The paintings of Velazquez are an extraordinary balance of apparent opposites - of modesty and importance, of publicity and privacy, of familiarity and dispassionate objectivity, of direct impact and quiet, patient harmonies.
He has been described by Allan Braham as ''a painter's painter'' making pictures so ''detached in character'' that ''it is as a technician that he can be most easily understood.'' Such a comment does, however, suggest that the quality of his art is somehow to be found in his skill and technique - and yet it is as true to say that few artists have made technique of such secondary considerations.
He treats it as no more than a means to an end - carefree, nimble, and direct , but always subservient to the image. To call him a technician might almost be an insult. It overlooks his undemonstrative humanity, his disregard for conventions - still refreshing today - not to mention the inspiration his works were to later painters like Goya and Manet, who were deliberately nonacademic and anti-technique.
Mr. Braham does, however, happily qualify this notion by referring to the ''power'' of some of Velazquez' images as depending on ''an ability to re-create in paint the essence of the living world that is given to few painters'' and also to his ''unnerving freedom from preconception.''
This last phrase certainly touches on some of the more indefinable qualities of his art, as well as on his charming and immediately apparent ones.
''Prince Baltasar Carlos in the Riding School'' is not one of his better known works. This is partly because it is privately owned and has not been shown in public much until recently, and partly because until it was cleaned in the early '70s it was relegated to ''workshop of Velazquez.''
Now, however, it is confidently considered his work. An exhilarating picture, not large in comparison with his more important records of the court of Philip IV, it is painted with a deft assurance, airiness, and color-harmony that are masterly and persuasive. The apparently almost instantaneous characterizations - from the King's son himself, perched with such confidence on his mount, to the middle-distance figures, in particular the bulky form on the right of the prime minister, the Conde-Duque de Olivares, to the King and Queen watching from the balcony in the background - are unlikely to be by any other hand: They have that ''essence of the living world.''
Velazquez was Philip IV's favorite painter, but he also owed much to Olivares , through whose influence he had first been recommended to the King. It seems possible that this painting was done for Olivares (it is known to have been in the collection of Olivares' nephew in the latter part of the 17th century). Until his downfall the prime minister was an immensely powerful figure, and apart from being a picture of the heir to the Spanish throne early displaying that symbolic accomplishment of kingship, a mastery of the horse, this painting is also a tribute to the Conde-Duque's status, not to say self-esteem.
The prancing boy equestrian with his white-plumed hat, white hose, black costume, and crimson sash may dashingly upstage everyone else in the scene. But Olivares comes a close second, receiving the lance in his capacity as ''Master of the Horse'' - and also, therefore, as riding instructor to the Prince.
Enriquetta Harris, in the Burlington Magazine, has suggested that Baltasar Carlos ''is about to be put through his paces . . . in the art of running at the ring.'' She also points to a particular French print as a precedent for this as a pictorial theme - so that Velazquez's spontaneity, or ''lack of preconception, '' is here not quite as total as it might appear to be. But the boy's enjoyment of riding and its attendant royal skills are true to life: In a letter written a year or two after this painting was made, Olivares described to the prince's uncle the boy's inexhaustible enthusiasm for las lanzas: ''Even Lent,'' he says, ''brought no rest from tilting.''
This is not the only painting in which Velazquez places the King and Queen in a paradoxically ''subordinate'' background position. In his famous 'Las Meninas'' they are blurry images reflected in a distant mirror while the painter gives his main attention to himself and other members and offspring of the court. There is in such deliberate rearrangement of status an element of humor, perhaps, or at least a trait in the artist's makeup that wants to study and portray the less prominent, relatively ordinary people around him. He is fascinated with ''behind the scenes.'' His role was as an official recorder of a formal court while his inclination seems to have been for the informal. It is in his balance of these ''opposites'' that the truthful vitality of his art emerges.
Of Prince Baltasar Carlos this painting seems to ask, how can a small boy be one of the most important figures in the land? And it answers, conversely - and not without a silent touch of amusement - that, after all, this superior personage is only a child.