The term double embedding could refer to any processing system which uses two support media at the same time. Usually, however, it refers to Peterfyi's celloidin-paraffin wax technique. Gelatin-paraffin wax and agar-paraffin wax methods are usually referred to by those names, rather than the general term. It is advisable to check what form of double embedding was used if trying to follow the details of a project in which some variant of it has been employed.
The basis for these techniques is to obtain increased support to the tissues, the first inclusion procedure often being used to hold the tissues in place while the second infiltrates. It is not as cut and dried as that would infer, however.
Peterfyi's double embedding
In Peterfyi's technique, the celloidin is more than just a glue to stick the tissue pieces together. It also supports it in the sense of protecting it from the harsh effects of hot paraffin. The double embedding sequence results in less shrinkage than paraffin alone, but not as little as celloidin alone. It is, however, considerably faster.
Kultchitzky's double embedding
Kultchitzky also proposed a technique, which involved regular celloidin processing, hardening with chloroform vapour, then infiltrating with paraffin wax. It is noted as being recommended for embryos and hard insects (flees, ticks).
Gatenby, J. B. and Beams, H. W., (1950)
The Microtomist's Vade-Mecum Ed. 11, pp. 100-108, (para. 187-203).
J. & A Churchill Ltd., London, UK.