Alexander Jackson Downing, the man who designed the Mall, called cemeteries "the first really elegant public parks and promenades formed in this country." Nineteenth-century guidebooks always praised Washington's famous cemeteries for "the elevating effect of ornate and well-preserved mortuary monuments on the moral taste and general sentiments of all classes." A quiet and elevating walk among the tombstones became so popular in the 1890s that most cemeteries issued admission tickets to control the crowds.

But times change, and tastes with them. Now those same cemeteries are likely to be particularly empty, with a semi-neglected, almost seedy air, full of marble stones and monuments melting or cracking from a century's exposure to the weather.

Which only makes them better. A graveyard walk is still a wonderful way - sometimes spooky, sometimes hilarious - to spend a sunny afternoon. And October, as if in honor of Halloween, is when Washington cemeteries are at their best. Weedy wildflowers like blue chicory, sprays of drying aster of Queen Anne's lace - here and there a rosebush bare and skeletal-looking, but covered with bright orange rose hips, or sometimes the Last Rose of Summer - left blooming alone. Ride through in a car and you rouse the bluejays, who rattle the trees and scold you. On foot, you will almost certainly flush a rabbit or chipmunk, maybe stumble on a very late or early-rising raccoon, surprise a crow, a dove, a quail. If you're lucky, a mockingbird will follow you along for company. And if you walk very slowly and quietly and let it get to know you, it will answer you, whistle for whistle, providing a little life in the midst of death.

Congressional Cemetery (1801 E St. SE), a good place to start, is amont the oldest existing cemeteries, founded in 1807 and filled with many graves from before the Civil War - when Americans were democratic even in death, and tombstones tended to be all of the same size and shape.It plots and roads run at right angles, like city streets, and the cenotaphs designed by Benjamin Latrobe in 1815 are an exampele of the plain, early American view of death. Squat little cubes of sandstone with a marble insert for the name of the congressman or senator underneath, they are more glum than grand, and determinedly antimonumental.

Congressional does, however, have plenty of the ornate mortuary monuments that delighted the old guidebook writers: The Elbridge Gerry Monument, built in 1823 to mark the tomb of the man who left us the word "gerrymander," is a giant truncated pyramid topped with an ornamental base, topped with an urn, topped with a flame or something just as ornamentally preposterous. The tomb of Alexander Macomb (1841) is a whole collection of symbols for death and the military: a broken sword, a Roman helmet, a draped broken column, an hourglass symbolizing time's fleet passage, and a butterfly and snake - both symbols of resurrection. That of John T. McLaughlin (1847), an upended cannon barrel on a base of stout cannonballs, is an impressively spartan marker, and would be even more impressive if not for its unfortunate resemblance to a giant anatomical model. John Philip Sousa is buried here, and Thadders Stevens, the great architect of Reconstruction and of the 14th and 15th amendments, altough all the biographies have him buried in a Negro cemetery in Pennsylvania, the only one he could find that was not racially restrictive.

Finally, Congressional is where you can visit the modest family tomb that houses the remains of J. Edgar Hoover, with a raised flat platform of earth in front of it that seems designed to invite dancing.

Now out to Glenwood (2219 Lincoln Rd. NE) to see what the Industrial Revolution did for death. Chartered in 1854, Glenwood is a romantic garden cemetery: Roads follow the contours of the land; trees are planted to look natural, but as you round a bend, open suddenly to reveal a prospect of faraway hills and valleys - most of them now filled with D.C. townhouses, but that's not the designer's fault. Glenwood is divided into neighborhoods, and the neighborhoods were divided by price: High ground cost most, and large plots more than small ones. The rich lived differently, and were buried differently, from the poor.

Glenwood is the place to get your Victorian symbolism straight: A broken column means an early death, a lamb a dead child, an infant that the child was under a year old. Anchors mean fidelity, wheat sheaves resurrection, naked woman that there is some pretense to public mourning, ivy eternal life . . . and obelisks - Glenwood has a whole forest of them - mean that the Washington Monument was getting close to completion when the dier died. A whole row of mausoleums seems to imitate 1870 townhouses - unless it's the other way around: The mausoleums look better and probably give more usable space for the money.

