We inherited from ancient Rome and Greece the custom of honoring military heroes, horsemen or not, with equestrian statues. Not quite so old, but apparently as durable, is the widespread belief that the fate of the rider is indicated by the position of the horse's hooves.

As the theory goes, if one hoof is raised, the rider was wounded in battle, possibly dying later. Two raised hooves indicate death in battle. If all four are on the ground, the rider survived all battles unharmed.

Most art historians disclaim the existence of any such convention, and point out the many statues that violate it. Others disagree, and history is not much help.

The first such statues we know of were created by the Greek sculptor Lysippus to commemorate the generals of Alexander the Great; the mounted figures proved popular and became customary. In Roman times, emperors and generals literally waited in line to have their likenesses immortalized in stone. Possibly the most famous equestrian statue from classical times is that of the Roman emperor Marcus Aurelius, found on the Capitoline Hill.

As the pall of the Middle Ages spread over Europe, monumental and memorial statuary was destroyed or retired to the recesses of churches and tombs. Sepulchral sculpture, advanced through Christian influence, came to occupy an important position in the world of art. It became the practice to attach symbolic and allegorical meanings to statues, a custom that still endures.

Leading Renaissance sculptors such as Donatello and Verrocchio of Florence revived equestrian statuary. Donatello's statue in Padua, honoring condottiere (leader of mercenaries) Erasmo Gattemelata, is credited with bringing such sculpture back into the open. Such statuary again took on civic as well as religious significance. The great Leonardo designed an equestrian statue of Francesco Sforza, another condottiere who became the ruler of Lombardy. The re- emerging skills of Renaissance sculptors are attested in the graceful lines of Verrochio's horseback statue of Bartolommeo Colleoni.

Equestrian statues of the Baroque period abounded with ornate decoration, and allegorical figures soon grew to assume an importance equal to that of the persons being honored; the pedestals frequently overshadowed the equestrians.

Nineteenth century England was a barren period for equestrian sculpture but in the United States, especially after the Civil War, monumental sculpture proliferated.

Americans honored Civil War heroes here there and everywhere there was a group of citizens willing to sponsor a statue. Generals who never had forked a horse in life soon sat in saddles of bronze or stone. We even put religious leaders on horseback.

Apparently as part of this wretched excess came the development of the custom, myth or legend of relating the position of the horse's hooves to the fate of the rider.

The question remains, are the horses symbolically sculpted? Although the supposed convention appears be American in origin, similar arguments have been advanced in England, which has statuary conventions aplenty: ivy symbolizes the bonds of memory; a broken column extinction of a family line; cut or broken flowers, a child or young wife from off this mortal coil untimely ript.

If ornate symbolism was once the rage on the Continent, our statuary has been more literal. Our heroes are -- were, anyway -- heroes, and to hell with metaphor.

One way to test the hoof convention is to look at a lot of statues. Go to Gettysburg and it seems to prove out. The statue of General John F. Reynolds, slain in battle, has two raised hooves. That of General Winfield Scott Hancock, wounded severely but surviving until 1886, has one raised.

Generals George G. Meade, John Sedgwick, O.O. Howard and Henry W. Slocum, all of whom passed through Gettysburg unscathed, are shown astride horses with all hooves planted firmly. But there are deviations: Sedgwick later died in action at Spotsylvania, and Howard already had lost his right arm at Fair Oaks.

Washington contains more equestrian statues than any other city in the nation; it is significant that only perhaps 10 out of 30 or more follow the convention. The most striking example of noncompliance is Andy Jackson on his rearing steed in Lafayette Park, although he came through of the War of 1812 in fine fettle.

An interesting contrast is the statue of Confederate General Stonewall Jackson on the Manassas battlefield; unveiled in 1940, it has Jackson's mount standing foursquare. The General survived First and Second Bull Run only to be fatally wounded by his own troops at Chancellorsville.

In general our statuary suggests that, if the purported convention is real, it applies to the outce of a particular feat of arms, not to the rider's ultimate fate. More likely, sculptors just do as they please. STALKING THE STATUES Washington's equestrian statues are not much help in testing the validity of the so- called "hoof convention." Here's a sampling: SOME THAT FOLLOW THE "RULES" FRANCIS ASBURY: 16th and Mount Pleasant NW (1924). All hooves on ground; died in peace. FIELD MARSHAL SIR JOHN DILL: Arlington National Cemetery (1950). All hooves on ground; died of leukemia. GEN. ULYSSES S. GRANT: Union Square, at the east end of the Mall (1922). All hooves on ground; died in peace. MAJ. GEN. WINFIELD SCOTT HANCOCK: Seventh and Pennsylvania NW (1896). One hoof raised; wounded in battle. MAJ. GEN. JOHN A. LOGAN: Logan Circle, Vermont Avenue, 13th and P Streets NW (1901). One hoof raised; died in peace, twice wounded. LT. GEN. WINFIELD SCOTT: Scott Circle, 16th and Massachusetts and Rhode Island NW (1874). All hooves on ground; died in peace. GEN. PHILIP H. SHERIDAN: Sheridan Circle, 23rd and Massachusetts NW (1908). All hooves on ground; died in peace. GEN. WILLIAM TECUMSEH SHERMAN: 15th and Pennsylvania and Treasury Place NW (1903). All hooves on ground; died in peace, pneumonia. MAJ. GEN. GEORGE H. THOMAS: Thomas Circle, 14th and Massachusetts NW (1879). All hooves on ground; died in peace. JOHN WESLEY: Wesley Theological Seminary (1961). All hooves on ground; died in peace. SOME THAT DON'T GEN. SIMON BOLIVAR: 18th at C and Virginia NW (1959). One hoof raised; died in peace of tuberculosis. MAJ. GEN. NATHANIEL GREENE: Stanton Square, Maryland and Massachusetts NE (1877). One hoof raised; died in peace, unwounded. MAJ. GEN. ANDREW JACKSON: Lafayette Park (1853). Two hooves raised; died in peace. LT. GEN. THOMAS J. (STONEWALL) JACKSON: Manassas (1940). All hooves on ground; wounded by own men and died. MAJ. GEN. PHILIP KEARNEY: Arlington National Cemetery (1914). One hoof raised; died in battle. MAJ. GEN. GEORGE B. McCLELLAN: Connecticut Avenue and Columbia Road NW (1907). One hoof raised; died in peace, unwounded. BRIG. GEN. JAMES B. McPHERSON: McPherson Square, 15th between K and I streets NW (1876). One hoof raised; shot and killed in battle. BRIG. GEN. COUNT CASIMIR PULASKI: 13th and Pennsylvania NW (1910). One hoof raised; died in battle. LT. GEN. GEORGE WASHINGTON: Washington Circle, at 23rd and K and Pennsylvania and New Hampshire NW (1860). One hoof raised; died in peace of cynache trachealis. Washington Cathedral (1959). One hoof raised. graphic /photo: Andrew Jackson (By James A. Parcell)