The arguments started before the holidays, when gift ideas were being hawked by everyone with something to sell and gifts were on everyone's mind. What would we give the boss, who was leaving Jan. 20, and taking all our jobs with her?

There was no question about whether. We all felt we owed her something beyond thanks for hiring us. She had freely shared her abilities and her knowledge, and we were all a little better for it and for having worked together. On the other hand, we all had responsibilities and our futures were uncertain. We had to buy something meaningful, but not too expensive.

That ruled out the international short-wave radio her husband said she had always wanted.

The alternative, several of us decided, was a jogger's earphone radio set to accompany her on her fitness regimen. We knew she would enjoy it, and we felt that made up for its relatively low cost.

But some had second thoughts, and the arguments began:

"We have to engrave something so she doesn't forget us."

"She won't forget us. Besides, why does she need another engraved dohickey around the house?"

Why indeed? The question prompted a debate on the whole philosophy of an office gift to a valued boss. My philosophy finally prevailed, not because I argued best, but because I volunteered to do the shopping and to keep within a strict budget.

My theory is that a gift to a boss -- or any corporate gift, from a gold watch to a bronze plaque -- is a Kilroy gift. It says "I was here."

During World War II American soldiers all over Europe left their mark on lavatory walls and roadside fences. American graffiti in those days showed little originality. Most of it said, "Kilroy was here."

Kilroy began as a '30s nebbish, the Alfred E. Newman of his generation. According to the Dictionary of Americna Slang, Kilroy was a nonentity, an inconsequential person. He was a voice crying in the crowd, "I'm here. I exist."

And that is the purpose of a boss gift. It is the graffito of the workplace, the plea for remembrance. A jogger's radio, a sweater, a pair of gloves, a bonbon dish or an electric radial saw are personal gifts, to be incorporated into the home, the life and the persona of the giftee. Kilroy gifts stand apart. They defiantly proclaim their individuality.

A silver bowl with the signatures of ll members of Congress given to a parting congressman is a Kilroy gift. A leather attache case with the name of the grateful corporation tooled in gold on the file section inside is a Kilroy gift. A letter of appreciation signed by the president is a Kilroy gift. A framed handprint of a grandchild, age 3, is a Kilroy gift.

Boss gifts are more difficult. Most bosses already have attache cases, and don't care to have the handprints of all the staffs. Silver bowls are too expensive, unless the staff is very large and/or very grateful (and keeping their jobs when the boss goes). A letter of appreciation from the staff doesn't have the cachet necessary for framing and hanging.

We had to find something that we could engrave that would stand apart and be identifiable, yet not be as ostebtatious (and self-congratulatory) as a bronze plaque.

Bowls and trays have been overdone, brass and pewter are hardly elegant enough.

I finally decided on glass: a glass ice bucket with glass handles. Even when filled, with ice, flowers or pistachio nuts, the engraving would be visible.

The message was the most difficult.

This was not the time, place or person for gushy sentimentality. We had prided ourselves on our professionalism as a staff, and on our ability to do our work crisply and cleanly. We needed to immortalize that tradition.

The message took the form of one of our inter-office memos, using our initials as we always did in our office. It looked good, it wasn't too wordy, and it retained the flavor of our time together.

I hope she likes it.

Now if we can come up with an appropriatte gift for the secretaries we are leaving behind, the women who were the backbone of our office.

They don't want Kilroy gifts. The philosophy is a little different there, but I haven't figured it out. Yet.