The performer places an open newspaper on the stage and sets an armless wooden chair on it, facing the audience. His lady assistant sits upon the chair. He covers her with a heavy silk veil, intones an appropriate incantation and on the count of three whips off the veil to show that the lady has vanished!
As in the Appearing Lady, there's a trapdoor in the stage. The newspaper is placed over the trapdoor and the chair positioned so that its four legs straddle the trapdoor. The newspaper has also a trapdoor cut out of it (note, not a cutout). At the back of the chair is a framework made of very fine wire, which can't be detected by the audience. The performer covers the lady, and in doing so lifts the frame over the back of the chair and over the lady's head & shoulders. The chair has a seat that is moveable, which will tilt downwards so that the lady can slide down it, through the trap in the paper and through the trapdoor in the stage. Once below the stage, she seals the newspaper trap shut with tape of some sort, and closes the stage trapdoor.
The performer stand behind the chair, and during the act of covering his assistant contrives to flip the wire frame over her. Its purpose is to maintain the correct silhouette and therefore the illusion that she's still there. Of course, as soon as she is adequately covered she begins to get out of the chair. It may be found necessary to have a couple of stiff wires extended from the chair to keep the veil extended where her knees go when she sits down, otherwise there may be a slight collapse in the veil when she vacates the chair. The chair seat should be spring-loaded, so that it will move back into place when her weight comes off it. There must be sufficient slack in the veil to cover completely the lady's feet as well as to prevent movement when she slides down. Finally, when the performer yanks the veil off the chair, he must flip the wire assembly back behind the chair. For dramatic effect a small smoke bomb could be contrived to go off when the chair seat flips back into place.