Southern Railway Co. reported yesterday a modest increase in first-quarter earnings but two other major railroads reported dismal results because of the 110-day coal strike.

Norfolk & Western Railway of Roanoke reported a quarterly loss of $12.7 million while Seaboard Coastline Industries, based in Richmond, announced that profits plumetted to $1 million from $20 million in the same period last year.

Washington-based Southern reported record first-quarter profits of $28.8 million ($1.89 a share), up 4.5 percent from $27.6 million ($1.82) in the 1977 period. Revenues rose 5.6 percent to $287.5 million.

Southern President L. Stanley Crane said the earnings growth occurred despite a 56 percent decline in coal shipments during the quarter and a 10 percent decline in overall freight carloadings because of the severe winter weather.

He attributed the higher profitability to a mixture of freight business which helped to moderate effects of the coal strike and to a 4 percent rate increase last Nov. 30. Since the strike ended, freight business has picked up sharply, he added.

Norfolk & Western's loss of $12.7 million was in contrast with earnings a year earlier of $17.7 million (57 cents a share), and was the first operating loss during an initial quarter since N&W began reporting consolidated earnings in 1969. Revenues declined 22 percent to $226 million.

President John Fishwick attributed the loss to the coal strike and said coal traffic levels have been running about 7 percent above normal levels since the United Mine Workers strike ended.

Seaboard President Prime Osborn told stockholders at the annual meeting in Richmond yesterday that first quarter revenues rose 6 percent to $436 million, despite the coal strike and winter weather.

But coal tonnage was off 32 percent and expenses were boosted sharply by the weather, he said. The quarterly earnings were equal to 7 cents a share compared with $1.38 in the 1977 period.

Maryland National Corp., parent firm of Maryland National Bank, yesterday reported a 23 percent increase in first-quarter profits. Earnings totaled $5.36 million (75 cents a share) compared with $4.35 million (61 cents) in the 1977 period. Total assets were up $300 million in the past 12 months to $2.6 billion on March 31, as deposits increased 6.5 percent to $2.16 billion. Marynat, the state's largest bank, now operates 143 offices around the state.

Central National's net income was 3 cents a share less than that, however, because of a program of selling some securities at a loss to allow reinvestment at higher interest rates. That program has been completed and will lead to higher future investment incme, the bank said.

Total resources for the corporation were $502 million, up from $460 million.

Rowe Furniture Corp., of Salem, Va., reported first-quarter earnings of $145,000 or (six cents a share) down from $219,000 (nine cents) because of what chairman Gerald M. Birnbach called "fierce competition" in the upholstered furniture business.

Shipments by the medium price furniture maker increased from $11.5 million to $12.7 million.