# R Sentence Examples

**R**seemed to be more distant but no less attentive, and perhaps under his veil of discretion, is even more technically adroit.Orchestral wind-parts have been discovered belonging to Haydn's string-quartet Op.

**r**, No.In 1875 a number of Russian Mennonites (descendants of the Anabaptists of the Reformation) came to the

**r**.If the tangent at P meets the asymptotes in

**R**,**R**', then CR.CR' = CS 2.When a current passes through

**R**the armature A is attracted and the local circuit is closed through the armature at b.Advertisement**R**1 and R2 are relays for receiving the FIG.He died in Vienna on the

**r**7th of December 1888.The smoother we make the pulley the more nearly does the amount of useful work which the weight is capable of doing approach ro foot-pounds, and if we take into account the work done against the friction of the pulley, we may say that the work done by the descending weight is ro foot-pounds, and hence when the weight is in its elevated position we have at disposal

**r**o foot-pounds more energy than when it is in the lower position.If the looped lines are both in good condition and free from leakage, the current sent out on line

**r**will be exactly equal to the current received back on line 2; and as these currents will have equal but opposite effects on the galvanometer needle, no deflection of the latter will be produced.In practice the resistances

**r**,**r**' are 9 Earth FIG.AdvertisementThe earliest successful form was " Bright's bell " sounder, which consisted of two bells of distinct tone or pitch, one of which was sounded when the current was sent in one [[International Code O]] --- 4 - 5 p-- - 6

**R**- 7 '...'As we have already stated, the distribution of the capacity along the resistance

**R**must in submarine cable work be made to correspond very accurately with the distribution of the capacity along the resistance of the cable.At the receiving station Marconi connected a single voltaic cell B 1 and a sensitive telegraphic relay

**R**in series with his tube of metallic filings C, and interposed certain little coils called choking coils.In the second period the gutturals have been palatalized, but there yet is no change of final s to

**r**.In the third period final s has everywhere become

**r**.AdvertisementThis is shown by the occasional appearance of

**r**instead of final s.The operator, whose attention is thus attracted, inserts a peg in the jack, then throws over the speaking key of the cord circuit, and having ascertained particulars of the requirement places the other peg of the pair in the nearest multiple jack of the wanted subscriber, whom she proceeds to ring up. In the meantime the callinglamp has darkened; and each subscriber's line being equipped with a cut-off relay whose function it is to disconnect tl, e calling apparatus while the circuit is in use, the insertion o

**r**a peg is immediately followed by the disappearance of the calling signal.The surface of the leaf, especially the laminar wing, bears glands which in spring exude large glistening dr„

**r**, s of nectar.But in all moral qualities the brilliant adventurer of the

**r**5th was infinitely superior to the brilliant adventurer of the r9th century.A law passed on the 22nd of March 1900 gave a B a, special impulse to this form of enterprise by fixing the ratio

**r**naze.AdvertisementAccording to Cicero (Timaeus,

**r**), Figulus endeavoured with some success to revive the doctrines of Pythagoreanism.Marx, puts forward the theory that Cicero and the Auctor have not produced original works, but have merely given the substance of two

**r**xvai (both emanating from the Rhodian school); that neither used the '**r**xvat directly, but reproduced the revised version of the rhetoricians whose school they attended, the introductions alone being their own work; that the lectures on which the Ciceronian treatise was based were delivered before the lectures attended by the Auctor.In the Babylonian Talmud (Babhli) there is no gemara to the smaller tractates of Order

**r**, and to parts of ii., iv., v., vi.Constant use, increased friction (m o

**r**e especially at high speeds), and damage to the rotator will alter an ascertained log error; head or following seas, strong winds, currents and tidal streams also FIG.The town dates from the beginning of the

**r**7th century, and the older part consists of a flagged causeway called Commercial Street, running for 1 m.AdvertisementFor purposes of provincial administration Russia is divided into 78 governments (guberniya), 18 provinces (oblast) and

**r**district (okrug).During the reign of Michael (1613-45) the new dynasty came to be accepted by all classes, and the country recovered to some extent from the disorders and exhaustion -4 f

**r**om which it had suffered so severely; but it was not 1613-45.The slopes of the sides vary according to the nature of the ground, the amount of moisture present, &c. In solid rock they may be vertical; in gravel, sand or common earth they must, to prevent slipping, rise

**r**ft.The gradient or grade of a line is the rate at which it rises or falls, above or below the horizontal, and is expressed by stating either the horizontal distance in which the change of level amounts to

**r**ft., or the amount of change that would occur in some selected distance, such as roo ft., r000 ft.In America a gradient of

**r**in roo is often known as a**r**% grade, one of 2 in roo as a 2% grade, and so on; thus a 0-25% grade corresponds to what in England would be known as a gradient of**r**in 400.An incline of

**r**in 400 is reckoned easy, of**r**in 200 moderate and of**r**in roo heavy.Between A and B, A and C, and A and D, there may be a string of stations, p, q,

**r**, s, &c., all receiving goods from a, b, c and d, and it would manifestly be inconvenient and wasteful of time and trouble if the trains serving those intermediate stations were made up with, say, six wagons from a to p next the engine, five from b to p at the middle, and four from c to p near the end.If the total resistance against which the train is maintained in motion with an instantaneous velocity of V feet per second is

**R**, the rate at which energy is expended in moving the train is represented by the product RV, and this must be the rate at which energy is supplied to the train after deducting all losses due to transmission from the source of power.Thus if

**R**is equal to 10,000 lb when the velocity is 44 ft.The relation between the b.h.p. and the torque on the driving-axle is 55 o B.H.P. =Tu., (9) It is usual with steam locomotives to regard the resistance

