Chimney Stacks and Pots in Kilcullen

Chimney stacks, some topped with pots, on buildings along Kilcullen’s Upper Main Street. 

I've been reading the cover article from the April edition of The Bridge about the planned streetscape survey of Kilcullen's Upper Main Street. Zooming in on a c. 1900 image of the street, it appears that many of the chimney stacks were devoid of chimney pots—the same is true for Lower Main Street. A chimney pot serves several functions beyond mere aesthetics. It improves airflow by effectively raising the chimney's height without requiring the entire stack to be built taller. Since a chimney pot is narrower than the flue inside the stack (these chimney stacks were often wide and sometimes flue-less; in fact, children used to climb the stacks to sweep the chimneys), it creates a venturi effect, increasing airflow speed and improving suction.

Chimney pots became more common in the 18th century, with the peak of the fashion occurring in the 19th century.

Another feature of the chimney stacks is that many of them appear to have been constructed from brick, rather than rough stone. Over the intervening 130 years or so since the Lawrence Collection photo was taken, most of the stacks have been rendered.

Images courtesy The National Library of Ireland.

 

Brick-constructed chimney stacks on buildings along Kilcullen's upper main street.

 

Lawrence Collection photo, c. 1900, of Kilcullen's Upper Main Street, 

 

How to Calculate Arc Length of a Circle, Segment and Sector Area

Circumference, diameter and radius. © Eugene Brennan

 

What You'll Learn

In this tutorial you'll learn about:

• names for different parts of a circle
• degrees and radians and how to convert between them
• chords, arcs and secants
• sine and cosine
• how to work out the length of an arc and chord
• how to calculate the area of sectors and segments
• the equation of a circle in the Cartesian coordinate system

What Is a Circle?

"A locus is a curve or other figure formed by all the points satisfying a particular equation."

A circle is a single-sided shape, but it can also be described as a locus of points where each point is equidistant (the same distance) from the centre.

Angle Formed by Two Rays Emanating From the Center of a Circle

An angle is formed when two lines or rays that are joined together at their endpoints, diverge or spread apart. Angles range from 0 to 360 degrees. We often "borrow" letters from the Greek alphabet to use in math and science. So for instance, we use the Greek letter "p" which is π (pi) and pronounced "pie" to represent the ratio of the circumference of a circle to the diameter. We also use the Greek letter θ (theta) and pronounced "the - ta", for representing angles.

An angle is formed by two rays diverging from the centre of a circle. This angle ranges from 0 to 360 degrees. © Eugene Brennan

360 degrees in a full circle. © Eugene Brennan

Parts of a Circle

• A sector is a portion of a circular disk enclosed by two rays and an arc.
• A segment is a portion of a circular disk enclosed by an arc and a chord.
• A semi-circle is a special case of a segment, formed when the chord equals the length of the diameter.

Arc, sector, segment, rays and chord. © Eugene Brennan

What Is Pi (π) ?

Pi represented by the Greek letter π is the ratio of the circumference to the diameter of a circle. It's a non-rational number which means that it can't be expressed as a fraction in the form a/b where a and b are integers.

Pi is equal to 3.1416 rounded to 4 decimal places.

What's the Length of the Circumference of a Circle?

If the diameter of a circle is D and the radius is R.

Then the circumference C = πD

But D = 2R

So in terms of the radius R

C = πD = 2πR

What's the Area of a Circle?

The area of a circle is A = πR ²

But R = D/2

So the area in terms of the radius R is

Scroll to Continue

A = πR ² = π (D/2)² = πD ²/4

What Are Degrees and Radians?

Angles are measured in degrees, but sometimes to make the mathematics simpler and elegant it's better to use radians which is another way of denoting an angle. A radian is the angle subtended by an arc of length equal to the radius of the circle. ( "Subtended" means produced by joining two lines from the end points of the arc to the center).

An arc of length R where R is the radius of a circle, corresponds to an angle of 1 radian.

So if the circumference of a circle is 2πR i.e 2π times R, the angle for a full circle will be 2π times 1 radian or 2π radians.

And 360 degrees = 2π radians.

