ABOUT 15 years ago, Sy Larkin of A Brooklyn walked into a police auction in New York City, saw an old violin on sale, and outlasted other bidders until he took it for $80. He had no chance to examine it until he had become its owner, but later he took it to a appraiser who offered him $3,500 for it.

"That made me think it was probably worth more than $3,500," says Larkin, "so I kept it and I play it regularly; I own 14 violins and I play them all for enjoyment."

Larkin was very lucky, with a kind of luck you hear about in old stories but not usually from living people. That's because old violins are vanishing from the marketplace. They are no longer just musical instruments; they have become investment properties, increasing in value more rapidly than a lot of stocks or real estate. This is putting them out of the reach of musicians who do not have the income of a Stern or Perlman and making them hard to get at any price. While an ever-growing number of players want to buy them, some of these instruments are being taken out of the musical life of Europe and the United States, being stored in vaults or sent off to unknown destinations in other parts of the world.

Larkin's violin is a product of the Tononi family, Giovanni and his son Carlo, who are not among the big three names of the craft but produced many highly regarded instruments in northern Italy during the early 18th century. The big three names for violins, violas and cellos are Amati, Guarneri del Gesu and, above all, Stradivari, all of whom worked in Cremona, Italy, in the 17th or early 18th century.

Some of these violins could be had for bargain prices two centuries ago. The famous "Betts" Stradivari, now in the Library of Congress, was reportedly bought by an English dealer in 1820 for one guinea, from a stranger who walked in off the street. Larkin's Tononi is certainly worth more than $3,500--perhaps 10 times that much--and the longer he keeps it the more it will be worth. That's what's happening to old violins. Around the turn of the century, Fritz Kreisler paid $4,000 for a Strad that he found "antagonistic to me," and later called this purchase "a costly error." In the 1960s, it would have been a $40,000 error, and today it would probably be $400,000 or more.

Jacques Francais, a New York dealer who is one of the world's leading experts on old stringed instruments, negotiates the sale of six to 10 Strads and Guarneris each year--perhaps one-third to one-half of the world's total annual traffic. Last year, he sold a Guarneri del Gesu for $800,000, but that is not the record price for an old violin. The record is the $1.2 million paid for the famous "Allard" Stradivarius by an unidentified buyer.

Francais does not know who bought it--or, if he knows, observes a code of professional secrecy. "It was an anonymous purchaser," he says. "My guess is that it went to the Orient, and I think it went to Hong Kong. There are more violins per square foot in Hong Kong than anywhere else in the world."

It's not only Hong Kong. Japan has become very interested in Western violins, and so has Korea. Iran, too. A case is currently pending in U.S. District Court here concerning a Strad that used to belong to National Iranian Radio and Television and changed hands mysteriously during the revolution there.

There also seem to be investors--individuals or groups--who are buying old instruments as investment properties in the Orient. One such collector is rumored to own 29 or 30 Strads. Dealers expect a similar level of demand to develop in Latin America during the next few years.

The Cremonese stringed instruments in the East constitute a small but not insignificant fraction of the total in existence, for which no precise figures are available. Various numbers are given, ranging from about 600 to about 800, when you ask the experts how many Strads there are. There are about 250 Guarneris, and an unknown number of Amatis.

There are also some instruments called "composites," which are partly but not entirely the work of a Cremonese master, possibly because part of the instrument was destroyed and had to be replaced.

Strictly speaking, most of the Cremonese instruments could be called composites, since most have been modified in one way or another during their centuries of existence. Some have been cut down or enlarged, which can reduce their value. Almost all have been altered to accommodate the bigger sound necessary for large, modern concert halls or to accept the higher tension of metal strings tuned to modern concert pitch, which is higher than it was in the 18th century. This apparently does not reduce their cash value, but it does make Cremonese instruments in their original condition the rarest of the rare.

Old violins, violas and cellos do not seem particularly rare in Washington. But that may be because they are more visible--treated as a public trust rather than an investment property to be hidden away in a vault. Most can be seen and heard with some regularity in the hands of the world's greatest string quartets. Five Strads at the Library of Congress are played regularly there by the Juilliard Quartet. Also at the Library are an Amati and a Guarneri del Gesu , which was donated by its former owner, Fritz Kreisler, and is played by visiting violinists. Some say it is the finest violin in the world.

The Corcoran Gallery has four Strads that were formerly the property of Niccolo' Paganini and are now used by the Cleveland Quartet, and four Amatis that are played by the Tokyo Quartet. The Smithsonian has dozens of old instruments--not only strings but horns and woodwinds--that are played by its resident ensembles, the Smithson Quartet and the Smithsonian Chamber Orchestra.

