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.
Comparing this equation with ux 2 +vy 2 +w2 2 +22G'y2+2v'zx+2W'xy=0, we obtain as the condition for the general equation of the second degree to represent a circle :- (v+w-2u')Ia 2 = (w +u -2v')/b2 = (u+v-2w')lc2 In tangential q, r) co-ordinates the inscribed circle has for its equation(s - a)qr+ (s - b)rp+ (s - c) pq = o, s being equal to 1(a +b +c); an alternative form is qr cot zA+rp cot ZB +pq cot2C =o; Tangential the centre is ap+bq+cr = o, or sinA +q sin B+rsinC =o.
Within the crust of the earth, whether by the contraction of the interior or in any other way, tangential pressures were set up. Since the crust is not of uniform strength throughout, only the weaker portions yielded to the pressure; and these were crumpled up against the more resisting portions and sometimes were pushed over them.