The Cross-Staff

The cross-staff was used by ancient astronomers to measure angular separation between celestial objects. It also served a secondary function of aiding to determine distances, latitudes and heights of terrestrial objects such as hills, mountains and islands. The earliest recorded use of this object was by the German mathematician, cartographer and navigator Martin Behaim, and this was in the 1480s. To find out more about Martin Behaim, check out this link:
New Advent: Martin Behaim

Using the Cross Staff

In simple terms, the cross-staff is a cross made from two pieces of wood, one long and the other short, with the shorter piece being movable. The longer piece comprises a long, squarish staff, made of hardwood, while the shorter length, also called the crosspiece or transom is made of the same material and it slides along the staff. The staff is then held up to the eye level and viewed. The crosspiece is adjusted so that the celestial object is just visible above the upper part of the crosspiece. For a better picture of this, take a look at the diagram below.

Using the Cross Staff

From the diagram, using a little trigonometry, the angle A can be found. If the star being viewed were Polaris, angle A would actually give the latitude of the observer in the Northern hemisphere.

The picture below shows the use of the cross-staff to calculate the distance of an island which is known to be 5miles in charted length. The calculation is done by taking the ratio of similar sides, using the concept of similar triangles.

Using the cross Staff to estimate distance

The cross-staff was simple to construct, light and portable, making it a handy and cheap navigational tool. It did frustrate some who were trying to measure the sun's altitude in the sky, as that required them to look into the sun. Of course, this problem was soon overcome by the use of smoked glass for the crosspiece. Navigators were also susceptible to parallax errors. For a description of how you can make your own cross-staff at home, follow this link:
The Event Inventor Cross Staff Projects

References
1. Dennis Fisher Latitude Hooks and Azimuth Rings 1995, International Marine
2. The Event Inventor Cross Staff Projects
3. New Advent: Martin Behaim