Opening five new Dart Drug stores and launching its Crown Books operation helped give Dart Drug a 24 percent increase in earnings for the nine months ended Dec. 31,

The Washington chain reported yesterday earnings of $1,710,000 or 93 cents a share, up from $1,378,000 or 75 cents a share for the same period a year ago, as sales rose from $129 million to $139 million.

For the third quarter, Dart showed a 33 percent increase in net income, from $475,000 or 26 cents a share to $634,000 or 34 cents a share; sales climbed from $47 million to $52 million.

President Herbert H. Haft said Dart remodeled nine stores during the nine months, in addition to the new openings. Last month the Crown Books operation, run by Haft's son Robert, opened three more stores and additional Crown Books units are planned this year, the company said.

Haft said Dart will change its fiscal year, which now ends March 31, to January 31, bringing it into line with common retailing practices.

Haft said January'e earnings statement will show a loss for the month because of the after-Christmas sales slump and high utility bills, but earnings for the abbreviated 10-month fiscal year will still exceed those for the full year ended March 31, 1977.

United Services Life Insurance Co. reported 12.9 percent rise in 1977 profits over the previous year, increasing from $6,026 million ($1.92 a share) to $6,802 million ($2.71).

The earnings increased resulted from an 11 percent gain in premiums and a 10.8 percent gain in investment income, said Leslie Schultz, president.

United Services Life, an International Bank affiliate, said new life insurance sales increased 5 percent to $224.5, bringing total life insurance in force to $2.78 billion. Total assests increased 8.4 percent to $322 million.

Atlantic Research Corp. of Alexandria reported its profits more than doubled last year, increasing to $1.01 million from $463,000 in 1976.

Sales for the year were $32.6 million, up from $27.6 million. Atlantic Research, formerly a subsidiary of The Susquehanna Corp., now is privately owned.

January was a warmer month than normal, but that was bad news for Washington Gas Light, which said the depressing the company's earnings.

For the 12 months through January, the gas company's net income was $13.5 million, ($2.42 a share) down from $16.2 million ($3.39) before extraordinary items for the previous 12-month period.