**R**as including the frictional resistances between the cylinders and the driving-axle, so that the rate at which energy is expended in moving the train is expressed either by the product RV, or by the value of the indicated horse-power, the relation between them being 55 0 I.H.P. =RV (Io) or in terms of the torque 55 0 I.H.P.X€=RVe=TW (II) The individual factors of the product RV may have any value consistent with equation (to) and with certain practical conditions, so that for a given value of the I.H.P.**R**must decrease if V increases.Thus if the maximum horse-power which a locomotive can develop is woo, the tractive resistance

**R**, at 60 m.Hence Engine resistance,

**R**e = 80 X20 = 1600 lb Vehicle resistance,**R**v =200 X8.5 = 1700 „ Train resistance,**R**= 3300 „ The speed, 40 m.Dividing thr Hugh by V and multiplying through by 550, 2240W 2240Wa

**R**=Were+W vry t G (23) ' 'an expression giving the value of**R**the total tractive resistance.If the draw-bar pull is known to be

**R**v, then applying the same principles to the vehicle alone which above are applied to the whole train, total draw-bar pull = Wvry 2240Wv 2240Wva.The best way of deducing

**r**„ is to select portions of the dynamometer record where the speed is constant.On steam-worked lines the speed of trains is about i

**r**to 15 m.In the most developed forms, such as the offering of soma, they assumed a great importance; (

**r**) the sacrificer had to pass from the world of man into a world of the gods; consequently he was separated from the common herd of mankind and purified; he underwent ceremonies emblematic of rebirth and was then subject to numberless taboos imposed for the purpose of maintaining his ceremonial purity.Other noteworthy churches are the Jakobskirche, an i

**r**th-century Romanesque basilica; the St Martinskirche; the Marienkirche or Obere Pfarrkirche (1320-1387), which has now been restored to its original pure Gothic style.Theodoric, who, ten days after his entry into the city, slew his rival at a banquet in the palace of the Laurel Grove (March

**r**5, 493).Harwich received charters in 1 547, 1 553 and

**r**560.The Mayas have left no

**r**cord of their institutions or of the causes of their decline, beyond what may be deduced from their ruined structures.He had left Paris during the whole of 1520, and, removing to Meaux, was appointed (May

**r**, 1523) vicar-general to Bishop Brigonnet, and published his French version of the New Testament (1523).Among interesting ancient buildings may be mentioned the palace within the fort, containing an armoury and fine library; and the Brihadiswaraswami temple, of the

**r**rth century, enclosed in two courts, surmounted by a lofty tower and including the exquisitely decorated shrine of Subrahmanya.Then Sweden assigned her German possessions to Denmark in exchange for Norway, whereupon Prussia, partly by purchase and partly by the cession 4

**r**of the duchy of Lauenburg, finally succeeded in uniting the whole of Pomerania under her rule.Naturally, it is among the free living forms that the parapodium is best developed, and least developed among the tubicolous belongs typically a long tentacle, the cirrus, which '

**r**podium or neuropodium, and may be developed into an arborescent gill or into a flat scale-like process, A the elytron (in Polynoe, &c.).His general formula for getting at the number of units in any sensation is S = C log

**R**, where s stands for the sensation,**R**for the stimulus numerically estimated, and c for a constant that must be separately determined by experiment in each particular order of sensibility.Near this and less advanced into the branchial chamber is the single renal organ or nephridium

**r**with its opening to the exterior**r**'.B, The diblastula has become a trochosphere by the development of the ciliated ring y

**r**(optical section).After the disastrous defeat of Leipzig (

**r**7th-19th Dctober 1813), when French domination in Germany and Italy -vanished like an exhalation, the allies gave Napoleon another opportunity to come to terms. The overtures known as the Frankfcrt terms were ostensibly an answer to the request for information which Napoleon made at the field of Leipzig.It lies between the rivers Frome and Piddle,

**r**2 m.For example, the con Head muscles y traction of the tergo A 's sternal muscles, connect

**r**.Gloger brought out at Breslau the first (and unfortunately the only) part of a Vollstandiges Handbuch der Natur- In th e Introduction to

**r**t his?His coins of 270 struck at Alexandria bear the legend v(ir) c(onsularis)

**R**(omanorum) im(perator) d(ux)**R**(omanorum) and display his head beside that of Aurelian, but the latter alone is styled Augustus.Its cartesian equation, when the line joining the two fixed points is the axis of x and the middle point of this line is the origin, is (x 2 + y 2)2 = 2a 2 (x 2 - y 2) and the polar equation is

**r**2 = 2a 2 cos 20.The pedal equation is

**r**3 =a 2 p, which shows FIG.Nisibis early became the seat of a Jacobite bishop and of a Nestorian metropolitan, and under the Arabs (when it continued to flourish and became the centre of the district of Diya`

**r**Rebi`a) the population of the town and neighbourhood was still mostly Christian, and included numerous monasteries.The uneasiness caused by the excessive dependence of Great Britain upon the United States for cotton, coupled with the Recent belief that shortages of supply are more frequent than

**R**they ought to be, and the fear that diminishing returns attempts to open may operate in America, occasioned the formation in England of the British Cotton Growing Association on.The rotary system of drilling which is in general use in the oilfields of the coastal plain of Texas is a modification of that invented Rotary by Fauvelle in 1845, and used in the early years of the

**R**.It is a chapter very difficult to write, for while on the one hand an ingenious and speculative historian may refer to the influence of the Crusades almost everything which was thought or done between

**r**too and 1300, a cautious writer who seeks to find Brehier, L'Eglise et l'Orient, p. 347.Over against its want of originality must be set the fact, not merely that Syrian culture ultimately spread extensively towards the West, but that the Syrians (as is shown by the inscriptions of Teima, &c.) long before the Christian era exercised over the northern Arabs a perceptible influence which afterwards, about the beginning of the

