Dominion Resources Inc., the Richmond-based utility holding company, yesterday reported a 12 percent increase in profits for 1987 to $430.5 million ($4.54 cents per share) from $385.2 million ($4.16) in 1986.

The company's revenue increased 10 percent to $3.3 billion from $3 billion.

However, the company said, its profits declined 10 percent in the fourth quarter, to $84.3 million (88 cents) from $93.8 million ($1), while revenue fell 5 percent to $760.5 million from $799.4 million in the quarter.

The company's chairman, William W. Berry, attributed the increase in profits for the year to a 5.5 percent increase in the kilowatt-hour sales by Dominion's electric utility, Virginia Power, and increased earnings from the company's nonutility operations.

The Virginia Power increase resulted from more than 77,000 new customer connections, a robust economy, and this year's weather conditions, which boosted electricity use.

The company attributed the fourth-quarter decline in profits and revenue to a one-time adjustment to reflect a new method for calculating electricity used but not yet paid for.

Media General Inc., the Richmond-based communications conglomerate, said its profits more than doubled in 1987, the company's strongest year of growth after several years of relatively flat results as acquisitions and diversification moves were absorbed.

The company -- whose holdings include newspapers in Richmond and Winston-Salem, N.C., the Fairfax County cable television system and several broadcast stations -- said it earned $42.9 million ($1.50) in 1987, compared to $17.1 million (60 cents) a year ago.

Revenue increased 13 percent to $715.3 million from $634.6 million.

In the fourth quarter, Media General said, it had profits of $11.4 million (40 cents), compared to a $8.4 million loss in the 1986 fourth quarter, when the company took a $16.8 million charge to cover a restructuring.

Legg Mason Inc., the Baltimore brokerage, said its earnings fell sharply in the quarter ending Dec. 31 in the wake of the Oct. 19 stock market crash.

Bad debts in client accounts wiped out nearly the entire profit in the quarter, the company said.

The company said it earned $236,000 (3 cents) in the quarter, compared to $2.3 million (31 cents) a year earlier, as clients' bad debts totaled $2.5 million in the most recent period.

Revenue increased to $55.4 million from $34.7 million.

"The December quarter was the most difficult and volatile period in recent history for the securities industry," said Raymond A. Mason, the firm's chairman.

"We are fortunate that we had limited exposure to areas which caused very large losses at some other firms."

For the first nine months of its fiscal year, Legg Mason earned $5.7 million (66 cents), compared to $7.3 million ($1.06) a year ago. Nine-month revenue rose about 60 percent to $164 million from $101 million.

Halifax Engineering Inc., an Alexandria-based professional services firm, said its profits nearly tripled in the quarter ending Dec. 31.

The company said it earned $279,000 (23 cents) in the quarter, compared to $95,000 (8 cents) a year ago. Revenue rose to $7.8 million from $6.4 million.

For the first nine months of the fiscal year, Halifax said, it earned $703,000 (59 cents), compared to a $216,000 loss a year ago. Revenue rose to $23.1 million from $19.4 million.