The Triumphant Cross is a composite symbol of a cross and an orb, representing Christ's triumph over the world
The Triumphant Cross is a cross atop an orb. The cross represents Christ's sacrifice and the orb (often with an equatorial band) represents the world. It symbolises Christ's triumph over the world, and prominent in images of Christ as Salvator Mundi - the Saviour of the World. (See also Earth Symbol.)
The symbol is used by the Carthusian monks1, with the motto Stat crux dum volvitur orbis ('The cross is steady while the world is turning.') The cross and orb have also been adopted by other denominations, as shown below.
When used as royal regalia, it takes the Latin name Globus Cruciger and is often encrusted with jewels (see also Jewelled Cross). The holder of the Globus Cruciger shows he or she takes responsibility as the titular head of the state religion and is defender of the faith. The orb (or the absurd 'Holy Hand Grenade' in Pythonesque) is also a great way to symbolise a monarch ominously holding an empire.
Before Christianity, Pagan rulers would hold a similar orb in their hands to symbolise their power over the world. When Christian rulers adopted this practice, they added the cross to show Christ's dominion over the world. In this way, it symbolises Christianity's triumph over Paganism.2
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Note: The Triumphant Cross should not be confused with the identical symbol for the element antimony, used in alchemy.
The globe, often squashed3, forms part of numerous church emblems. These usually represent the church's mission to spread the Gospel worldwide. Such emblems include:

Anglican Church in North America

Baptist Union of Great Britain

Batak Christian Protestant Church

Christian Methodist Episcopal Church

Christian Protestant Church in Indonesia

Evangelical Lutheran Church in America

Evangelical Lutheran Church in Tanzania

National Baptist Convention of Mexico
| 1: | For more information about Carthusian monks, see www.chartreux.org/en/ or www.parkminster.org.uk/. Alternatively, if you're in the mood for a monk joke... |
| 2: | This adds support to the notion that the ancients had calculated that earth was spherical |
| 3: | Even though the earth is more or less spherical, for some reason we say "worldwide" and not "worldlong", but we go a "long way" and not a "wide way". Perhaps it's something to do with this... |