ALEXANDRIA'S City Council has now enacted an ordinance setting a few simple rules for gold and silver dealers. That's good beginning. But to be effective, these laws need to cover the whole metropolitan area. The other local governments, and state legislatures, need to follow Alexandria's lead promptly.

The purpose is to make it a little less easy and safe for a thief to sell stolen goods -- either in their original form or in the little bars that used to be somebody's antique tea service before it went into the melting pot.With the vast rise in the prices of precious metal, a new and unwholesome traffic has developed. Itinerant dealers come through the area, placing large newspaper ads offering cash for gold and silver. Next comes a wave of burglaries. The dealer does a brisk trade out of a motel room for a few days and then departs. How was the dealer to know that all those soup spoons were stolen?

There are four basic requirements that every jurisdiction ought to adopt -- at once. The first is, like Alexandria, to make all dealers register, get permits and keep records of all purchases.

The second is to prohibit dealers from buying lumps of melted metal, or ingots of amateur manufacture, or any article with serials or jeweler's marks obliterated.

Third, dealers should be required to hold all goods for 15 days while notifying police of each purchase. That's already the law in the District of Columbia and, as of last Wednesday, in Alexandria. Some dealers protest that holding the goods is too risky because the price of gold and silver might fall in that time. Baloney. Dealers who don't want to risk inventory losses can hedge on the futures market. That's what the futures market is for.

Fourth, and most important of all, sellers must be required to identify themselves. The District requires a name and address, but these are often fake. Alexandria requires a physical description, but why not go a step further? One large and well-established dealer, Federal Gold Exchange, Inc., insists on seeing a driver's license. In some cities, Federal Gold has begun to accept a driver's license only if it has a photograph. If there's no photograph, this dealer takes a fingerprint. If the seller doesn't want to be identified, there's no sale. That's the right way to do it.

These requirements alone won't end burglaries. But they will take some of the ease and profit out of them. The present lack of law is an invitation to a crime wave. Thousands of people in this area, having returned to stripped and ransacked homes, can testify, unhappily, to that.