Atlantic Richfield Co., the sixth-largest U.S. oil company, reported yesterday that it earned $403 million ($1.98 a share) in the third quarter compared with a $519 million loss a year earlier. Arco attributed the gain to higher profit margins on petroleum products and reduced exploration expenses.

And Unocal Corp., which is ranked 12th in the U.S. oil industry, reported that its third-quarter earnings declined 12 percent largely because of lower domestic natural gas and crude oil prices and reduced production.

Meanwhile, in Seattle, Boeing Co. yesterday reported a year-to-year increase of more than 50 percent in third-quarter earnings that it said was spurred by $3 billion in orders for more than 100 planes.

Other major companies posting their latest results yesterday included Merrill Lynch & Co. Inc., which said third-quarter and nine-month operating profits improved; UAL Inc., Trans World Airlines Inc. and Greyhound Corp., which said their third-quarter profits fell.

Arco's net earnings in the third quarter last year would have been $317 million ($1.23) had it not been for unusual items and losses on discontinued operations totaling $836 million. Third-quarter revenue slipped 8.6 percent to $5.50 billion from $6.02 billion.

Earnings on worldwide oil and gas operations rose 5 percent to $300 million in the quarter from $286 million in the year-earlier period. Worldwide production of oil and natural gas liquids declined slightly to 707,800 barrels a day. Domestic natural gas sales also slipped moderately to 1.207 million cubic feet a day.

For the first nine months, Arco had a net loss of $344 million, compared with a profit of $282 million ($1.09) in the same period last year. Revenue was off 8 percent to $17.04 billion from $18.59 billion.

*Los Angeles-based Unocal Corp., parent of Union Oil of California, earned $158.7 million ($1.37 a share) in the third quarter, down from $181.2 million ($1.04) on a greater number of shares outstanding in the third quarter of 1984. Revenue rose 5 percent to $3.04 billion from $2.89 billion.

Unocal Chairman Fred L. Hartley said third-quarter operating earnings were down only 8 percent despite adverse conditions in the crude oil and natural gas market.

The company had improved geothermal production, increased refining and marketing profit margins and higher sales of petroleum products. But these factors were offset by lower prices for domestic gas, crude oil and chemicals and lower foreign petroleum results.

Unocal had a $91 million after-tax gain on the sale of units in Union Exploration Partners Ltd., its new oil and gas limited partnership. Unocal said the gain offset expenses incurred in fighting off a hostile takeover attempt by Texas oilman T. Boone Pickens Jr.

Hartley said the debt-for-equity swap that foiled Pickens, a higher quarterly cash dividend and other steps "significantly improved the yield to shareholders."

For the first nine months of 1985, Unocal earned $459.8 million ($3.17), down from $547 million ($3.15) a year earlier. Nine-month revenue rose to $8.72 billion from $8.57 billion.

*Boeing Co.'s earnings for the third quarter were $132 million (85 cents a share) on sales of $3.1 billion, compared with 1984 third-quarter earnings of $86 million (59 cents) on sales of $2.2 billion.

Nine-month earnings were $378 million ($2.53) on sales of $9.4 billion, compared with $266 million earned on sales of $7 billion for the same period in 1984.

The healthy third-quarter figures were given a boost by orders for 104 commercial jets from 10 airlines and two leasing firms. Third-quarter orders in 1984 totaled 55 planes. Third-quarter sales included orders for 97 of the company's most popular airliner, the 737-300.

The announcement of a $2 billion deal for the purchase by Northwest Airlines of 10 of Boeing's new 747-400 jumbo jets and 10 of the slower-selling 757s came just after the quarter's end and will be included in year-end figures.

*Merrill Lynch & Co. Inc. announced that its profits soared 146 percent in the first nine months of the year even though its third-quarter income totaled less than half of the amount earned in the same 1984 period.

For the third quarter, which ended Sept. 27, the worldwide financial services firm reported after-tax earnings of $38.4 million (38 cents a share), down from $80 million (87 cents) a year earlier.

But last year's results benefited from the sale of the building housing Merrill Lynch headquarters in the Wall Street financial district. Sale of the One Liberty Plaza building added $46 million (50 cents) to 1984 third-quarter net income. A gain of $9 million (10 cents), stemming from tax-law changes also was added to last year's third-quarter income. Without those one-time gains, Merrill Lynch would have earned $25 million (27 cents) in the 1984 third quarter.

