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Vernier ScalesLet's get back to estimating between the marks while making measurements. Back in 1631 a French mathematician named Pierre Vernier developed a way of making those estimates more reliable. That method is called a Vernier scale, as shown in Example 5 in your workbook. In parts a, b and c, the Vernier scale is on top and the standard scale is on the bottom. (Note: Due to scanning and digital reconstruction of the following analog diagrams, many of the lines are dashed or have dashed attachments. It is the position of these lines and not their appearance that is important in the following discussion. This technical difficulty can be avoided by using the diagrams in Example 5 of your workbook.)
In the next section, we'll get into how you actually make some of these measurements you've been reading about.
E-mail instructor: Eden Francis Clackamas Community College
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In the simplest form 10 units on the Vernier
scale equal 9 units on the Standard scale. I have numbered the top sequence of lines from
0 to 10, and I have numbered the bottom sequence of lines from 0 to 15. Notice that with
the 0 marks on both scales lined up, the 10th mark on the Vernier scale lines up with the
9th mark on the Standard scale. 
Notice what happens in part b when the
Vernier scale is shifted slightly. I would estimate that the 0-mark on the Vernier scale
is one-tenth of the way between the marks on the Standard scale. The Vernier scale
confirms this because the number 1 mark on the Vernier scale lines up with a mark below it
on the Standard scale. If the 0-mark on the Vernier scale is slid two-tenths of the way
over to the next Standard mark, then the number 2 mark on the Vernier scale would line up
with a mark below it on the Standard scale. Note that however far the Vernier scale
slides, the position of the 0-mark of the Vernier scale will be indicated by the number of
the Vernier mark that lines up with a mark on the Standard scale. How that works might be
apparent to you. More likely, you will want to look at and manipulate the sample we have
in the lab. 
Now look at part c. Let's figure out the
position of the Vernier-0-mark on the Standard scale. It is between the 5th and 6th marks
so it is at five-point-something, maybe 5.7 or 5.8. By noting that the number 7 mark on
the Vernier scale lines up with a mark on the Standard scale, we know the reading should
be 5.7. If you have any questions about this see an instructor. You will be using a
modified Vernier scale in the lab when you use a Dial-O-Gram balance. 