In Kircher's diagram, above, the copper sphere appears considerably larger than the aperture at the top of the glass sphere -- a physical impossibility. This effect is due to the magnification of the copper sphere in the liquid, and is also visible in the reconstruction -- it is not a mistake made by the engraver, as we originally believed.
 

Zdenco Vrscaj enlarging the aperture of the glass sphere in the reconstruction

The first technique involves using a silk thread or one made from filament extracted from Aloes leaves, attached to the cap on the top of the glass sphere (which is open, to allow the inner sphere to be inserted).

Kircher's second technique was more ambitious. He suggested floating the hollow copper globe at the junction between two clear immiscible liquids of different densities. The copper globe would have to be carefully weighted with ballast to ensure it had an intermediate specific gravity or "gravitas in specie". He suggested a number of liquids that would work for this purpose, including a combination of "terebinth", or turpentine, and water. Kircher also suggested various extracts derived from plants through distillation, but claimed that his favourite combination consisted of  "spirit of wine" -- grape alcohol -- and "spirit of tartar". He even went so far as to give a detailed recipe for the alchemical preparation of spirit of tartar, used in the pharmacy of the Collegio Romano.

In attempting to reconstruct Kircher's clock, we consulted with three chemical experts about the immiscible liquids: Prof. Laurence Principe of Johns Hopkins University, Prof. John Brauman of Stanford University and Dr. Justin Du Bois, also of Stanford University. Not having a ready supply of spirit of tartar, we considered using other liquids in conjunction with water, Tetrahydrofuran (THF) and Acetonitrile, both organic solvents, both having refractive indices close to that of water, to minimize the phase difference and enhance the illusion. However, due to the safety issues associated with using these highly volatile liquids in a public space, we eventually resorted to using mineral oil, with the advice of Tom Tompkins of the Exploratorium. Mineral oil has the convenient property of having a refractive index very close to that of pyrex, particularly if you mix heavy and light viscosities of mineral oil. This allowed us to suspend the copper globe not with a silk thread, but with a thin glass rod.