O Sentence Examples

The assignats had now become totally valueless - the abolition of the "maximum" the previous year (1795) had produced no effect, and, though, by various payments into the treasury, the total number had been reduced to about 24,000,000,000 francs, their face-value was about 3 o to I of coin.

From Garmat Ali, where the Tigris and Euphrates at present unite,' under the title of Shattel-Arab, the river sweeps on to Basra, Ex p o yds.

In 616 it was taken by Chosroes, king of Persia; and in 6 4 o by the Arabians, under `Amr, after a siege that lasted fourteen months, during which Heraclius, the emperor of Constantinople, did not send a single ship to its assistance.

The calcium salt, CaN 2 O 2.4H 2 O, formed by the action of calcium chloride on the silver salt in the presence of a small quantity of nitric acid, is a lustrous crystalline powder, almost insoluble in water but readily soluble in dilute acids.

But the definition of the cardinal number of a class applies when the class is not finite, and it can be proved that there are different infinite cardinal numbers, and that there is a least infinite cardinal, now usually denoted by o where to is the Hebrew letter aleph.

This last number exemplifies the fact that one signed real number, such as o, may be correlated to many of the n cardinals, such as 2.

The new sultan's reign marked, if not the beginning, at least the high tide Aba-ui-Aziz, o f that course of improvident and unrestrained 1861-1876.

The Kurds, the constant oppressors of that people, had received official recognition and almost complete immunity from the control o f the civil law by being formed into a Y g eo Y manry frontier-guard known as the Hamidian cavalry.

This island, which is separated by Waigat Strait from the Nugsuak peninsula, is o lofty, and has an area of 3005 sq.

To this period also belongs the massive rampart, over o ft.

Battle of In this battle the French numbered about 20,000 with Corunna, 4 o guns; the British 15,000 with 9 very light guns.

Hamburg has comparatively few secular buildings of great architectural interest, but first among them is the new Rathaus, a huge German Renaissance building, constructed of sandstone in 1886-1897, richly adorned with sculptures and with a spire 33 o ft.

In i i i o Hamburg, with Holstein, passed into the hands of Adolph I., count of Schauenburg, and it is with the building of the Neustadt (the present parish .of St Nicholas) by his grandson, Adolph III.

The mean result of the best determinations shows that when a current of one ampere is passed for one second, a mass of silver is deposited equal to o ooi i 18 gramme.

The hydrogen at the cathode is developed by the secondary action 2Na+2H 2 O =2NaOH+H2.

Thus, diminishing the concentration of the cadmium iodine solution from normal to one-twentieth normal changes the transport number from I 12 to o 64.

The mean values of k for other common acids were - formic, 0.0000214; acetic, o 0000180; monochloracetic, 0.0.0155; dichloracetic, 0.051; trichloracetic, 1.21; propionic, 0.0000134.

If we take as an example a concentration cell in which silver plates are placed in solutions of silver nitrate, one of which is ten times as strong as the other, this equation gives E = o 060 X Io 8 C.G.S.

The result is that a high electromotive force is set up, which has been calculated as o.

These formulae are supported by many considerations, especially by the selective CH 2 OH CH20H CH OH CH OH C C H O

If ozone is passed into a solution of rubber in chloroform the caoutchouc combines with a molecule of ozone forming a compound of the empirical composition C 5 H 8 O 8.

Of the total in 1897, 81.4% were Russians, 8.3% Turko-Tatars, 5% Mongols and o 6% " indigenous " races, i.e.

The last-named form is in the female o 36 mm.

Resultants.-When we are given k homogeneous equations in k variables or k non-homogeneous equations in k - i variables, the equations being independent, it is always possible to derive from them a single equation R = o, where in R the variables do not appear.

Since dp4+(-)P+T1(p +q qi 1)!dd4, the solutions of the partial differential equation d P4 =o are the single bipart forms, omitting s P4, and we have seen that the solutions of p4 = o are those monomial functions in which the part pq is absent.

For a single quantic of the first order (ab) is the symbol of a function of the coefficients which vanishes identically; thus (ab) =a1b2-a2bl= aw l -a1ao=0 and, indeed, from a remark made above we see that (ab) remains unchanged by interchange of a and b; but (ab), = -(ba), and these two facts necessitate (ab) = o.

On the one hand, assuming the quartic to have the form 4xix 2, we find i=j=o, and on the other hand, assuming i=j=o, we find that the quartic must have the form a o xi+4a 1 xix 2 which proves the proposition.

We will write the cubic covariant (f, i) 2 =j, and then remark that the result, (f,j) 3 = o, can be readily established.

When C vanishes j has the form j = pxg x, and (f,j) 3 = (ap) 2 (aq)ax = o.

Remark.-The invariant C is a numerical multiple of the resultant of the covariants i and j, and if C = o, p is the common factor of i and j.

Forms.-Taking the two forms to be a o xi + pa l x i 1x2+p(p-1)a2xr2x2-I-...

Galena (q.v.), the principal lead ore, has a world-wide distribution, and is always contaminated with silver sulphide, the proportion of noble metal varying from about o of or less to o 3%, and in rare cases coming up to 2 or i %.

Such slags contain S10 2 =3033%, Fe(Mn)O =27-50%, Ca(Mg, Ba)O =12-28%, and retain less than 1% lead and I oz.

A third addition becomes necessary to remove the rest of the silver, when the lead will assay only o I oz.

The desilverized lead, which retains o 6-0.7% zinc, has to be refined before it is suited for industrial use.

A hydrated oxide, 2PbO H 2 O, is obtained when a solution of the monoxide in potash is treated with carbon dioxide.

O, which, in turn, when boiled with a solution of boric acid, gives PbB407.4H20.

Vertical section to show the ovules o, attached to the parietes.

For the mean motion of the earth in one second in circular measure, we have n 8149' l o g.

From the equation K=(µ - I)/47r, it follows that the magnetic susceptibility of a vacuum (where µ = I) is o, that of a diamagnetic substance (where, u I) is positive.

Demagnetizing Force.-It has already been mentioned that when a ferromagnetic body is placed in a magnetic field, the resultant magnetic force H, at a point within the body, is compounded of the force H o, due to the external field, and of another force, Hi, arising from the induced magnetization of the body.

Since H, generally tends to oppose the external force, thus making H less than H o, it may be called the demagnetizing force.

In such cases H i = o and H =Ho.

If a hollow sphere 7 of which the outer radius is R and the inner radius r is placed in a uniform field Ho, the field inside will also be uniform and in the same direction as Ho, and its value will be approximately 3 i - R 3 For a cylinder placed with its axis at right angles to the lines of force, 2 = Ho (41) 2 +4(-2)(i - R2) These expressions show that the thicker the screen and the greater its permeability o, the more effectual will be the shielding action.

The value of the constant / 7 ranges in different metals from about o ooI to 0.04; in soft iron and steel it is said to be generally not far from 0.002.

Thin sheet iron o 367 mm.

Since the demagnetizing factor was o 052, the strongest field due to the coil was about 1340; but though arrangements were pro vided for cooling the apparatus by means of o ice, great difficulty was experienced owing to heating.

