The Compound number is the two-digit total a name reaches before the final reduction, and its existence is an admission that reduction costs something.
A name summing to forty-seven and one summing to twenty-nine both reduce to two. The doctrine attached to two then applies equally to both, which is the whole point of a system that assigns meanings to nine digits. The Compound number is the tradition's way of saying that the two people are nevertheless not the same, and that what was discarded on the way to the two is worth keeping.
Cheiro built much of his popular system on compound numbers, giving each two-digit total its own character and its own fortune, and that layer of the tradition is largely his. It sits somewhat awkwardly beside the Balliett material that supplies the rest of this chart, because the two authors were working from different letter tables and different assumptions about what a number is.
The same instinct produces the master numbers, which are compounds exempted from reduction altogether, and the karmic debt numbers, which are compounds singled out as unlucky. Three separate devices exist to rescue information from the reduction the system otherwise insists on.
A reader can take that two ways. It is either a system enriching itself through experience, or a system repeatedly patching a rule it will not abandon. The atlas records both readings and prefers neither, since the tradition itself contains both and has never resolved them.