Sporting a new less-moppy hairstyle, the world's richest man had his day in the big city yesterday to promote his new book "Business @ the Speed of Thought."

While he was being chauffeured around the Big Apple, Microsoft lawyers sent a formal antitrust settlement offer to the government

But when you're worth $92.7 billion, you don't have to worry about the time. A throng of fans waited for more than a half hour for the Gates to appear at Barnes & Noble in Rockefeller Center.

Gates had a Q&A session at 2, but didn't show until well after 2:30.

A Microsoft spokeswoman said they weren't sure why he was late for the book store appearance, which he cut short to a half hour.

"I thought it was too short," said Cheryl Stinerock, who was standing in a side aisle for more than 40 minutes waiting for Gates to arrive.

"What he said was interesting," said Stinerock diplomatically, "but he arrived late and I expected him to stay a little longer."

Another elderly gentleman in a fedora, who declined to give his name, fumed. "He robbed us of a half hour."

Gates quickly left by a back door. But most people didn't seem to be rushing to buy the book. Still, the book hit No. 1 yesterday on Amazon.com, pushing George Stephanopoulos' All Too Human to No. 2.

The Microsoft co-founder began his day on NBC's "The Today Show," where Matt Lauer grilled him about the Department of Justice's antitrust suit against the software giant.

"We'd love to have this thing settled," Gates told Lauer. "But the key principles haven't changed and that's because what Microsoft is all about is building great software. And that freedom to innovate is important to us and every other company."

Lauer moved on to other topics in Gates' book, such as increasing the use of e-mail and asked him whether he'd rather e-mail or telephone his wife.

Gates, sporting a new haircut and new glasses, smoothly replied he'd rather see her.

Gates' next audience - at a Microsoft sales event - was tailored to a more technonology-minded audience.

The liveliest part of this appearance was a video starring Gates and President Steve Ballmer jamming in their own "Night at the Roxbury," where they pumped up the volume all over Manhattan and even danced in "The River Dance."

Gates next move was to rush over to an investor conference sponsored by Schroder & Co. and Variety, where he was interviewed by Sir David Frost.

Gates was able to cast a spell on the hundreds of media execs and investors assembled at The Plaza.

After lunch he stopped at the Ziegfeld to deliver a speech to a packed theatre filled with business students from New York University and Columbia.

-- Jon Elsen, Mary Huhn, and Keith Kelly - 3/25/99