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CHAPTER II.

The Polar Planimeter.

Integrating Wheel and Recording Mechanism.

The Integrating Wheel W with its attachments and adjusting mechanism form by far the most important part of the Planimeter and on their condition and on the delicacy and accuracy of their adjustment depends to a very large extent the value of the Instrument.

The Wheel itself is usually about three-quarters of an inch in diameter and is made of very highly polished metal, hard nickel being the material usually selected owing to its freedom from tendency to rust. The Wheel is mounted on a spindle or axis of hard steel having at each end very fine conical points which fit into conical receptacles in bearing boltsó which are set into the Carriage frame at both ends of the spindle. As the accuracy of the Planimeter demands that this axis of the Integrating Wheel shall be exactly parallel both to the surface on which the wheel moves and to the Tracer Arm of the instrument, these bolts which form the bearings of the axis are capable of very accurate adjustment both horizontally and vertically by means of very fine adjusting screws in the Carriage or frame which act on the bolts and bring them to the desired position.

It is also a strict essential that the axis shall be so adjusted in its hangings that friction shall be reduced to a minimum and that the wheel shall revolve with the greatest possible freedom but without perceptible play or shake in its bearings.

To the wheel and its axis is attached the recording mechanism of the instrument by means of which the total number of revolutions and fractions of a revolution made by the Integrating Wheel during any given operation may be accurately measured and recorded.

Attached to the Wheel and of slightly less diameter than the rim of the Wheel is a drum, usually of white celluloid. The circumference of this drum is accurately divided into ten equal parts and the lines marking such parts are subdivided each into ten other equal parts marked by smaller marks, thus dividing the circumference of the Wheel into one hundred equal parts. Each one of these one hundred divisions is marked by a black line cut on the white drum

Attached to the Carriage in such a manner that the edge lies along the graduated edge of the drum is a white celluloid plate having vernier cut along its edge. By means of this vernier the space between two consecutive lines on the drum is divided into ten other equal parts. This arrangement of graduated drum and its vernier divides the circumference of the drum into one thousand equal parts and since one complete revolution of the Integrating Wheel causes the drum to move over one thousand of the equal parts into which its edge is divided, it follows that the drum and its vernier will give at once the fractional part of any revolution made by the wheel in terms of these parts.

At U on the axis of the wheel is cut a worm screw which engages with a pinion which forms the axis of the small graduated white celluloid wheel O. This worm is so arranged that one complete revolution of the Integrating Wheel and its axis will cause the wheel O to make one-tenth of a revolution about its center, and since the circumference of the wheel O is divided into ten equal parts it is evident that the wheel O will record the number of whole revolution of the Wheel W made during any operation.

It is then evident that the wheel O together with the graduated drum and its vernier will give at once and accurately the whole number of complete revolution and the tenths, hundredths and thousandths of a revolution made by the Integrating Wheel W during any operation of the Planimeter. It further follows that if we know the circumference of the Wheel W, the number of revolution and fractions of a revolution thus recorded will give us accurately the length of any path rolled over by the wheel during the operation which caused those revolutions.

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