Yakov's staff

For a more accurate measurement of angles, rather than a protractor "with your own hands", you can make a simple and convenient device that once served our ancestors. This so-called "Yakov's staff" - a device that was widely used by seafarers before the 18th century - until such time as it was gradually replaced by more convenient and accurate goniometers.

The Yakov's staff is one of the first instruments for astronomical observations, serving to measure angles. Used in astronomy, navigation and geodesy. In navigation, the tool is called a transverse rod and is used to determine the breadth of the vessel by measuring the height of the North Star or the Sun. Nowadays the name "Yakov's staff" is used mainly in relation to the tool for geodesy.

The origin of the name of the instrument is not clear. Some refer to the biblical patriarch Jacob. Perhaps the name came from the similarity of the instrument to Orion, which on some medieval stellar maps was called Jacob. The name cross-staff is associated with the cross-shaped tool form.

Yakov's staff consists of a long ruler of 70-100 centimeters (AB), along which a CD bar perpendicular to it can slide, both parts of the CO and OD of the sliding bar are equal to each other. If you want to determine the angular distance, for example between the stars S and S', using Yakov's staff, then put the end A of the ruler to the eye (where for the convenience of observation a drilled plate can be attached) and direct the ruler so that the star S' end of its B, then move the crosspiece CD along the ruler until the star S is visible at the end of C. Now it only remains to measure the distance AO so that, knowing the length of the CO, calculate the value of the angle SAS'. The tangent of the desired angle is equal to the ratio CO/AO: calculate by the Pythagorean theorem the length of the AC, and then find the angle whose sine is CO/AC.

Why do we need the other half of the crossbar, which has a Yakov's staff? In the case when the measured angle is too large, so that it can not be measured now by this way. Then the line S 'is directed not by the ruler AB, but by the straight line AD, moving the crosspiece so that its end C falls at the same time for the star S. It is of course not difficult to find the value of the angle SAS' by calculation or construction.

Calculations or constructions can be performed in advance, making the Yakov's staff, so that at each measurement you do not have to do them, and designate the results on the ruler AB: then, by sending the Yakov's staff to the stars, you read only the reading recorded at point O, measured angle.