Southern Railway Co.'s earnings continued on a growth track during the second quarter, advancing 14 1/2 percent to a record $50.8 million, the Washington transportation firm said yesterday.

The quarterly earnings were equal to $3.31 a share and were the highest for any three-month period in the company's history. The previous record was $44.3 million ($2.94 a share) in the same quarter last year.

Revenues rose 9 percent to $366 million, which President L. Stanley Crane said reflected rate increases as well as a higher volume of business. All commodities except transportation equipment (new automobiles and parts), coal and waste or scrap material contributed to higher revenues in the recent period.

Ton-miles rose about 2 percent in the quarter, even though the 1978 period included a surge in coal shipping after a three-month miners' strike was ended (a ton-mile is one ton of freight moved a mile).

For the first six months of 1979, the railroad's profits rose 18 percent to a record $86.6 million ($5.64) from $73.1 million ($4.83) a year earlier, as revenues rose more than 14 percent to $704 million.

Spending for maintenance of plant and equipment also was at record levels in the first half - up 22 percent from a year ago to $261 million. Total expenses increased by 15 percent in the recent six months.

In addition to higher outlays for maintenance, Crane said there have been sharp increase for wages and fuel. Diesel fuel costs alone have jumped more than 50 percent a gallon since the start of the year.

Southern's directors voted a regular quarterly dividend of 80 cents on common stock payable Sept. 15 to owners of record Aug. 15. Regular payouts on preferred and preference shares also were approved.

MCI Communications Corp., a Washington-based national communications firm, reported yesterday a 148 percent increase in profits for its first quarter ended June 30. Earnings were $2.1 million (4 cents a share) compared with $851,000 (3 cents) a year ago. Revenues jumped 44 percent to $29.6 million.

Per-share earnings for the recent period were affected adversel by payment of dividends on convertible preferred stock and by the existence of 8 million more common stock equivalent than last year. MCI said the gains reflects an expansion of private communications business and the impact of a recent agreement on the purchase of local telephone interconnection facilities.

Union Trust Bancorp of Baltimore and half a dozen other regional banking firms generally reported substantial increases in profits during recent months because of higher volumes of lending at near-record interest rate yields.

The Maryland bank holding company, which owns Union Trust Co. and financial services subsidiaries, reported one of the more modest gains in operating profits - up 5 percent in the second quarter to $2.28 million (93 cents a share) from $2.18 million (89 cents) a year earlier.

Six-month earnings, not counting gains or losses from selling securities, rose 2 percent to $4.36 million ($1.78) from $4.27 million ($1.74).

Chairman J. Stevenson Peck said yesterday that average assets grew 11 percent in the first half to a record $1.2 billion, while loan volume increased 9 percent to an average $744 million. Deposits at Union Trust's 82 offices averaged $866 million in mid 1979 compared with $836 million a year ago. Second-quarter reports from other bank firms included:

New Virginia Bancorp. of Springfield, operating earnings of $515,446 (39 cents) vs. $514,417 (39 cents); deposits of $164 million on June vs. $157 million; loan volume of $109 million vs. $104 million.

Central Fidelity Banks Inc. of Richmond, operating earnings of $3.94 million (74 cents) vs $3.29 million (64 cents); deposits and loan volume rose 8 percent in the past year to $1.43 billion and $994 million, respectively, on June 30.

First American Bank of Virginia, a unit of Financial General Bankshares based in McLean, earnings of $2.09 million ($1.31) vs. $1.17 million ($1.04); deposits rose $58 million in the past 12 months to $711 million, while loan volume increased $48 million to $430 million.

National Bank of Fairfax, earnings of $421,451 ($1.05) after accounting for effects of an offering of convertible debentures in December; assuming no dilution, earnings were $1.26 a share vs. $1.41. Deposits rose to $152 million from $148 million a year ago, and loan volume increased to $102 milliom from $88 million.

Bank of Columbia of Washington, six-month operating earnings of $167,509 (38 cents) vs. $64,814 (14 cents); deposits rose $6 million to $45 million, while loan volume increased to $31.5 million from $27.8 million.

Farmers & Mechanics National Bank, Frederick, six-month earnings of $1.1 million (1.87) vs. $872,300 ($1.47); deposits increased to $200 million from $191 million, while loan volume rose to $140.5 mililion from $124.1 million. CAPTION: Graph, Big Oil Profits By Alice Kresse - The Washington Post