Two of the nation's strongest railroad companies -- Southern Railway and Union Pacific Corp. -- yesterday reported booming business and record profits during 1978.

In another major development for the depressed rail industry, Southern Pacific Co. said it will not oppose a proposed merger of Chessie System Inc. and Seaboard Coastline Industries to form the largest railroad system in the country.

In effect, Southern Pacific abandoned a potential takeover fight for Seaboard, of which it owns 10 percent of the common stock. Benjamin F. Biaggini, chairman of San Francisco-based Sopac, said mergers are vital to survival of the rail industry and that this goal was more important than his own firm's disappointment that it couldn't merge with Seaboard.

Washington-based Southern said profits jumped 54 percent in the fourth quarter and 19 percent for all of 1978 to record levels in both periods. Based on this performance and "the outlook for continued growth in 1979," Southern directors yesterday voted an 11 percent increase in quarterly dividend rates -- starting with a payout of 80 cents a share (up from 72 cents) on March 15 to owners of record Feb. 15.

In 1978, Southern earned $127 million ($8.35 a share) compared with $107 million ($7.04) the previous year, with revenues up 10 percent to $1.26 billion. Fourth-quarter profits were $30.8 million ($2.00) vs. $20 million ($1.29) on a revenue increase of 17 percent to $337 million.

President L. Stanley Crane noted that Southern's gains occurred despite a 110-day coal strike that reduced business for the firm's leading freight commodity, coal. In the final quarter, coal revenues jumped 17 percent and chemical shipping revenues were up 19 percent.

A late-year surge in freight carloadings has continued into January and "currently shows no signs of abating," Crane added. In the first two weeks of January, carloadings jumped 16 percent over the 1978 period.

Union Pacific officers also were optimistic about business in 1979 after looking over their annual earnings statement, which showed profits up 19 percent to $264 million ($5.55 a share) from $221.9 million ($4.68) in 1977. Revenues rose 17 percent to about $3 billion.

In the fourth quarter, the gain was much stronger: Profits up 25 percent to $79.6 million ($1.67) vs. $63.8 million ($1.34) and revenues up 20 percent to $834 million. All Union Pacific operations posted record profits for the year with railroad earnings up 21 percent, Champlin Petroleum up 13 percent and Rocky Mountain Energy up 19 percent.

Chairman James Evans said coal and grain shipments have been particularly heavy and "we remain, on balance, optimistic about our prospects for 1979."

Southern Pacific's announcement yesterday, which virtually assures approval of the $1 billion Chessie-Seaboard merger by stockholders at special meetings next month, came less than a week after Chessie and Seaboard submitted formal merger applications to the Interstate Commerce Commission, which also must approve the plan.

Biaggini said SoPac will vote its 1.4 million shares in favor of the combination, ending speculation that Seaboard's largest single block of shares might be voted against the combination at a meeting where a majority vote in necessary.

"While we are disappointed that we were not able to work out an affiliation between Southern Pacific and Seaboard Coast Line to form the nation's first transcontinental railroad, we have long recognized and endorsed the concept of railroad mergers as necessary to restore health to the industry," Biaggini stated.

Top officers of Chessie and Seaboard hailed the SoPac announcement as a "statesmanlike" decision by Biaggini that recognizes the proposed merger as one that "can only help" U.S. transportation.