Pickett Model N600-ES Log Log Speed Rule

Engineering; Mechanical Engineering; Mathematics

Physical Description:

The Pickett Model N600-ES Log Log slide rule is constructed using three yellow painted aluminum bars. The “ES” in the model name means “Eye-Saver” and refers to the yellow painted construction. The two outer bars are called the stators and are attached by a brace on both ends. The braces create a gap between the two stators where the third aluminum bar, called the slide, fits into the grooves between the two stators. A clear plastic cursor slides along the outside of the stators. The cursor has a vertical hairline marker on both sides of the slide rule for lining up the scales between the slide and stators. The upper stator has LL1 and A scales on the front side and LL2 and DF scales on the backside. The lower stator has D, DI, and K scales on the front side and D and LL3 scales on the backside. The slide has B, ST, T, S, and C scales on the front side and CF, Ln, L, CI, and C scales on the backside. The scales are usually logarithmic with a few exceptions such as the L and Ln scale which are log operations with a linear scale. The index of a scale is the furthest left number for the left index or the furthest right number for the right index. The scale ranges and operations are described under inscriptions.

Functional Description:

The Pickett Model N600-ES Log Log slide rule is a duplex slide rule. A duplex slide rule has scales on both sides of the slide rule and a dual-faced cursor. The dual-faced cursor allows for relating one side of the scale to the other side for a greater number of calculations. Logarithmic scales have a multiplication and division property discovered by William Oughtred in 1630 that allow for the operations of multiplication and division instead of addition and subtraction of linear scales. Multiplication is the simplest operation on a slide rule using the two fundamental scales, C and D. To multiply two numbers, x and y, the left index of C is positioned over x on the D scale. Then the cursor is position over y on the C scale. The value of the cursor on the D scale is the solution to x multiplied by y. The decimal place may need to be adjusted to get the correct order of magnitude since the C and D scale has values ranging from 1 to 10. The other scales are used to perform different operations such as squares, reciprocals, exponentials, and sines, cosines, and tangents.

The Pickett Model N600-ES Log Log slide rule is constructed using three yellow painted aluminum bars. The “ES” in the model name means “Eye-Saver” and refers to the yellow painted construction. The two outer bars are called the stators and are attached by a brace on both ends. The braces create a gap between the two stators where the third aluminum bar, called the slide, fits into the grooves between the two stators. A clear plastic cursor slides along the outside of the stators. The cursor has a vertical hairline marker on both sides of the slide rule for lining up the scales between the slide and stators. The upper stator has LL1 and A scales on the front side and LL2 and DF scales on the backside. The lower stator has D, DI, and K scales on the front side and D and LL3 scales on the backside. The slide has B, ST, T, S, and C scales on the front side and CF, Ln, L, CI, and C scales on the backside. The scales are usually logarithmic with a few exceptions such as the L and Ln scale which are log operations with a linear scale. The index of a scale is the furthest left number for the left index or the furthest right number for the right index. The scale ranges and operations are described under inscriptions.

Functional Description:

The Pickett Model N600-ES Log Log slide rule is a duplex slide rule. A duplex slide rule has scales on both sides of the slide rule and a dual-faced cursor. The dual-faced cursor allows for relating one side of the scale to the other side for a greater number of calculations. Logarithmic scales have a multiplication and division property discovered by William Oughtred in 1630 that allow for the operations of multiplication and division instead of addition and subtraction of linear scales. Multiplication is the simplest operation on a slide rule using the two fundamental scales, C and D. To multiply two numbers, x and y, the left index of C is positioned over x on the D scale. Then the cursor is position over y on the C scale. The value of the cursor on the D scale is the solution to x multiplied by y. The decimal place may need to be adjusted to get the correct order of magnitude since the C and D scale has values ranging from 1 to 10. The other scales are used to perform different operations such as squares, reciprocals, exponentials, and sines, cosines, and tangents.

