June 21, 1987

LEAD: Six years ago Eugene Lang, a millionaire industrialist, offered 61 sixth-grade students in East Harlem a chance to reach an impossible dream. If they stuck to their school work, he said, he would guarantee them a college education.

LEAD: AS municipalities on Long Island and across the country continue to move toward garbage-to-energy incineration as a solution to their mounting solid-waste problems, a debate is emerging over whether the ash produced by incinerators is toxic enough to be classified as hazardous waste.

LEAD: AFTER six weeks of hearings into the Iran-contra affair, the members of the joint Congressional committees have begun to emerge as familiar personalities. Some have been eloquent, like Representative Lee H. Hamilton, the chairman of the House panel. Some have proved to be doughty defenders of the Reagan Administration, like Senator Orrin G.

LEAD: To those major borrowers of mortgage money who think that interest rates will soon tumble, a new financing product called the Tokyo Takeout might be appealing.

LEAD: MANY years and housing trends ago, well-off Manhattan families lived primarily in established residential areas and the less-well-off lived on the fringes.

LEAD: WHEN Marianne Rusche and Jane Reynolds, who work at the Quail Ridge Country Club in Boynton Beach, decided early last year to invest in a home together, they went to an agent for the Westbury Homes Corporation, one of the largest home builders in thriving Palm Beach County.

LEAD: IMPOSING American morality on other countries' political systems is a ticklish business, and the United States has rarely done it well, whether the Administration be Republican or Democratic. There is a peculiar interplay between Washington's regard for democracy and its anxiety over Communist expansion.

LEAD: HOWARD AND MARION BUTTERS retired to Fort Lauderdale, Fla., from Pittsburgh about 20 years ago. But when they started looking for a community in which to spend their later years - both are in their 80's - they looked north to Williamsburg, Va. ''It just wasn't the same place,'' Mrs. Butters said of

LEAD: IN 1968, Harry Edwards was a young activist who tried to persuade black American athletes to boycott the 1968 Olympics. Though that effort failed, it led to the black-power salute on the victory stand by Tommie Smith and John Carlos and helped dramatize Edwards's message: that black Americans were being denied equal opportunity in the land of opportunity.

LEAD: THE Long Island Lighting Company will pursue Federal permission to operate the Shoreham plant year-round at a quarter of its full power as an interim measure to meet electric demand, the company's chairman, William J. Catacosinos, said last week.

LEAD: President Reagan today vetoed a bill that would write into law the fairness doctrine requiring broadcasters to present divergent views on controversial topics.

LEAD: FOR the sixth graders at the Cecil H. Parker Elementary School in Mount Vernon, the graduation ceremony last week had all the usual ingredients. There were awards and speeches by city and school officials. Camera lights flashed and toddlers in the audience grew restless.