| SCALES ... |
A scale can be thought of as a tool to let us compare two different views of the same object. Scales allow us to perform calculations and measurements without requiring the object to be its actual size. A scale can also be thought of as a ratio.
A biologist uses a scale in another way. Often small life forms and bacteria are microscopic. This scale is used to produce an enlargement so that we are better able to see the details of the organism.
Two of the most important scales on any slide rule are the C and D scales. These two scales are used mainly for multiplication and division. The Kid's Rule C and D look like this  for a close-up ...  You will notice that the distance between the marks is smaller at the left than at the right. This is because these scales are based on logarithms. At the very left of each of these scales you will see the number 1. This is called the left index. At the very right you will see another number 1, this is called the right index and is written as 10 on some other slide rules. Answers to problems depend on which of these indices (plural of index) we use. The neat thing about the indices is if a number goes off scale (that's when the sliding part sticks out too far) then you can use the other index and continue with your problem.
Reading the Scales:
The hairline of the cursor is used to help read our answers after we perform all the sliding operations. In the explanations, we will refer to the hairline simply as the cursor; so instructions will be like move the cursor and read a result from the cursor. Now you need to be careful reading the scales because it's very easy to slip up and put the cursor on the wrong value and then what happens?? We get the wrong answer!! Let's look at the C scale a bit more closely ... You will notice on your slide rule that there are ten large numbers on it 1, 2, 3, 4, 5, 6, 7, 8, 9 and another 1 (remember sometimes this could be a 10). These are the main markings or if you really want to show off their technical name is primary graduations. Now on your Kid's Rule you will notice more smaller numbers between the big 1 and the big 2. These are called the secondary graduations (You might like to invent a better name for them. What would you call them? Let me know!) Now these smaller numbers surely can't be the same as the bigger numbers! And they're not! The smaller ones actually let you count more accurately between 1 and 2. So they would represent numbers like 1.1, 1.2, 1.3 and so on up to 1.9. But what happened to the numbers between 2 and 3, then 3 and 4 and the rest? Well as you know the spacing gets smaller as we go from the left-hand side of the scale to the right-hand side, so it gets a bit hard to print all the numbers without making a big mess. So all you see are the markings, but I'm sure you will be able to work out what numbers these marks stand for. (I might test you a little bit later.) |
For example, an architect uses a scale to produce drawings of a building and by using the scale the drawing corresponds to what the actual building will be like. Can you imagine the difficulty if your plan had to be the same size as the building? This type of scale used here produces what is called a reduction.
Not all scales are linear. Sometimes it is better to use non-linear scales so that information can be analyzed easily and other relationships discovered. Most scales on a slide rule are not linear because they make use of mathematical properties. In fact the scales on a slide rule are based on what is known as the logarithm (that's such a neat name, pronounced 'log'-rhythm) and we will investigate the properties of logarithms as we proceed.