Revenue in the third quarter grew to $1.75 billion from $1.66 billion the year before.

Chairman William A. Schreyer and President Daniel P. Tully said Merrill Lynch has improved its financial posture this year. Merrill Lynch's improvements occurred in all areas, especially in its real estate business.

Merrill Lynch said its 1985 nine-month net income totaled $161.6 million ($1.64), up from $65.8 million (72 cents) in the corresponding 1984 period. Revenue was $5.10 billion, compared with $4.40 billion.

*UAL Inc., the holding company that owns United Airlines, Hertz Corp. and Westin Hotels, reported third-quarter consolidated net earnings of $22.2 million (46 cents a share) on consolidated operating revenue of $1.7 billion.

The third-quarter results compare unfavorably with those a year earlier, when UAL Inc. reported consolidated net earnings of $66.6 million ($1.75) on consolidated operating revenues of $1.8 billion.

But Richard J. Ferris, UAL Inc. chairman, president and chief executive officer, said a comparison of the results is "significantly distorted" by the second-quarter pilots' strike against United Airlines.

The agreement that ended the strike established lower pay rates for new pilots. "The long-term savings to be produced for United Airlines by a pilots' contact with more competitive wages will enhance the airline's ability to succeed in the marketplace," Ferris said in a statement.

Consolidated third-quarter results do reflect improved earnings from Westin Hotels and one month of the operations of Hertz Corp., which was acquired in August.

For the first nine months of 1985, UAL Inc. reported a consolidated net loss of $69.4 million ($2.52), compared with consolidated net earnings of $215.3 million ($5.70) during the same nine-month period in 1984. Consolidated operating revenue was $4.4 billion, 15 percent less than the $5.2 billion for the first nine months of 1984. Consolidated operating expenses were $4.5 billion, a 5 percent decrease from $4.8 billion a year ago.

*Trans World Airlines Inc. reported a $13.5 million third-quarter loss, blaming it on a $42.9 million charge for terminating a merger pact with Texas Air Corp., fare discounts and lower volume partly due to passenger concerns about international air piracy.

New York-based TWA said its loss compared with a profit of $91.2 million ($2.61 a share) in the third quarter of 1984. Sales totaled $1.08 billion, a 1.8 percent increase over the comparable period last year.

A TWA statement said earnings were "negatively affected" by the charge for annuling the Texas Air merger prior to financier Carl C. Icahn's takeover of the carrier in August.

"In addition to the impact of merger related activities, results for 1985's third quarter were adversely affected by concern with terrorist activities overseas, while domestic revenues were diluted by industry discounts and general traffic softening," Richard D. Pearson, TWA president and chief operating officer, said in the statement. He apparently was referring to the June hijack of a TWA jetliner by Lebanese Shiite terrorists to Beirut.

The statement said TWA lost $69.7 million in first nine months of 1985 on sales of $2.88 billion, compared with a $59.3 million profit, $1.27 a share, on sales of $2.69 billion for the same period last year.

"On the basis of nine-month results, 1985 will be a substantial loss for TWA," Pearson said.

*Greyhound Corp. said in Phoenix that a 35 percent year-to-year drop in its third-quarter profits was caused partly by a $19.5 million loss for its leasing subsidiary.

Greyhound, which is the parent of several consumer products and service companies and the manufacturer of MCI intercity buses, reported third-quarter net income of $27.4 million (56 cents a share) and revenue of $862.2 million. Net income during the third quarter of 1984 was $42.2 million (87 cents) and revenue was $732.3 million.

Greyhound said its third-quarter earnings reflected a previously announced after-tax loss of $19.5 million (40 cents) charged to a subsidiary, Greyhound Leasing & Financial Corp.

The loss resulted from a lease-purchasing deal in which Greyhound has obtained a $79 million consent judgment against a Utah partnership. Greyhound said earlier this month it had recovered $45 million but decided to charge the unusual loss to its subsidiary because of "uncertainties surrounding further recoveries."

Greyhound said its net income for the first nine months of 1985 totaled $85.3 million ($1.75) compared with $88.5 million ($1.81) for the first nine months of 1984. Nine-month sales were $2.43 billion, compared with $2.1 billion for the same period last year.