According to "HP Compaq 8200 Elite Series QuickSpecs" document (p. 12), the memory DIMMs are populated starting from A(black) socket, then B(black), then A(white) and B(white).
Table 8-1 of "8200/6200 Maintenance and Service Guide" document provides us the slot numbers:
DIMM4 (Channel A) DIMM4 white Memory Module
DIMM3 (Channel A) DIMM3 black Memory Module
DIMM2 (Channel B) DIMM2 white Memory Module
DIMM1 (Channel B) DIMM1 black Memory Module
So, the proper order is DIMM3, then DIMM1, then DIMM2 and DIMM4.