Middleton-on-Lune railway station Middleton-on-Lune railway station Middleton-on-Lune railway station was located in Westmorland (now Cumbria), serving the hamlet and rural locale of Middleton on the Ingleton Branch Line. It was opened as Middleton in 1861 and renamed Middleton-on-Lune on 19 July 1926, closing in 1931. The Lancaster and Carlisle Railway built the Ingleton Branch Line from the existing Ingleton Station to . By the time the branch was completed in 1861, the L&CR was operated by the London and North Western Railway (L&NWR). After formal closure the line was still on occasions used for weekend excursions and to transport pupils to and from
Spherical lune two polar opposite points. Common examples of great circles are lines of longitude ("meridians") on a sphere, which meet at the north and south poles. A spherical lune has two planes of symmetry. It can be bisected into two lunes of half the angle, or it can be bisected by an equatorial line into two right spherical triangles. The surface area of a spherical lune is 2θ "R", where "R" is the radius of the sphere and θ is the dihedral angle in radians between the two half great circles. When this angle equals 2π radians (360°) — i.e., when