The aluminium-iron attained its greatest permeability in a field of o 5, about that of the earth's force, when its value was 9000, this being more than twice the maximum permeability of the Swedish iron.

Its hysteresis-loss for B =9000 was o 236 per pound.

It was, however, found that the behaviour of this alloy was in part due to a layer of pure iron (" ferrite ") averaging o 1 mm.

If V is the volume of a ball, H the strength of the field at its centre, and re its apparent susceptibility, the force in the direction x is f= K'VH X dH/dx; and if K',, and are the apparent susceptibilities of the same ball in air and in liquid oxygen, K' Q -K'o is equal to the difference between the susceptibilities of the two media.

Whilst the chances are in favour of some one homoplastic coincidence or structural agreement occurring between some member or other of a large group a and some member or other of a large group b, the matter is very different 2 a o FIG.

The segmentation of the prosoma and the form of the appendages bear a homoplastic similarity to the head, pro-, meso-, and meta-thorax of a Hexapod with mandibles, maxillary palps and three pairs of walking legs; while the opistho io i e d c b o a S' S" 2 I VT V S IV III II I Opisthosoma Prosoma FIG.

Its specific gravity is 0.8009 (o C.).

It is one of the most favoured regions of English Miles 400 o L; Barcellos rd o?

There were 155 of these factories in 1895, but in 1905 only 108 were in operation, with 715,000 spindles, and about 37, 00 o operatives.

Generally, while there is a relative poverty of zoological groups, there is a great wealth of species within the group. Of gammarids, there are as many as 300 species, and those living at great depths (33 o to 380 fathoms) tend to assume abyssal characters similar to those displayed by the deep-sea fauna of the ocean.

An important instance in which the calculation can be made is that of an elongated ellipsoid of revolution placed in a uniform field H o, with its axis of revolution parallel to the lines of force.

This'step caused excited public meetings in the capital, o which were joined in by the troops, and deputations i., x831.

Next to these two books his study, Do Estado das classes servas na Peninsula desde o VII.

His protest against the Concordat of the 21st of February 1857 between Portugal and the Holy See, regulating the Portuguese Padroado in the East, his successful opposition to the entry of foreign religious orders, and his advocacy of civil marriage, were the chief landmarks in his battle with Ultramontanism, and his Estudos sobre o Casamento Civil were put on the Index.

A single sentence in Porphyry's Isagoge or " introduc tion " to the Categories of Aristotle furnished the i o, s text of the discussion.

Meanwhile the negotiations continued, Ministry, s o secretly that when, on the 9th of April, the appoint- 1906.

The grammatical forms are expressed, as in Turkish, by means of affixes modulated according to the high or low vowel power of the root or chief syllables of the word to which they are appended-the former being represented by e, o, S, ii, i l l, the latter by a, d, o, 6, u, it; the sounds e, i, i are regarded as neutral.

Similarly the equalities 99 X I o I = 9999 = wow - I 98 X 102 = 999 6 = moo() - 4 97 X 10 3 =9991 =1 0000 - 9 lead up to (A - a) (A+a) = A 2 - a 2.

If any power is absent, we treat it as present, but with coefficient o.

This is the foundation of the use of recurring decimals; thus we can replace = s s = 1 o o /(' - 1 + 0 -)1 by .363636(=36/102 +36/ 104 +3 6 / 106), with an error (in defect) of only 36/(10 6.99).

Thus, to solve the equation ax e +bx+c = o, we consider, not merely the value of x for which ax 2 +bx+c is o, but the value of ax e +bx+c for every possible value of x.

The special symbols o and I are used to denote a - a and a=a.

Each symbol a is associated with its supplement a which satisfies the equivalences a+a = i, aa = o, the latter of which means that a and a have no region in common.

The values of x and y are different, unless V (qq o) = o.

If A 1 = X a i e i, B i = /if i e i, the distributive law of multiplication is preserved by assuming A1B1=E(a0 i 3)eiej; it follows that A 1 B 1 = - B 1 A 1, and that A l 2 = o.

In ordinary algebra we have the disjunctive law that if ab = o, then either a = o or b= o.

All such single-fact systems have proved to be departures from the true line of o€ growth of the zoological system which was shaping itself year by year - unknown to those who so shaped it - as a genealogical tree.

We imagine a wave-front divided o x Q into elementary rings or zones - often named after Huygens, but better after Fresnelby spheres described round P (the point at which the aggregate effect is to be estimated), the first sphere, touching the plane at 0, with a radius equal to PO, and the succeeding spheres with radii increasing at each step by IX.

When u = o, it takes the value unity.

At the focal point (E =o, n = o) all the secondary waves agree in phase, and the intensity is easily expressed, whatever be the form of the aperture.

When, as in the application to rectangular or circular apertures, the form is symmetrical with respect to the axes both of x and y, S = o, and C reduces to C = ff cos px cos gy dx dy,.

It is thus sufficient to determine the intensity along the axis of p. Putting q = o, we get C = ffcos pxdxdy=2f+Rcos 'px 1/ (R2 - x2)dx, R being the radius of the aperture.

The mean brightness varies as z3 (or as r3), and the integral found by multiplying it by zdz and integrating between o and co converges.

On either side of any one of them the illumination is distributed according to the same law as for the central image (m = o), vanishing, for example, when the retardation amounts to (mn t 1)X.

In these instruments the lines are ruled upon a spherical surface of speculum metal, and mark the intersections of the surface by a system of parallel and equidistant planes, o; of which the middle member passes through the centre of the sphere.

If w now relate to the edge of the grating, on which there are altogether n lines, no- = 2a sin w, and the value of the last term in (I o) becomes no- sin 3w sin O'tan 0', - 1 1 - 6 mnX sin' w tan 0'.

The aperture of the unretarded beam may thus be taken to be limited by x = - h, x = o, y= - 1, y= +1; and that of the beam retarded by R to be given by x =o, x =h, y = - 1, y = +l.

For the retarded stream the only difference is that we must subtract R from at, and that the limits of x are o and +h.

It appears therefore that there are no bands at all unless a lies between o and +4h,, and that within these limits the best bands are formed at the middle of the range when us =21 4 .

When, in order to apply Huygens's principle, the wave is supposed to be broken up, the phase is the same at every element of the surface of resolution which lies upon a line perpendicular to the plane of reference, and thus the effect of the whole line, or rather infinitesimal strip, is related in a constant manner to that of the element which lies O in the plane of reference, and may be considered to be represented thereby.

For example, when u = o, M = o, N =o, and consequently G =H = 2.

It has long been known from observation that there are no bands on the interior side of the shadow of the O edge.

We will now apply (18) to the investigation of a law of secondary disturbance, when a primary wave = sin (nt - kx) (19) is supposed to be broken up in passing the plane x = o.

He was the author of an 'Eirvro o' TWv HX aTcwos Soy s6TC.wv, an analysis of Plato's philosophy according to later writers.

Dilute sulphuric acid precipitates uranium yellow, Na 2 U 2 0 7.6H 2 O, from the solution so obtained.

