Usage of the travelling microscope

In an instrument with vernier scales, if $n$ divisions of the main scale coincides with $N$ divisions of the vernier scale, then,

$$Least~count = \frac{length~of~a~smallest~division~of~the~main~scale}{N}$$

• Mean internal diameter of capillary tube $=\frac{(X_{2}-X_{1})+(Y_{2}-Y_{1})}{2}$
• Mean internal diameter of rubber tube $=\frac{(X_{2}-X_{1})+(Y_{2}-Y_{1})}{2}$
• Mean external diameter of rubber tube $=\frac{(X_{4}-X_{3})+(Y_{4}-Y_{3})}{2}$

1. First determine the least count of the travelling microscope and note it down. Using a spirit level and adjusting the levelling legs, level the microscope.
2. Fix the capillary tube co-axially with the microscope part of the instrument on a stand and focus the face of the capillary tube by the microscope.
3. Move the microscope horizontally until the cross wires of the microscope get adjusted as shown in Figure 4.2 and using the horizontal scale observe readings $X_{1}$ and $X_{2}$. Next move the microscope vertically until its cross wires get adjusted as shown in Fig 4.3 and using the vertical scale observe readings $Y_{1}$ and $Y_{2}$.
4. Remove the capillary tube, insert the rubber tube in that position. Measure the internal horizontal diameter of the tube as shown in Figure 4.4 and obtain readings $X_{1}$ and $X_{2}$. Next obtain the internal vertical diameter of the tube as shown in Figure 4.5 and obtain readings $Y_{1}$ and $Y_{2}$.
5. When measuring the external diameter of the rubber tube arrange it so that the cross wires are in contact with its external surface and obtain readings $X_{3}$ and $X_{4}$ as shown in Figure 4.4. and also readings $Y_{3}$ and $Y_{4}$ as shown in Figure 4.5.