**r**st century, became much stronger through the kingdom of the Nabataeans.C. 11 (

**r**400) .As has been said, however, the contention of the common law judges prevailed, and the Admiralty Court (except for a temporary revival under Cromwell) sank into comparative Modern in si insignificance during the

**r**th century.Its consonants are k, g, ng, ch, j, n, t, d, n, p, b, m, y,

**r**, l, w, s, h.By geometrical consideration it can be shown that the angle subtended by p, as seen from F, must be inversely as the square of its distance

**r**.He discharged the duties of an envoy with equal magnificence and dexterity; the treaty of May

**r**r60, which put an end to the war, was of his making.Considering derivatives primarily concerned with transformations of the hydroxyl group, we may regard our typical acid as a fusion of a radical

**R**CO - (named acetyl, propionyl, butyl, &c., generally according to the name of the hydrocarbon containing the same number of carbon atoms) and a hydroxyl group. By replacing the hydroxyl group by a halogen, acid-haloids result; by the elimination of the elements of water between two molecules, acid-anhydrides, which may be oxidized to acid-peroxides; by replacing the hydroxyl group by the group. SH, thio-acids; by replacing it by the amino group, acid-amides (q.v.); by replacing it by the group - NH NH2, acid-hydrazides.Hantzsch (Ber., 1889, 22, p. 1238) succeeded in ob

**R**taining derivatives of o-diketo-**R**-hexene, which yield**R**-pentene and aliphatic compounds on decomposition.Experiment, however, showed that while the quotient on the left hand of this equation was fairly constant for a great number of substances, yet its value was not gR but 7

**R**; this means that the critical density is, as a general rule, 3.7 times the theoretical density.From the relation between the critical constants Pk Vk/Tk = 37

**R**or T k /P k = 3 .This value does not hold in the case of

**r**- ?The relation they suspected to be of the form -yS = KT, where K is a constant analogous to

**R**, and S the surface containing one gramme-molecule, y and T being the surface tension and temperature respectively.In the

**r**i th tablet, Ut-Napishtim tells the famous story of the Babylonian flood, which is so patently attached to Gilgamesh in a most artificial manner.The chief of these ministers is denoted 6 E7rl

**r**&o' 7r pay µarwv, and he corresponds to the vizier of the later East.A distinguished philosopher or man of letters would find them bidding f o

**r**his presence, and most of the great names are p ?Of Russia in Europe only the more densely peopled governments have been surveyed, since 1816, in the manner of other European countries, while for most regions there

**R**are only so-called "military surveys."A relation (

**R**) is serial when (I) it implies diversity, so that, if x has the relation**R**to y, x is diverse from y; (2) it is transitive, so that if x has the relation**R**to y, and y to z, then x has the relation**R**to z; (3) it has the property of connexity, so that if x and y are things to which any things bear the relation**R**, or which bear the relation**R**to any things, then either x is identical with y, or x has the relation**R**to y, or y has the relation**R**to x.The "field" of the relation

**R**is the class of things ranged in order by it.Two relations

**R**and**R**' are said to be ordinally similar, if a one-one relation holds between the members of the two fields of**R**and**R**', such that if x and y are any two members of the field of**R**, such that x has the relation**R**to y, and if x' and y are the correlates in the field of**R**' of x and y, then in all such cases x has the relation**R**' to y', and conversely, interchanging the dashes on the letters, i.e.**R**and**R**', x and x', &c. It is evident that the ordinal similarity of two relations implies the cardinal similarity of their fields, but not conversely.The addition and multiplication of two relation-numbers is defined by taking two relations

**R**and S, such that (I) their fields have no Cf.Thus the rational number one, which we will denote by '

**r**, is not the cardinal number I; for t**r**is the relation I/I as defined above, and is thus a relation holding between certain pairs of cardinals.Accordingly this class is a real number; it will be called the real number 2

**R**.In the above example 2

**R**is an integral real number, which is distinct from a rational integer, and from a cardinal number.Shortly before, a revolutionary attack by an Armenian band on the Ottoman bank

**r**at Constantinople brought about a general massacre of Armenians in the capital (where a widespread revolutionary organization undoubtedly existed), in which at least 3000 victims fell, and the persecution of Armenians became the order of the day.On the i

**r**th of October, when they began their march, the road along the Danube was swept into the river, carrying with it several guns and teams, and hours were consumed in passing the shortest distances.Lestocq was, meanwhile, driven through Konigsberg (which surrendered on the

**r**5th) on Tilsit, and now that he was no longer supported by the Russians, the Prussian commander gave up the struggle.Aided by lucky changes of wind, he reached Cadiz, was joined by 1 French and 6 Spanish ships under Admiral Gravina, which, added to the 1

**r**he had with him, gave him a force of 18 sail.The British admiral, delayed by contrary winds, had not been able to start from the entry to the Straits of Gibraltar till the 1

**r**th of May..Considerable additions of later date, in the Decorated and Perpendicular styles, are due to the Despensers and to Beauchamp, earl of Warwick, while the present residential part is of various dates ranging from the 15th century down to the last half of the

**r**9th, when a thorough restoration, including the addition of a superbly ornamented clock-tower, was carried out.Massena failed to dislodge the Allies, and on the 8th of May withdrew to Salamanca, Almeida falling to Wellington on the

**r**ith of May 181**r**.On the 28th of October r8

**r****r**, Hill, by a very skilful surprise, captured Arroyo de los Molinos (between Badajoz and Trujillo), almost annihilating a French corps under Gerard; and in December 181r the French were repulsed in their efforts to capture Tarifa near Cadiz.He wrote a biographical memoir for an edition of his father's writings, which was published in 187

**r**.Now this ratio is the same as that which gives the relative chemical equivalents of hydrogen and copper, for

**r**gramme of hydrogen and 31.8 grammes of copper unite chemically with the same weight of any acid radicle such as chlorine or the sulphuric group, SO 4.When the solutions may be taken as effectively dilute, so that the gas laws apply to the osmotic pressure, this relation reduces to E _ nrRT to c1 ey gE c2 where n is the number of ions given by one molecule of the salt,

