How it Works (from Steve's site):
Since this protractor uses a bubble level it can only measure vertical angles. The bubble is zeroed up on a reference surface by rotating the disc that the vial is attached to until the bubble is aligned with a mark and the front wing-nut is locked down. Then the protractor is placed on a tilted surface and the larger disc is unlocked (using the wingnut on the back) and the disc is rotated until the bubble is again aligned in the same position, then the rear wingnut is locked back down. The angle is read to a degree where the long line on the left side of the vernier points to the degree scale - read the smaller number. The angle is then read to a tenth of a degree by seeing which of the vernier lines matches up best end-to-end with the degree markings and added to the degree measurement. The markings on the vernier are 0.9 degree apart.
Here is the link with details on how to make your own compact protractor accurate up to 0.1 degree.