention to the under side of the leaves. With house plants, I do this in the shower, and then I clean the shower so that no one gets concussed from slipping on the oil that was sprayed everywhere.