The Library of Congress Strads are a gift of Gertrude Clarke Whitall, who also gave the Library an endowment to have them played regularly--a key point and one that set an example for the enlightened treatment of old stringed instruments in Washington. In the same spirit but without an endowment, the Corcoran lends its instruments to great string quartets, believing that an old instrument must be played regularly to maintain its quality. In return for the loan, the Tokyo and Cleveland quartets perform regularly at the gallery free of charge. The Cleveland, which could not afford the insurance on its borrowed instruments, also plays at the University of Maryland in return for insurance payments. These eight instruments travel around the world with their players; the Library of Congress Strads can be heard only on the premises.

Ask any string player how he feels about Strads and Gesu s lying unused and accumulating capital gains, and the reaction is one of sheer horror. Whether or not instruments deteriorate when they are not played (most players think so, but opinions differ), the feeling is that they were meant to be played, not looked at in museums or stored away as investments.

Some investors feel that way, too--for example, Fort Worth businessman Bill Davis, who bought a Stradivari violin about a year and a half ago as a multifaceted investment. The instrument was selected by a search committee organized by the Fort Worth Symphony, whose concertmaster now uses it in the orchestra's performances.

"I wanted several things," says Davis. "I want it to go up in value, of course, but I also wanted the orchestra to have a fine instrument to set a standard for the other players, and I wanted to stimulate interest on the part of other people to do the same thing. It has turned out to be a good deal for everybody." Another fan of the orchestra, Fred Grimes, has bought a second Strad, which is being used by the leader of the second violins.

What does a player do who is not a millionaire and does not have a library, museum or orchestra to lend him a Strad or Guarneri? "I'm going through the process of looking for an instrument right now," says cellist Kenneth Slowik of the Smithsonian Chamber Orchestra, "and I'm doing it very carefully. You really have to love an instrument before you mortgage your life to buy it." Slowik has to buy an old instrument; his orchestra plays 18th-century music on instruments of the period.

Many other orchestral musicians and some star soloists are turning to modern instruments. "Modern," in this field, means something made during approximately the past 100 years, such as the turn-of-the-century instrument owned by cellist Fred Zenone of the National Symphony. But an instrument doesn't have to be that old to be good; Zenone and many other musicians believe that some instruments being made today may be recognized as classics in the future.

One name that comes up repeatedly when string players talk about new instruments is that of Sergio Peresson, an Italian-born luthier who now lives and works in New Jersey. (Violin-makers are called "luthiers"; the term dates back to before the violin was invented, when their predecessors made lutes.) Dealers in old violins will tell you that the new ones are not worth talking about, and an icy tone comes into Francais' voice when the name of Peresson is mentioned. "These instruments will not last," he says. "Chemicals are used to enhance the tone, and they sound very good for a while, but after five years the tone will collapse."

A growing number of players disagree--notably virtuoso violinist Eugene Fodor, who has played a Peresson since 1975. "The dealers are promoting a mystique about the irreplaceable quality of old fiddles," he says. "It helps to raise the price and it's a lot of malarkey. I used to play a Guarneri that formerly belonged to Joachim the famous virtuoso for whom Brahms composed his Violin Concerto . I could have played it for the rest of my career, but I have switched to a Peresson. Jacqueline Du Pre' owned two Strads cellos , but for the last few years of her career she played only her Peresson. These instruments are owned by Menuhin and Rostropovich and half the string section of the Philadelphia Orchestra, and the dealers hate to have anyone know about it."

Fodor should be getting a commission from Peresson, but most of what he says is verifiable. There are, in fact, 23 Peresson instruments in the string section of the Philadelphia Orchestra, which is particularly noted for the quality of its string tone, and some of them have been in use for 15 years. There are also several Peressons in the National Symphony, including one owned and used by concertmaster William Steck, who finds its tone "getting stronger if anything, really opening up and getting richer" in the fourth year after it was made.

The choice of an instrument, for those who demand top quality, is as personal as the choice of a human life companion. Ultimately, it is based on intangibles. One New York violinist, Diana Halprin, finally settled on a Guadagnini after trying out a number of Strads and other old violins that were not only more expensive but also less to her taste. "There are good Strads," she says, "but there are also some that I wouldn't give you $2 for, and I tried some costing up to $350,000." She was trading up from a Tonino that had cost her $40,000, but she still had to take out a $70,000 loan--the first loan ever given by Citibank of New York for the purchase of a musical instrument.

"Every morning now," she says, "I wake up and look at my Guadagnini and I say, 'Thank you, God,' then I say, 'Thank you, Citibank.' Banks don't like to take violins as security; they made me insure the violin, insure my life, even insure my hands so that no matter what happens, the payments will be made. I actually auditioned for my loan; I played the violin for the loan officer, right in the bank's lobby, while the employes and the customers listened. At the end, I got applause and $70,000."