It makes me feel truly old to say I was trained in using these – it always fascinated me how rotation in a single axis could derive a two dimensional area. It is a very precisely made instrument and a delightful piece of precision engineering. I have kept two for this reason alone!
The planimeter should come with a small rotating arm on a fixed central pad and having a dimple in the arm and a pointer line scribed at the arms outer end which you use to ensure you start and finish its rotation at precisely the same point. The arm would have an area stamped on it being unique to this 'test piece'. You put the pointer of the planimeter in the arm's dimple and rotate the arm of the test piece exactly 360 degrees and this will turn the wheel on the planimeter a certain number of divisions. That can then be related as a proportion to the 'standard area' stamped on the test arm and used to establish your own calibration chart.
If the test piece is missing it would be possible to make your own as it depends only upon a very precise measurement of the distance between the arms central pivot point to the 'dimple' and multiplying this by itself (pi r squared) and then again by Pi (3.1416) to give the test area figure.
The table simply relates that ratio to various drawing scales and settings of the 'elbow joint' of the planimeter along its arm.
The tool is still useful for obtaining areas and perimeter lengths from style plans and maps, but has been largely replaced by digital drawings and computer aided design software which calculate perimeters and areas of complex shaped items with even greater accuracy and far less effort.