It is therefore difficult to suppose that the Jewish Church as a whole passed through a stage in which it was felt desirable to substitute o'n'7 H in writing for n¦n'.

Between 1902 and 1907 about 55 o families were placed on the land, their holdings aggregating over 500,000 acres.

Alcoholic potash decomposes it into piperidine, C5H,1N, and piperic acid, C 12 H 10 O 4.

The chloride readily combines with water to form a crystallizable hydrate SnCl 2.2H 2 O, known as "tin salt" or "tin crystals."

The total length of the works is about 44 o yds.

He wrote some good hymns, including "O Throned, 0 Crowned" and a beautiful version of Urbs Beata.

Privileges It is only necessary to mention these here, but each fthe lord of the privileges requires an exhaustive examination o, as to its origin.

The levels are supposed to be I o fathoms (60 ft.) apart.

With weak and thin beds forming the roof the working-places are often not wider than 20 or 3 o ft.

The Max Kohl pumps are based on the same principle, but are constructed with more elaborate detail, leading to a greater efficiency, an exhaust of o 0008 mm.

In a well-made apparatus the pressure in the exhausted vessel is now reduced to I t o or 2 1, of a millimetre, or even less.

The general conformation of the Hindu Kush system south of the Khawak, no less than such fragmentary evidence of its rock composition as at present exists to the north, points to l its construction under the same conditions of upheaval and subsequent denudation as are common to the western o Himalaya and the whole of the trans-Indus borderland.

Indo-Chinese (1) Tibet-Burman family sub-family (2) Siamese-Chinese sub-family (3) Mon-Annam sub-family Railways Divisional Headquarters O District Headquarters .....

The gross revenue of Lower Burma from all sources in 1871-1872 was Rs.1,36,34,520, of which Rs.1,21,70,5 o was from imperial taxation, Rs.3,73,200 from provincial services, and Rs.10,90,790 from local funds.

The following is an analysis of a specimen of English pressed glass; S102, 70.68%; Na 2 0, 18.38%; CaO, 5.45%; BaO, 4.17%; Al 2 0 3, 0.33%; and Fe203, o.

The solution on evaporation deposits a hydrated form, H 2 SiF 6.2H 2 O, which decomposes when heated.

To give an idea of what can be done in this way, it may be stated that gold can be beaten out to leaf of the thickness of - j g - mm.; and that platinum, by judicious work, can be drawn into wire 2?o o mm.

Water, at ordinary or slightly elevated temperatures, is decomposed more or less readily, with evolution of hydrogen gas and formation of a basic hydrate, by (I) potassium (formation of KHO), sodium (NaHO), lithium (LiOH), barium, strontium, calcium (BaH 2 O 2, &c.); (2) magnesium, zinc, manganese (MgO 2 H 2, &c.).

By the joint action of water and air, thallium, lead, bismuth are oxidized, with formation of more or less sparingly soluble hydroxides (ThHO, PbH 2 O 2, BiH303), which, in the presence of carbonic acid, pass into still less soluble basic carbonates.

Tin and antimony (also arsenic) are converted by it (ultimately) into hydrates of their highest oxides Sn0 2, Sb205 (As 2 O 5) - the oxides of tin and antimony being insoluble in water and in the acid itself.

Bismuth and antimony give (the latter very readily) sesquioxide (Bi 2 O 3 and Sb203, the latter being capable of passing into Sb204).

Aluminium, when pure and kept out of contact with siliceous matter, is only oxidized at a white heat, and then very slowly, into alumina, Al 2 O 3.

Manganese dioxide and sulphuric acid oxidize it to benzoic and o-phthalic acid; potassium chlorate and sulphuric acid breaks the ring; and ozone oxidizes it to the highly explosive white solid named ozo-benzene, C 6 H 6 O 6.

Suppose the ship turns about an axis through F in the water-line area, perpendicular to the plane of the paper; denoting by y the distance of an element dA if the water-line area from the axis of rotation, the change of displacement is EydA tan 8, so that there is no change of displacement if EydA = o, that is, if the axis passes through the C.G.

The time rate of increase of momentum of the fluid inside S is )dxdydz; (5) and (5) is the sum of (I), (2), (3), (4), so that /if (dpu+dpu2+dpuv +dpuw_ +d p j d xdyd z = o, (b)` dt dx dy dz dx / leading to the differential equation of motion dpu dpu 2 dpuv dpuv _ X_ (7) dt + dx + dy + dz with two similar equations.

Taking the axis of x for an instant in the normal through a point on the surface H = constant, this makes u = o, = o; and in steady motion the equations reduce to dH/dv=2q-2wn = 2gco sin e, (4) where B is the angle between the stream line and vortex line; and this holds for their projection on any plane to which dv is drawn perpendicular.

Then 4, =o over the cylinder r = a, which may be considered a fixed post; and a stream line past it along which 4, = Uc, a constant, is the curve (r - ¢2) sin 0=c, (x2 + y2) (y - c) - a 2 y = o, (3) a cubic curve (C3).

An ellipse interior to n = a will move in a direction opposite to the exterior current; and when n = o, U = oo, but V = (m/c) sh a sin 13.

Motion symmetrical about an Axis.-When the motion of a liquid is the same for any plane passing through Ox, and lies in the plane, a function ' can be found analogous to that employed in plane motion, such that the flux across the surface generated by the revolution of any curve AP from A to P is the same, and represented by 2s-4 -11'o); and, as before, if d is the increase in due to a displacement of P to P', then k the component of velocity normal to the surface swept out by PP' is such that 274=2.7ryk.PP'; and taking PP' parallel to Oy and Ox, u= -d/ydy, v=dl,t'/ydx, (I) and 1P is called after the inventor, " Stokes's stream or current function," as it is constant along a stream line (Trans.

Similarly, with the function (19) (2n+ I) 3 ch (2n+ I) ITrb/a' (2) Changing to polar coordinates, x =r cos 0, y = r sin 0, the equation (2) becomes, with cos 0 =µ, r'd + (I -µ 2)-d µ = 2 ?-r3 sin 0, (8) of which a solution, when = o, is = (Ar'+) _(Ari_1+) y2,, ?

As an application of moving axes, consider the motion of liquid filling the ellipsoidal case 2 y 2 z2 Ti + b1 +- 2 = I; (1) and first suppose the liquid be frozen, and the ellipsoid l3 (4) (I) (6) (9) (I o) (II) (12) (14) = 2 U ¢ 2, (15) rotating about the centre with components of angular velocity, 7 7, f'; then u= - y i +z'i, v = w = -x7 7 +y (2) Now suppose the liquid to be melted, and additional components of angular velocity S21, 522, S23 communicated to the ellipsoidal case; the additional velocity communicated to the liquid will be due to a velocity-function 2224_ - S2 b c 6 a 5 x b2xy, as may be verified by considering one term at a time.

Ja - u  ?I a -a b -u' sh nS2=sh log (Q)=?a - b a - a' b - u' At x where = co, u = o, and q= go, (O n b - a ' a + a -b a' cio) - ?a-a'?b a-a' q In crossing to the line of flow x'A'P'J', b changes from o to m, so that with q = Q across JJ', while across xx the velocity is qo, so that i n = go.

