THE ROYAL CROWN Derby tureen given by Queen Elizabeth II to President Ford as a Bicentennial gift last year helps one understand why President and Mrs. Carter have asked that state gifts be limited only to an exchange of photographs.

The soup tureen is decorated with his and hers official seals (Ford's and Elizabeth's) and pictures of the rear end of Philadelphia's Independence Hall and the front of the White House. It also has eight gold corncopies, two wreathed circles with the dates 1976 and 1776, four acanthus leaves lopped with gold rings, four rows of 14 gold stars on blue backgrounds, eight borders of red and white stripes and a rose (Tudor? Cabbage?) on the top, along with various and assorted curlicues too numerous to mention.

The tureen, a perfect 1876 Victorian pastiche, was presented during the British royal couple's visit to the United States last year but mercifully withheld from the public gaze until now.

The British gift may have been retaliation for the Stueben engraved-glass "Merry-Go-Round" covered bowl the Trumans gave to Princess Elizabeth in November 1947, when she married Prince Philip. The bowl is remarkable for being one of the better (or worse) examples of Steuben's late-'40s Muscle Modern period, engraved bulbous-kneed maidens, bumpy legged fire-eating steeds and knolty dwarfs. The bowl is topped with plumed-glass lumps and bottomed with left-over crystal bumps.

The British tureen and the American bowl are among a group of objects linked to American relations with the British Crown - mostly royal visits to the former colonies - that will go on view Wednesday at the Smithsonian's Museum of History and Technology. The exhibit, "Silver Jubilee," may be the only American museum show no mark Elizabeth's 25th year of reign with objects and documents from the queen's private collections in Buckingham Palace and Windsor Castle. It also includes objects such as the tureen from American presidential libraries and archives. A twin of the Steuben bowl given to Elizabeth, lent by Steuben, is also in the show.

The exhibit, on the museum's first floor, will continue through Labor Day. Its organizer, Silvio Bedini, the museum's deputy director, seems to be an expert at extracting rare and wonderful (See FORM, F4, Col. 1> objects from royal archives. He also arranged, not long ago, loans of the Leonardo da Vinci drawings from the queen of England and Columbus artifacts from the king of Spain.

The Fords, the exhibit shows, in return for the tureen, gave the queen a handsome rodeo rider bronze sculpture, "Two Champs," by the well-known American sculptor Harry Jackson.)

The state gifts - since they are so rarely shown to the public outside presidential libraries - are the most interesting part of the show.

A splendid gift is the ormolu candelabra, presented by the then-Princess Elizabeth in 1951 to President Truman as a gift from her father, King George VI. They were a housewarming present for the newly remodeled White House. The candelabra were made by the master metalsmith Matthew Boulton around 1770. The 35-inch high objets vertu have inserts of spar, a purplish stone that resembles amethyst. Normally they sit upon the handsome marble mantlepiece, also given by King George, in the Queen's Bedroom, one of the two ceremonial guest bedrooms at the White House. The candelabra were lent by Mrs. Carter.

A literally dazzling gift is the gold pin set with five scattered diamonds and five marquise-shaped diamonds centered with the queen's own ER (Elizabeth Regina) cypher given to Mrs. Ford by Queen Elizabeth.

Scaling down are gold cufflinks given by the queen to the Fords' son Jack and a silver compact to his sister Susan. The Queen Mother gave the Dwight Eisenhowers a snuffbox when they visited her in Scotland in October 1946, and Mrs. Eisenhower got a silver compact from the Queen Mother on Nov. 10, 1954.

Dutiful letters of the last century from the Prince of Wales to his mother, Queen Victoria, offer an unusual (and painfully polite) glimpse into those royal visits. On Oct. 7, 1860, the Prince wrote from Richmond:

The President's house is a very nice one, & the rooms are really very fine, & comfortably furnished. Washington is a fine looking town & contains some striking buildings; the finest is the Capitol, in which the Congress sits . . . Mt. Vernon . . . is unfortunately in very bad repairs & is rapidly falling into decay; we saw all the different rooms & the one is wh. Washington died.

That Queen Victoria herself was, as a young princess, somewhat of a hero-worshiper can be seen by the answers to her requests for autographs from President James Madison and John Quincy Adams. The letters remind us how poor and weakly worded are our modern epistles:

It being intimated that an autographic specimen from me, as from some others of my countrymen, would be acceptable for a collection which the Princess Victoria is making; these few lines, with my signature, though written at a very advanced age, and with Rheumatic fingers are offered for the occasion. They will be an expressions at least of the respect due to the young Princess who is understood to be developing, under the wise Counsels of her august Parent, the endowments & virtues which give beauty & value to personal character, and are auspicious to the high station to which she is destined., James Madison, Feb. 1, 1834.

Bedini believes the first individual American association with British royalty was in 1616 when Pocahontas, an Indian, went with her husband John Rolfe to England. That event is represented by an engraved portrait of Pocahontas (1595?-1617) by an unknown artist in 1793, based on a 17th-century engraving from life by Simon van de Passe. Alas, this royal visit ended most tragically of all, Pocahantas died just before she was to leave England.

For the history buff, the show has delights in every glass case. The teletype tapes between President Buchanan and Queen Victoria on the completion of the Atlantic cable in 1858 include the apologetic explanation of why the President didn't get the queen's entire message. Here, too, is the "Trent Memorandum," the last official act of Victoria's Prince Consort, which averted war between the British and the Union during the Civil War. The exchange of letters between Queen Victoria and Mary Todd Lincoln on the death of President Lincoln shows how an official act can be done in a personal manner - the queen speaks of her own grief for her husband's death:

No one can better appreciate than I can, who am myself utterly broken-hearted by the loss of my own beloved Husband, who was the Light of my Life, - my Stay - my all - what your sufferings must be . . .

The show - from the arrow heads, in 1632 specified as rent and fealty to the crown from Lord Cecil Calvert, Baron of Baltimore for the land that became Maryland, to the 1976 official photograph of the royal pair - marks this country's endless fascination with the royal family we could not live with nor without.