This is my new square finished and ready to use.
Step 1: Cut Materials
The chop saw is from an earlier Instructable.
Step 2: Fit Up the Sides of the Handle
Weld the edges of the pieces at their ends with little more than a tack weld. These welds are visible in the photo from step 4. Welding a bead where the pieces lay next to each other is not necessary and will only complicate matters later.
UPDATE--The square worked out quite well, but had a slight inaccuracy when comparing lines scribed after flipping the handle over to the other direction. Upon close examination I discovered the square steel tubes used to make the handle were not uniform, but actually had a little bit of a diamond shape to them in places. I broke the welds holding the blade to the handle. Then I used a sanding drum on my radial arm saw to grind the front and back faces of the handle so they were flat and true over their entire length. See this Instructable for how I can do the same process with a piece of wood to be glued. Then I welded the handle back onto the blade. But, instead of working with the handle in two halves as shown here, I worked with both halves joined together in one piece. Now the square is quite precise. (Aug. 20, 2011).
Step 3: Welding the Blade to the Handle Half -- What Not to Do
Step 4: Weld the Blade to the Handle
Step 5: Fit the Other Side of the Handle
Step 6: The Moment of Truth
At this point your project looks like a square, but you cannot assume the handle and blade are precisely 90 degrees from one another. I am checking by scribing a line on a piece of paper taped down so it cannot move. The handle of the square is resting against the edge of a piece of machine cut plywood I use as a reliable straightedge.
Step 7: Flip the Square and Make a Second Line
A geometrical theorem states that two lines perpendicular to the same line are parallel. Flip the handle of the square to the right and scribe a second line with a very small amount of space between it and the first line.
Step 8: Check for Convergence
I wish I could say my square was perfect when I checked it. But, it was not. I had to cut into the welds shown in step 4 at the top of the handle to loosen them on both sides of the square. The welds at the other end of the 3/4" lengths of 1/2" x 1/2" tubing were still intact and I was able to tap the square's blade enough to make the square accurate without breaking these welds. Then I made the welds I had cut apart again and checked the square for accuracy once more. I do not know if heat had caused the blade to twist out of position with respect to the handle, or if my alignment was not as good as I had thought. But, eventually I got it right and the square is very accurate now.
I could scribe the blade with markings to denote graduations of 1/8", and I could drill a hole in the blade for hanging the square, but those things do not seem very important right now.