How to Convert From Degrees to Radians

1. 360 degrees = 2π radians
2. Dividing both sides by 360 gives
3. 1 degree = 2π /360 radians
4. Then multiply both sides by θ
5. θ degrees = (2π/360) x θ = θ(π/180) radians
6. So to convert from degrees to radians, multiply by π/180

A radian is the angle subtended by an arc of length equal to the radius of a circle. © Eugene Brennan

How to Convert From Radians to Degrees

1. 2π radians = 360 degrees
2. Divide both sides by 2π giving
3. 1 radian = 360 / (2π) degrees
4. Multiply both sides by θ, so for an angle θ radians
5. θ radians = 360/(2π) x θ = (180/π)θ degrees
6. So to convert radians to degrees, multiply by 180/π

How to Find the Length of an Arc

You can work out the length of an arc by calculating what fraction the angle is of the 360 degrees for a full circle.

1. A full 360 degree angle has an associated arc length equal to the circumference C
2. So 360 degrees corresponds to an arc length C = 2πR
3. Divide by 360 to find the arc length for one degree:
4. 1 degree corresponds to an arc length 2πR/360
5. To find the arc length for an angle θ, multiply the result above by θ:
6. 1 x θ = θ corresponds to an arc length (2πR/360) x θ

So arc length s for an angle θ is:

s = (2πR/360) x θ = πRθ /180

The derivation is much simpler for radians:

By definition, 1 radian corresponds to an arc length R

So if the angle is θ radians, multiplying by θ gives:

Arc length s = R x θ = Rθ

Arc length is Rθ when θ is in radians. © Eugene Brennan

What Are Sine and Cosine?

A right-angled triangle has one angle measuring 90 degrees. The side opposite this angle is known as the hypotenuse and it is the longest side. Sine and cosine are trigonometric functions of an angle and are the ratios of the lengths of the other two sides to the hypotenuse of a right-angled triangle.

In the diagram below, one of the angles is represented by the Greek letter θ.

The side a is known as the "opposite" side and side b is the "adjacent" side to the angle θ.

sine θ = length of opposite side / length of hypotenuse

cosine θ = length of adjacent side / length of hypotenuse

Sine and cosine apply to an angle, not necessarily an angle in a triangle, so it's possible to just have two lines meeting at a point and to evaluate sine or cos for that angle. However sine and cos are derived from the sides of an imaginary right angled triangle superimposed on the lines. In the second diagram below, you can imagine a right angled triangle superimposed on the purple triangle, from which the opposite and adjacent sides and hypotenuse can be determined.

Over the range 0 to 90 degrees, sine ranges from 0 to 1 and cos ranges from 1 to 0

Remember sine and cosine only depend on the angle, not the size of the triangle. So if the length a changes in the diagram below when the triangle changes in size, the hypotenuse c also changes in size, but the ratio of a to c remains constant.

Sine and cosine are sometimes abbreviated to sin and cos.

Sine and cosine of angles. © Eugene Brennan

How to Calculate the Area of a Sector of a Circle

The total area of a circle is πR ² corresponding to an angle of 2π radians for the full circle.

If the angle is θ, then this is θ/2π the fraction of the full angle for a circle.

So the area of the sector is this fraction multiplied by the total area of the circle

or

(θ/2π) x (πR ²) = θR ²/2 with θ in radians.

Area of a sector of a circle knowing the angle θ in radians. © Eugene Brennan

How to Calculate the Length of a Chord Produced by an Angle

The length of a chord can be calculated using the Cosine Rule.
For the triangle XYZ in the diagram below, the side opposite the angle θ is the chord with length c.

From the Cosine Rule:

c ² = R ² + R ² -2RRcos θ

Simplifying:

c ² = R ² + R ² -2R ²cos θor c ² = 2R ² (1 - cos θ)

But from the half-angle formula (1- cos θ)/2 = sin ² (θ/2) or (1- cos θ) = 2sin ² (θ/2)

Substituting gives:

c² = 2R ² (1 - cos θ) = 2R ²2sin ² (θ/2) = 4R ²sin ² (θ/2)

Taking square roots of both sides gives:

c = 2Rsin(θ/2) with θ in radians.

A simpler derivation arrived at by splitting the triangle XYZ into 2 equal triangles and using the sine relationship between the opposite and hypotenuse, is shown in the calculation of segment area below.

