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# Measurement of a Base-Line

The object of this experiment, which is a working model of the measurement of a geodetic base-line, is to determine with accuracy the distance between the scratches on two plugs so far apart that the methods of accurate measurement described above are impracticable.

The general plan of the method is to lay ivory scales end to end, fixing them by placing heavy weights on them, and to read by means of a travelling reading microscope the distance between the extreme graduations of the two ivory scales, or between the mark on the plug and the extreme graduation of the ivory scale placed near it. We have then to determine the real length of the ivory scales, and by adding we get the total length between the plugs.

The experiment may therefore be divided into three parts.

(1) To determine the Distance between the End Graduations of the Ivory Scales placed end to end.

This is done by means of the travelling microscope. Place the scales with their edges along a straight line drawn between the two marks and perpendicular to them, and fix them so that the extreme graduations are within 1/5 inch. Next place the microscope (which is mounted on a slide similar to the slide-rest of a lathe, and moved by a micrometer screw the thread of which we will suppose is 1/50th of an inch) so that the line along which it travels on its stand is parallel to the base line, and focus it so that one of its cross-wires is parallel and coincident with one edge of the image of the end graduation of the one ivory scale. (It is of no consequence which edge is chosen, provided it be always the same in each case.)

Read the position of the microscope by its scale and micrometer screw, remembering that the fixed scale along which the divided screw-head moves is graduated to 50ths of an inch, and the circumference of the screw-head into 200 parts; each part corresponds, therefore, to 1/10000 inch. So that if the reading on the scale be 7, and on the screw-head 152, we get for the position

7 divisions of the scale= 7/50 in.
152 divisions of the screw-head =0.0152 in.

Next turn the micrometer screw-head until the last division on the other ivory scale comes into the field of view, and the corresponding edge of its image is coincident with the cross-wire as before. Read again; the difference of the two readings gives the required distance between the two graduations.

In the same way the distance between the scratch on the plug and the end division of the scale may be determined.

Place one ivory scale so that one extremity is near to or coincident with the scratch on the plug; read the distance between them; then place the other scale along the line and end-on with the first, and measure the distance between the end divisions of the two scales. Then transfer the first scale to the other end of the second; measure the distance between them again; and so on.

(2) To Estimate the Fraction of a Scale over.

This may be done by reading through the microscope the division and fraction of a division of the scale corresponding to the scratch on the second plug. This gives the length of a portion of the scale as a fraction of the true length which is found in (3).

(3) To Determine the true Length of the Ivory Scales.

This operation requires two reading microscopes. Focus these two, one on each extreme division of the scales to be measured, taking care that the same edge of the scratch is used as before. Then remove the scale, introduce a standard whose graduation can be assumed to be accurate, or whose true length is known, and read by means of the micrometer the exact length, through which the microscopes have to be moved in order that their cross-wires may coincide with two graduations on the standard the distance between which is known accurately.(1)

The lengths of all the separate parts of the line between the marks, which together make up the whole distance to be measured have thus been expressed in terms of the standard or of the graduations of the micrometer screw. These latter may be assumed to be accurate, for they are only used to measure distances which are themselves small fractions of the whole length measured (see p. 41). All the data necessary to express the whole length in terms of the standard have thus been obtained.

Experiment. - Measure by means of the two given scales and the microscope the distance between the two given points.

Enter the results thus:

 (1) For less accurate measurements the lengths of the scales may also be determined by the use of the beam-compass.

Last Update: 2011-03-27