Helmholtz, of the efflux of a jet between two edges A and A 1 in an infinite wall, is obtained by the symmetrical duplication of the above, with n = 1, b = o, a' = - oo, as in fig.

When the liquid is bounded externally by the fixed ellipsoid A = A I, a slight extension will give the velocity function 4 of the liquid in the interspace as the ellipsoid A=o is passing with velocity U through the confocal position; 4 must now take the formx(1'+N), and will satisfy the conditions in the shape CM abcdX ¢ = Ux - Ux a b x 2+X)P Bo+CoB I - C 1 (A 1 abcdX, I a1b1cl - J o (a2+ A)P and any'confocal ellipsoid defined by A, internal or external to A=A 1, may be supposed to swim with the liquid for an instant, without distortion or rotation, with velocity along Ox BA+CA-B 1 -C1 W'.

The determination of the O's and x's is a kinematical problem, solved as yet only for a few cases, such as those discussed above.

The system of forced loans was abolished and a 1 o% tax on real property introduced in its stead, and a law of amnesty for political offenders enacted.

Extraction of cane juice by diffusion (a process more fully described under the head of beetroot sugar manufacture) is adopted in a few plantations in Java and Cuba, in Louisiana Etr cti o n and the Hawaiian Islands, and in one or two factories y f i in Egypt; b u t hitherto, except under exceptional conditions (as at Aska, in the Madras Presidency, where the local price for sugar is three or four times the London price), it would not seem to offer any substantial advantage over double or triple crushing.

Outline of the ventral surface to show the external apertures and nervous system; a, rosette-organ; b, uterine pore; c, terminal sucker; e, vaginal pore; g, male gonopore; n, o, p, nervous system.

The term clay is often used by chemists to denote hydrated silicate of alumina (Al 2 O 3 2SiO 2.2H 2 O), of which kaolin or china clay is a fairly pure form.

About 57 o the dynasts of Yemen, who had been subdued by the Ethiopians of Axum, applied to Chosroes for help. He sent a fleet with a small army under Vahriz, who expelled the Ethiopians.

Two of them, r o to r2 ft.

Such a furnace, to take a current of 4 H.P. (say, of 60 amperes and so volts), measured externally about 6 by 6 by 7 in., and the electrodes were about o 4 in.

Protestants of the Augsburg and Helvetic Confessions numbered 54,364; members of the Church of England, 49 o; Old Catholics, 975; members of the Greek Orthodox Church, 3674; Greek Catholics, 2521; and Mahommedans, 889.

It forms several oxides, TiO 2, Ti 2 O 3 and TiO 3 being the best known; others (some of doubtful existence) have been described from time to time.

Titanium sesquioxide, Ti 2 O 3, is formed by heating the dioxide in hydrogen.

H 2 O, forms white, shining, monoclinic scales.

Boudard's Etudes sur l'alphabet iberien (Paris, 1852), and Numismatique iberienne (Beziers, 1859); Aloiss Heiss, Notes sur les monnaies celtiberiennes (Paris, 1865), and Descriptionenerale des monnaies antiques de l'Espagne (Paris, 1870); Phillips, O Ober das iberische Alphabet (Vienna, 1870), Die Einwanderung der Iberer in die pyren.

The Tatra Mountains extend through the Hungarian counties of Lipt6 and Szepes, and with their northern extremities also through the Austrian crownland of Galicia, and have a length of 4 o m.

Under the guidance of General Caceres a junta was then formed to carry on the government until an election for the presidency should be held and the senate and cham- Ch o eres in ber of deputies constituted.

A hydrated dioxide, approximating in composition to SrO 2.8H 2 O, is formed as a crystalline precipitate when hydrogen peroxide is added to an aqueous solution of strontium hydroxide.

Strontium chloride, SrC1 2.6H 2 O, is obtained by dissolving the carbonate in hydrochloric acid, or by fusing the carbonate with calcium chloride and extracting the melt with water.

A, Fasciola hepatica, from the ventral surface (X 2); the alimentary and nervous systems only shown on the left side of the figure, the excretory only on the right; a, right main branch of the intestine; c, a diverticulum; g, lateral ganglion; n, lateral nerve; o, mouth; p, pharynx; s, ventral sucker; cs, cirrus sac; d, left anterior dorsal excretory vessel; m, main vessel; v, left anterior ventral trunk; x, excretory pore.

A, Dorsal view showing the nervous system and digestive system; a, mouth; b, pharynx; c, d, e, gut; E, post-genital union of two limbs of gut; f, excretory pore; g, vaginal pore; h, j, k, brain and nerves; 1, dorsal nerves; m, ventral nerves; n, adoral sucker; o, posterior sucker; p, hooks on posterior sucker; r, vitello-intestinal duct.

In other Entoprocta the buds on a horseshoe retain a high degree of individuality, a shaped l o p h o - thread-like stolon giving off the cylindrical phore; stalks, each of which dilates at its end i, Ectocyst; into the body of a zooid.

The ovary (o) and the testis (t) of Ectoprocta are developed on the body-wall, on the stomach, or on the funiculus.

The central nervous system (x) is highly developed, and in Loxosoma bears a pair o` eyes.

The word Morashtite (Morashti) was therefore obscure to them; but this only gives greater weight to the traditional pronunciation with o in the first syllable, which is as old as the LXX., and goes against the view, taken by the Targum both on Micah and on Jeremiah, and followed by some moderns (including Cheyne, E.B., 3198), that Micah came from Mareshah.

He was born before the year 99 o, in Cordova, studied in Lucena, left his native city in 1012, and, after somewhat protracted wanderings, settled in Saragossa, where he died before 1050.

On the 23rd of January 1874 Gladstone announced the dissolution in an address to his constituents, declaring that the authority of the government had o f187atioa g y g of 1874.

The general election resulted o in a majority of forty for Home Rule, heterogeneously composed of Liberals, Labour members and Irish.

The double election to the German throne in 141 o first brought Frederick into relation with Brandenburg.

The small eyes are some- T y p h l o p s bra- times covered by transparent shields.

The difficulty is increased by the fact that in some cases several towns were grouped together in one payment (o vv-rcXEZr).

Hence the density v is given by 47rabc (x2/a4+y2/b4-I-z2/c4), and the potential at the centre of the ellipsoid, and therefore its potential as a whole is given by the expression, adS Q dS V f r 47rabc r' (x2/a4-I-y2/b4+z2/c4) Accordingly the capacity C of the ellipsoid is given by the equation 1 I J dS C 47rabc Y (x 2 +y 2 + z2) V (x2/a4+y2/b4+z2/c4) (5) It has been shown by Professor Chrystal that the above integral may also be presented in the form,' foo C 2 J o J { (a2 + X) (b +X) (c 2 + X) } (6).

