At the end of the rainbow sits a pot of gold -- and Robert Sheets.

Each year Sheets, who operates out of a musty suite of offices on 14th Street near the Treasury Department, calls on hundreds of people, offering them small -- and often not-so-small -- fortunes.

It can be theirs, he tells them, if they'll give him about one-third of the total.

Most people do. The result has made Sheets and his profit-making American Archives Association one of the nation's most successful tracers of missing heirs.

Although neither Sheets nor the 11 members of his staff will discuss the firm's annual income, his critics and his competitors alike concede that it is large. Sheets says the firm, now in its 30th year, has settled unclaimed estates valued from $3,000 to $11 million.

The searches, often conducted in secrecy because of the competitive nature of the trade, have taken Sheets' staff and his investigators to courthouses, attics, newspaper morgues, cemeteries and old photographic studios seeking biographical records and clues that might lead to distant relatives and heirs.

Sheets is willing to discuss how his methodical step-by-step efforts have paid off, but is not willing to release the names of heirs for fear it would expose them to unwanted publicity. A self proclaimed "baron" of the industry, he now turns his nose up at any estate under $10,000 but says he would gladly have his staff spend years looking for an heir to a larger estate. w

As an example, he cites the work his staff has done locating the heirs of a Washington woman who died in 1975, leaving an estate valued in excess of $300,000. Like an estimated half of all Americans, the woman did not have a will, nor did she have any known heirs.

Until Sheets took the case, it looked as if District of Columbia government was going to get the estate under an "escheat" statute, which permits it to claim estates in the absence of heirs.

From old Who's Whos and social registers, his staff discovered the woman had been married to a foreign diplomat and that they had lived for a time in New York City. In New York investigators began what was to become a five-state hunt for missing heirs as they followed the trail of court records -- a second marriage in New York in 1946 that referred to a 1941 divorce decree in Chicago that led to a 1933 marriage in Indiana noting her 1904 birth in Missouri.

In St. Louis, investigators discovered the woman's parents divorce decree and a suit filed by her father that bore a Fort Worth, Tex., notary public's stamp. That took the investigators to Texas where they eventually located seven first cousins of the deceased, each of whom is expected to bring a claim for the estate before a District of Columbia court within the next few months.

Some cases call for delicate diplomacy as Sheets and his investigators unearth illegitimate children, secret first marriages, and a host of peccadilloes that some heirs would rather leave undisclosed. Such facts emerge early in the investigation as Sheets reconstructs the decedent's family tree in an effort to identify potential heirs.

The discovery of an ancestral philandering rarely stops a potential heir, Sheets says. His staff, however, concedes that tact and diplomacy are often needed.

Says Jayne Tucker, the firm's genealogist: "I always tell them [the heirs] that I don't care whether they have been married one, two or nineteen times. All I want is proof [of heirship]. Now we can't help what great-grandpa did. If it's touchy, we try to be diplomatic."

Sheets tries to ignore whatever unseemly side there is to his business. He sloughs off the hostility of state administrations of abandoned property who call those in his trade "ferets" and says such epithets refer to his competitors who operate out of their homes. These he calls "scavengers."

Some 20,000 volumes of yellowing city directories and telephone books lone the walls of his offices, spilling over into what used to be a shower room. On the shelves are such oddities as "Harvard Class of 1924," "Thom's Directory of Ireland 1945," and a Fort Wayne, Ind., directory of 1889 -- each a tool in the search for heirs.

Sheets boasts of the firm's necrological collection -- the obituaries. There are hundreds of them neatly filed in alphabetical order in 730 library trays, each two feet long.

On the wall of Sheets' office hangs a kinship chart, a sort of family tree that shows what degree of kinship a mother, cousin, or aunt is to the deceased, marked by a blank in the middle of the chart.

"That's my Bible," says Sheets, who calls himself a "forensic genealogist" rather than an heir tracer.

But amid such sobriety there is room for humor. "Contested wills make for heirs splitting," reads a sign on a wall in a next door office. On the desk top is a sign asking "Is your will up to date?" Taped across the bottom is "I hope not."

It is those who die without wills who keep American Archives in business.

"Lawyers die without wills, doctors die without wills, the whole spectrum right down to the recluse and the derelict. Some of the derelicts on the street leave behind $20,000 to $30,000," Sheets said.

"We had a derelict in Who's Who. He had been a very successful businessman. He went through a very bad marital situation, turned to liquor, and died of acute alcoholism on the streets of Chicago," Sheets recalls.

From interviews with other derelicts that knew him, American Archives investigators discovered that the man had said he was a member of Phi Beta Kappa.

"We checked the Phi Beta Kappa lists and there he was," Sheets said. The man left behind a $90.000 estate, a portion of which went to American Archives for locating the man's children.

But it is Sheets' first large estate -- "the one that made me" -- that he will never forget. Sheets, who had been a title researcher for a Chicago real estate firm, began tracking down the heirs of Mae Haas, a widow who died in Cleveland in 1950, leaving a $250,000 estate. Sheets discloses the name because the case is so old.

Initially he found no trace of heirs. Shortly after a portion of the estate was sold off, a junk man who had bought a stove from the estate discovered a packet of tintypes tucked into the stove's asbestos lining. He notified the estate's administrator, who notified Sheets.

Sheets had the old photos enlarged and found the photographer's name and "Poughkeepsie, N.Y." on a corner of the pictures. Knowing that Haas had worn a crucifix, Sheets went to New York and searched parish after parish for baptismal records. Finally he found what he was looking for. From there he tracked down two elderly sisters who had in their family albums photographs indentical to the tintypes found in the Haas stove. The sisters were the heirs.

Sheets refers to firms like his as "gentlemen," but acknowledges that the business of tracing heirs can be a sticky affair that provokes intense emotions.

There is often keen competition among heir tracers for the larger estates. "It is a footrace sometimes. If someone gets the solution first, the others back off," says Jim Gleason of the Sacramento, Calif., tracing firm of Brandenburger and Davis.

Competitors of American Archives agree that Sheets' Washington firm is one of the largest in the nation. "If it's not the first, it's the second largest," says Gleason. That assessment is shared by Larry Morrow of Finders Diversified, an Ohio firm, and others in the field.

Tracers are also the rivals of state officials who, in the absence of identifiable heirs, can claim estates under state "escheat" statutes and add them to state treasuries. Some 30 estates that would have gone to the District of Columbia, in the absence of heirs, went instead to American Archives and the heirs the firm found, according to Sheets.

But the business isn't what it used to be, according to Sheets. "It's unbelievable, this inflation," he said. "An individual that would have left an estate of $50,000 now leaves an estate of $10,000. He's had to use his savings." CAPTION:

Pictures 1 and 2, Robert Sheets, who calls himself a "forensic genealogist," in his 14th Street office, and some of his 20,000 city directories and telephone books. Photos by James M. Thresher -- The Washington Post; Picture 3, Therese Weber checks for information in obituary files covering Chicago area. By James M. Thresher -- The Washington Post