Southern Railway and Allegheny Airlines, two large transportation companies with headquarters in Washington, yesterday reported higher profits in the third quarter of 1977.

Profits of Southern were up by a modest 6.7 per cent from the same period last year at $21.8 million ($1.42 a share) compared with $20.4 million ($1.33) Revenues rose to a record $283 million from $252 million.

Southern President L. Stanley Crane said the quartely earnings were the second highest on record for the period, while nine-month profits rose 35 per cent to a record high of $87.1 million ($5.75 a share) from $64.6 million ($4.23) last year. Revenues were up 12 per cent to a record $851.5 million.

Allegheny Airlines reported record September and third-quarter profits, which president Edwin 1. Colodny attributed to increased personal travel and the impact of new discount fare in some markets.

Third-quarter earnings rose to $5.4 million (87 cents a share) from $3.8 million (60 cents) last year, as revenues increased to $130 million from $116 million.

For the first nine months, Allengheny reported profits of $274,000 (1 cent) - off sharply from $5 million (55 cents) in the 1976 period.

Results reported by other transportation firms were as follows:

Union Pacific Corp - Third-quarter profits rose 11 per cent to $55.9 million ($1.08 a share) from $50.4 million ($1.08), with revenues up 25 per cent to $628 million ($3.34) vs. $19.7 million ($2.78), as revenues rose 24 per cent to $1.8 million.

Santa Fe Industries - Third-quarter profits were $36.4 million ($1.36) vs. $39.1 million ($1.49), and revenues rose to $472 million from $4.15 million.

Southern Pacific Co. - Net income fell to $24.8 million (92 cents a share)from $31.2 million ($1.17) because of higher income taxes: revenues increased by 7 per cent to $514 million.

AUL, Inc. - The holding company for United Air Lines and Western International Hotels reported third-quarter profits of $85.3 million ($3.42 a share) vs. $48 million ($1.92) last year, with revenues up to $912 million from $831 million.

Eastern Air Lines - Third-quarter profits dipped to $3.2 million (16 cents a share) from $10.6 million (54 cents) a year earlier, with revenues up slightly to $495 million from $448 million. Eastern benefitted last year from a wage-freeze program.