Union Pacific Corp. and Southern Railway, in terms of revenues the largest and ninth largest companies in the railroad business, reported steady but modest increases in profits for the third quarter and first nine months.

Earnings of UP, which has subsidiaries engaged in petroleum and other energy resources, increased 16 percent in the July-September period to $65 million ($1.36 a share) from $56 million ($1.18) in the 1977 period as revenues rose 16 percent to $730 million.

Washington-based Southern reported record third-quarter profits of $23 million ($152 a share), up about 8 percent from $21.8 million ($1.42) a year earlier. Revenues increased 9 percent to $308 million.

Executives of both companies said yesterday that freight traffic continues at strong levels. UP Chairman James Evans said record shipping volumes reflected significant gains in the corn, wheat, coal and auto sectors.

"The railroad expects its strong traffic patterns to continue in corn and wheat quarter continued to rise at a faster rate than in 1977, with gains of 19 percent in farm products and 15 percent in stone, clay and concrete products.

He noted that the quarter included a four-day rail strike and accelerated maintenance program spending to compensate for work deferred because of unusual cold weather last winter.

Southern, which paid $5.1 million to an industry insurance program to aid the strike-bound Norfolk & Western in the recent quarter, earned $96.6 million ($6.35) in the first nine months compared with $97 million ($5.75) a year earlier. Revenues rose 8 percent to $924 million.

UP earned $184.5 million ($3.88) in the recent nine months vs. $158 million ($3.3) as sales rose 16 percent to $2.16 billion. s.