Gideon Hoekstra, Nick Renke, Donovan Doran, Erik Madson

1962

English

Minimum: 152.4mm X 38.1mm X 7.9mm

Maximum Extended: 279.4mm X 38.1mm X 7.9mm

Maximum Extended: 279.4mm X 38.1mm X 7.9mm

Aluminum, Plastic

Pickett & Eckel - Chicago, Illinois, US

MODEL | N600-ES | LOG LOG | SPEED RULE | PICKETT | MADE IN USA | PICKETT | ALL METAL | SLIDE RULES | PICKETT & ECKEL. | INC. | CHICAGO, ILL | © 1962

Scale Label Inscription in Order (Description, Function, Range)

LL1 (Log Log, e0.01x, greater than 1: 1.01-1.15 and less than 1: descending 0.99-0.91, Logarithmic) |

A (Scale of squares, x2, two repeated 1-10 scales, Logarithmic) |

B (Scale of Squares, x2, two repeated 1-10 scales, Logarithmic) |

ST (Scale of sines and tangents, sin(x) tan(x), 0.6-5.5, Logarithmic) |

T (Scale of tangents and cotangents, tan(x) cot(x), 6-45 ascending and 84-45 descending, Logarithmic) |

S (Scale of sines and cosines, sin(x) cos(x), 5.8-90 ascending and 20-84 descending, Logarithmic) |

C (Fundamental Slide Rule Scale, x, 1-10, Logarithmic) |

D (Fundamental Slide Rule Scale, x, 1-10, Logarithmic) |

DI (Reciprocal D scale, 1/x, descending 1-10, Logarithmic) |

K (Scale of cubes, x3, three repeated 1-10 scales, Logarithmic) |

LL2 (Log Log, e0.1x, greater than 1: 1.11-e and less than 1: descending 0.90-0.40, Logarithmic) |

DF (Folded D scale, x*pi, pi-10 then 1-pi, Logarithmic) |

CF (Folded C scale, x*pi, pi-10 then 1-pi, Logarithmic) |

Ln (Natural log scale, ln(x), 0-2.3, Linear) |

L (Log scale, log(x), 1-10, Linear) |

CI (Reciprocal C scale, 1/x, descending 1-10, Logarithmic) |

C (Repeated) |

D (Repeated) |

LL3 (Log Log, ex, greater than 1: e-20M and less than 1: descending 0.37-0.0001, Logarithmic)

Scale Label Inscription in Order (Description, Function, Range)

LL1 (Log Log, e0.01x, greater than 1: 1.01-1.15 and less than 1: descending 0.99-0.91, Logarithmic) |

A (Scale of squares, x2, two repeated 1-10 scales, Logarithmic) |

B (Scale of Squares, x2, two repeated 1-10 scales, Logarithmic) |

ST (Scale of sines and tangents, sin(x) tan(x), 0.6-5.5, Logarithmic) |

T (Scale of tangents and cotangents, tan(x) cot(x), 6-45 ascending and 84-45 descending, Logarithmic) |

S (Scale of sines and cosines, sin(x) cos(x), 5.8-90 ascending and 20-84 descending, Logarithmic) |

C (Fundamental Slide Rule Scale, x, 1-10, Logarithmic) |

D (Fundamental Slide Rule Scale, x, 1-10, Logarithmic) |

DI (Reciprocal D scale, 1/x, descending 1-10, Logarithmic) |

K (Scale of cubes, x3, three repeated 1-10 scales, Logarithmic) |

LL2 (Log Log, e0.1x, greater than 1: 1.11-e and less than 1: descending 0.90-0.40, Logarithmic) |

DF (Folded D scale, x*pi, pi-10 then 1-pi, Logarithmic) |

CF (Folded C scale, x*pi, pi-10 then 1-pi, Logarithmic) |

Ln (Natural log scale, ln(x), 0-2.3, Linear) |

L (Log scale, log(x), 1-10, Linear) |

CI (Reciprocal C scale, 1/x, descending 1-10, Logarithmic) |

C (Repeated) |

D (Repeated) |

LL3 (Log Log, ex, greater than 1: e-20M and less than 1: descending 0.37-0.0001, Logarithmic)

Slides rules were used in math intensive engineering courses to perform calculations. Slides rules were eventually replaced by calculators and are now mostly obsolete.