A cycle such as ABCD enclosed by parts of two isothermals, BC, AD, and two adiabatics, AB, CD, is the simplest form of cycle for theoretical purposes, since all the heat absorbed, H', is taken in during the process represented by one isothermal at the temperature o', and all the heat rejected, H", is given out during the process represented by the other at the temperature 0".

If the substance in any state such as B were allowed to expand adiabatically (dH = o) down to the absolute zero, at which point it contains no heat and exerts no pressure, the whole of its available heat energy might theoretically be recovered in the form of external work, represented on the diagram by the whole area BAZcb under the adiabatic through the state-point B, bounded by the isometric Bb and the zero isopiestic bV.

Combining this with the first law, for a Carnot cycle of finite range, if H is the heat taken in at 0', and H" is the heat rejected at 0", the work W done in the cycle is equal to the difference H' - H", and we have the simple relations, W/(0' - o") =H'/o' =H" o".

Then by relations (2) the heat, H, absorbed in the isothermal change BC, is to the work, W, done in the cycle ABCD in the ratio of o to (o' - o").

Substituting these symbols in the expression for the area, the relation becomes H=o(p' - p„)(v„_v')/(o' - o").

The heat evolved in this process may be represented by s"(o' - o"), where s" is the specific heat of the substance in the second state at saturation pressure.

By the application of the second law, relations (2), the same work area is equal to (o' - o")L'lo'.

Dividing by (0' - e"), and writing dp/do and dL/do for the limiting values of !the ratios (p' - p")/(o' - o") and (L' - L")/(o' - o"), we obtain the important relations s' - s"+dL/do= (v" - v')dp/do=L/o,..

The whole quantity of heat required to raise the temperature from 0" to 0' at constant pressure along the path EC is H+h, which is equal to S(0' - o"), where S is the specific heat at constant pressure.

Since h = s (o' - 0"), the difference S - s between the specific heats at constant pressure and volume is evidently H/(o' - o").

We thus obtain the expressions dH = sdo +0 (dp I dO) dv = Sd0 - o (dv/do) dp..

We thus obtain the relation ds/dv(o const) =od 2 p/d0 2 (v const),.

The equation to these lines in terms of v and 0 is obtained by integrating dE=sd0+(Odp/de - p)dv = o .

Denoting by So, so, these constant limiting values at p=o, we may obtain the values at any pressure by integrating the expressions (27) and (28) from co to v and from o to p respectively.

In the limiting case of a long fine tube, the bore of which varies in such a manner that U is constant, the state of the substance along a line of flow may be represented by the line of constant total heat, d(E+pv) = o; but in the case of a porous plug or small throttling aperture, the steps of the process cannot be followed, though the final state is the same.

The value of B is determined by observing the latent heat, Lo = F"o - F'0, which gives B =B" - B' =L0+(s' - So)00+(n+r)copo - bpo+dho (45) This constant may be called the absolute latent heat, as it expresses the thermal value of the change of state in a manner independent of temperature.

The sieges of Perinthus and Byzantium (34 o, 339) ended in Philip's meeting with a signal check, due in some measure to the help afforded the besieged cities by Athens and her allies.

Not far distant, on a conspicuous position close by the banks of the Doon, stands the Grecian monument to Burns, in the grounds of which is the grotto containing Thom's figures of Tam o' Shanter and Souter Johnnie.

The loose aggregation of agricultural households gives place t o the organized community with new needs and new g y ideals, and at the same time in religious thought the old vague notion of the numen is almost universally superseded by the more definite conception of the dens - not even now quite anthropomorphic, but with a much more clearly realized personality.

The alloys of the formulae AuAg, AuAg 2, AuAg 4 and AuAg 2 o are perfectly homogeneous, and have been studied by Levol.

It dissolves in alkalis to form well-defined crystalline salts; potassium aurate, KAu0 2.3H 2 O, is very soluble in water, and is used in electrogilding.

The gold chloride of commerce, which is used in photography, is really a hydrochloride, chlorauric or aurichloric acid, HAuC1 4.3H 2 O, and is obtained in long yellow needles by crystallizing the acid solution.

Light-yellow monoclinic needles of 2KAuC1 4 H 2 O are deposited from warm, strongly acid solutions, and transparent rhombic tables of KAuCl 4.2H 2 O from neutral solutions.

By crystallizing an aqueous solution, red crystals of AuC1 3.2H 2 O are obtained.

Potassium auricyanide, 2KAu(CN) 4.3H 2 O, is obtained as large, colourless, efflorescent tablets by crystallizing concentrated solutions of auric chloride and potassium cyanide.

Sodium aurosulphide, NaAuS 4H 2 O, is prepared by fusing gold with sodium sulphide and sulphur, the melt being extracted with water, filtered in an atmosphere of nitrogen, and evaporated in a vacuum over sulphuric acid.

Sodium aurothiosulphate, 3Na 2 S 2 O 3 Au2S203.4H20, forms colourless needles; it is obtained in the direct action of sodium thiosulphateongoldinthe presence of an oxidizing agent, or by the addition of a dilute solution of auric chloride to a sodium thiosulphate solution.

In the Transvaal the operation occupies 32 to 4 days for fine sands, and up to 14 days for coarse sands; the quantity of cyanide per ton of tailings varies from 0.26 to 0.28 lb, for electrolytic precipitation, and o 5 lb for zinc precipitation.

In the process employed at the Worcester Works in the Transvaal, the liquors, containing about 150 grains of gold per ton and from 0.08 to o 01% of cyanide, are treated in rectangular vats in which is placed a series of iron and leaden plates at intervals of 1 in.

Between s o and 176 the authority of the episcopate had been immensely strengthened, and along with it a settled order had been introduced into the Churches.

Every endeavour is made to gloss over, or modify, expressions which seemed derogatory to the ancestors of ' According to Zunz, Gottesdienstliche Vortrdge, 2nd ed., p. 80, its contents bear the following proportions to Genesis, z o o to Exodus, about 1 1 4 to Leviticus, s to Numbers, and 4 to Deuteronomy.

Although the duke strove after peace at almost any price, he was nearly always involved in war and l o st many possessions, including Geneva and Vaud.

The city walls attained a circuit of 1 o m.

But even if we date the rise of heresies in the reign of Domitian instead of Trajan, 2 the attributing of this epistle against 2 O n this point (date of the outbreak of heresy) there is some inconsistency in the reported fragments of Hegesippus.

In 1897 the sum o was subscribed by citizens to found a hospital (1903) to commemorate the Diamond Jubilee of Queen Victoria, and named after her.

In 1908 this city had a park system of 75 o acres.

The oxide, bismuth ochre, Bi 2 O 3, and the sulphide, bismuth glance or bismuthite, are also of commercial importance.

Bismuth dioxide, BiO or Bi 2 O 2, is said to be formed by the limited oxidation of the metal, and as a brown precipitate by adding mixed solutions of bismuth and stannous chlorides to a solution of caustic potash.

Bismuth tetroxide, Bi 2 O 4, sometimes termed bismuth bismuthate, is obtained by melting bismuth trioxide with potash, or by igniting bismuth trioxide with potash and potassium chlorate.

