If BQ be the direction for the first minimum (the darkness between the central and first lateral band), the relative retardation of the extreme rays is (mn+1)X.
Suppose now that X+SX is the wave-length for which BQ gives the principal maximum, then (mn+1)A=mn(X+SX); whence OX/X= limn.
With sufficient approximation we may regard BQ and b as rectangular co-ordinates of Q.
4 let AB be the axis of composition, AP be the vapour pressure of pure A, BQ the vapour pressure of pure B.
A =p n, b= aq, c- 2n bq, and so on.
2, we obtain lap, bq, cr} 2 2= 2 t(lp+mq+nr)/(l-1-m+n)} 2, the accents being dropped, and p, q, r regarded as current co-ordinates.
This equation, which may be more conveniently written tap, bq, cr} 2 = (Ap+pq+vr) 2, obviously represents a circle, the centre being Xp+µqt-vr=o, and radius 20/p(X+µ+v).
If we make =,u=v o, p is infinite, and we obtain lap, bq, cr} 2 =o as the equation to the circular points.
The equation of the latter, referred to its principal axes, being as in II (41), the co-ordinates of the point J where it is met by the instantaneous axis are proportional to p, q, r, and the direction-cosines of the normal at J are therefore proportional to Ap, Bq, Cr, or X, u, v.
At any point of this we have x y I = Ap. Bq: Cr, and the equation is therefore (I ~~r) x1+ (1 ~lll) yf+ (1 ~ 12=0.
If we now apply them to the case of a rigid body moving about a fixed point 0, and make Ox, Oy, Oz coincide with the principal axes of inertia at 0, we have X, u, v=Ap, Bq, Cr, whence A (B C) qr = L,
If we multiply theta by p, q, r, respectively, or again by Ap, Bq, Cr respectively, and add, we verify that the expressions Ap2 + Bqf + Cr1 and A1p2 + Bfqi + Ciri are both consta~it.
R)=ap. io 4 --(aq+bp)Io 3 -l-(ar-1-bq-1-cp) io 2 +(br+cq) Io+cr.
To show the cause of this motion, let BQ represent a section of an oblate spheroid through its shortest axis, PP. We may consider this spheroid to be that of the earth, the ellipticity being greatly exaggerated.