One vivid memory from high school is my physics teacher, Mr. Upchurch, teaching us how to use slide rules. He did it in such a way that made finding answers to calculations with a couple of sticks fun and easy. First, he showed us how to add with two meter sticks. It was pretty simple really. Put the "end" of the top stick over a number on the bottom stick, move your finger over to another number on the top stick, read the sum of the two numbers under your finger on the bottom stick. WOW, that really worked!Things got a little fuzzy for me when he made us do the math to convert the linear meter stick scale to a logarithm scale. But when I realized the only thing that changed was the scale on the sticks, I was back on track.

I never did like logarithms, but I got really good at using a slide rule. In fact, for several years after my own physics students started using calculators, I could get the answer to most problems quicker on my slide rule than they could on their calculators.

Mr. Upchurch lived to see calculators make slide rules obsolete and his problem student teaching another generation of physics students, but never dreamed of having his slide rule curriculum on something called the World Wide Web.

Mr. Upchurch, this is for you.

Parts of a slide rule:

Body- upper and lower fixed barsSlide- the movable middle barCursor- the hairline

To use a slide rule, one must know the following:

- How to read the scales.
- How to "set" the slide and cursor for each operation.
- How to estimate the result and determine the decimal point.

- Estimation: convert the problem to round numbers that can be easily estimated.
- Common Sense: for most practical problems, there is usually only one place for the decimal point in which the answer is reasonable.
- Scientific Notation: carry out the indicated operations then use the laws of exponents to combine the exponents until a single power of 10 is indicated.

A Personal Opinion:I am convinced that the problems many of today's students have with fractions and decimals can be traced directly to the replacement of the slide rule by calculators. Students punch numbers into a calculator and expect it to provide the correct answer. The skills of estimation and carrying decimals are no longer practiced.

Slide Rule Scales:The number of different scales, their length, and the number of subdivisions are largely determined by the size of the slide rule. Larger slide rules are better than smaller slide rules because of the detail of the scales.

C and D scales:used for the common operations of multiplication, division, and proportion.

- These scales are also used to convert between radians and degrees.
- Log formula for these scales is d = M Log
_{10}n- For this equation, M is the length of the rule (10 inches), and d is the distance between 1 and n on the rule.

- This produces a graduated scale.

- Slide two of these scales across each other to begin calculating.

CF and DF scales:"folded" C and D scales beginning withpie. The index is near the middle of the scale.

- Using "folded" scales increases operation speed by allowing the calculation without resetting the slide.
- The circumference of a circle is found with the DF and D scales.
CI and DI scales:just like the C or D scale except it increases from right to left.

- Using "inverted" scales increases operation speed by allowing calculations to be done with the slide always on one side of the body, instead of moving back and forth during an operation.
- This is helpful when multiplying a string of numbers or doing combined multiplication and division.
- The CI and C scales are combined to find the reciprocal of a number.
A and B scales:these scales are shrunk to half the length of the C and D scales and printed twice on the same line.

- Finding square and square root is done by combining the A and D scales, or the B and C scales.
- The area of a circle is found with a combination of the A, B, and C scales.
K scale:this scale is shrunk to one third the length of the D scale and printed three times on the same line.

- Finding cube and cube root is done by combining the K and D scales.
L scale:used with the C or D scales to find the mantissa of the common logarithm (base 10) of a number.

- The logarithm of a number is the exponent to which a given base (10) must be raised to produce the number.
- A logarithm consists of two parts:

- The characteristic is the integer (left of the decimal).
- The mantissa is the decimal fraction (right of the decimal).
S scale:used to find the approximate value of the sine or cosine of any angle between 5.7 and 90 degrees.

- Since sin X = cos (90 - X), the same graduations serve for both sines and cosines.
T scale:used to find the tangent or cotangent of any angle between 5.7 and 84.3 degrees.

- Since tan X = cot (90 - X), the same graduations serve for both tangents and cotangents.
ST scale:used to find trig functions for small angles, less than 5.7 degrees.

