I guessed him to be about sixty, but his age was difficult to estimate since it was obvious that he was no stranger to facials, manicures, and massages. What was most impressive was his air of assurance. This was a man, I decided, who never had a doubt in the world. It was rather daunting to a goof like me whose theme song could be "What's It All About, Archy?"

We chatted casually for a few minutes and, without my asking, he remarked that he was semi-retired and that he and his daughter were so impressed by Palm Beach they were determined to make it their permanent home.

"Y'see, Archy," he said, "we've lived all over the world. As a mining engineer I was forced to travel a great deal, and I think we're both ready to settle down."

I nodded understandingly, mentally adding mining engineer to his growing list of former occupations.

Our conversation was interrupted when Theo returned with our drinks. Hector had been exactly right; she did have a way with a gimlet: not too tart, not too heavy on the vodka, and with a delightful slice of fresh lime in each glass.

We toasted each other, sipped appreciatively and, again without my asking, he began to describe the type of dwelling he and his daughter would like to inhabit.

"On Ocean Boulevard," he said definitely, "or close to it. A view of the sea, if possible, or at least a short stroll to the beach. Three bedrooms at a minimum. Florida room, of course. A pool is not necessary, but I would like a nice piece of lawn, front and back. Wouldn't you say, Theo?"

"Room for a gazebo," she replied, almost dreamily. "A flower garden. Perhaps a small greenhouse. My private gym, of course. And an enormous kitchen."

Hector laughed. "Perfection is not for this world, sweet," he said, "but perhaps we can find a reasonable facsimile."

"I'm sure you can," I said. "Let me go through our listings, talk to colleagues, and bring you a very limited selection for your consideration."

"We're not ready to buy," he said. "I warned you about that."

"Of course," I said. "I understand completely. It sometimes takes a year, or even more, of viewing, evaluating, and finally making a decision. After all, you're choosing a home you'll probably live in for the rest of your lives, and you want it to be right. Believe me, I'm not going to pressure you. I have one client who's been debating a final choice for almost three years."

"You're a very patient man, Archy," Theo said.

"Yes," I agreed, "I am."

"Are you an attorney?" Heck asked suddenly.

"No, I am not," I said. "But my father is. His law firm represents some of the most reputable people in Palm Beach." (And a few disreputable, I was tempted to add.) "I do hope you'll ask friends and neighbors about McNally and Son. We're proud of our reputation."

They smiled at me encouragingly. They were seated close together on the couch, a rather hideous number covered with flowered cretonne. I could see little resemblance between father and daughter, and I wanted to ask about the missing Mrs. Johnson but naturally I didn't. Not quite comme il faut, y'know.

Our glasses were almost empty when I saw Hector peek at his watch. I would have expected it to be a gold Rolex, but from where I sat it appeared to be an old, clunky digital, which surprised me.

I finished my drink and rose. "I know you have another appointment, Heck," I said, "and I don't want to take up more of your time. Thank you for seeing me and for your kind hospitality. The gimlet was splendid!"

"Our pleasure, Archy," he said, standing. "When you have something special you think we should see, do give us a call."

"I'll certainly do that," I said. "And thank you again."

"I'll walk you to your car," Theo said, and I could have screamed with delight.

We went outside, she preceding me, and I saw how her tanned legs gleamed in the sunlight. As an experienced aesthetician I notice such things.

She laughed when she saw my red Miata. "What a little beauty!" she said.

"Isn't it?" I said, happy that she approved of my wheels. "They're producing new models in black and British racing green. I may trade it in."

"Don't you dare," she said, patting the hood. "This one is you. Where do you live, Archy?"

"Ocean Boulevard. The Atlantic is practically lapping at our doorstep."

"How wonderful," she said. "I'd love to see your home."

"Of course," I said, almost spluttering with pleasure. "Whenever you like." I handed her a business card. "Do give me a call."

"I shall," she said, looking at me thoughtfully. "Perhaps we could make an afternoon of it. There are so many places in the Palm Beach area I'd love to see and haven't had the chance."

"I'd be happy to serve as your cicerone," I said warmly. "Perhaps we might start with lunch."

"That would be fun," she said.

The thought then occurred to me that maybe the Chinless Wonder was bonkers in describing Theodosia as his soon-to-be fiancee. That might be his fantasy, but the way this Lorelei was coming on, it certainly didn't seem to be hers.

"Theo," I said, "there is something I'd like to ask and I do hope it won't upset you. I'm acquainted with Silas Hawkin's widow and daughter, and in his ledger they found a notation of a painting he had been working on at the time of his death. It's listed merely as 'Untitled.' They can't find the painting and have no idea what the subject matter might be. They requested I ask you if Si ever discussed it while he was doing your portrait."

She shook her head. "No, Si never mentioned anything else he was working on. I have no idea what 'Untitled' might be."

"I didn't think you would," I assured her, "but I promised to ask. Thank you so much for welcoming me to your home. I do appreciate it."

"I'm looking forward to that lunch," she said lightly.

She shook my hand, turned, and walked back to her condo. I watched her stroll away. An entrancing sight.

I sat a moment on the hot cushions of the Miata, trying to cool off and calm down. Madam X was fascinating, no doubt about it.

I had confused impressions of both the Johnsons. Despite his air of surety Hector struck me as the type of man who constantly has to reassure himself by exaggerating his wealth, accomplishments, and prospects. Not exactly bragging, you understand, but just keeping his illusions about himself intact.

As for Theo, I ruefully admitted I may have made an initial error by equating her beauty with sweetness, purity, modesty, innocence-all that swell stuff. Now I began to wonder if there might not be a darker side to her nature, including unbridled hedonism, willfulness, cold ambition, and other attitudes that added up to a self-centered young lady with an eye out for the main chance.

Maybe, just maybe, the suspicions of crabby Mrs. Gertrude Smythe-Hersforth were justified.

Musing on the complexities of human temperament I started up the Miata and headed slowly out of the parking area. As I did, another car entered. I glanced, drove on a few yards, stopped, and made a great show of lighting a cigarette while I watched in the rearview mirror.

The newcomer stopped in front of the Johnsons' town house. The driver alighted, rang the doorbell, and was immediately admitted. Apparently Hector's expected business associate.

The car he was driving was a gunmetal Cadillac de Ville. And he was a saturnine bloke with a profile like a cleaver. Undoubtedly the gink who had spoken so familiarly to Shirley Feebling in Fort Lauderdale.

I sat there, shaken, and looked up to the heavens for revelation.

Nothing.

I returned to the McNally Building and found on my desk a message requesting that I call Sgt. Rogoff immediately. I did, finding him at police headquarters, an edifice the sergeant called the Palace but which looks to me as if it should be in the hills overlooking the Cote d'Azur.