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bq

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.

Newton m m _ _ there states that (p+ pq) - = p n -}- T naq ?- m 2n n bq -?

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.

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.

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.

Newton m m _ _ there states that (p+ pq) - = p n -}- T naq ?- m 2n n bq -?

a =p n, b= aq, c- 2n bq, and so on.

+214'(37+2V 'ya+2w'a(3=o, it is readily seen that for by the relation Ea 2 (p - q) (p - r) = 4 0 2 (see Geometry: Analytical, which is generally written lap, bq, cr} 2 = 4 z.

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.

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.

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