The length of a chord. © Eugene Brennan

How to Calculate the Area of a Segment of a Circle

To calculate the area of a segment bounded by a chord and arc subtended by an angle θ , first work out the area of the triangle, then subtract this from the area of the sector, giving the area of the segment. (see diagrams below)

The triangle with angle θ can be bisected giving two right angled triangles with angles θ/2.

sin(θ/2) = a/R

So a = Rsin(θ/2) (cord length c = 2a = 2Rsin(θ/2)

cos(θ/2) = b/R

So b = Rcos(θ/2)

The area of the triangle XYZ is half the base by the perpendicular height so if the base is the chord XY, half the base is a and the perpendicular height is b. So the area is:

ab

Substituting for a and b gives:

Rsin(θ/2)Rcos(θ/2)

= R ²sin(θ/2)cos(θ/2)

But the double angle formula states that sin(2θ) = 2sin(θ)cos(θ)

Substituting gives:

Area of the triangle XYZ = R ²sin(θ/2)cos(θ/2) = R ² ((1/2)sin θ) = (1/2)R ²sin θ

Also, the area of the sector is:

R ²(θ/2)

And the area of the segment is the difference between the area of the sector and the triangle, so subtracting gives:

Area of segment = R ²(θ/2) - (1/2)R ²sin θ

= (R ²/2)( θ - sin θ ) with θ in radians.

To calculate the area of the segment, first calculate the area of the triangle XYZ and then subtract it from the sector.. © Eugene Brennan

Area of a segment of a circle knowing the angle. © Eugene Brennan

Equation of a Circle in Standard Form

If the centre of a circle is located at the origin, we can take any point on the circumference and superimpose a right angled triangle with the hypotenuse joining this point to the centre.
Then from Pythagoras's theorem, the square on the hypotenuse equals the sum of the squares on the other two sides. If the radius of a circle is r then this is the hypotenuse of the right angled triangle so we can write the equation as:

x ² + y ² = r ²

This is the equation of a circle in standard form in Cartesian coordinates.

If the circle is centred at the point (a,b), the equation of the circle is:

(x - a)² + (y - b)² = r ²

The equation of a circle with a centre at the origin is r² = x² + y². © Eugene Brennan

Equation of a Circle in Parametric Form

Another way of representing the coordinates of a circle is in parametric form. This expresses the values for the x and y coordinates in terms of a parameter. The parameter is chosen as the angle between the x-axis and the line joining the point (x,y) to the origin. If this angle is θ, then:

x = cos θ

y = sin θ

for 0 < θ < 360°

Summary of Equations for a Circle

Table 1. Circle formulas. θ is in radians.

Quantity	Equation
Circumference	πD
Area	πR²
Arc Length	Rθ
Chord Length	2Rsin(θ/2)
Sector Area	R²θ/2
Segment Area	(R²/2) (θ - sin(θ))
Perpendicular distance from circle centre to chord	Rcos(θ/2)
Angle subtended by arc	arc length / (Rθ)
Angle subtended by chord	2arcsin(chord length / (2R))

Example

Here's a practical example of using trigonometry with arcs and chords. A curved wall is built in front of a building. The wall is a section of a circle. It's necessary to work out the distance from points on the curve to the wall of the building (distance "B"), knowing the radius of curvature R, chord length L, distance from chord to wall S and distance from centre line to point on curve A. See if you can determine how the equations were derived. Hint: Use Pythagoras's Theorem.

© Eugene Brennan

References

Harris, J., & Stöcker Horst. (1998). Handbook of Mathematical Formulas and Computational Science. Springer.

This article is accurate and true to the best of the author’s knowledge. Content is for informational or entertainment purposes only and does not substitute for personal counsel or professional advice in business, financial, legal, or technical matters.

© 2018 Eugene Brennan

 

Q&A From Readers 

George Dimitriadis from Templestowe on May 18, 2018:

Hi.

A good introduction to the basics of circle properties.

Diagrams are clear and informative.

Just a couple of points.

You have So C = πD = πR/2, which should be C = πD = 2πR

and A = πR^2 = π (D/2)2 = πD^2/2

should be A = πR^2 = π (D/2)2 = πD^2/4

Eugene Brennan (author) from Ireland on May 18, 2018:

Thanks George, I should have proof read before publishing, instead of beta testing on the readers !!

Larry Rankin from Oklahoma on May 19, 2018:

Very educational.

Troy Sartain on March 19, 2019:

How about a similar article for ellipses? Just a thought. Obviously, another level of complexity, even if not rotated.