MEEM, Third floor display case, 3rd case from the right, 2nd shelf

MacKenzie, D. Scott. “Illustrated Self-Guided Course On How To Use The Slide Rule.” Sliderulermuseum. November 18, 2019. https://www.sliderulemuseum.com/SR_Course.htm

Marcotte, Eric. “Types of Slide Rules and their Scales.” Sliderule. November 18, 2019. https://www.sliderule.ca/scales.htm

Marcotte, Eric. “Types of Slide Rules and their Scales.” Sliderule. November 18, 2019. https://www.sliderule.ca/scales.htm

Wang Laboratories Model 370 Programming Calculator

Mathematics; Science; Engineering; Financial Services.

A rectangular shaped (304.4 Length X 165.1Width X 355.6 Height mm) device. This frame is made of metal that is painted everywhere except the stainless steel bottom. The front of the calculator contains a panel and display board. The panel holds 56 plastic keys of different shapes (Key Shape 1: 17.5 X 9.5 X 17.5 mm & Key Shape 2: 38.1 X 9.5 X 17.5 mm) and colors (black, gray, white, and blue) and 12 small white switches. The display board is a clear plastic sheet with a 14-digit display of nixie tubes behind it. On top there are multiple openings, likely for ventilation. On the back near the bottom is a black plastic knob, a switch for power, 2 slots for inputting cords, and 2 cords that go out.

Functional Description:

The Wang Model 370 Programmer is a primitive calculator that was capable of being programmed for adding loops, logical tests, jumps, and subroutine calls. This turned the calculator into a small computer.

On the keyboard are many different commands for programming and many basic calculator operations (such as add, subtract, multiply, divide, etc.). The 370 Programmer calculates operations and displays them on through the clear plastic screen via lighting up different nixie tubes shaped into numbers.

The 370 was capable of programming and reading code. It could use the programming keys on the keyboard to create a code. It could attach to a card reader that would read punch out sheets and translate the card into code for the 370 to use. Both methods could then store the code on the 370 to be used later.

Functional Description:

The Wang Model 370 Programmer is a primitive calculator that was capable of being programmed for adding loops, logical tests, jumps, and subroutine calls. This turned the calculator into a small computer.

On the keyboard are many different commands for programming and many basic calculator operations (such as add, subtract, multiply, divide, etc.). The 370 Programmer calculates operations and displays them on through the clear plastic screen via lighting up different nixie tubes shaped into numbers.

The 370 was capable of programming and reading code. It could use the programming keys on the keyboard to create a code. It could attach to a card reader that would read punch out sheets and translate the card into code for the 370 to use. Both methods could then store the code on the 370 to be used later.

Gideon Hoekstra, Donovan Doran, Erik Madson, Nick Renke

1967-1968

English

Length 304.4 X Width 165.1 X Height 355.6 mm

Key Shape 1: 17.5 X 9.5 X 17.5 mm Key Shape 2: 38.1 X 9.5 X 17.5 mm

Key Shape 1: 17.5 X 9.5 X 17.5 mm Key Shape 2: 38.1 X 9.5 X 17.5 mm

Metal, plastic, paint, glass, and rubber.

WANG Laboratories, Inc.

FRONT: PROGRAMMING KEYBOARD | MODEL 370 ELECTRONIC CALCULATOR WANG LABORATORIES, INC. MASS. U.S.A. WANG PROPERTY OF | 41904 MICHIGAN | TECHNOLOGICAL | UNIVERSITY BACK

FUSE TURN OFF | ON POWER 115 AC | 60 CPS I/O E.P. READER

BOTTOM: Wang Laboratories Inc. | ELECTRONIC CALCULATOR | 370 SYSTEMS | MODEL NO. 370/370-2 | SERIAL NO. 700185 | TEWKSBURY, MASS, U.S.A. AUG 14 1968

FUSE TURN OFF | ON POWER 115 AC | 60 CPS I/O E.P. READER

BOTTOM: Wang Laboratories Inc. | ELECTRONIC CALCULATOR | 370 SYSTEMS | MODEL NO. 370/370-2 | SERIAL NO. 700185 | TEWKSBURY, MASS, U.S.A. AUG 14 1968

Likely used as an early programming device and calculator at the school before being replaced by better computers.

