The Cosmosphere consists of a printed terrestrial globe, set inside a revolving glass celestial globe. It was invented by Dr William Muller, a major of the Royal Hanoverian Engineers from Woolwich, and made by the Cary brothers. In a pamphlet of 1829 called "The Cosmosphere: an Instrument substituting an Orrery, a Planetarium, a Tellurium, a Lunarium, an Armillary Sphere, a Celestial and a Terrestrial Globe, for Self-Instruction and for Schools.", Muller described it as "an apparatus that will represent and explain the universe". The full version of the Cosmosphere would have included a planetarium that could replace the terrestrial globe within the glass celestial sphere.

The glass sphere is attached to a brass meridian ring which is clamped to a column and base and can be adjusted to the desired latitude. It is engraved with a degree scale and inscribed "MULLER'S PATENT". The clamp also secures the terrestrial globe and brass rings with degree scales to indicate longitude. The glass celestial sphere depicts constellations and graduated lines marking the ecliptic and the equator. The terrestrial sphere, dated 1824, includes the tracks of all Cook's voyages, outlines of the continents and eight named oceans.