JUSTICES of the Supreme Court do not often write doggerel. But tucked away Tuesday in a footnote to a dissenting opinion by, of all people, strait-laced Byron R. White, were these lines: Will you walk into my parlour?" said a spider to a fly; (You may find out you have consented, without ever knowing why.)

Jsutice White's ascent (or descent) into poetry was triggered by the court's curious decision upholding the conviction of a woman in Detroit for possessing heroin. He and three of his colleagues thought she had been illegally arrested and therefore wrongly convicted. Three other justices found nothing wrong with the search or the conviction because they thought she was legally arrested. The deciding votes were those of two justices who said she had not been arrested at all and had voluntarily consented to a strip search that revealed a packet of heroin in her underwear.

These are the facts. Sylvia Mendenhall was the last passenger off an early morning airline flight from Los Angeles to Detroit. Nervous, she looked all around the terminal before walking slowly toward the baggage area. She claimed no luggage but asked a skycap for directions to the Eastern ticket counter. There she exchanged a ticket on an American flight to Pittsburgh for an Eastern ticket to the same city.

That, said five justices, was sufficient evidence on which two experienced drug officers could legitimately decide she might be a drug courier and stop her for questioning. Nonsense, said Justice White and his three colleagues. That kind of behavior can reasonably be expected "of anyone changing planes in an airport terminal." Surely not all, or even a majority, of passengers who do those things are drug couriers.

But then: Miss Mendenhall's nervousness increased after she was stopped. When she produced, at the request of the agents, a ticket with one name on it and a driver's license with another, they asked her to accompany them to their office, where they asked her to consent to a strip search in front of a policewoman.

Miss Mendenhall, according to five justices, "voluntarily" went to the agents' office and voluntarily took off her clothes after being told by the officer to do so. That was what pitched Justice White into doggerel. It's also too much for us. Surely Miss Mendenhall was under arrest, and just as surely she did not undress voluntarily in any normal meaning of the word.

The finespan theory to the contrary, devised by Justice Potter Stewart, is a way of salvaging a conviction without having to accept the idea that drug agents can arrest anyone who gets off an airplane from Los Angeles last, scans the terminal, goes to the baggage counter without claiming baggage and trades in a ticket. Miss Mendenhall, no doubt, got what she deserved for possessing heroin. But there is a moral in this tale for everyone else: if you're flying in from L.A. and looking for a friend in the terminal, don't be last off the plane.