CHAPTER IV.
Measurement of Plane Areas.
III. Measurement of Large Areas.
Movements of Integrating Wheel.
While tracing the periphery of the figure, in the
manner described, if the Integrating Wheel be watched, it will be found
that the direction of rotation of the wheel may not be the same throughout
the tracing. At some places of the periphery the tracing may cause a forward
or positive rotation while at other places it may cause a backward or negative
rotation and hence the final Reading will really be the difference between
the amount of the forward or positive rotations and the amount of the backward
or negative rotations; or taking into account the algebraic signs
of the two directions of rotation, the positive rotations being +, and
the negative –, the final Reading will be the Algebraic sum of the two,
and the proper sign being given to the resultant or Reading for the given
area, it is algebraically added to the given Constant. It is evident
that the algebraic sign of the Constant will always be positive or +.
Applied to an actual measurement this operation would be as
follows: