This invention relates to a complete double lap lapping and polishing machine particularly to an apparatus designed to finish to a required thickness and/or finished polish workpiece such as thin silicon and/or ceramic wafers. The machine includes improvements in all of it's substructure components, including it's overall housing design, planetary gear drive, fluid cooling systems, positioning and locking of the upper lap plate in an inoperative position, an automatic thickness or sizing control, rotary union with automatic fluid liquid indicator and a slurry delivery and recovery system, all of which result in a more automated efficient use of the machine so as to produce a closer tolerance finished product.