**r**the transport ratio of the anion,**R**the gas constant, T the absolute temperature, y the total valency of the anions obtained from one molecule, and c i and c 2 the concentrations of the two solutions.To pass a steady current in the direction opposite to this electromotive force of polarization, the applied electromotive force E must exceed that of polarization E', and the excess E - E' is the effective electromotive force of the circuit, the current being, in accordance with Ohm's law, proportional to the applied electromotive force and represented by (E - E')/

**R**, where**R**is a constant called the resistance of the circuit.According to Nordenskjold

**r**it numbers only twenty-nine species of mammals, of which seven are marine and seventeen or eighteen may be safely considered as living beyond the forest limit.For since A 11 A 22 -Ar 2 =,,a 33, with similar relations, we have a number of relations similar to A 11 A 22 =AM 2, and either Ars = +11 (A rr A ss) or - (A

**r**.A ss) for all different values of**r**and s.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.**R**is a function of the coefficients which is called the " resultant " or " eliminant " of the k equations, and the process by which it is obtained is termed " elimination."This expression of

**R**shows that, as will afterwards appear, the resultant is a simultaneous invariant of the two forms.By solving the equations of transformation we obtain rE1 = a22x1 - a12x1,

**r**= - a21x1 + allx2, aua12 where**r**= I = anon-anon; a21 a22**r**is termed the determinant of substitution or modulus of transformation; we assure x 1, x 2 to be independents, so that**r**must differ from zero.From these formulae we derive two important relations, dp4 = or the function F, on the right which multiplies

**r**, is said to be a simultaneous invariant or covariant of the system of quantics.In fact, if f and 4, have these forms, it is easy to verify that (f, 4,)i= (A j z) (rs)

**r**x s x .This method of solution fails when the discriminant

**R**vanishes, for then the Hessian has equal roots, as also the cubic f.T = (j, j) 2 jxjx; 0 = (iT)i x

**r**x; four other linear covariants, viz.Further, in the case of invariants, we write A= (1, i') 2 and take three new forms B = (i, T) 2; C = (

**r**,**r**`) 2;**R**= (/y).On this principle the covariant j is expressible in the form

**R**2 j =5 3 + BS 2 a+4ACSa 2 + C(3AB -4C)a3 when S, a are the above defined linear forms.Hence, solving the cubic,

**R**2 j = (S -m i a) (S - m 2 a) (S - m3a) wherein m 1 m2, m 3 are invariants.To determine them notice that

**R**= (a6) and then (f, a 5) 5 = -**R**5 (k1 +k2+k3) (f, a 4 5) 5 = - 5R5 (m 1 k 1+ m 2 k 2+ m 3 k 3), (f, a352) 5 = -10R5 (m21ke +m2k2+m3k3) three equations for determining k 1, k2, k3.When

**R**=0, and neither of the expressions AC - B 2, 2AB -3C vanishes, the covariant a x is a linear factor of f; but, when**R**=AC - B 2 = 2AB -3C =0, a x also vanishes, and then f is the product of the form jx and of the Hessian of jx.For the case 8=1, 0' =2, the condition is a i

**r**1 72 = A032=0; and the simplest perpetuant, derived directly from the product A 1 B 21 is (I)a(2)b-(21)b; the remainder of those enumerated by z3 I z.Between 1808 and 181

**r**he travelled much both in England and the south of Europe, and in 1812 published a blank verse translation of the Inferno.This experiment suggested to Faraday the conception of '

**r**,?The magnetic field due to a long straight wire in which a current of electricity is flowing is at every point at right angles to the plane passing through it and through the wire; its strength at any point distant

**r**centimetres from the wire is H = 21/**r**, (2) i being the current in C.G.S.The field at the centre of a circular conductor of radius

**r**through which current is passing is H = 27ri/**r**, (3) the direction of the force being along the axis and related to the direction of the current as the thrust of a corkscrew to its rotation.If the coil has the form of a ring of mean radius

**r**, the length will be 21rr, and the field inside the coil may be expressed as H = 2ni/**r**.The potential due to a single pole of strength m at the distance

**r**from the pole is V = m/**r**, (7) the equipotential surfaces being spheres of which the pole is the centre and the lines of force radii.The potential due to a thin magnet at a point whose distance from the two poles respectively is

**r**and**r**' is V =m(l/**r**=l/**r**') (8) When V is constant, this equation represents an equipotential surface.If

**r**and**r**' make angles 0 and 0 with the axis, it is easily shown that the equation to a line of force is cos 0 - cos B'= constant.The potential due to a small magnet of moment M, at a point whose distance from the centre of the magnet is

**r**, is V=M cos 0/**r**2, (io) where 0 is the angle between**r**and the axis of the magnet.If F T is the force along

**r**and F t that along t at right angles to**r**, F**r**=X cos 0+ Y sin 0=M 2 cos 0, F t = - X sin 0+ Y cos 0 = -**r**3 sin 0.Although the above useful formulae, (io) to (15), are true only for an infinitely small magnet, they may be practically applied whenever the distance

**r**is considerable compared with the length of the magnet.At a point whose distance from the axis of the wire is

**r**the tangential magnetic force is H = 21r /a 2 (39) it therefore varies directly as the distance from the axis, where it is zero.'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.Thus if the magnet is suspended horizontally by a fine wire, which, when the magnetic axis points north and south, is free from torsion, and if 0 is the angle through which the upper end of the wire must be twisted to make the magnet point east and west, then MH = CB, or M = C6/H, where C is the torsional couple for

**r**0.If two magnets having moments M, M' are arranged at right angles to each other upon a horizontal support which is free to rotate, their resultant

