The Travelling Microscope

The sliding carriage of the traveling microscope rides on carefully machined ways, pushed by a nut under the carriage which rides on the micrometer screw. The nut must not fit tightly on the screw or it will bind; hence there is always some slack built into the mechanism.

For the microscope set initially on the same line for both directions of motion, the readings will differ by distance S, the backlash (slop) in the mechanism.

One way to avoid trouble with this slack is always to make settings after turning the screw more than the slack in one direction, say the direction of increasing readings. If one overshoots on a reading, go back by more than the slack and then turn forward again. The screw will then always press on the same side of the nut and no error arises.

A much better experimental technique is to take readings both ways. Suppose one wants to measure the distance between two lines, 1 and 2. Call the reading turned toward larger readings on line 1, $D_{1}$ and when turning in the reverse direction, $R_{1}$; similarly for $D_{2}$ and $R_{2}$. Then the distance between the lines will be $D_{2} - D_{1}$ and also $R_{2} - R_{1}$ so that one has immediately two independent readings to compare. More important, $D_{1} - R_{1}$ is the slack in the mechanism; it should equal $D_{2} - R_{2}$ and should be the same for all pairs of readings. If $D - R$ changes by more than the experimental error in setting, you know immediately you have made a blunder in either setting or reading and can immediately repeat the measurement. The constancy of D - R is actually an excellent measure of the uncertainty in the measurements you are taking.