PLANIMETER is a machine for deter mining the area of any plane figure drawn to scale such as maps, sections, diagrams, indi cator diagrams. There are two kinds, and (trolling.'" The polar planimeter invented by Amsler in 1850 consists of two principal parts, viz., the tracer arm carrying the tracing point and a carriage with the computing wheel and the pole arm, a rod mounted on a pivot on which the instrument revolves. The area of any figure is obtained accurately by tracing its boundary line with the tracing point, reading off the graduations on the measuring wheel and multiplying by a suitable factor to give square feet, square miles or other desired unit. The original instrument has been considerably im proved as to usefulness and accuracy and in being set to any desired scale, but as all polar plammeters revolve around a fixed point, their scope is limited by the length of arms of the instrument. Therefore, a large figure has to be divided into sections. The rolling planimeter moves on two broad rollers from one of which the movement is imparted to the recording mechanism. The measuring wheel revolves by contact with a polished sphere segment. Onlv the rollers and the tracer arc in contact with the drawing and the results are, therefore, not affected by irregularity of the paper. Accord ingly it will measure with one operation the area of a figure of any length, the width of which does not exceed the length of the ex tended tracer-arm. Wider areas can be sub
divided by lines and each subdivision measured separately. Figure 1 shows the simplest form of polar planimeter. A higher grade machine is shown in figure 2. The compensating plani meter is a modification of the polar instrument in which the pole arm is held in the wheel car riage of the tracer arm by a pivot which ends in a steel ball fitting nicely in a socket of the wheel carriage. This gives rigidity and the tracer arm has an angular motion of 180 de grees, or much greater than in old forms.. By measuring a figure with pole on the left and then again with pole on the right side of the tracer arm and taking the mean the instru mental errors are compensated. The pantograph polar planimeter has two arms, one about seven and one-half inches long for measuring very small figures and one 11 inches long which covers a circle 38 inches in diameter for measuring large figures. The machine is so compensated that when the smaller arm is used the result is more accurate. The disc plani meter is another form in which the motion of the measuring wheel is independent of the con dition of the paper on which the figure is drawn as the measuring wheel revolves by contact with the plane disc.
For mechanical integrators or integraphs which work on nearly the same principle as the planimeter see INTEGRATORS.