President Reagan becomes an honorary member of the Society of the Cincinnati this evening in one of the capital's remarkable settings, the ballroom of Anderson House, at 2118 Massachusetts Ave.

He is in good presidential company in accepting the affiliation, since George Washington himself became the patriotic society's first president general in 1783, retaining the office till his death at the close of the century. A group of officers of the Continental Army, as the Revolution drew to a close, established the society to keep alive the comradeship and the revolutionary ideals of the war, and took its name from the pure-spirited Roman dictator Lucius Quinctius Cincinnatus, a patrician farmer who left his plow to take a military command and restore order in Rome in the 5th century B.C., and who relinquished all power and refused all trappings once his mission was finished.

It seemed to the men of 1783, and to Americans thereafter, that the republic was lucky in Gen. Washington, who preferred his farm to power, but who was prevailed on to become the country's first president chiefly because nobody else seemed able to fill the job.

The French Maj. Pierre Charles L'Enfant, who later designed the plan for the capital, designed the society's insignia, a diamond-studded gold eagle suspended from a blue-and-white ribbon. Washington wore this jewel, which was evaluated at $367 in his estate at his death. Presidents general of the society have in turn worn it, to this day.

President Monroe was an original member, and Zachary Taylor and Franklin Pierce were members. President Jackson was the first presidential honorary member, and others have included Benjamin Harrison, Grover Cleveland, Theodore Roosevelt, William Howard Taft, Woodrow Wilson, Warren G. Harding and Franklin Delano Roosevelt.

Membership otherwise is hereditary.

A handful of guests, maybe 120, have been asked to arrive at Anderson House at 5:30 this afternoon and to be in their seats in the ballroom by 6. Investiture ceremonies will be followed by the president's greeting guests, if his schedule permits, in the second-floor English Drawing Room, and a reception will follow, which the president is not expected to attend.

The room itself is remarkable, 30 by 60 feet, the ceiling about 28 feet high, and although it was originally called the Great Hall, its rococo splendor and suitability for parties have caused most people to call it the ballroom.

It is only one of several spectacular rooms of Anderson House, a limestone mansion built between 1902 and 1905 by the Boston firm of Little and Browne for Larz Anderson and his wife.

Anderson was among the more widely known diplomats of the early 20th century, serving as ambassador to Japan and minister to Belgium, among other posts. He was born in Paris in 1866, was educated at Exeter and Harvard, served in the Spanish-American War and became second secretary of the embassy at London when he was 25. When he was 31 he married Isabel Weld Perkins, who inherited a fortune estimated at $17 million from her grandfather, Stephen Weld, who had grown rich from East Indian tradings. Isabel Perkins was one of the world's richest young women at that time.

The house promptly became the scene of elaborate entertaining. Anderson once observed that his was the only house in town in which servants still wore livery. The Andersons were not personally flamboyant, but they astounded the capital when in 1908 they bought a car that went almost 60 miles an hour and had toilet facilities, a writing desk, a heating system, a fan and other wonders.

Marshal Foch, the king of Siam and an almost endless list of notables were entertained in the house.

Anderson was a member of the Cincinnati, whose insignia is carved over the front door, and it is thought that from the beginning he planned to leave the building to the society. The deeds were to his wife, but Anderson suggested she might give it to the society, which she did in 1938 after congressional action made the transfer tax-free. The house is virtually unaltered from the Andersons' day and is one of a handful of great mansions remaining in the town. People can never quite remember how many different marbles are used in the floors--17 is perhaps the consensus.

The room in which the president will be invested has a wooden floor, marquetry squares surrounded by great borders of herringbones. Along the north wall of the room a stairway rises gently in 26 steps to a balcony level. The stair rail is wrought bronze, and the balcony is supported by twisted columns of rose-colored marble.

Anderson, though quite a society figure, is said to have had only a limited appetite for large parties and is supposed to have scratched a peephole or two in one of the mirrored panels of the ballroom, through which he could see who was present, and to gauge the best time for his entrance. There is a secret door, which is not much pointed out nowadays since people got in the habit of playing with it, through which Anderson could come and go with surprising and, to him, agreeable celerity.

Apart from its architectural decorations, which are fairly fabulous by present standards, the building houses an important research library of 10,000 volumes and many priceless original papers connected with the Revolution. There is also a collection of 16th-century Flemish tapestries and a number of portraits of early Cincinnatians by Gilbert Stuart and others, as well as a few paintings by Reynolds, Hoppner, Raeburn and Lawrence, from the days of the Andersons.

Since the house has become the society's national headquarters, there have been various occasional displays (such as rare battle flags) and lectures. The house is a museum, open 2 to 4 on most weekdays.

From time to time there have been beautiful dinners, dances and so forth at the house, given by members of the society, and it has been available for government use from time to time. In 1974 the visiting king of Jordan used it for a grand dinner honoring President Ford and Henry Kissinger, at which Pearl Bailey sang after supper.

Upstairs there are suites of rooms named for the various state societies of the national organization, including 15 or 20 bedrooms (depending on whether you count the old servants' rooms), one of them 26 feet square.

There used to be a wonderful malachite table in the Winter Garden (a gallery running along the south side of the ballroom); it was moved because people kept setting drinks on it at parties. Martinis are bad for malachite. The glorious old stable no longer stands. It was nice to be a horse there. The stalls were rendered festive by a number of huge polished brass balls, and the feed buckets were dark wood with dazzling white bands. Nothing, of course, lasts forever.