The primal characteristic of a good self-portrait is (rather obviously) self-appraisal. This issue can be dodged, though the result is usually theatrical, a kind of flourish like an overconfident signature, a narcissistic attempt at self-advertisement which cannot ring true. There is too much awareness of a third party in such self-portraiture; not just the artist and his mirror-image, but the ''viewer'' as well.
One of the extraordinary things about Rembrandt's many self-portraits (and one writer has calculated that he made on average two pictures of his own features each year of his career) is that the ''viewer,'' of whom no artist can of course be entirely unconscious, has very little bearing on what is happening. Among 17th-century art collectors there was not much interest in the self-portrait.
Rembrandt's persistent practice of this branch of art was therefore essentially private. Unquestionably what he learned, from all this self-portrayal, about human expressiveness, emotion, and painting itself, was fed back into more outward aspects of his work. But here, in fact, was an artist working for no master but himself, and studying nothing more (nor less) than himself. Yet the paintings do not strike the outsider as egocentric: they seem to carry in them something universal. They represent a searching effort to discover his own identity hidden in that unlikely face.
Increasingly, these enquiries into the art of knowing himself become visible ''question marks.'' He confronts his mirrored reflection with a kind of dissatisfied, sometimes even quizzically amused, frown. He evidently looked at that image, each time, not only with frank familiarity, but as though he had never met this person before.
''Who are you?'' is the crux of the enquiry, rather than ''How do you do?'' These paintings span the passage from youth to old age with a kind of acceptance not dissimilar to Shakespeare's melancholy Jacques tracing the ''seven ages of man.'' They also demonstrate something unconquerable. Perhaps they can be seen as typical of many human beings who grow from youthful rebelliousness to success to failure to a new kind of assurance to a late mingling of cosiness and cynicism. But through all these changes and moods there runs what could be described as the potential of the man. These plain features never quite satisfy their owner's sense of puzzlement, they remain an arena of the possible, of the maybe or the could-be. They are the features, as the paintings make increasingly clear, of an artist - and an artist is persistent, continuous, forever developing, never coming to an end.
The self-portrait at Kenwood House in London was probably painted about 1660, and is often shown as an example of the so-called ''classical'' phase of Rembrandt's art. Just after it was cleaned in the late 1940s, the Burlington Magazine described it in an editorial as ''the most structurally rigid'' of Rembrandt's self-portraits, and said that its ''geometry'' was ''the solid framework in which fierce sensations are left to glow.'' It brought to the writer's mind the style of the mature Cezanne.
It is true that this is a strikingly monumental work. Beautifully hung at Kenwood, it can be experienced almost as an impressive audience with a great artist. All the same, it is only Rembrandt, without illusion, looking at Rembrandt - an unpretentiously straightforward man, honest, abrupt perhaps, but not unkind - a strange mixture of the very positive and the uncertain.
The unmistakable structure of the picture doesn't for a moment remove that ''question mark'': the nature of appearance is still impenetrable, and the intangible qualities of a man can still do no more than play secretly in the soft shadows of his face.