Southern Railway Co. announced an increase in profits of nearly 73 percent for the third quarter of 1979 over the previous year.

In a meeting held here today for railroad analysts, the District-based rail freight company reported profits of $40.7 million ($2.63 a share) for the quarter, up from $23.4 million ($1.52) in the 1978 quarter despite steep increases in expenses, particularly fuel costs.

Revenues also set a record at $367.1 million for the quarter, 19.1 percent higher than 1978 third-quarter revenue of $308.2 million.

Nine-month net income of $127.3 million ($8.27) also was a record for Southern and was almost exactly the same as earnings for all of 1978. Revenue rose 16 percent to a record $1.071 billion from $923.6 million for the same nine months of 1978.

Leading analysts said they were somewhat surprised by Southern's results, and noted that its per-share earnings for the year would exceed their predictions by about $1.

Despite the continuing rosy earnings reports, Southern officials and other analysts cautioned that a recession could affect the company next year.

Further, Stanley Crane, Southern's chairman, said in an interview that he is concerned about the effects of rising interest rates on the company's prospects. Crane took a cautious approach toward 1980 in a presentation for several hundred analysts.

Crane said that 1979 earnings would top those for the previous year by a "very acceptable margin," but that "as far as 1980 is concerned -- let's wait and see."

"I'm concerned about the general level of the economy in the next six to nine months," Crane said in the interview. "The Federal Reserve actions are bound to have a negative effect, which I support if it will cut inflation."

The analysts attending today's meeting -- representatives of the nation's leading investment companies and banks -- echoed the cautious optimism expressed by Crane, but suggested that Southern -- which last year was the nation's second-most-profitable railroad -- might share industry-wide uncertainties in 1980.

The analysts said that passage of deregulation legislation might make Southern in effect share the losses absorbed by the Conrail system because of increases in various joint rate agreements.

Asked by an analyst about deregulation, Crane predicted that a bill would be passed by Congress some time next year. But Crane also noted that the most controversial proposal, which would allow unilateral adjustments of these joint rate agreements, could cut Southern profits.