Norfolk Southern Corp. yesterday reported record profits of $482.2 million, the highest in the railroad's three-year history, while both Legg-Mason Inc. and D.C. National Bancorp Inc. reported an increase in quarterly profits.

Norfolk Southern's earnings for the year ended Dec. 31 represented an increase of 35 percent over 1983 earnings of $356.5 million, company Chairman Robert Claytor told industry analysts in New York.

Profits in 1984 came to $7.66 per share of common stock, the highest since Norfolk & Western and Southern railroads merged in 1982. Operating revenue for 1984 was $3.53 billion, up from $3.15 billion last year.

Net earnings in the fourth quarter were $108.2 million ($1.72 a share) versus $101.3 million ($1.61) for the same period last year. Operating revenue for the quarter was $814.7 million, down slightly from $815.7 million last year.

Claytor attributed the increase in earnings and overall revenue to an increase in traffic volume and only a slight increase in operating expenses.

* Legg Mason Inc. yesterday said its revenue had increased by about 20 percent in the third quarter ended Dec. 31, while profits declined 13 percent in the same period.

Legg Mason Inc. of Baltimore, parent company of Legg Mason Wood Walker Inc., a major securities firm, said revenue for the quarter ended Dec. 31, rose to $18.9 million from $15.8 million in 1983. Profits for the quarter were $854,000 (20 cents a share), compared with $990,000 (23 cents) for the same period last year.

Results of the third quarter include those of subsidiaries C. C. Collings & Co. Inc. and Legg Mason Masten Inc., also securities firms.

For the nine-month period, revenue was $49.9 million, compared with $48.8 million in the corresponding 1983 period. Profits for the period were $1.5 million (36 cents), compared with $3.9 million ($1.02) for the nine-month period last year.

Many brokerage firms have reported a loss this year, said Chairman Raymond Mason. Losses have resulted from industry costs going up while revenue has not, he said. The poor performance of the stock market last year offset the increase in commission revenue, he said.

* D.C. National Bancorp Inc., parent company of D.C. National Bank, reported that earnings in the fourth quarter ended Dec. 31 rose 13.5 percent to $775,000 from $683,000 for the same period in 1983.

Annual earnings for the year ended Dec. 31 are up 40.3 percent over the same period in 1983, the company said. Annual earnings this year were $3.17 million ($3.94 a share), compared with $2.26 million ($3.59) in 1983.

At the same time, total assets increased 26.5 percent to $327.9 million, up from $259.2 million in 1983. Total loans were $231.4 million, up 40 percent, and total deposits were $290.6 million, up 25.9 percent.