**R**will set itself in the magnetic meridian.The outer coil derives current, through an adjustable resistance

**R**, from a xvii.If the conductor consists of a coil of wire the ends of which are connected with a suitable galvanometer, the integral electromotive force due to a sudden increase or decrease of the induction through the coil displaces in the circuit a quantity of electricity Q=SBns

**R**, where SB is the increment or decrement of induction per square centimetre, s is the area of the coil, n the number of turns of wire, and**R**the resistance of the circuit.Let s be the area of a single turn of the standard coil, n the number of its turns, and

**r**the resistance of the circuit of which the coil forms part; and let S, N and**R**be the corresponding constants for a coil which is to be used in an experiment.The reversing key K having been put over to the left side, the short-circuit key S is suddenly opened; this inserts the resistance

**R**, which has been suitably adjusted before hand, and thus reduces the current and therefore the magnetizing force to a known value.In a similar manner, by giving different values to the resistance 4 F

**R**, any desired number of points**R**= between a and c in the curve can FIG.But though a formula of this type has no physical significance, and cannot be accepted as an equation to the actual curve of W and B, it is, nevertheless, the case that by making the index e =1.6, and assigning a suitable value to

**r**t, a formula may be obtained giving an approximation to the truth which is sufficiently close for the ordinary purposes of electrical engineers, especially when the limiting value of B is neither very great nor very small.Since t horse-power= 746 watts, and

**r**ton = 2 240 lb, the factor for reducing horse-power per ton to watts per lb is 746/2240, or just 1/3.In the case supposed therefore the total force per square centimetre is H2 F =2712-f-HI+B ?

**r**(4 7r I +H)2 8?**r**B2 =87r.The play of the beam is limited by a stop S and a screw

**R**, the latter being so adjusted that when the end Y of the beam is held down the two air-gaps are of equal width.The whole of the rod will therefore be subject to a compressive longitudinal stress P, the associated contraction

**R**, expressed as a fraction of the original length, being**R**= P/M = (B 2 -H2)/87-M, where M is Young's modulus.B

**r**(S) = strongly magnetized.The History of Johannes Hyrcanus is mentioned in

**r**Macc. xvi.Segesvar was founded by Saxon colonists at the end of the

**r**2th century; its Latin name was Castrum Sex.In gold, 19,053,861

**r**(say) Floating indebtedness (a/es current, bills, &c.) Total, not funded, approx.But after the beginning of the

**r**5th century Scholasticism was divorced from the spirit of the time, and it is useless to follow its history further.The Austro-Russian

**R**alliance was announced at the beginning of May, and before the end of the month the common plan of campaign had been arranged.The problem of finding the sum of

**r**terms is aided by graphic representation, which shows that the terms may be taken in pairs, working from the outside to the middle; the two cases of an odd number of terms and an even number of terms may be treated separately at first, and then combined by the ordinary method, viz.Having obtained

**R**, which is less than Q, we now repeat with Q and**R**the process that we adopted with P and Q; i.e.Suppose we find Q = sR+T, then we repeat the process with

**R**and T; and so on.Similarly the statements P+Q -

**R**- S = T and P+ Q -**R**= T+ S are the same.Now suppose that the formula (2) has been established for every power of A+a up to the (n-i)th inclusive, so that (ii_ I) = (n- I) (

**r**), (y I) = (n -1) (**r**_ l).This decreases as

**r**increases; its value ranging from na/A to al(nA).Some writers, for instance, use the symbol n, in place, in some cases, of n (

**r**), and, in other cases, of n (**r**).It is convenient to retain x, to denote x

**r**/**r**!, so that we have the consistent notation xr =x**r**/**r**!, n (**r**) =n(**r**)/**r**!, n[**r**] =n[**r**]/**r**!.If

**r**is greater than m or n (though of course not greater than m+n), some of the terms in (22) and (23) will be zero.This is sometimes called the number of homogeneous products of

**r**dimensions formed out of n letters; i.e.Suppose that there are a number of arrangements of

**r**terms or elements, the first of which a is always either A or not-A, the second b is B or not-B, the third c is C or not-C, and so on.Then, since nr rl is also a rational integral function of n of degree

**r**, we can find a coefficient c**r**, not containing n, and such as to make N-c**r**nr ri contain no power of n higher than n**r**- 1.Every unit of the rth species which does not vanish is the product of

**r**different units of the first species; two such units are independent unless they are permutations of the same set of primary units e i, in which case they are equal or opposite according to the usual rule employed in determinants.If E is any extensive unit, there is one other unit E', and only one, such that the (progressive) product EE' =-

**r**.The method of solving equations geometrically was considerably developed by Omar Khayyam of Khorassan, who flourished in the 1

**r**th century.We have seen that the problem before us is independent of the law of the secondary wave as regards obliquity; but the result of the integration necessarily involves the law of the intensity and phase of a secondary wave as a function of

**r**, the distance from the origin.For the aggregate effect of the secondary waves is the half of that of the first Fresnel zone, and it is the central element only of that zone for which the distance to be travelled is equal to

**r**.In order to obtain the effect of the primary wave, as, retarded by traversing the distance

**r**, viz.When the primary wave is plane, the area of the first Fresnel zone is 7rXr, and, since the secondary waves vary as

**r**1, the intensity is independent of**r**, as of course it should be.Since the distance to be travelled by the secondary waves is still

**r**, we see how the effect of the first zone, and therefore of the whole series is proportional to al(a+**r**).Thus in the case of the circular disk, equidistant (

**r**) from the source of light and from the screen upon which the shadow is observed, the width of the first exterior zone is given by = X(2r)/4(2x), 2x being the diameter of the disk.The amplitude of the light at any point in the axis, when plane waves are incident perpendicularly upon an annular aperture, is, as above, cos k(at-

**r**1)-cos k(at-**r**2) =2 sin kat sin k(r1-r2), r2,**r**i being the distances of the outer and inner boundaries from the point in question.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.Trans., 1834) in his original investigation of the diffraction of a circular object-glass, and readily obtained from (6), is z z 3 25 27 J1(z) = 2 2 2.4 + 2 2.4 2.6 2 2.4 2.6 2.8 + When z is great, we may employ the semi-convergent series Ji(s) = A/ (7, .- z)sin (z-17r) 1+3 8 1 ' 6 (z) 2 3.5.7.9.1.3.5 5 () 3 1 3.5.7.1 1 3 cos(z - ?

