July 13, 1982

At 7 A.M., when the miners gather here at the edge of the Bitterroot Mountains, the air is sweet with the smell of Douglas fir. By 7:15, the men have descended 5,000 feet in a narrow elevator shaft and walked 800 feet along the muddy quartzite corridors to a work space where the 85-degree air is thick with humidity. For six to eight hours, they will drill, dynamite and clear away ore. Silver miners, like businessmen, prefer to return to the same work space every day, but lately at the Hecla Mining Company's Lucky Friday Mine here, many have been shifted around to drill at the richest part of the vein. Two major mines and a smelter have already been closed in the Silver Valley, a sliver of wooded land 20 miles long and 5 miles wide. Given the low quality of the ore at the mines, along with rising production costs and declining metals prices, they were no longer economical to operate. Another mine has been closed temporarily.

AS public attention focuses on such land-based missiles as the MX and the Pershing 2, the United States Navy is accelerating development of a submarine-launched ballistic missile expected to dramatically increase naval destructive power. The missile, known as Trident 2, is intended to give the Navy's missile submarines a potency comparable to virtually any land-based weapons system. It also may complicate efforts to bring the arms race under control. ''Trident 2 will be the most destabilizing first-strike weapon ever built,'' Representative Thomas J. Downey, a member of the House Budget Committee study group on defense, asserted early this year. The Suffolk Democrat's opinion is shared by some, but by no means all, arms controllers.

David Begelman was removed today as chairman and chief executive officer of United Artists, the second major movie studio he has been forced to leave. Mr. Begelman resigned under pressure from Columbia Pictures in 1978 some months after he had been accused of embezzling $61,008 from Columbia by forging checks and of taking an additional $23,000 in improperly documented expenses. He pleaded no contest to those charges. Although no reason was given for his latest departure, most of the 11 films that were made by United Artists under Mr. Begelman's leadership have failed to make money at the box office.

Giddings & Lewis Inc., one of the nation's largest machine tools manufacturers, rejected today as ''inadequate'' a $260 million takeover offer by the American subsidiary of AMCA International Ltd. of Montreal and urged its shareholders to vote against the bid. However, the AMCA International Corporation of Hanover, N.H., said it would continue with its $25-a-share offer for all of Giddings's 10.4 million shares outstanding. Some analysts said that AMCA could raise its bid. ''It's the weakest rejection I've ever seen,'' said Peter von Ond, a securities analyst at Nesbitt, Thomson, Bongard Inc., a brokerage firm in Montreal. ''Giddings can't find a 'white knight' to come to its rescue; they don't have any legal challenges and investors are ready to take the money and run.''

The provision in the Senate Finance Committee's tax bill authorizing the withholding of income taxes on stock dividends and interest payments, once given little chance of success, is gaining adherents, and passage by the House now seems likely, House Demoratic sources said over the weekend. ''The opposition we expected isn't there yet,'' a Democratic aide said. Similarly, the ranking Republican on the Ways and Means Committee, Barber B. Conable Jr. of upstate New York, was reported by industry and Congressional sources to have tempered his earlier opposition. ''It's something he thinks is worth looking at,'' said a source close to Mr. Conable.