## Problems Involving Averaging.

### Special Attachment for Measuring Av. Ht. of Diagrams.

In the best forms of Polar Planimeter there is often a special attachment or arrangement (See Pg. 93) by which the Tracer Arm can be accurately and quickly adjusted so that its length shall be equal to the length of the base of any figure to be measured and without the necessity of measuring the base. In one form this attachment consists of two fine needle points which project upwards from the Tracer Arm, one needle point being at the Tracer and is usually the Tracing needle itself prolonged upwards, while the other is at the Carriage Pivot F and attached to the Carriage.

The adjustment of the length is then made by turning the Planimeter upside down, and having pushed the needle point at the Tracer end into the paper at one end of the base of the given figure, the Carriage is slid along the Tracer Arm until the second needle point is brought to the other end of the given base, when the Carriage is clamped and the instrument turned over. It is evident that by this operation the Tracer Arm length FT is made equal to the length AB of the base of the diagram.

Other forms of this attachment are modifications of the form just described and usually require a corrective factor by which the Reading for the given figure must be multiplied.

M. Coradi has adopted for his Compensating Planimeter a very simple but effective means for making this adjustment, and which is made possible by the particular form of construction of this instrument. It consists simply of making a very fine hole in the bottom of the receptacle, into which the ball joint end of the Polar Arm fits. The Tracer can then be placed at one end of the base of the given diagram and the carriage moved until the other end is seen through this small hole.

Although of no more importance than many other operations made possible by the principle of the Planimeter we have been discussing, the finding of the average or mean height of an indicator diagram is perhaps that operation with which the Planimeter is most commonly associated. This use of the instrument and its value in obtaining the most accurate results has caused the production of a number of simple forms of planimeters designed especially for the measurement of indicator diagrams, and by whose use a degree of accuracy in this class of calculation is attained impossible by any other method.