Minutes at Chanonry Point

Chanonry Point near Inverness is an amazing place to go to watch dolphins. Hence the large crowd gathered in the bottom photograph. The latitude is given as 57 degrees and 34.44'. The ' stands for "minutes". Each degree is subdivided into 60 smaller divisions called minutes of arc, and indeed each minute can be further subdivided into 60 seconds of arc, meaning that 1 degree is worth 3600 seconds of arc (denoted ''). I've never seen decimal fractions of a minute before, though. That's like mixing metaphors. It suggests that the precision of the measurement is +- 0.01 minutes of arc. A whole circle is 360 degrees or 21600 minutes. So there are 2.16 x 10^6 lots of 0.01 minutes of arc in a whole circle. A whole circle is worth 2 x pi radians so 0.01 minutes of arc is worth 2.9 x 10^-6 radians. Arc length = angle in radians x radial distance. The radius of the Earth is 6400 km. That means that the latitude of the lighthouse is given to a precision of +- 19 metres.