Southern Railway Co. and Norfolk & Western Railway, whose proposal to merge is scheduled for Interstate Commerce Commission hearings starting in two weeks, both reported yesterday that the first quarter of 1981 produced substantial increased in profitability.

At the same time, officers of the two railroads cautioned that second-quarter results would adversely affected by the current United Mine Workers strike against the coal industry. Roanoke-based N&W long has been a major hauler of coal and Southern's list of principal revenue-producing commodities also has been headed by coal in the last year.

Southern, a Washington-based corporation, reported record profits of $59.1 million ($3.79 a share), exceeding by 15 percent the previous record quarter in the same period last year of $51.2 million ($3.29). Operating revenues rose 9 percent to $437 million.

Profits of N&W rose 63 percent to $78.6 million ($2.45 a share) from $48.4 million ($1.55) a year earlier, which was the previous best first quarter. Revenues jumped 21 percent to $449 million.

Southern President Harold Hall credited higher freight rates and tight budgetary controls as main factors in higher earnings, given a lower level of freight business in the recent quarter. Revenues ton-miles (one ton carried a mile) on Southern fell 3 1/2 percent in the January-March period. Only coal among the 12 leading commodity groups escaped the decline in volume; coal shipping was up 10 percent from last year.

Freight revenues, on the other hand, were higher because of increased rates, in all major commodity groups but transportation equipment (including autos) and construction aggregates. Freight volume continues to trail the 1980 level and this situation "is aggravated by the loss of coal tonnage due to the UMW strike," Hall sated, adding:

N&W Chairman John Fishwick said his railroad "will be severely impacted" by the UMW strike that began March 27. Coal accounts for about half of the railroad's revenues, and coal traffic has been curtailed sharply in recent weeks. "We expect that a good deal of this traffic will not be permanently lost but will move after the strike is over," Fishwick added.

To some extent, both railroads benefited from heavy prestrike coal shipments in the recent quarter, as customers built inventories in the case the mines were closed. In N&W's case, first-quarter coal volume was up 13 percent from a year ago.

A. H. Robins Co. of Richmond, a pharmaceutical manufacturer, said earnings rose 36 percent in the first quarter to a record $12.1 million (48 cents a share) compared with $8.9 million (35 cents) a year earlier. The previous record was $9.7 million (37 cents) in 1976. Sales rose 10 percent to $114.7 million.

President E. Claiborne Robins Jr. told the annual meeting yesterday that operating profits from health-care products rose 11 percent. "While we do not expect to maintain the earnings pace of the first quarter, we nevertheless expect 1981 to be one of our best years," he added.

Dynalectron Corp. of McLean reported yesterday that first-quarter profits rose slightly to $1.03 million from $1.008 million in the same period last year. Per-share earnings fell to 12 cents from 14 cents, because of more shares outstanding. Revenues rose to $107.7 million from $97.2 million, and the engineering, energy and technical services firm had a backlog of contacts on April 2 totaling $290 million, down from $325.5 million a year ago.