Eugene Brennan (author) from Ireland on March 19, 2019:

Thanks Troy, I'll keep it in mind. Parabolas will probably come first though.

Mazin G A on April 01, 2019:

Hi,

How can I calculate the angle at the center of an arc knowing radius and center, start, and end points? I know how to do that if I have the length of the arc, but in my case I don't have it.

Eugene Brennan (author) from Ireland on April 05, 2019:

If you mean you know the coordinates of the start and end points of the chord, you can work out the length of the chord using Pythagoras's theorem. Then use the equation for length of a chord (2Rsin(θ/2) to find θ.

Lakshay on September 19, 2019:

Good efforts

darrell on April 06, 2020:

how do i calculate the length of a segment of a circle

Eugene Brennan (author) from Ireland on April 07, 2020:

If you mean the chord length, it's 2Rsin(θ/2).

See the derivation above.

Austen SMITH on April 28, 2020:

Hi I have a simple but frustrating problem- I want to build a regular curved wall a set distance from a straight wall - the centre of the circle /arc of the wall falls within the building.

I need to work out distance from the straight wall to measure, at regular intervals, to create the perfect curve starting and ending on the chord (2nd) forming the distance from the straight wall.(1st chord)

Hope you can help.

Eugene Brennan (author) from Ireland on April 30, 2020:

Hi Austen, I spent hours trying to figure this out using angles, but it turned out that since the chord length is known between two ends of the curved wall (is this correct?), it can easily be worked out using Pythagoras's Theorem. I've drawn it up as an example at the bottom of the article, hope it helps.

Suggestion, you could put the values into a spreadsheet to do the calculations.

Austen on May 31, 2020:

Many thanks for solving the curved wall issue.

I’ racked my brains back 45 plus used the existing formulae on your website to crack it- but as always when someone who “knows” tells you “how” - it becomes so clear you wonder how you couldn't see it before.

Thanks for relighting the knowledge thirst.

A

Eugene Brennan (author) from Ireland on May 31, 2020:

Thanks Austen.

I worked out D in the diagram above knowing R and L/2. In reality that's probably not necessary because you may already know the distance from the centre of the arc to the inside of the wall. Adding this to S gives you D.

Driving Slower to Reduce Fuel Consumption

Created by ChatGPT

In theory, according to Newton's first law, a body remains at rest, or in motion at a constant speed in a straight line, unless it is acted upon by a force. So if you kicked a ball in space and there were no planets or stars to influence the ball, it would go on forever.

How to Use a Multimeter to Measure Voltage, Current, and Resistance

A multimeter measures voltage, current, and resistance and can also trace breaks in wires and test diodes, capacitors, and fuses. © Eugene Brennan

 

What Is a Multimeter?

Multimeters are measurement instruments widely used by professionals in several fields including industrial maintenance and testing, research, appliance repair, and electrical installation. However, a digital multimeter (or DMM) is also an invaluable test instrument for home and DIY use.

Conversations With ChatGPT: Air Drag and Surface Topology

Created by Grok.

Eugene: Is it possible to make a material that has a huge amount of drag that could allow a human to float? And what topology of surface has the most drag, a plane? I know that drag is proportional to cross-sectional area and also that there is a coefficient that depends on the surface shape of an object.

Parabola Equations and Graphs, Directrix and Focus and How to Find Roots of Quadratic Equations

© Eugene Brennan

In this tutorial, you'll learn about a mathematical function called the parabola. We'll cover the definition of the parabola first and how it relates to the solid shape called the cone. Next, we'll explore different ways in which the equation of a parabola can be expressed.

Conversations With ChatGPT: Converting Garden Waste to Electricity

Created by ChatGPT

Eugene: Is it possible to convert the energy stored in garden waste directly into electricity?

Special Relativity and Angle Grinder Disks

© Eugene Brennan

The theory of special relativity was postulated by Einstein in his 1905 paper, "On the Electrodynamics of Moving Bodies". While things behave seemingly "normal" at speeds we experience in our daily lives, bizarre things happen at near-light speeds.

Where Does Water Come From in an Air Compressor Tank?

Graph of temperature versus max water storage capacity of air.

Anyone who owns an air compressor knows that one of the regular maintenance chores is to drain the tank to release water. This is essential to prevent eventual corrosion of the tank.

