His claim that memory is “unaccountable” could be understood in at least two different ways.  He might mean only that he doesn't have an account of the actual workings of the faculty, that he lacks a psychological theory of the operation of the mechanism by which we remember. Yet this would not be a reason for thinking that memory is “unaccountable,” but only “presently unaccounted for”. So the most plausible interpretation is that memory is unanalyzable.  Reid's insistence that memory cannot be accounted for via a relationship to an image, but that it is instead an immediate knowledge of the past would seem to support the unanalyzablity reading.  To call memory “unanalyzable” in the sense Reid has in mind is to say that it cannot be analyzed or reduced to component parts, at least not over and above its characterization as direct knowledge of the past.