What is the measuring principle behind the strain gauge plethysmograph?

Plethysmograph stams from the Greek word "plethysmo", to increase, and "graphos" to write.
A plethysmograph is "an instrument for recording and measuring the variation in the volume of a part of the body".
The measuring principle behind the strain gauge plethysmograph is amazingly simple : the relative volumechange of a (supposed cilindrical) limb equals the relative resistance change of the strain gauge wrapped around this limb.
Indeed the volume of a cilindrical object with constant length changes with 2 % if the circumference change with 1 %.
The change in circumference can be measured as a change in length of a strain gauge filled with InGa wrapped around the object to be measured. If the lenght of the strain gauge changes it's electrical resistance changes also because the strain gauge gets longer and thinner. It can be calculated that for a 1 % change in lenght, the resistance changes with 2 %.
This means that to know the relative volume variation of an extremity (DV/Vo) it is sufficient to measure relative resistance variation of the strain gauge (DR/Ro).