Rules of Logarithms and Exponents With Worked Examples and Problems

A graph of a log function. Krishnavedala , CC BY-SA 3.0 via Wikimedia Commons

An Introduction to Logarithms, Bases and Exponents

In this tutorial you'll learn about

• exponentiation
• bases
• logarithms to the base 10

Another Use for AI: Reading Tables From Images and Converting to HTML

Screenshot of a table. © Eugene Brennan

Artificial intelligence gets a lot of bad press, so I need to write a proper article at some stage about how beneficial I’ve found it to be for all sorts of tasks.

Summary of Ideal Gas Laws

Thanks to ChatGPT for creating the table to my design. There's a long discussion with ChatGPT about the gas law equations here, where I revise my limited knowledge from school. (which was basically just understanding Boyle's Law and Charles's Law)

Law / Equation	Form / Equation	Derived From	Notes / Conditions
Boyle’s Law	P V = constant	Ideal Gas Law P V = n R T, with T = constant	Isothermal: pressure inversely proportional to volume
Charles’s Law	V / T = constant or V ∝ T	Ideal Gas Law P V = n R T, with P = constant	Isobaric: volume directly proportional to temperature
Gay-Lussac’s Law	P / T = constant or P ∝ T	Ideal Gas Law P V = n R T, with V = constant	Isochoric: pressure directly proportional to temperature
Ideal Gas Law	P V = n R T	Fundamental definition of ideal gases	Connects pressure, volume, temperature, and moles
Combined Gas Law	P V / T = constant P1 V1 / T1 = P2 V2 / T2	Ideal Gas Law, general form combining Boyle, Charles, Gay-Lussac	Relates pressure, volume, and temperature for a fixed amount of gas
Adiabatic PV Relation	P Vγ = constant	First Law dU = -P dV + Ideal Gas Law, γ = Cp/Cv	No heat transfer; pressure rises faster than 1/V
Adiabatic T–V Relation	T Vγ-1 = constant	PV adiabatic relation + Ideal Gas Law	Temperature rises when volume decreases (or vice versa)
Adiabatic T–P Relation	T = constant × P(γ-1)/γ	From PV and T–V adiabatic relations	Temperature as a function of pressure
Adiabatic PV Relation (states)	P1 V1γ = P2 V2γ	PV adiabatic relation applied to two states	Useful for calculating compression/expansion between two points
Adiabatic T–V Relation (states)	T1 V1γ-1 = T2 V2γ-1	T–V adiabatic relation applied to two states	Temperature change for volume change between two states
Adiabatic T–P Relation (states)	T2 = T1 (P2/P1)(γ-1)/γ	T–P adiabatic relation applied to two states	Temperature change for pressure change between two states

Unorthodox Fire Starting Devices

A fire plunger. Image courtesy eBay

Two gadgets for those who need to light a fire when camping or otherwise and want to show off (although a cigarette or gas lighter is perfectly adequate):

How to Understand Calculus: Integration Rules and Examples

© Eugene Brennan

What Is Calculus?

Calculus is a study of rates of change of functions and accumulation of infinitesimally small quantities. It can be broadly divided into two branches:

What Is Calculus? A Beginner's Guide to Limits and Differentiation

 © Eugene Brennan

Calculus is a study of rates of change of functions and accumulation of infinitesimally small quantities. It can be broadly divided into two branches:

• Differential Calculus. This concerns rates of changes of quantities and slopes of curves or surfaces in 2D or multidimensional space.
• Integral Calculus. This involves summing infinitesimally small quantities.

What Would Happen if You Fell Down a Hole That Went Through the Centre of the Earth?

Created by Grok

Well you'd be incinerated as you pass through the hot and molten core! But imagine if the core wasn't there or you had a special suit that protected you from the heat—what would happen then? Would you suddenly stop when you got to Oz?

Science Friday Podcast — Jim Lovell Interview

NASA astronaut Jim Lovell, photographed in 1969. Image credit: NASA, public domain, via Wikimedia Commons

The late Jim Lovell, commander of the ill-fated Apollo 13 mission talks with Ira Flatow of SF in an interview from 1995.
Apollo 13 was the seventh crewed mission and would have been the third operation to land humans on the Moon. However an explosion in an oxygen tank caused loss of electrical power and cut short the mission. The crew had to slingshot the spacecraft around the Moon to gain enough momentum to get back to Earth. In the interview, Jim explained the details of the event, we hear recordings of radio comms between flight control and the the spacecraft and Commander Lovell answers questions from callers. 

