This is one of the most curious items in my collection: a pocket size watch slide rule. This two inches diameter circular slide rule or Model KL-1, was manufactured by the Technical and Lights Company "Sunrise", in the old Soviet Union. These watch type circular slide rule was fabricated by different companies from 1918 to possibly 1978. T The manufacturer's logo is on the rules front face. There is nothing else on the rule itself that allow to determine the manufacturing year.
The KL-1 is a double sided circular slide rule with two rotating "hairlines". There are a double log (outer) and a single log (inner) standard scales paired on the front face [ A - C ]}. On the back face a single standard log scale (outer) paired with two inner concentric scales: a circular sine scale and a long spiral tangent scale [ C - S - T ] . These trigonometric scales are divided in degrees-minutes. Only the front disk can be rotated with one of the a knurled knobs, the disc with the trigonometric scales does not move. The second knob rotates the two hairlines; these are aligned and point to opposite directions. On the crystal covering the front disk there is engraved a reference line aligned with one of the knobs.
The operation of this little circular rule is a little bit cumbersome at the beginning, but once you are familiar of the operation, is possible to perform multiplications, divisions, squares and square roots, find values of sine, tangent and their inverses, and calculate circles' areas. Next is a translation of the KL-1 User Manual done by the ISRM:
With this rule, an skillful user can solve the net problem with a precision of two-three decimals:
https://www.sliderulemuseum.com/Circular/C19_Soviet_KL-1_PocketWatch.jpg