MEEM 3rd Floor, Hallway Display Case

Bensene, Rick. “Wang Laboratories: From

Custom Systems to Computers.” The Old Calculator Web Museum. September 8, 2019. Accessed November 18, 2019. https://www.oldcalculatormuseum.com/d- wangcustom.html

Wang Calculators – History.” DoPECC.

Accessed November 18, 2019. https://dopecc.net/calculators/wang/

Custom Systems to Computers.” The Old Calculator Web Museum. September 8, 2019. Accessed November 18, 2019. https://www.oldcalculatormuseum.com/d- wangcustom.html

Wang Calculators – History.” DoPECC.

Accessed November 18, 2019. https://dopecc.net/calculators/wang/

Picket Model 1000 Slide Rule

Mathematics

Physical Description: The Pickett 1000 slide rule is made of three rectangular bars of aluminum alloy coated in plastic with grooved slides. Two bars are connected at the end with braces that are mounted to the flat side of the bars and the third bar is free to slide between them, held in place by slide tension springs. The two outer bars are called stators and the inner bar is referred to as the slide. The slide rule also has a courser made of two flat lenses held together by aluminum above and below the upper and lower stators. Each bar of the Pickett 1000 slide rule has at least one scale on it. The front side of the slide rule has the DF scale on the upper stator CF, CIF, CI and C scales on the slide and D and L scales on the lower stator. The back side of the slide rule has an A scale in the top stator B, T, ST, and S scales on the slide and K and D scales on the lower stator.

Functional Description: Slide rules work on a system of logarithms. In order to do multiplication the slide rule adds two logarithms and takes the antilog to determine the answer. Because the slide rule uses logarithmic scales, the operation is simplified. If the user wanted to multiply two numbers together they would move one of the indices on the C scale to the first number that they wish to multiply on the D scale .They would then move the cursor to the second number in the multiplication on the C scale and look at the corresponding number on the D scale. So, if you wanted to multiply 2 and 4 you would move the left index of the C scale to the 2 on the D scale, move the cursor to the 4 on the C scale and see that the answer Is 8. To do division the inverse is done. To find the square and square root the A or B scale and the D scale are used. Locate the number of the square root you want to find using the cursor, when found the corresponding number on the D scale is the answer. To find the square the inverse is found. cube and cube root K scale and the D scale are used. To find the cube root take the number and find it on the K scale read the corresponding number on the D scale. To find the cube the inverse is performed. Scales available on the slide C and D used for multiplication and Division, CF and DF used for multiplication and division when the C and D scales run out. The CI and CIF scales are the inverse of the C scale and CF scale respectively. The S T slides are used for sine and tangent of greater than 5.7 degrees while the ST slide is used for degrees less than 5.7 degrees. The A and B scales are used in the calculation of squares and square roots. The L scale is used for the Log base 10 of a number..

Trevor Cretney, Adam Kausch, Matthew Luebke, and Adam Miller

International Slide Rule Museum. ISRM is the world's largest free digital repository of all things concerning slide rules and other math artifacts. There are over 7000 Images or PDF's in the ISRM Galleries">. Web. 22 Mar. 2017. <http://sliderulemuseum.com/SR_Scales.htm>.

Konshak, Mike. Pickett Chronology. JPG.

Hartung, Maurice L. How to use the Ortho-phase duplex slide rule. Pickett & Eckel, 1948. PDF.

Konshak, Mike. Pickett Chronology. JPG.

Hartung, Maurice L. How to use the Ortho-phase duplex slide rule. Pickett & Eckel, 1948. PDF.

1957

English

physical object

United States

Body: 31 x 306 x 7 mm

Slide: 306 x 14 x 3 mm

Cursor: 25 x 41 x 7 mm

Slide: 306 x 14 x 3 mm

Cursor: 25 x 41 x 7 mm

Aluminum, Plastic

Pickett & Eckel Inc, Alhambra, CA

U.S.A. COPYRIGHT 1948 | PICKETT. A.F. ECKEL | ALHAMBRA. CALIF., U.S.A. [front face, left side of slide]

PICKETT & ECKEL INC. | ALHAMBRA CALIF U.S.A. [front face right side of slide]

MODEL NO. 1000 | ORTHO – PHASE DUPLEX [back face left side of slide]

