Lord Rayleigh has shown that there is a tangential motion as well as a motion in and out.
Luminous arcs (T), tangential to the upper and lower parts of each halo, also occur, and in the case of the inner halo, the arcs may be prolonged to form a quasi-elliptic halo.1 The physical explanation of halos originated with Rene Descartes, who ascribed their formation to the presence of icecrystals in the atmosphere.
This is called the tangential area, and will be denoted by T1.
The - - 4X + g tangential area may be expressed in terms of chordal areas.
Some of the formulae obtained by the above methods can be expressed more simply in terms of chordal or tangential areas taken in various ways.