The basic carbonate, 2(B10) 2 CO 3 4H 2 O, obtained as a white precipitate when an alkaline carbonate is added to a solution of bismuth nitrate, is employed in medicine.

Astronomers denote the year which preceded the first of our era by o, and the year previous to that by 1 B.C.; but chronologers, in conformity with common notions, call the year preceding the era 1 B.C., the previous year 2 B.C., and so on.

But the earl of Lennox, Darnley's father, understood Moray to mean that as early as January 21-22, 1567, the house of Kirk o' Field, where Darnley was slain, had already been mined.

Lord Robert was the only friend of Darnley in Mary's entourage; and he even, according to the accusers, warned him of his danger in Kirk o' Field, to which they said that a Casket Letter (III.) referred.

In this alphabet the Greek letter p (or rather a very similar letter with the loop a little lower down) is used to represent sh, and there are some peculiarities in the use of o apparently connected with the expression of the sounds h and w.

The reason for this is readily seen; if a mass M of any gas occupies a volume V at a temperature T (on the absolute scale) and a pressure P, then its absolute density under these conditions is O = M/V; if now the temperature and pressure be changed to l and P,, the volume V l under these conditions is VPT/PIT1, and the absolute density is MP,T/VPT I.

There are several corrections of the formula O =W/(W - W1) necessary to the accurate expression of the density.

The free acid may be obtained by decomposing the barium salt with sulphuric acid and concentrating the solution, when a crystalline mass of composition H 2 Te04.2H 2 O separates.

But no such suggestion occurs in the Basis Astronomiae of Peter Horrebow (Copenhagen, 1735), which contains the only works of Roemer that re e o main to us.

By heating with sodium amalgam and separating with hydrochloric acid, the dichloride, TaC1 2.2H 2 O, is obtained as emerald green hexagonal crystals.

In the north tropical belt of high pressure south of the Azores the atmospheric pressure in January is o 87 in.

According to Knudsen the salinity is given in weight per thousand parts by the expression S = o 030+ I.

Observations with the xanthometer have not hitherto been numerous, but it appears that the purest blue (o--I on Forel's scale) is found in the Sargasso Sea, in the North Atlantic and in similarly situated tropical or subtropical regions in the Indian and Pacific Oceans.

According to Thoulet and Chevallier the specific heat diminishes as salinity increases, so that for io per mille salinity it is o 968, for 35 per mille it is only o 932, that of pure water being taken as unity.

Ruppin's analysis of Baltic water, which has an alkalinity of 16 to 18 instead of the 5 or 6 which would be the amount proportional to the salinity, while the water of the Vistula and the Elbe with a salinity of o 1 per mille has an alkalinity of 28 or more.

Thus in the Central American Sea below 93 o fathoms, the depth on the bar, no water is found at a temperature lower than that prevailing in the open ocean at that depth, viz.

The yield per man on the working faces was 4.5 tons, and for the whole of the working force underground, o 846 tons, which is not less than that realized in shallower mines.

Cs 2 S 4H 2 0, Cs 2 S 2 H 2 O, Cs 2 S 3 H 2 0, Cs 2 S 4 and, Cs 2 S 5 H 2 0, are also known.

It appears tolerably safe to conclude that, whatever errors 'may have affected the determination, the diameter or distance of the particles of water is between the two thousand and the ten thousand millionth of an inch " (= between 125 X I o 8 and 025 X 10 -8 cms.).

Thus the contribution to the total impulsive pressure exerted on the area dS in time dt from this cause is mu X udtdS X (11 3 m 3 /,r 3)e hm (u2+v2+w2 )dudvdw (I o) The total pressure exerted in bringing the centres of gravity of all the colliding molecules to rest normally to the boundary is obtained by first integrating this expression with respect to u, v, w, the limits being all values for which collisions are possible (namely from - co too for u, and from - oo to + oo for v and w), and then summing for all kinds of molecules in the gas.

The aggregate amount of these pressures is clearly the sum of the momenta, normal to the boundary, of all molecules which have left dS within a time dt, and this will be given by expression (pp), integrated with respect to u from o to and with respect to v and w from - oo to +oo, and then summed for all kinds of molecules in the gas.

The molecules of gases for which n = o must accordingly be spherical in shape and in internal structure, or at least must behave at collisions as though they were spherical, for they would otherwise be set into rotation by the forces experienced at collisions.

Instead of this we have n = o, and -y = I I.

The chloride, SmCl 2, is a brown crystalline powder which is decomposed by water with liberation of hydrogen and the formation of the oxide, Sm 2 O 3, and an oxychloride, SmOC1.

The value of farms on which dairying was the chief source of income in 1900 was 46% of the total farm value of the state; the corresponding percentages for livestock, vegetables, hay and grain, flowers and plants, fruit and tobacco, being respectively 14.6, 10 2, 8 o, 4.2, 3.2, and 1 8%.

Taking quinquennial periods from1856-1905the birth-rates were 29.5, 25.3, 26 o, 27.6, 24.2, 25.0, 25.8, 27.6, 27.0 and 24.2 per r,000; and the death-rates 17.7, 20.7, 18.2, 20 8, 18.8,19.8, 19.4, 19.8, r 8 o and 16.4.

There is no dividing line between first-contact ethnology and -s y g gY gy Th J o pre-contact archaeology.

O Areois were also a social force.

To the more strictly exegetical lectures the names E nyncmtc, 4-07-Amara, i nynTuca, O o€t, were sometimes applied.

In the notation of the integral calculus, this area is equal to f x o udx; but the notation is inconvenient, since it implies a division into infinitesimal elements, which is not essential to the idea of an area.

This will be seen by taking the mid-ordinate as the ordinate for which x = o, and noticing that the odd powers of x introduce positive and negative terms which balance one another when the whole area is taken into account.

If m = 4, and the data are ul, u2, Us, U4, we have area = h (7 u o + 3 2u 2 -112/42 + 3 2u 3 + 7u4).

In the case of the sphere, for instance, whose radius is R, the area of the section at distance x from the centre is lr(R 2 -x 2), which is a quadratic function of x; the values of So, Si, and S2 are respectively o, 7rR 2, and o, and the volume is therefore s.

To extend these methods to a briquette, where the ordinate u is an algebraical function of x and y, the axes of x and of y being parallel to the sides of the base, we consider that the area of a section at distance x from the plane x = o is expressed in terms of the ordinates in which it intersects the series of planes, parallel to y=o, through the given ordinates of the briquette (§ 44); and that the area of the section is then represented by the ordinate of a trapezette.

If the transformation is made first, and if the resulting raw moments with regard to the (approximate) central ordinate are o, 72, 71-3, ..., the true moments µ1, u2, /13, ...with regard to the central ordinate are given by Lo=o 1 i / h2,3 83.

In cases other than those described in § 82, the pth moment with regard to the axis of u is given by Pp = XPrA where A is the total area of the original trapezette, and S 2 _ 1 is the area of a trapezette whose ordinates at successive distances h, beginning and ending with the bounding ordinates, are o, x1P -1A, x2 P-1 (AI+AI),.

