Mathematical Derivation
The operation of a linear planimeter can be justified by applying Green's theorem onto the components of the vector field N, given by:
where b is the y-coordinate of the elbow E.
This vector field is perpendicular to the measuring arm EM:
and has a constant size, equal to the length m of the measuring arm:
Then:
because:
The left hand side of the above equation, which is equal to the area A enclosed by the contour, is proportional to the distance measured by the measuring wheel, with proportionality factor m, the length of the measuring arm.
Read more about this topic: Planimeter
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