‘Pickett logo’ [back face right side of slide]

D204318 [cursor]

PICKETT & ECKEL INC. | ALHAMBRA CALIF U.S.A. [front face right side of slide]

MODEL NO. 1000 | ORTHO – PHASE DUPLEX [back face left side of slide]

‘Pickett logo’ [back face right side of slide]

D204318 [cursor]

Scales

A: 1-20 logarithmic scale

B: 1-20 logarithmic scale

T: logarithmic scale from 0-90

ST: logarithmic scale 0.56-5.73

S: logarithmic scale from 0-90

K: 1-30 logarithmic scale

D: 1-10 logarithmic scale with notation at pi

DF: folded scale ranging from pi-10 and then 1-pi

CF: folded scale ranging from pi-10 and then 1-pi

CIF: descending logarithmic scale pi-1 followed by 10-pi

CI: descending logarithmic scale 10-1

C: 1-10 logarithmic scale with notation for pi

L: 1-10 linear scaleThe history of this object at Michigan Tech is unknown. It is a calculation tool used before the calculator became an affordable tool.

Alumni House

American Thompson Steam Gauge

Steam Engines; Pressure Systems; Artillery

Physical Description:

The Thompson Improved Steam Indicator comes in a dark stained wooden box 285mm wide, 207mm deep, and 240mm tall. It opens about halfway up its height to reveal a number of objects. The box, as well as various components, are serial numbered 4994. Inside the box there are pockets as well as mounts for the various objects to go into which can be seen in the images provided.

In the center is the steam indicator, which resembles two off-center attached cylinders screwed onto a mount. The cylinders are both 90mm in height and 50mm in diameter. The top cylinder has a slot to affix a cardstock, a stylus arm and pull string. The bottom cylinder has the arm holding the stylus and a spring inside to control the stylus arm. The bottom of the bottom cylinder has threads and ties to the mount on the bottom of the box, as well as thumb bars on the bottom to attach or unattach it by hand.

The steam indicator comes with 6 springs numbered 10, 20, 30, 40, 60, and 80, which range in length from 53-63mm long. These springs are threaded onto mounts on the upper half of the box and can replace the spring inside the bottom cylinder of the steam indicator. This allows the system to make more precise graphs depending on the pressure that the engine is putting out.

In addition to the above, there are also two globe shut-off valves with thread sizes of 20 and 25mm. The valves come with caps for one side to prevent damage to the threads that could result in inadequate attachment . There is also a torque wrench used to tighten the lower cylinder onto the engine that the indicator will be attached to. There is also a small vial of oil, for the joints of the stylus arm or the springs. There was also a specialized wrench designed to tighten the components in order to prevent gas leaks. The final component was a ruler with a screw driver end that allowed for the dismantling of the indicator as well as measuring the height of the graphs drawn by the arm allowing the user to find the pressure in the system.

Functional Description:

In order to use the Thompson steam indicator, the user fastened the stainless-steel ball valve to the steam engine being analyzed. The indicator was then be fastened to the open end of the ball valve via a threaded connection. With the ball valve opened, the steam within the engine’s piston exerts pressure on a spring enclosed within a 100 mm tall, 30 mm diam. cylinder of the indicator. A plunger connected to the spring is forced upward depending upon the force received by the spring. The motion of the plunger moves the 80 mm long arm vertically, which determines the markings made by the attached pencil. The pencil marks a piece of paper, which is wrapped around the upper cylinder (90 mm tall and 51 mm dia) of the indicator. Wrapped around this upper cylinder is a string whose function is to rotate the cylinder about its center. If the string were left free to hang, the steam pressure pushes the pencil upward, making a straight vertical line on the paper. However, the string was fastened to a component of the engine to allow for the engine piston and the cylinder to move in unison. The string moves the cylinder of the steam indicator in unison with the piston throughout the entire stroke, and a continuous marking is made to illustrate the pressure at each point of the stroke as the pencil is moved upward and downward while the cylinder pivots throughout the process. Thus, the vertical motion of the pencil graphs changes in pressure, while the rotation of the cylinder indicates the phase of the piston cycle, and so in unison the pencil plots a diagram of the pressure cycle in the engine.