Here is the monument to Benjamin C. Grenup, the first fireman killed in the line duty (run over by the fire engine he was pulling): column (truncated, of course) carved with the scene of his death and flanked with three antique fireplugs. Here are all those dark granite things that look like the newel posts on Victorian staircases, topped with a plume; smug-looking statues of little children, and obelisks that have cracked and fallen over, so they remind you of Shelly's "Osymandias." Stones with Chinese characters, Beaux Arts, Art Nouveau, Art Deco stones - simple, clear designs with lumpy curves and rigid lines, like a bedstead in a Ginger Rogers movie - all dated at least 20 years after the style's fad had passed.

Prospect Hill, right behind Glenwood (enter from North Capitol Street) and much smaller, has a couple of oddities of the 1880s - cast-iron tombstones, designed by building firms trying to demonstrate that they could do everything the stonemason could, in equally Gothic splendor. One selling point of cast iron was that you did not have to keep paying a stonemason to cut names of additional family members as they joined the old ones in death - you just had a new plate cast and bolted to the pedestal.

St. Mary's Cemetery, right across Lincoln Road from Glenwood, is also small - but it is Catholic. I am proaably just prejudiced, since I went to Catholic schools, but it seems to me that Catholics have a much richer iconographic vocabulary than American Protestants - especially when it comes to death. St Mary's has Virgins, Holy Families, Infants of Prague, great rugged crosses, and some stuff I've never seen anywhere else. A handsome pair of larger-than-life maenads seem to do a serious but very lively dance, holding aloft a triple-size beachball. A husband who was obviously a bricklayer built his own tombstone for a departed wife, out of yellow fire-brick, so it looks something like an ornate Victorian backyard barbecue. Three or four stones are not carved but faced with gold and green and red and black tile, showing stylized lilies in a really spectacular Art Nouveau design.

Rock Creek Cemetery (Rock Creek Church Road and Webster Street) is a very early cemetry and a very late one. A small burial ground attached to the church dates back to the 1770s, but most of it was added in the 1870s. The most famous work here is the monument to Marian, the wife of Henry Adams, sculpted by Augustus Saint-Gaudens in a setting designed by Stanford White. There is no inscription, not even a signature on the statue of the hooded woman who sits facing a semicircular marble bench. You can cut off from the outside by a high hedge of holly, in a place at once very gloomy and austerely grand.

The success of the Adams monument inspired much of the other late Victorian art at Rock Creek - and hardly anyone has come up to the inspiration. The Thompson-Harding grave shows a rugged cross, an angel in the act of dropping a stone flower, and a statue of a portly gentleman trying hard to look celestial in a coat and tails. Many other mourning figures sit on semi-circular benches like the one White designed in attitudes of despair that strain credulity and must have strained every muscle on the model when they were carved. The mausoleums are very late, backed with stained glass that is like most Victorian craftwork - considerably better than the stuff that pretends to be fine art.

Rock Creek is the best-kept of the old cemeteries, which gives it a kind of barren golf-course look after Glenwood of Prospect Hill. But it has some delightful stuff: the door to the Sherwood mausoleum, done in 1928, a late but flawless example of Art Nouveau; the Hardon Monument, a single stone carved to look like a rough pile of uncarved stones, a cross, an anchor and an angel. By the 1890s there was a movement away from the ornate cemetery art, and Rock Creek has lots of examples of simple rough stones - simple rough stones of very expensive marble - cut with nothing more than the name of the deceased.

These are only a few of the area cemeteries - Washington has always had a compulsion to honor death. There's also Arlington, of course. But Arlington is full of all those orderly military rows - and it seems depressing that all those poor soldiers are not allowed to break ranks, even in death. National Memorial Park (Route 29, south of Falls Church) is worth a visit also, if only to see the Four Chaplains Memorial - which demonstrates that great bad tombstone tast will always be with us, even when art tuns to abstraction.

This weekend offers two chances to tour some of these historic graveyards:

Saturday the National Trust for Historic Preservation has a bus tour of Rock Creek and Oak Hill cemeteries, 9:30 to 3:30. Some seats are still open, and the $17.50 fee includes lunch at the Woodrow Wilson House. 387-4062 or 673-5363.

Sunday the Congressional Cemetery Association is holding an All Hallows' Eve festival, noon to 3, after the sheep have finished grazing. The sheep were called in, we're told, after Congress failed to appropriate grass-cutting money. Also: the Alma Temple clowns and tax-deductible box lunches at $12 and free food for accompanied children under 14. 839-3633.