Lacking a vernier, tightly wrap a strip of paper, 1 cm. wide by 10 cm., around a clean, unmarred section of the post, tasking care to align the edges. Mark where they overlap with a very sharp pencil. Remove the paper strip and measure from the end to the mark, in millimetres. Now, divide the result by pi (3.14) to determine the diameter. Repeat the process to ensure the result are consistent.

Using this method, you should be able to measure the circumference accurately to the nearest 0.5mm. This will result in a diameter accurate to within 0.15 mm, provided care is taken during the measurement process.

However, it you are going to be working on vintage bicycles, I would suggest that you invest in a set of calipers, as they are an invaluable aid. Places like Harbour Freight routinely sell 6" digital calipers for under $20 US. Shorter, 4" versions, which are typically satisfactory for most cycling applicationd, can be had for under $15 US and plastic, vernier calipers are under $5.00 US.