**r**) 8 ' z (z) 3.5.7.9.11.1.3.5.7 1 5 + 8.16.24.32.40 (zThe value of C for an annular aperture of radius

**r**and width dr is thus dC =271-Jo(Pp)pdp, (12).In these expressions we are to replace p by ks/f, or rather, since the diffraction pattern is symmetrical, by kr/f, where

**r**is the distance of any point in the focal plane from the centre of the system.We will now investigate the total illumination distributed over the area of the circle of radius

**r**.If

**r**, or z, be infinite, Jo(z), J 1 (z) vanish, and the whole illumination is expressed by 71-**R**2, in accordance with the general principle.In any case the proportion of the whole illumination to be found outside the circle of radius

**r**is given by J02(z)+J12(z).If 2R be the diameter of the objectglass and D the distance of the object, the angle subtended by AP is E/D, and the angular resolving power is given by X/2 D sin a = X/2

**R**(3) This method of derivation (substantially due to Helmholtz) makes it obvious that there is no essential difference of principle between the two cases, although the results are conveniently stated in different forms. In the case of the telescope we have to deal with a linear measure of aperture and an angular limit of resolution, whereas in the case of the microscope the limit of resolution is linear, and it is expressed in terms of angular aperture.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.E is then the co-ordinate relatively to 0 of any focal point 0' for which the retardation is

**R**; and the required result is obtained by simply integrating (5) with respect to from - cc to +oo.Then the displacement at 0 will take place in a direction perpendicular to 0 1 0, and lying in the plane Z0 1 0; and, if 1' be the displacement at 0, reckoned positive in the direction nearest to that in which the incident vibrations are reckoned positive, = 4?y (1 +cos 0) sin 4 f' (bt -

**r**).For a disturbing force of given integral magnitude it is seen to be everywhere about an axis perpendicular to

**r**and the direction of the force, and in magnitude dependent only upon the angle (43) between these two directions and upon the distance (**r**).This displacement, which we may denote by; is in the plane containing z and

**r**, and perpendicular to the latter.By all real estate deeds the sale of intoxicating liquors is for ever prohibited in the city; and an act of the state legislature in 1909 prohibited the sale of intoxicating liquor within

**r**z m.Moreover, it is very doubtful whether the word

**r**y ?c can be translated " Director."All Gerbert's dreams for the advancement of church and empire were cut short by the death of Otto III., on the 4th of February 1002; and this event was followed a year later by the death of the pope himself, which took place on the

**r**2th of May 1003.At the various churches such elementary schools as existed were to be found, but they did not profess to teach more than a smattering of the three "

**R**'s " and the principles of Christianity.A number of British subjects resident in Comman- the Transvaal, in spite of their having no political status, were commandeered to suppress a native

**r**i s i ng.But the flank attack became entangled in mass in a loop of the river and suffered heavily, and two batteries that formed part of the frontal attack came into action within a few hundred yards of unsuspected Boer trenches, with the result that ten guns were lost, as well as in all some

**r**roo men.Buller's operations, too, had cost at Colenso

**r**roo men, at Spion Kop**r**700, at Vaalkrantz 400, and now in the last long-drawn effort 16 oo more - over s000 in all.Then the deviation experienced by the ray at A is i -

**r**.The total deviation of the ray is consequently given by D =2(i -

**r**) +7r - 2r.Similarly it may be shown that each internal reflection introduces a supplementary deviation of 7r - 2r; hence, if the ray be reflected n times, the total deviation will be D =2(i -

**r**) +n (7r - 2r) .Taking the refractive index of water for the red rays as 0;, and for the violet rays as 1

**r**, we can calculate the following values for the minimum deviations corresponding to certain assigned values of n.Among the works which he translated into Syriac and of which his versions survive are treatises of Aristotle, Porphyry and Galen, 3 the Ars grammatica of Dionysius Thrax, the works of Dionysius the Areopagite, and possibly two or three treatises of Plutarch.4 His own original works are less important, but include a " treatise on logic, addressed to Theodore (of Merv), which is unfortunately imperfect, a tract on negation and affirmation; a treatise, likewise addressed to Theodore, On the Causes of the Universe, according to the Views of Aristotle, showing how it is a Circle; a tract On Genus, Species and Individuality; and a third tract addressed to Theodore, On the Action and Influence of the Moon, explanatory and illustrative of Galen's IIEpi rcptaiµwv

**r**t µepwv, bk.He became in 1005 the first abbot of Eynsham or Ensham, near Oxford, another foundation of ZEthelma

**r**'s.In ordinary life it was generally pulled up through the girdle and formed a KC)

**R**?ros (Greek Art, fig.The Kauo

**r**ia, or Macedonian hat, seems to have been similar to this.Sainte-Beuve calls Terence the bond of union between Roman urbanity and the Atticism of the Greeks, and adds that it was in the

**r**7th century, when French literature was most truly Attic, that he was most appreciated.Sigismondo,

**r**2 m.The quelling of the insurrection of the

**r**5th of May was his last successful act.He reversed the Hippocratic maxim "art is long," promising his scholars to teach them the whole of medicine in six months, and had inscribed upon his tomb iaTpovLKc, 7

**r**, as being superior to all living and bygone physicians.But, without discussing the general philosophical position or historical importance of Bacon, it may safely be said that his direct influence can be little traced in medical writings of the first half of the