The indicator was designed to record the stroke of a steam engine, particularly locomotives. At the start of the stroke, the inlet valve opens completely, allowing the maximum force to be applied to the spring by the steam. The pencil marks a horizontal line at its highest point in the cycle from left to right. At cut-off, the inlet valve closes and expansion of the steam occurs, during which the force gradually decreases. This phase is indicated by a pencil mark resembling an exponential decay curve. At release, the exhaust valve opens, releasing the steam and the force is at its minimum, resulting in a straight horizontal pencil mark at the lowest point of the curve—this time from right to left. When the exhaust valve closes, compression occurs, causing a gradual rise in pressure. When the inlet valve opens again, the gradual increase in pressure becomes a sharp increase, causing the pencil to mark a straight vertical line returning to the first point of the cycle when the steam pressure exerts its greatest force on the spring. The end product of this device is a card illustrating the change in pressure throughout the continuous cycle of the steam engine. For an engine operating at 250 RPM, the device could generate one cycle plot (or card) per minute.

The spring within the indicator can be replaced with a larger spring to record higher steam engine pressures. The set of springs are marked according to their compressive strength: the spring marked #100 converts the force from 100 psi gauge-pressuresteam into a pencil movement of one inch, a #80 spring converts 80 psig steam into a movement of one inch, and so on.

Though the steam indicator was primarily used on locomotives, it could also be applied to traction engines and artillery. Due to the high cost of the indicator, it was seldom used on traction engines beyond the confines of the factory in which it was produced. When applied to heavy artillery, the oil in the recoil chamber would replace the steam as the working fluid and exert a pressure on the spring. The string would be fastened to the barrel to allow for the recoil movement to pull on the string.

Elsa Schwartz, Collin Graf, Sarah Hartman, Joel VanLanen, and Patrick Demorest.

1904

English

Physical object

Serial no. 4994

United States of America

Box: 285 x 240 x 207 mm

Cylinders: height of 90 mm, diam. 50 mm

Springs: 53-63 mm long

Valves: thread sizes of 20 and 25 mm

Cylinders: height of 90 mm, diam. 50 mm

Springs: 53-63 mm long

Valves: thread sizes of 20 and 25 mm

Indicator: bronze, steel, rope, graphite

Box: Wood, brass

Box: Wood, brass

American Steam Gauge Co., Boston, MA.

AMERICAN | STEAM GAUGE &. V. MFG.CO | BOSTON, U.S.A. | PAT'D. JAN. 31. 1899. | PAT'D. JUNE 7. 1904 | J.W. THOMPSON | PAT'D AUG. 31. 75 | 4994 [Indicator]

312 | 25 [Cylinder]

4994 [Box]

10 | 20 | 30 | 40 | 60 | 80 [Springs]

312 | 25 [Cylinder]

4994 [Box]

10 | 20 | 30 | 40 | 60 | 80 [Springs]

The object was made by the firm the American Steam Gauge Company of Boston, MA. The indicator was initially invented by James Watt, who also is credited with the invention of the steam engine. Joseph Thompson is the creator of this steam engine indicator with his patent being granted on Aug 31, 1875. The instrument was manufactured by The American Steam Gauge Company, which was founded in 1851. The instrument was sold as the “American Thompson Improved Indicator”, and was considered to be high end among steam indicators of the time. The improvements of the Thompson indicator over previous models were that the writing component followed an elliptical pattern to maintain a straight line on the recording barrel. This resulted in less inertia and increased the engine speeds, and pressures that the indicator could be used at. The patent granted in 1904 to Earl Vaughn had the benefits of making the indicator easier to disassemble for adaptability of the indicator. For this reason it is believed that this indicator was manufactured sometime after 1904.

MEEM, 3rd floor display case

"The Story of the Steam Engine Indicator." last modified July/August 2001 http://www.farmcollector.com/steam-traction/story-steam-engine-indicator

*Engineer: with which is incorporated steam engineering, volume 35* .. Vol. 42. (Chicago: The Engineer Publishing Company, 1905).

Dorn, Harold. *Dictionary of Scientific Biography*. Vol. 14. (New York: Charles Scribner's Sons, 1976), 196-99.