Prism constants are defined differently by Leica than for all other manufacturers. They use a default reference prism with an absolute correction of -34.4mm as the reference. This means that:
Leica Constant = Absolute Constant +34.4mm
If you are using prisms from different manufacturers you will need to be careful to identify if the reported constant is a Leica or Non-Leica constant and adjust the definition accordingly.
SA’s Sokkia interfaces expect you to enter the Absolute Constant while within the Leica Interface we expect the Leica Constant. This means that an open air corner cube will have a zero constant in the Sokkia interface and a 34.4mm offset in the Leica interface.