**r**7th century.The Turks were in strong force in that quarter, and, as the hours passed and the defenders (3rd and

**r**ith Divs.) massed, the situation became such as to render any French advance out of the question; indeed, but for the fire of the warships the troops who had landed could barely have maintained themselves.Edward Dillon (Glass, 1902) has very properly laid stress on the importance of the enamelled Saracenic glass of the r3th, 14th and

**r**5th centuries, pointing out that, whereas the Romans and Byzantine Greeks made some crude and ineffectual experiments in enamelling, it was under Saracenic influence that the processes of enamelling and gilding on glass vessels were perfected.In the edition of 158

**r**of the De re metallica by Georg Agricola, there is a woodcut showing the interior of a German glass factory, and glass vessels both finished and unfinished.Let P, Q denote the normal thrust across the sides bc, ca, and

**R**the normal thrust across the base ab.Then, since these three forces maintain equilibrium, and

**R**makes equal angles with P and Q, therefore P and Q must be equal.It is used to determine the density of a body experimentally; for if W is the weight of a body weighed in a balance in air (strictly in vacuo), and if W' is the weight required to balance when the body is suspended in water, then the upward thrust of the liquid (I) (2) "F

**r**an Minim ' 'i n or weight of liquid displaced is W-W, so that the specific gravity (S.G.), defined as the ratio of the weight of a body to the weight of an equal volume of water, is W/(W-W').These equations can be made to represent the state of convective equilibrium of the atmosphere, depending on the gas-equation p = pk =RA (6) where 0 denotes the absolute temperature; and then d9 d p

**R**dz - dz (p) n+ 1' so that the temperature-gradient deldz is constant, as in convective equilibrium in (I I).Thus if the plane is normal to Or, the resultant thrust

**R**=f fpdxdy, (**r**) and the co-ordinates x, y of the C.P. are given by xR = f f xpdxdy, yR = f f ypdxdy.For instance, in a uniplanar flow, radially inward towards 0, the flow across any circle of radius

**r**being the same and denoted by 27rm, the velocity must be mfr, and 0=m log**r**,, y=m0, +4,i =m log re ie, w=m log z.If other vortices are present, any one may be supposed to move with the velocity due to the others, the resultant stream function being = gy m log

**r**=log IIrm; (9) the path of a vortex is obtained by equating the value of 1P at the vortex to a constant, omitting the rm of the vortex itself.For example, a pair of equal opposite vortices, moving on a line parallel to a plane boundary, will have a corresponding pair of images, forming a rectangle of vortices, and the path of a vortex will be the Cotes' spiral

**r**sin 20 = 2a, or x-2+y-2=a-2; (io) this is therefore the path of a single vortex in a right-angled corner; and generally.If the liquid is stirred up by the rotation

**R**of a cylindrical body, d4lds = normal velocity reversed dy = - Rx- Ry ds (5) ds 4' + 2**R**(x2 + y2) = Y, (6) a constant over the boundary; and 4,' is the current-function of the relative motion past the cylinder, but now V 2 4,'+2R =o, (7) throughout the liquid.Consider the motion given by w=U(z+a2/z), (I) 4,=U(

**r**+-**r**) cos 0= U + a1x, so that (2) = U (**r**-)sin 0= U(i -¢) y.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).Over a concentric cylinder, external or internal, of radius

**r**=b, 4,'=4,+ Uly =[U I - + Ui]y, (4) and 4" is zero if U 1 /U = (a 2 - b2)/b 2; (5) so that the cylinder may swim for an instant in the liquid without distortion, with this velocity Ui; and w in (I) will give the liquid motion in the interspace between the fixed cylinder**r**=a and the concentric cylinder**r**=b, moving with velocity U1.Consequently the inertia to overcome in moving the cylinder

**r**=b, solid or liquid, is its own inertia, increased by the inertia of liquid (a2+b2)/(a2,..b2) times the volume of the cylinder**r**=b; this total inertia is called the effective inertia of the cylinder**r**=b, at the instant the two cylinders are concentric.When the cylinder

**r**=a is moved with velocity U and**r**=b with velocity U 1 along Ox, = U b e - a,1**r**+0 cos 0 - U ib2 - 2 a, (**r**+Q 2 ') cos 0, = - U be a2 a2 (b 2 -**r**) sin 0 - Uib2 b1)a, (**r**- ¢2 sin 0; b and similarly, with velocity components V and V 1 along Oy a 2 b2 ?= Vb,_a,(**r**+**r**) sin g -Vi b, b2 a, (**r**+ 2) sin 0, (17) = V b, a2 a, (b2**r**) cos 0+Vi b, b, a, (**r**- ¢ 2) cos h; (18) and then for the resultant motion z 2zz w= (U 2 + V2)b2a a2U+Vi +b a b a2 U z Vi -(U12+V12) b2 z a2b2 Ui +VIi b 2 - a 2 U1 +Vii b 2 - a 2 z The resultant impulse of the liquid on the cylinder is given by the component, over**r**=a (§ 36), X =f p4 cos 0.ad0 =7rpa 2 (U b z 2 + a 2 Uib.2bz a2); (20) and over**r**=b Xi= fp?The expression for w in (i) § 29 may be increased by the addition of the term im log z =-m0 + im log

**r**, (1) representing vortex motion circulating round the annulus of liquid.Taking two planes x = =b, and considering the increase of momentum in the liquid between them, due to the entry and exit of liquid momentum, the increase across dy in the direction Oy, due to elements at P and P' at opposite ends of the diameter PP', is pdy (U - Ua 2 r2 cos 20 +mr i sin 0) (Ua 2

