## Various Forms of Planimeters and their Characteristics.

### Polar Planimeter.

The next higher form of Planimeter to the simple instrument just described differs from the simpler form in having a tracer arm whose length can be increased or diminished. Since any change in the length of the Tracer Arm produces a change in the number of units recorded for the tracing of any given area, this form of instrument admits of the adjustment of the tracer arm so as to give the area of any figure traced in more than one unit of area, and to allow of its use in measuring figures drawn to different scales.

No. 3.

Index marks are usually engraved upon the tracer arm to which the arm must be adjusted in order to give the area traced in terms of the unit of area desired. Thus, when set to one such mark the area recorded will be in square inches, in another square yards, in another square decimeters and so on, the unit given by any given index mark being engraved on the arm at that mark.

Owing both to the adjustable length of arm and the larger size of this form of Planimeter this instrument is capable of measuring much larger areas at one operation than is possible to the simpler form and with the same degree of accuracy, thus largely increasing its usefulness in all such operations.

While any of the forms of Planimeter so far referred to may be used to find the mean height of an indicator or similar diagram, the operation is evidently an indirect one and necessitates more or less mathematical computation to arrive at the desired results.

To obviate this a special form of the kind of Planimeter under discussion is made by means of which the Planimeter is enabled to give the average height of these diagrams, without having to submit the results to subsequent calculation.

No. 4.

This special form of the instrument has two conical needle point projections extending upward from the Planimeter. One of these projecting points is attached to the Frame or Carriage of the instrument while the other is attached to the top of the Tracer Arm and moves with it. By loosening the binding screws of the Tracer Arm and placing the Carriage Point at one end of the base of the diagram the Tracer Arm is slid through its bearings in the Carriage until the needle point on the top of the Arm is brought to the other end of the base of the diagram, in which position the Tracer Arm is firmly fastened by means of the clamping screws of the Carriage.

By this operation the distance between these two needle points is made equal to the length of the diagram, the mean height of which is to be measured. The points on the planimeter at which these needle points are attached are so arranged that the instrument having been thus adjusted and the outline of the diagram traced, the resulting reading when multiplied by a certain Constant given for each instrument will be the average mean height of the diagram traced.

As this special attachment in no way interferes with the use of the Planimeter in any other of its applications, this attachment is one of very great convenience and importance where there is much use of the Planimeter in this form of operation.