If we write -fxo f yox s yiu dx dy, we first calculate the raw values coo., ai,o, 0.1,1,

Thus we find (e.g.) -2x1,1 52,1 2 x2,1 - i h2a o, .

Proofs of the Inquiry into the Life and Writings of Homer, p. 33 o (London, 1736).

The lowest current weight is 1 22.5 grains for sovereigns and 61.125 grains for half-sovereigns corresponding to losses by wear of about o.

The amount of copper removed from silver blanks containing 900 to 925 parts of silver per moo is from o 6 to I o per 1000.

The balance turns to o oi grain.

As stated under Phosphorus, phosphoric oxide, P 2 0 5, combines with water in three proportions to form H 2 O P 2 0 5 or HP03, metaphosphoric acid; 2H 2 O P 2 0 5 or H4P207, pyrophosphoric acid; and 3H 2 O P 2 0 5 or H 3 PO 4, orthophosphoric or ordinary phosphoric acid.

Pyrophosphoric acid, 'H' 4 P 2 0 7, is a tetrabasic acid which may be regarded as derived by eliminating a molecule of water between two molecules of ordinary phosphoric acid; its constitution may therefore be written (HO) 2 0P O PO(OH) 2.

It forms monoclinic prisms (with IoH 2 O) which are permanent in air.

Metaphosphoric acid, HP0 3, is a monobasic acid which may be regarded as derived from orthophosphoric acid by the abstraction of one molecule of water, thus H 3 PO 4 - H 2 O = HP0 3; its constitution is therefore (HO)P0 2.

Live-stock and dairy products are important factors in the T C t o L %i, aa.

If the velocity U is so chosen that E - poU 2 = o, then X = o, or the wave travels on through the action of the internal forces only, unchanged in form and with velocity U = (E/p).

Buti o Pdt = P is the normal pressure, and as we only wish to find the excess we may leave this out of account.

We also have pu t =p o u t /(I +dy/dx).

But f o 2dx=0 since the sum of the displacements = o.

The temperature of the air traversed and its humidity were observed, and the result was finally corrected to the velocity in dry air at o C. by means of equation (ro).

In the memoir cited above Regnault gives an account of determinations of the velocity in air in pipes of great length and of diameters ranging from o 108 metres to i i metres.

Regnault also set up a shorter length of pipes of diameter o 108 m.

Let the forks be numbered o, I, 2,.

If the frequency of o is n, that of N is 2n.

That is, the length of the pipe must be increased by o 82 R before applying Bernoulli's theory.

Then we have Ya,ody/dx +p& (U - u) 2 = p o&,oU 2.

Since no angular momentum goes out on the whole Z nwra 4 d0/dx -?- 2 pwra 4 Ud0/dt = o.

Taking the squares of the amplitude to represent the intensity or loudness of the sound which would be heard by an ear at the point, this is 4a 2 cos t ir(ni - n2)t =2a 2 {1 -cos 27r(n l - n2)t}, a value which ranges between o and 4a 2 with frequency .n1 - n2.

If, instead of considering one point in a succession of instants, we consider a succession of points along the line of propagation at the same instant, we evidently have waves of amplitude varying from 2a down to o, and then up to 2a again in distance U/(ni - n2).

The first census, taken in 1880, showed a total population of 133,518; in 1890 there were 207,503 inhabitants - an increase in ten years of 55.41%o and at the census of 1904 there were 387,315 inhabitants, a further increase of 85.56%.

The effect of his exhortations, as well as of his personal character and public acts, upon the standards and spirit of official life in the United States, was a pronounced one in attracting to the federal service a group o men who took up their work of public office with the same spirit of enthusiasm and self-sacrifice that actuates the military volunteer in time of war.

Two spheres intersect in a plane, and the equation to a system of spheres which intersect in a common circle is x 2 + y 2 + z 2 +2Ax -fD = o, in which A varies from sphere to sphere, and D is constant for all the spheres, the plane yz being the plane of intersection, and the axis of x the line of centres.

In addition to voluntary submissions and references by rules of court there are in America, as in the United Kingdom, various statutes which provide for arbitration in particular o cases.

Itl ' At first girders had soli or plate webs, but for spans o 9 over ioo ft.

In some girder -1 o bridges the members are connected entirely by riveting, in others the principal members are con nected by pin joints.

In the specification for bridge material, drawn up by the British Engineering Standards Committee, it is provided that the steel shall be acid or basic open-hearth steel, containing not more than o.

If a footway is added about o 4 ton per ft.

Let t be the statical breaking strength of a bar, loaded once gradually up to fracture (t = breaking load divided by original area of section); u the breaking strength of a bar loaded and unloaded an indefinitely great number of times, the stress varying from u to o alternately (this is termed the primitive strength); and, lastly, let s be the breaking strength of a bar subjected to an indefinitely great number of repetitions of stresses equal and opposite in sign (tension and thrust), so that the stress ranges alternately from s to -s.

For shearing stresses the working stress may have o 8 of its value for tension.

In the Forth bridge for members in which the stress varied from o to a maximum frequently, the limit was 5.0 tons per sq.

On the 3rd of May Griffenfeldt was tried not by the usual tribunal, in such cases the Hojesteret, or supreme court, but by an extraordinary tribunal of 1 o dignitaries, none of whom was particularly well disposed towards the accused.

About 15% of a volatile oil is obtained by distilling cubebs with water; after rectification with water, or on keeping, this deposits rhombic crystals of camphor of cubebs, C 15 H 26 O; cubebene, the liquid portion, has the formula C15HV4.

Meyerdahl obtained 4% of palmitic acid, 20% of jecoleic acid, C19H3602, and 20% of therapic acid, C 17 H 28 O 2; other investigators have recognized jecoric acid, C 18 H 30 O 2, asellic acid, C17H3202, and physetoleic acid, C16Hn02, but some uncertainty attends these last three acids.

It consisted of a glass vessel, containing a solution of sulphate of zinc, in which were placed two plates of pure amalgamated zinc. These plates were connected by means of a german-silver shunt, their size and the distance between them being so adjusted that about ii 0 - 0 - part of the current passing through the meter travelled through the electrolytic cell and -j o i j of the current passed through the shunt.

The vowel signs have no sound by themselves, but act upon the vowel sound" aw "inherent in the consonants, converting it into" a," i," o," ee," ow,"&c. Each of the signs has a name, and some of them produce modulations so closely resembling those made by another that at the present day they are scarcely to be distinguished apart.

The sulphydrate or hydrosulphide, Ca(SH)2, is obtained as colourless, prismatic crystals of the composition Ca(SH) 2.6H 2 O, by passing sulphuretted hydrogen into milk of lime.

A British naval squadron arrived in the Moluccas in February 181 o and captured Amboyna, Banda, Ternate and other islands.

An ice-cold solution of this substance kept at o C. and having sulphuretted hydrogen continually passed through it gives the hydrosulphide.

From 1792 to 1799 he was occupied with the measurement of the arc of the meridian extending from Dunkirk to Barcelona, and published a detailed account of the operations in Base du systeme metrique (3 vols., 1806, 1807, 1810), for which he was awarded in 181 o the decennial prize of the Institute.

