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.

M _ c Q du dO dt - rrqu 2r qu AB _ Q du L **bq** (u -a') +V (b -a')1,l (a -u)11/ndu) L 1,1 (a-a/),,1 (u-b), f u Along the wall Bx, cos n0 =I, sin n0 =o, b >u>o ch nSt = ch log () n=, , fb-a?, ?

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,

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.

R)=ap. io 4 --(aq+bp)Io 3 -l-(ar-1-**bq-**1-cp) io 2 +(br+cq) Io+cr.

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.