In general, there are two problems to solve here. You need to attach the base to something to hold it off the ground. I just use a nut and bolt, having drilled a suitable hole in the head of my photography tripod. It is a BIG help, when taking readings, to be able to adjust easily the direction the base is facing, and to get it horizontal. The pan head on my tripod takes care of that. My solution needs some work at present because, unless I am very careful, the base tends to rotate on the head of the tripod. Shouldn't be hard to fix, but be sure your design doesn't have a similar flaw. It helps to mount the base in a way that leaves the apparatus well balanced.
The 'secret' at the heart of my design depends on the shape of the base of the theodolite. It is shaped like a circle which has about 40 percent cut off by a straight line not quite through the center of the circle. I achieved a very good result by doing the hole in the center of my base first. A friend then clamped a piece of wood to the table of a band-saw. This piece of wood had a nail poking up from it. The piece of wood my theodolite base was cut from was then put on this nail, via the central hole. The wood was carefully swung 'round on the nail, thus cutting the slightly- more- than- semicircle edge that I needed.
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