Sextant

The Sextant: Math Solved the Longitude Problem

The Sextant

The Sextant

What does it look like?

Look at this interactive sextant model. This goes through the different parts of the sextant and what they do. Try clicking on the names of the parts to get a description.

Double Reflection Principle


Sextants use a very powerful princple called the double reflection principle. This principle uses the angles of rays reflecting off a mirror. Double Reflection Principle 1
As you can see in the figure above, an incoming ray (I) goes forwards and hits a mirror. This mirror then reflects the ray (R). From the mirror, we can draw a perpendicular line (N). The angle on either sides of N (x) is the same.
Now we will use this information to explain the double reflection principle. Double Reflection Principle 2
The figure above, we see two mirrors. The first mirror is the same, but there is also a grey mirror with its corresponding angles in grey as well. The grey mirror is exactly the same as the first mirror, but it has been rotated by an angle of z. I is the same as before, the ray is still coming from the same direction. R is now R', and N is now N'. N' is the normal line to the grey mirror. The new angle between N' and I is x+z. This makes sense becasue we just shifted x by z degrees. The angle between N and N' is z. Now we want to look at the angles between N and R'. Double Reflection Principle 3
As we said before, the angle between N and R' is x. We also said that the angle between N and N' is z. Using this information, we can find the angle between N' and R to be x-z. Double Reflection Principle 4
Now that we know the angle between N' and R is x-z and we know the angle between N' and R' is x+z, we can use this to find the angle between R and R'. The angle between R and R' (y) is going to be the angle between N' and R' minus the angle between N' and R.
y = (x+z) - (x-z) = 2z.
This means that the angle between R and R' is double the angle of rotation of the mirror. Double Reflection Principle 5
The figure above summarizes the double reflection principle in one drawing.
This principle is used in the design of the sextant because even though the sextant is only 60 degrees, it can measure angles up to 120 degrees. That means something that is relatively small, can measure angles that are double its size, making it easier to move and use. Imagine trying to hold a 120 degree instrument while measuring the angle of the sun. It would be very awkward.

Errors and corrections


There are some corrections that you have to account for when you take a measurement using a sextant. With all tools, there are errors. Some of these errors are correctable and some are not.

Correctable


Perpendicularity Error: index mirror is not perpendicular to the plane of the intrument
Fix: adjust screw on index mirror
Side Error: horizon mirror is not perpendicular to the plane of the instrument
Fix: adjust side-error screw on horizon mirror
Index Error: index and horizon mirrors are not parallel when index arm is at 0 degrees
Fix: adjust the screw on the index arm mirror

Non-correctable


Collimation Error: telescope not parallel to the plane
Centering Error: pivot point of pivot is not perfectly aligned with geometric center of instrument's frame arc
Prismatic Error: faces of the mirrors aren't parallel to each other so they create a prism
Shade Error: shades aren't parallel to eachother creating a prism (shades are used when looking at the sun so you don't burn your eye out and have to wear an eye patch)
Graduation Error: imperfections in the micrometer or the markings on the instrument's arc
Worm and Rack Error: imperfections in the movements of the index arm
Give it a try! Now that you know what a sextant is, and what the parts are, try using one below to find the angle of the sun in relation to the horizon. This tool will walk you through the steps.