The Gordon Jewelry Co., the nation's second-largest jewelry store chain, has bought the 105-year-old R. Harris & Co. jewelry stores and plans to expand them to three or four suburban malls within the next few years.

The four Harris stores - 11th and G streets, the White Flint Mall, Georgetown and Chevy Chase - were bought because Gordons wanted to expand in the Washington area with a company whose "name gives us more exposure in the Washington, D.C. market. Washington is a very good jewelry market," said Daniel P. Gordon, senior vice-president for the Houston-based chain.

"There's a very good disposable income in the area and it is considered a high fashion area. It's not New York as far as high fashion, but it's certainly in the next tier," Gordon said.

Gordons already has two stores with its name in Springfield Mall and Prince Georges Plaza, Gordon said, plus it owns the D.P. Paul jewelry store chain which also has a Springfield Mall store.

Another reason the Harris purchase was made was "we had trouble getting locations in the other (shopping) centers with those names," meaning Gordonw and D.P. Paul, Gordon said. That it because their names are not as established in the Washington area as Harris, Gordon said.

The malls Gordons hopes to expand the Harris stores into are Tysons Corner, Montgomery, Landover and Wheaton malls, Gordon said.

The Harris stores merchandise is targeted toward middle and upper-income customers and Gordon's market spans all levels of middle class, Gordon said.

Gordons owns about 475 stores, 265 of which bear the Gordons name, Gordon said. It also owns 145 traditional stores, which stock higher-priced jewelry, silver, china and crystal, 26 catalog storerooms and 48 jewelry outlets in major department stores, Gordon said.

Gordon would not disclose the stores' profits and the stores' owners could not be reached yesterday. During the 1978 fiscal year ending Aug. 31, Gordons had sales of $282 million and net profit of $19 million, Gordon said.