In the next ensuing session of Congress, in 1889-90, the Republicans passed a new tariff act, known as the McKinley Tariff Act, because Mr McKinley was then chairman of McKffinl o fey the House Committee in charge of the bill.

He wrote a fine descriptive work, Obrazy z zycia i podrozy (" Pictures of Life and Travel"), and also a poem, Piesn o ziemi naszej (" Song of our Land").

By the Treaty of Chaumont of March 1 o, 1814, these four powers bound themselves together in a bond which was not to be dissolved when peace was concluded.

In Colombia there occurs a double salt, Na 2 CO 3 CaCO 3.5H 2 O, known as gay-lussite.

Sodium trioxide, Na 2 O 31 is said to be formed from an excess of oxygen and a solution of sodammonium in liquid ammonia.

Common washing soda or soda-crystals is the decahydrate, Na2C03 IoH 2 O, which appears as large clear monoclinic crystals.

Pop. (1890), 53,230; (igoo), 79, 8 5 o, of whom 23,758 were foreign-born (including 8076 Irish, 2700 Germans, 2260 Russians, 1952 Italians, 1714 Swedes, 1634 English and 1309 English Canadians); (1910 census) 98,915.

It is also formed by the action of sulphuretted hydrogen on the isocyanic esters, 2CONC 2 H 5 +H 2 S=COS+CO(NHC 2 H 5) 2, by the action of concentrated sulphuric acid on the isothiocyanic esters, Rncs H 2 O = Cos Rnh 2, Or Of Dilute Sulphuric Acid On The Thiocyanates.

Gulf of Gabes I o g Lemg.W.of Greenwicir 0 Longitude East of Greenwich B 4 D very complete sequence of formations from the Lias to those of recent date.

Its specific gravity is o 865; hence it is the lightest metal known except lithium.

He left the university without taking a degree, and in 16 4 o was residing in the Middle Temple.

The peroxide, Pr 4 O 7, forms a dark brown powder, and is obtained by ignition of the oxalate or nitrate.

It should be mentioned that in most tables of trigonometrical functions, the number io is added to all the logarithms in the table in order to avoid the use of negative characteristics, so that the characteristic 9 denotes in reality 1, 8 denotes a, io denotes o, &c. Logarithms thus increased are frequently referred to for the sake of distinction as tabular logarithms, so that the tabular logarithm =the true logarithm -IIo.

The numerical value of this modulus is o 4342944 81 9 03251 82765 11289..

This equation defines log x for positive values of x; if o the formula ceases to have any meaning.

The function log x as x increases from o towards w steadily increases from - co towards +co.

It is positive for all values of y and increases steadily from o toward as y increases from -co towards + oo.

Thus even when the argument is real log x has an infinite number of values; for putting 71 =o and taking positive, in which case a = o, we obtain for log the infinite system of values log +2n7ri.

If 1 denotes the logarithm to base e (that is, the so-called "Napierian " or hyperbolic logarithm) and L denotes, as above, " Napier's " logarithm, the connexion between 1 and L is expressed by L = r o 7 loge 10 7 - 10 7 / or e t = I 07e-L/Ia7 Napier's work (which will henceforth in this article be referred to as the Descriptio) immediately on its appearance in 1614 attracted the attention of perhaps the two most eminent English mathematicians then living - Edward Wright and Henry Briggs.

The " liber posthumus " was the Constructio (1619), in the preface to which Robert Napier states that he has added an appendix relating to another and more excellent species of logarithms, referred to by the inventor himself in the Rabdologia, and in which the logarithm of unity is o.

Briggs pointed out in his lectures at Gresham College that it would be more convenient that o should stand for the logarithm of the whole sine as in the Descriptio, but that the logarithm of the tenth part of the whole sine should be Io,000,000,000.

But he considered that the change ought to be so made that o should be the logarithm of unity and io,000,000,000 that of the whole sine, which.

If a= logg = - log (1-10)' 81 (1) c = 10g 80 = log 1 +sr, 126 (8) e =10g1 o = log 1 +1000 then log 2=7a-2b+3c, log 3=IIa-3b+5c, log 5=16a-4b +7c, and log 7 =2(39a - IOb+17c - d) or=19a-4b+8c +e, and we have the equation of condition, a-2b+c=d+2e.

Being but a few miles south of Dunnet Head, John o' Groat's is a colloquial term for the most northerly point of Scotland.

The cowry-shell, Cypraca europaea, is locally known as "John o' Groat's bucky."

I o g.

The large sale of the New Testaments of Tyndale, and the success of Coverdale's Bible, showed the London booksellers that a new and profitable branch of business was o opened out to them, and they soon began to avail Matthew's P ?

The mineral nearly always contains a small amount of silver, and sometimes antimony, arsenic, copper, gold, selenium, &c. Argentiferous galena is an important source of silver; this metal is present in amounts rarely exceeding %, and often less than o 03% (equivalent to 104 ounces per ton).

In a region where there is no absorption, we have = o and therefore g=o, and we have only one equation, namely, x2_ A2m' which is identical with Sellmeier's result.

Pop. (1890) 3733; (190 o) 5155, of whom 1183 were foreign-born; (1910 U.S. census) 5936.

But this effect of participation in the bread and cup was not in Paul's opinion automatic, was no mere o, ', us operatum; it depended on the ethical co-operation of the believer, who must not eat and drink unworthily, that is, after refusing to share his meats with the poorer brethren, or with any other guilt in his soul.

Sodium nitroprusside, Na 2 Fe(NC) 5 N02H 2 O, is the commonest salt.

Jesus, 0 Lord, of waxing fame full moon, O Jesus.

The weir is opened by joining the needles of each bay by a chain passed through the eyes at the top and a line of wire through the central rings, so that when released at the top by the tilting of the escape bar by the derrick, they float down as a raft, and are caught by a man in a boat, or, when the cur rent is strong, they are 'mopes ?o drawn to the bank by a rope attached to them previously to their release.

These equations show that the circles touch where they intersect the lines x 2 +y 2 = o, i.e.

Analytically, the Cartesian equation to a coaxal system can be written in the form x 2 + y 2 + tax k 2 = o, where a varies from member to member, while k is a constant.

The radical axis is x = o, and it may be shown that the length of the tangent from a point (o, h) is h 2 k 2, i.e.

In this all able-bodied citizens between the ages of 18 and 6!o are nominally enrolled, but the active militia consists of about 45, 00 0 men of all ranks, in a varying state of efficiency.

The compounds containing this radical are treated under other headings; the hydride is better known as ethane, the alcohol, C 2 H 5 OH, is the ordinary alcohol of commerce, and the oxide (C 2 H 5) 2 O is ordinary ether.

Verneuil succeeded in imparting a sapphire-blue colour to artificial alumina by addition of i 5% of magnetic oxide of iron and o.

On Dividing By 28, The Remainder Is O, Or 28; And Opposite 28, In The First Column Of Letters, We Find D, C, The Dominical Letters Of The Year 1148.