"Now," said the Wizard of Oz, "having created something from nothing, I will make something nothing again."
Our friend Oz is merely a humbug wizard, for he once proved it to me.
"The girl that rules the marvelous Land of Oz," was the reply.
How stupid and ignorant you are, in the Land of Oz, and what dreadful things you feed upon!
Queensland's annual output is between 750,000 and 800,000 oz.; the number of men engaged in goldmining is io,000.
In New South Wales the greatest production was in 1852, soon after the first discovery of the precious metal, when the output was valued at £2,660,946; the production in 1905 was about 270,000 oz., valued at £1,150,000.
In 1905 the production amounted to 1,983,000 oz., valued at £8,300,000.
The electromotive force of each cell is i 07 volts and the resistance 3 ohms. The Fuller bichromate battery consists of an outer jar containing a solution of bichromate of potash and sulphuric acid, in which a plate of hard carbon is immersed; in the jar there is also a porous pot containing dilute sulphuric acid and a small quantity (2 oz.) of mercury, in which stands a stout zinc rod.
For the first oz., and i3/4d.
The internal rate is 15c. (i3/4d.) per 3/4 oz.; post-cards foe.
Gold-mining and quartz-mining are its principal industries, and in 1907 Nevada county's output of gold (104,J90.76 oz., worth $2,162,083) was second only to that of Butte county (134,813.39 oz., worth $2,786,840) in California; the county is the leading producer 1 Died the 21st of September, 1890, and Frank Bell became governor by virtue of his office as lieutenant-governor.
In West Siberia, however, quartz-mining is steadily increasing in importance: whereas in 1900 the output of gold from this source was less than 10,000 oz., in 1904 it amounted, to close upon 50,000 oz.
On the other hand gravel-washing gives a declining yield in West Siberia, for while in 1900 the output from this source was approximately 172,000 oz., in 1904 it was only 81,000 oz.
The total yield annually amounts to some 700,000 oz., the largest quantity coming from the Olekminsk, district in the province of Yakutsk, and this district is followed by the Amur region, the Maritime province, and Nerchinsk and Transbaikalia.
-, reduce s x2ax1 -x10x2 to the form j Oz ON 2 1 1 j 2 i The Binary Quintic.-The complete system consists of 23 forms, of which the simplest are f =a:; the Hessian H = (f, f') 2 = (ab) 2axbz; the quadratic covariant i= (f, f) 4 = (ab) 4axbx; and the nonic co variant T = (f, (f', f") 2) 1 = (f, H) 1 = (aH) azHi = (ab) 2 (ca) axbycy; the remaining 19 are expressible as transvectants of compounds of these four.
If the ray be parallel to OX, and the direction of vibration parallel to OZ, we have E =o, 7 7 = o, while I is a function of x and t only.
The force operative upon the positive half is parallel to OZ, and of amount per unit of area equal to - b 2 D = b 2 kD cos nt; and to this force acting over the whole of the plane the actual motion on the positive side may be conceived to be due.
According to (18), the effect of the force acting at dS parallel to OZ, and of amount equal to 2b2kD dS cos nt, will be a disturbance - dS sin cos (nt - kr) (20), regard being had to (12).
This therefore expresses the secondary disturbance at a distance r and in a direction making an angle cp with OZ (the direction of primary vibration) due to the element dS of the wave-front.
Deep. The yield of the Rand mines, in 1887 but 23,000 oz., rose in 1888 to 208,000 oz.
In 1892 the yield was 1,210,000 oz.: in 1896 it exceeded 2,280,000 oz.
In 1905 when a full supply of labour was again available the output was 4,760,000 oz., in which year the sum distributed in dividends to shareholders in the Rand mines was over £4,800,000.
Though several large nuggets have been found (the largest weighing 215 oz.), the total production is not great, the highest output obtained by washing being worth about £300,000 in one year.
Work was begun in 1895, and the yield of gold in that year was 274 oz., which increased to 893 oz.
As an example of the general equations, take the simplest case of a uniform field of gravity, with Oz directed vertically downward; employing the gravitation unit of force, 1 dp i dp t dp dp/dz = p = pzn (4) z n+I pz 1 /n p-p n-H ?t), (5) supposing p and p to vanish together.
If homogeneous liquid is drawn off from a vessel so large that the motion at the free surface at a distance may be neglected, then Bernoulli's equation may be written H = PIP--z - F4 2 / 2g = P/ p +h, (8) where P denotes the atmospheric pressure and h the height of the free surface, a fundamental equation in hydraulics; a return has been made here to the gravitation unit of hydrostatics, and Oz is taken vertically upward.
(7) Interchanging these values =m log r, 4, = mO, 4,+4,i =m log rei e (8) gives a state of vortex motion, circulating round Oz, called a straight or columnar vortex.
In plane motion the kinetic energy per unit length parallel to Oz T 2p J J [(d4)) 2+ (d dy (P)1dxdy=lpfl[ a) 2+ (=zp 4d ds=zp f, ydvds.
For in a rigid body, rotating about Oz with angular velocity the circulation round a curve in the plane xy is x ds yds) ds = times twice the area.
This is so when the axis of revolution is a principal axis, say Oz; when S21=0, t 2 =0, =o, o=0.
Similarly, the inertia parallel to Oy and Oz is NW' - 1 B W', B C (b2 +-X, c 2 ab and A +C abc/ZP, Ao For a sphere a=b=c, Ao= Bo=Co =, 'a' = Q = = z, (9) U from (II), (16) so that the effective inertia of a sphere is increased by half the weight of liquid displaced; and in frictionless air or liquid the sphere, of weight W, will describe a parabola with vertical acceleration W - W', g (30) W+ aW Thus a spherical air bubble, in which W/W' is insensible, will begin to rise in water with acceleration 2g.
Again, the components of angular momentum about OC, OA are Cn,A sin 0~, and therefore the angular momentum (u, say) about OZ is pA sini 0 ~+Cn cosU.
83 OZ is supposed to be vertical, and OC is the axis of the solid drawn in the direction 0G.
In the case of the top, the equation of energy and the condition of constant angular momentum (~l) about the vertical OZ are sufficient to determine the motion of the axis.
Now consider a system of fixed axes Ox, Oy, Oz chosen so as to coincide at the instant I with the moving system Ox, Oy, Os.
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,
J To prove these, we may take fixed axes Ox, Oy, Oz coincident with the moving axes at time t, and compare the linear and angular momenta E+E, ~ ~ ?~+~X, u+u, v+~v relative to the new position of the axes, Ox, Oy, Oz at time t+t with the original momenta ~, ~ ~, A, j~i, v relative to Ox, Oy, Oz at time t.
Let r be the distance of a point P from a fixed origin 0, 0 the angle which OP makes with a fixed direction OZ, il the azimuth of the plane ZOP relative to some fixed plane through OZ.
In the case of the spherical pendulum we have r=l, e= mgi sin 0, s=o, if OZ be drawn vertically downwards, and therefore sin 0 cos Ol1 ~ sin 0, ~- (23)
The latter equation expresses that the angular momentum mP sing O~t about the vertical OZ is constant.
The meaning of these quantities is easily recognized; thus X is the angular momentum about a horizontal axis normal to the plane of 0, u is the angular momentum about the vertical OZ, and s is the angular momentum about the axis of symmetry..
36, if OA, OB, OC be three mutually perpendicular lines in the solid, we may denote by O the angle which OC makes with a fixed direction OZ, by ~ the azimuth of the plane ZOC measured from some fixed plane through OZ, and by f~ the inclination of the plane COA to the plane ZOC In fig.