# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Biruni and the radius of the Earth by dip**

**From:**Marcel Tschudin

**Date:**2011 Jan 7, 20:23 +0200

I'm questioning myself why Biruni measured the height of the mountain in order to obtain the radius of the earth? Not knowing about refraction he must have thought of a geometry as shown in Fig. 2 of the Gomez paper. If he knew that the circumference of a circle is 2 r pi corresponding to 360 degrees and if he was able to measure distances in the plain he also could have proceeded as follow: 1) He decides from which hilltop he intends to measure the dip of the apparent horizon in the plain. 2) He searches the tangent point S in the plain where the hilltop just touches the apparent horizon. In Fig. 2 he looks from S to B assuming a straight line whereas in reality it is a refracted one. 3) He measures the distance between S and the base A of the hilltop knowing that this would be the length of the arc between those two points. If the hilltop was about 320m above the plain, then A would have been around 68km from S. (I neglect here that the plain was likely not completely flat.) 4) He climbs the hilltop and measures the refracted dip of the apparent horizon to be 34 or 35 moa imagining that he would measure the angle theta in Fig. 2. 5) He can now calculate the radius of the circle where 34 moa corresponds to an arc length of 68km. The question here is (appart from so many others) how distances of around 70km could be measured in those days? Marcel