A cross staff is easy enough to make. I take a piece of wood 3/4" square or so, and about 36" long. Then I make four cross pieces from strips of thin wood 1/4" thick by 2" wide. The lengths are important. The smallest is 21/2" long, the next is 5" followed by 10" and lastly a piece 20" long. I make a square hole in the centre big enough for the long stick to fit through so it slides up and down without sticking. On the back of each crosspiece I glue a small block again with a square hole so the crosspiece doesn't wobble when on the stick.
With my method you don't need the math to work out your latitude, I do it so the degrees are marked on the stick already. There are four sides to the stick, one for each of the crosspieces. The smallest one goes from two dgrees up to forty degrees, the five inch one goes from twenty degrees up to sixty, the ten inch crosspiece goes from thirty to eighty degrees and the twenty inch goes from forty to ninety degrees.
To use it, you fit the crosspiece to the stick, and hold the end of the stick up to your eye. You slide the crosspiece down the stick until the bottom edge of the crosspiece lines up with the horizon and the top edge of the crosspiece lines up with polaris. Then you take the reading off the stick where the crosspiece intersects it.
When you reach a latitude where you can't get a reading, you change to either a smaller crosspiece (if sailing south) or larger crosspiece (if sailing north).
So, to sumarise, you have a square stick with scales marked on all four sides. You have a crosspiece for each scale, four in all that you use depending on your latitude. The crosspieces are stiffened on the back with a block of wood to give stability on the stick.
To mark the scale you need to do the following:
Take a sheet of wallpaper lining paper and draw a line down one edge. Make it as long as the stick.
At one end of the line, mark it off as the eye end and the other mark off as polaris end.
At the eye end, take a protractor and draw lines outward every 5 degrees, so there are a series of equally spaced lines radiating out from the end of the line at the eye end of the paper. These lines will represent spacings of ten degrees on the stick. The reason for five degree spacings representing ten degrees on the stick is that we are only measuring half of the crosspiece, so we have to double up. (You'll see what I mean when you try it).
Once the degrees are drawn, mark a line parallel to the first line you drew, exactly half the length of the crosspiece, so the first will be 11/4" in from the main line. The next will be 21/2" in followed by a line 5" in and finally a line drawn 10" in.
Place the stick on the 11/4" line and mark where the line intersects with the degree lines. With five degrees being the radiating line nearest the original line, and ninety degree line being at forty five real degrees to the original line (if that sounds confusing remember that five real degrees is representing ten degrees on the stick, because we are only measuring one half of it.)
Once the intersection lines are marked, and the degrees noted, turn the stick over a quarter turn and do the same on the next line out, the 21/2" line representing the five inch crosspiece. Mark once again where the radiating lines intersect the parallel line and so on until all four side of the stick are marked off in varying degrees.
The best way to keep these marks from wearing away is to cut nicks across the stick with a knife and either stamp the degrees into the wood or use a dremel with an engraving bit to permanently mark the wood with the degrees.
Once made, give all pieces a good wax with beeswax to protect the wood and help with smooth sliding of the crosspiece.
So, to use the thing, you hold the stick up to your eye and slide the crospiece up or down until the bottom is on the horizon and the top is on polaris and read off the degrees on the stick. If you are on the equator, polaris will look like it is on the horizon so you'd have the smallest crosspiece way out on the end of the stick. If on the other hand you are up north and polaris is right above you, you'll need the longest crosspiece and it will be nearer your face when you take the measurement.
I really hope that is clear, I'm just typing it all from memory. Just ask if you need clarification on any aspect of it.
Oh yes, nearly forgot. This instrument is for astral navigation only. Never try to take a sun sighting with it or you'll end up with retinal burns. There's a different kind of cross staff for sun sighting that you use with your back to the sun and rely on the shaddow cast to give the reading, but that's for another day.
Eric