Leitz Petrographic Stage

"Yes, you might call it a planimeter. Leitz' name for it was "Integration Stage". It was developed under Berek as an aid to petrographers to determine the volumina of minerals in rock thin sections by measuring their surface areas. It attaches to the top of the microscope stage and permits one to meander through the specimen by any of the six micrometer spindles in X and one separate control in Y. You would assign specific minerals to the spindles, let's say quartz to spindle one, calcite to two etc. The specimen moves against a crossline in the eyepiece and whenever you pass from one mineral boundary to the next you change to the spindle assigned to it. When you are done each spindle shows a length that is the sum of the distances traversed inside mineral grains of the same species.

There was also an Integration Ocular where the cross line inside the ocular moved but the scans were necessarily confined to the field of view. When statistical methods like point counting with special 20 or 25 point graticules and point counting stages (Swift) became available, the Integration Stage fell into disuse. I have lost track of the technology but I would speculate that contemporary motor driven stages are even more attractive and that, in favorable cases, the volumina can be determined by image analysis.

There is a beautifully illustrated book "The Petrographic Microscope" by Daniel E. Kile that shows the Leitz and another stage on page 66 in the historical context of petrographic microscopes.