Another Few Stats on Poulaphouca Reservoir Water Levels and Volume

An ash tree growing on a trail beside the Poulaphouca Reservoir. © Eugene Brennan

In the period from 20th to 31st January, the volume of water in the Poulaphouca Reservoir increased by 52 million m³ of water, corresponding to a 2.3 m rise in level. In the same period, discharges from Golden Falls dam totalled 16 million m³. Since the level in the Golden Falls lake didn't change appreciably over those 12 days, and its surface area is much smaller than that of the Poulaphouca lake, the amount of water that flowed into Poulaphouca must have been equal to the increase in volume plus the amount that flowed out — 68 million m³. Over the 12 days, that gives an average inflow rate of 68/12 million or approximately 5.6 million m³/day. That's about 1.6 times the peak daily flow rate through Kilcullen last week. The Poulaphouca lake is fed by two rivers: The River Liffey and Kings River and so that's understandable. Some small streams also add to the water accumulated.
The ash tree above is on a nice section of path along the lake that leads to the car park on the N81, near the turn for Ballymore Eustace .
Stats are available on the ESB hydrometric website here.
 

Making a Bit Of Space : Golden Falls Lake Level Has Risen

Water level in Golden Falls Lake, Ballymore Eustace. Image courtesy ESB hydrometrics

The Golden Falls lake rose 1.44 m since yesterday. That's a bit of a jump since the downwards trend over the last week or so, and equivalent to approximately 370,000 cubic metres (m³) of water. The Golden Falls lake doesn't really provide a large storage capacity compared to the much larger Poulaphouca Reservoir, which has a surface area of approximately 22.6 square kilometres (km²), 86 times that of the Golden Falls lake. According to Esbarchives.ie, the head of the Golden Falls dam is 17.4 m. If the walls of the 256,000 m² lake were vertical, that would give a storage capacity of about 4.4 million m³ of water. To put that into perspective, if it were empty, it could store only about a day and a quarter's worth of the water that passed through Kilcullen at peak discharge last week. So dropping the level isn't a huge advantage as regards overall storage and I guess the objective is to try and make more "headroom" available in the Poulaphouca Reservoir to cater for extended periods of heavy rain.

Image courtesy ESB hydrometrics.

Kilcullen Town Hall's Film Projector

Movie projector from Kilcullen Town Hall Cinema. © Eugene Brennan

I was examining the nameplate (rating plate) of Kilcullen Town Hall's former film projector the other day, now located in a corner of the porch of the heritage centre. The Peerless Magnarc carbon-arc lamphouse, paired-with the projector and  manufactured by the J. E. McAuley Manufacturing Company of Chicago, Illinois, ran on DC electricity. A rectifier may have been built into the projector to convert mains AC to DC, or possibly it was a separate piece of equipment.
Arc lamps were used as an intense white light source for projectors, essential for producing a bright image on the screen. They were also used of course in search lights during WWII, for spotting enemy aircraft. Arc lighting generates large amounts of harmful UV radiation and filters would presumably have been used in the optics to block this. Electric arcs also produce a lot of heat, as anyone who has ever done electric welding would know, and again, filtering would have been necessary to protect the film. Carbon rods were consumable items used in arc lamps, just like the rods used for arc welding and had to be replaced frequently. In the early days of movies, film stock was manufactured on a highly flammable nitrate base and fires were common. It's thought that a candle ignited a reel of nitrate film, resulting in the Drumcollogher tragedy of 1926, in which 46 people perished.

I'm not sure what the "motor" is, referred to in the spec. Since the lamp was an add-on unit to the projector, it was probably not the film feed motor, but rather a motor powering a cooling fan for the lamp or one that fed the electrodes as they were consumed.

The photo mounted on the projector shows actor Paul Newman standing in front of it on the occasion of his visit to Kilcullen over 20 years ago. At that stage, the projector was still located in the projection room.

In 2006, Brian Byrne published a more detailed article in the Kilcullen Diary which provided more information about the projector’s projection unit.

Arc volts 31 - 46
Arc amps 32 - 100
Motor volts 31 - 110
Motor amps 0.5 - 1.4

J.E. McAuley Mfg. Co.
Chicago, ILL 
United States of America

Rating plate attached to the projector. © Eugene Brennan