Scale Graduations:

- Graduations - the subdivisions of a scale
- Primary graduations - lines on any scale with large numbers above or below them
- Secondary graduations - ten shorter line divisions between the primary graduations
- Tertiary graduations - shorter subdivision lines between secondary graduations
- Left index - the first numbered mark at the left of a scale
- Right index - the first numbered mark at the right of a scale
- Special graduations:

Pie- found on all basic scales'- representspie/4 or 0.7854 - found on A, B, C, and D scales near the right-hand end (just short of 8). Used for finding the area of circles- R - represents 57.3 - found on C, D, and CI scales. Used in changing from radians to degrees and conversely

Setting the Scales for Operations:Practice the setting below with avirtual slide rule.

- Pickett N1010-ES Trig (Classroom - 7 foot, yellow wood)
- Pickett N1010-ES Trig (Classroom - 4 foot, yellow wood)
Like the one on the wall in my first classroom in 1970.

- Pickett Trig (Overhead Projector - 10 inch scale, clear plastic)
Purchased in 1972 as an upgrade for the wall rule.

- Pickett N3-ES Power Log Exponential (10 inch scale, yellow aluminum)
- Pickett N1010-T Trig (10 inch scale, white aluminum)
- Pickett N902-T Simplex Trig (10 inch scale, white aluminum)
- Pickett N4-ES Vector-Type Log Log (10 inch scale, yellow aluminum)
- Pickett N-1080-ES (10 inch scale, yellow aluminum)
- Pickett 14 U.S. (10 inch scale, yellow aluminum)
- R. C. Pickett, A. F. Eckel 2 Deci Log Log (10 inch scale, white composite fiber)
- Pickett N1006-ES Trig (5 inch scale, yellow aluminum)

- K&E #4081-5 Log Log Duplex Decitrig (20 inch scale)
- K&E #4081-3 Log Log Duplex Decitrig (10 inch scale)
- K&E #N4081-3 Log Log Duplex Decitrig (10 inch scale)
- K&E #4092 with patent dates June 5 '00 and Dec. 22 '08 (10 inch scale)
- (2) K&E #4092-3 with patent dates June 5 '00 Dec. 22 '08 April 1 '24 (10 inch scale)
- K&E #N4053-3 Polyphase (10 inch scale)
- K&E K-12 Prep #68 1892 (10 inch scale, white plastic with green print)
- K&E Doric model 1992 (5 inch scale, white plastic)

- Post #1446 (10 inch scale)
- Post #1447 (10 inch scale)
- Post #1452W (10 inch scale)

- Dietzgen #1732 Maniphase Multiplex with Pats. 2,170,144 & 2,258,722 (10 inch scale)
- Dietzgen #1768-P (10 inch scale, white plastic with green slide)
- Dietzgen Phillips #1759 B (10 inch scale)
Others

- Charvoz-Roos #Sr-109, 1946 (10 inch scale)
- ACU-MATH #500 (10 inch scale, white plastic)
- ACU-MATH #1200 (5 inch scale, white plastic)
- Aristo #89 (5 inch scale, white plastic)
- C-THRU S888 (10 inch scale, white plastic)
This is the student model I still have in quantity to reward students if they master the basic slide rule operations.

- Disney Mickey Mouse - Walt Disney World
- Empire Pedigree (10 inch scale, white plastic)
- Engineering Instruments #250BT (10 inch scale, wood/white plastic)
- Sterling #587 (5 inch scale, white plastic)
- Sterling Precision (10 inch scale, white plastic)
I have also found the following slide rule books:

- The Standard Manual of the Slide Rule, Its History, Principle, and Operation

J. E. Thompson

Second Edition, 1952- The Log Log Duplex Slide Rule Self Teaching Manual

Keuffel & Esser Co.

1932- The Log Log Duplex Decitrig Slide Rule Manual #4081

Keuffel & Esser Co.

1943- How to use Trig Slide Rules

Maurice L. Hartung

1953- How to use Log Log Slide Rules

Maurice L. Hartung

1953- A Manual for the Slide Rule

Paul E. Machovina

1950

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