Physics 1103

Appendix A:  Linear Measurements

Perhaps the most common device for measuring lengths is the ruler or meter stick.  It is difficult, however, to estimate fractions of each division, so if greater precision is required, certain refinements must be made.

The Vernier caliper is a device that employs an auxiliary (Vernier) scale which permits more accurate measurements of small fractions of a main scale division.  The Vernier scale consists of N equally spaced divisions which have the same total length as (N - 1) main scale divisions.  On the Vernier caliper, the main (stationary) scale is divided in to millimeters.  The Vernier (moveable) scale is 9 mm long and consists of 10 divisions.  Each division on the Vernier scale, then, is 0.9 mm long, or 0.1 mm less than the main scale divisions.  Therefore, the number of the Vernier line which is best aligned with a line on the main scale is equal to the number of tenths of a millimeter beyond the the last reading of the main scale at the zero mark on the Verneir scale.

Fig. 1 - Vernier caliper

Study the above figure.  The caliper jaws are extended 11.7 mm.  First of all, you can tell that the zero mark of the Vernier scale (indicated by the left-most upward arrow) has passed the 11.0 mm mark (indicated by the downward arrow) on the main scale.  The number of the Vernier line which is best aligned with a line on the main scale is 7 (indicated by the right-most up arrow).  Therefore, the zero mark of the Vernier scale has gone 7 tenths of a millimeter past the 11.0 mm mark, giving a total reading of 11.7 mm.  The least count of the Vernier caliper is 0.1 mm.  That is, 0.1 mm is the smallest scale reading that can be made without estimation.

Practice reading the Vernier caliper below!  When the java applet loads, click and drag on the picture with the mouse to position the caliper for a new measurement.  You can read the value by using the above method.  To verify your measurement, type your reading in the provided box then press the enter key.  The "Reset" key sets the Caliper at the 0.0 mm position.  You can set the Caliber on tutorial mode by selecting  the "show" checkbox.  When in tutorial mode, three red arrows and number displays are provided, as above, to help you make the reading.  The first two arrows help you get the measurement in millimeters. The third helps you read the decimal.

This applet created by Fu-Kwun Hwang of the National Taiwan Normal University

If one requires greater precision than can be obtained with a Vernier caliper, a micrometer caliper is often used.  This instrument consists of an integral number of equally spaced divisions.  Consider as an example of the micrometer caliper shown below.

Fig. 2 - Micrometer caliper with closeup

The screw of this instrument has 20 threads per centimeter so that it advances 0.5 mm for each revolution.  Since there are 50 divisions around the rim of the head, the least count of this instrument is 1/50 x 0.5 = 0.01 mm.  In reading the rim of the instrument, one must determine whether the barrel is on its first or second revolution after a main scale division (one can determine this by simple inspection).  Some micrometers have the main scale subdivided into .05 mm intervals so no ambiguity arises.