The performer borrows a hat from someone — a pillbox hat or some style which has stiff sides several inches in height. He "sterilizes" it by dropping in a pinch of powder and lighting it — causing a fine puff of smoke. He takes a couple of eggs and some flour and mixes them up in a porcelain or light metal container; pours them into the hat; passes the hat over a flame a few times (taking care not to scorch it, of course); then removes a small cake which he can give samples of to the audience; he turns the hat upside down and shakes it to demonstrate there's nothing in it, then returns it to its owner, who is pleased to testify that there's nothing nasty in it and that it hasn't been damaged.
The porcelain container is perfectly innocent: it must be cylindrical in shape and have a slightly roughened interior. It can be shown to the audience. The trick is actually accomplished by use of a second cylinder with a diameter just slightly less than the first one. It has two compartments as shown in the illustration (B). The lower compartment is painted and treated to appear the same as the inside of the first cylinder. The cake and the two-part cylinder are slipped into the hat at some point — perhaps being suspended on the back of a chair and dropped in as the performer goes past it. The flour and eggs are poured into the top compartment; the first cylinder is slipped over the two-compartment one and the two are removed together. Thus there's nothing left in the hat but the cake.
The "sterilization" must of course be done when the second cylinder has been placed in the hat. The amount of flour used should be sufficient to soak up the eggs and make them into a lump — solid enough not to make fluid noises when the cylinders are moved about. The second cylinder must have on its outside surface tape or something that will cause it to stick inside the first cylinder when the latter is slipped over it; nothing grand but there must be sufficient friction to hold it in place.
(The diagram shows two springs ("r"). The original instructions call for four such springs to hold the second cylinder inside the first. No necessary these days).