Southern Railway and Union Pacific Corp., two of the nation's most profitable railroad firms, yesterday reported record earnings for the second quarter of 1977. Missouri Pacific Corp. also posted higher profits, and Norfolk & Western Railway boosted its quarterly dividend rate.

Washington-based Southern said profits in the three months ended June 30 soared 71 per cent to $37.7 million ($2.51 a share) from $22.1 million ($1.45) in the same period last year and $29.9 million in the second quarter of 1974, the previous high. Revenues jumped 16 per cent to $309 million in the recent period.

That brought profits for the first half to a record $65.3 million ($4.33 a share), an increase of 48 per cent over $44.2 million ($2.90) a year earlier. Revenues rose 12 per cent to $581 million.

Southern president L. Stanley Crane said freight car loadings were up strongly in recent months, with volume gains for all 12 leading groups of commodities carried on the firm's trains.

He said, however, the future appears clouded by projections of a slowdown in economic growth and the possibility of coal mine strikes (coal shipments account for about 10 per cent of Southern's annual revenues). A prolonged strike would "diminish the otherwise bright prospects in store for Southern and for much of the rail industry this year," Crane said.

Union Pacific Corp., a diversified rail and energy firm, reported second-quarter profits of $54.7 million ($1.15 a share) vs. $44 million (94 cents), as revenues rose to $605 million from $487 million. First-half profits were $102 million ($2.16 a share) on revenues of $1.19 billion vs. earnings of $79.3 million ($1.70) and revenues of $967 million.

Missouri Pacific Corp. second quarter-profits rose to a record $28 million ($2.09 a share) from $16.2 million ($1.56) a year ealier, as revenues rose to $369 million from $303 million.