(Also known as "She" from the novel "King Solomon's Mine" and others by H. Rider Haggard).
An assistant stands on a small table within an enclosure surrounded by some dark and heavy cloth ("to prevent the fire from spreading"). The table has four legs, and four candles are mounted beneath it. A cylindrical screen is suspended above the assistant, and is lowered so as to completely cover him or her and rest upon the table. The performer fires off a pistol or otherwise signals; at this point smoke and fire burst out from inside the screen; after a suitable interval, the screen is lifted and the fire put out; there is nothing left but a skull and assorted bone fragments and perhaps some scraps of costume.
As the original description correctly points out, the audience must conclude that the assistant has escaped somehow, since the performer couldn't afford to sacrifice an assistant each time the show is run.
The illusion is very simply performed: there are under the table two mirrors, attached to each other at an angle of 90 degrees to each other and 45 degrees to the sides of the enclosure. The table does in deed have four legs, but two of them are behind the mirrors; the two in front are reflected by the mirrors, as are the TWO candles mounted under the table. The side and back curtains are all of the same material and colour, and the stage is covered with some material or carpet that has no apparent pattern. There is a trapdoor in the back part of the table for the assistant to escape through; he or she simply gets down from the table, places the skull and other bits and pieces on the table, along with the fire and smoke maker, when the screen has been lowered; upon the pistol shot, she or he lights the firemaker and retires through the curtain at the back, which has a convenient cutout.
The skull, etc. are of course on the floor behind the table all along. The assistant can climb up on to the table from its front or its sides - obviously it must be sturdy! — which helps to establish the innocence of the scene. Of course it would be disastrous if the assistant touches the mirrors in any way! The cloth for the cylinder will have to be replaced fairly often, as even if it is fireproof it will get scorched eventually.