National Steel Corp. reported 1978 earnings of $112.4 million, an 87 percent increase over 1977, a generally weak year for the steel industry.

Last year's earnings amounted to $5.85 a share on sales of $3.8 billion.

In 1977, National earned $60.1 million ($3.12 a share) on sales of $3.2 billion. It is the nation's third largest steel producer.

"Strong demand for steel and continuing cost-reduction program results have enabled 1978 earnings to recover significantly from the previous year's level and from the impact of the coal strike," said Chairman George Stinson.

For the fourth quarter, National said it earned $38 million ($1.98), a 131 percent increase over earnings of $16.5 million (85 cents) in the 1977 quarter. Fourth-quarter sales rose from $769 million in 1977 to $1 billion in 1978.

American Airlines Inc. had record net income for 1978 that was 93 percent above 1977 resuits -- the previous record year -- according to preliminary, unaudited figures, the nation's third largest air carrier and fifth largest transportation company said yesterday.

Net income rose from $69.7 million ($2.11 a share) to $134.4 million ($4.27) during the full year and from a restated net loss of $12.1 million in the 1977 fourth quarter to about $8 million (17 cents).

Continental Oil Co. reported an 89.5 percent gain in fourth-quarter profits to $155.2 million ($1.45 a share) from $81.9 million (77 cents) a year earlier. Revenues were $2.8 billion, up from $2.4 billion a year earlier.

Profits for the year were $451.3 million ($3.20) on revenues of $9.9 billion compared with $380.6 million ($3.55) in 1977 on revenues of $9.1 billion.

Conoco is the nation's ninth largest oil producer and 17th largest industrial corporation.

Getty Oil Co. reported a 19.9 percent gain in fourth-quarter earnings, continuing the string of higher profits reported by most of the nation's oil companies in recent days.

Getty, the nation's 20th largest oil company, said fourth-quarter earnings totaled $102 million ($1.24 a share), up from $85.1 million ($1.04) a year before. Fourth-quarter revenues totaled $1.03 billion, up from $960 million in the fourth quarter of 19779

For the year, Getty's profits came to $327.8 million ($3.98) against $309.1 million ($3.78) in 1977. Revenues totaled $3.76 billion in 1978, up from $3.54 billion a year earlier.

United Technologies Inc. announced record earnings for the 1978 fourth quarter and year and raised the quarterly dividend on common stock by 5 cents to 55 cents a share.

The higher rate is payable March 10 to shareholders of record Feb. 23.

Chairman Harry Gray said net income for the quarter was up 25 percent to $62.04 million ($1.20 a share on a fully diluted basis) from $49.59 million ($1.08) a year earlier. Sales rose to $1.705 billion from $1.428 billion.

Profits for the year were $234.14 million ($4.76) on sales of $6.265 billion compared with $192.97 million ($4.26) in 1977 on sales of $5.55 billion. There were almost a million more shares outstanding in 1978 than in 1977.

Liggett Group Inc. announced record net earnings of $56.8 million in 1978, including a gain of $30.4 million after taxes from the sale of its foreign cigarette operations.

The earnings, which amounted to $6.26 a share, were up from $2.6 million (12 cents) in 1977.

Raymond J. Mulligan, president of Liggett Group, said the company had record revenues of $971 million in 1978, up from $878 million the previous year.

Liggett Group announced last Friday an agreement in principle to sell its domestic cigarette division to a firm owned by Dolph Overton of Smithfield, N.C. Officials said the sale would bring in net proceeds of about $122 million.

Earnings for 1978 included the $30.4 million ($3.43) after-tax agin from the sale of the foreign tobacco unit. Earnings from the foreign cigarette business amounted to $30 million and included a $17.3 million after-tax charge for a write-off of good will related to the "other products" group.

The earnings for 1977 included an after-tax charge of $30 million ($3.33) for the revaluation of assets of the Perk Pet Food subsidiary, and earnings of $3.1 million from the foreign cigarette business.