**r**2 sin 2 0+mr 1 cos 0) + pdy (- U+Ua 2**r**2 cos 2 0 +mr1 sin 0) (Ua 2**r**2 sin 2 0 -mr 1 cos 0) =2pdymUr '(cos 0 -a 2**r**2 cos 30), (8) and with b tan**r**=b sec this is 2pmUdo(i -a 2 b2 cos 30 cos 0), (9) and integrating between the limits 0 = 27r, the resultant, as before, is 27rpmU.For the liquid filling the interior of a rotating elliptic cylinder of cross section x2/a2+y2/b2 = 1, /(4) = m l (x 2 / a2 - - y2 /b 2) (5) with V21G1' =-2R =-2 m 1 (I / a2 + 21b2), 214 = m l (x2 / a2 + y2 / b2) - IR(x2+y2) = I

**R**(x2 - y2) (a 2 - b2)/(a2+b2), cp 1 = Rxy (a 2 - b2)/(a2 +b2), w1 = cb1 +% Pli = - IiR(x +yi)2(a2b2)/(a2+b2).An angular velocity

**R**, which gives components - Ry, Ix of velocity to a body, can be resolved into two shearing velocities, -**R**parallel to Ox, and**R**parallel to Oy; and then ik is resolved into 4'1+1'2, such that 4/ 1 -**R**-Rx 2 and 1//2+IRy2 is constant over the boundary.The polar equation of the cross-section being rI cos 19 =al, or

**r**+ x = 2a, (3) the conditions are satisfied by = Ur sin g -2Uairi sin IB = 2Uri sin 10(14 cos 18a'), (4) 1J/ =2Uairi sin IO = -U1/ [2a(**r**-x)], (5) w =-2Uaiz1, (6) and the resistance of the liquid is 2lrpaV2/2g.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,, ?For instance, with n = I in equation (9), the relative stream function is obtained for a sphere of radius a, by making it, y' =1y+2Uy 2 = 2U(

**r**2 -a 3 /**r**) sin?The components of velocity of the moving origin are denoted by U, V, W, and the components of angular velocity of the frame of reference by P, Q,

**R**; and then if u, v, w denote the components of fluid velocity in space, and u', v', w' the components relative to the axes at a point (x, y, z) fixed to the frame of reference, we have u =U +u' - yR +zQ, v =V +v -zP +xR, w=W +w -xQ +yP.Thus, for example, with = 4Uy 2 (

**r**2 a 2 -I), r2 = x2 +y 2, (13) for the space inside the sphere**r**=a, compared with the value of, i' in § 34 (13) for the space outside, there is no discontinuity of the velocity in crossing the surface.Between two concentric spheres, with a 2 +A =

**r**2, a2+A1=a12, A=B =C =a3/3r3, a 3 a 3 a3 _ a3 Cb _1U x**r**3 a13 Y'=2 Uy2 r3 3 a13 .The method of electrical images will enable the stream function, )' to be inferred from a distribution of doublets, finite in number when the surface is composed of two spheres intersecting at an angle 7r/m, where m is an integer (

**R**.Thus for m =2, the spheres are orthogonal, and it can be verified that a13 a2 3 aY3 i f /' = ZU (I - 13 - 7.2 3 + 3) ' (8) where a l, a2, a =a l a 2 /J (a 1 2 +a 2 2) is the radius of the spheres and their circle of intersection, and

**r**1,**r**2,**r**the distances of a point from their centres.Thus if T is expressed as a quadratic function of U, V, W, P, Q,

**R**, the components of momentum corresponding are dT dT dT (I) = dU + x2=dV, x3 =dW, dT dT dT Yi dp' dQ' y3=dR; but when it is expressed as a quadratic function of xi, 'x2, x3, yi, Y2, Y3, U = d, V= dx, ' w= ax dT Q_ dT dT dy 1 dy2 dy The second system of expression was chosen by Clebsch and adopted by Halphen in his Fonctions elliptiques; and thence the dynamical equations follow X = dt x2 dy +x3 d Y = ..., Z ..., (3) = dt1 -y2?y - '2dx3+x3 ' M =..I +W a W a), ' (k) 4 (I I) I+ w-

**R**For a shot in air the ratio W'/W is so small that the square may be neglected, and formula (II) can be replaced for practical purpose in artillery by tan26= n2 = W i (0 - a) (k ð)7()4, (12) if then we can calculate /3, a, or (3-a for the external shape of the shot, this equation will give the value of 6 and n required for stability of flight in the air.By act of Congress, approved in April 1904, the establishment of chaplains was fixed at 57 (15 with the rank of major), 12 for the artillery corps and

**r**each for the cavalry and infantry regiments.In the first Arabic and Ethiopic versions it is called

**r**Ezra; in some Latin MSS.Origen, Ambrosiaster, and Euthalius ascribe to it

**r**Cor.The uterus (X in figure C) begins in all cases at the shell gland (c, d) and may exhibit a swelling (

**R**S) for the retention of the spermatozoa..C, invaginated head of Cysticercus cellulosae, showing the bent neck and receptacle

**r**; X 30.Two of them,

**r**o to r2 ft.On his death in 1897 his nephew Abdul-Aziz, son of the murdered amir Matab, succeeded; during his reign a new element has been introduced into Nejd politics by the rising importance of Kuwet (Koweit) and the attempts

**R**t g P () P history.If titanic oxide be fused with excess of alkaline carbonate a titanate,

**R**2 T103, is formed.Hofmann), an alcoholic solution of stannous chloride (containing hydrochloric acid) (

**R**.The fame of this Belad-el-Jerid, or "Country of the Date Palms," was so exaggerated during the

**r**7th and 18th centuries that the European geographers extended the designation from this small area in the south of Tunisia to cover much of inner Africa.The Jethro Coffin House was built in 1686, according to tradition; the Old North Vestry, the first Congregational meeting-house, built in

**r**7**r****r**, was moved in 1767, and again in 1834 to its present site on Beacon Hill.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.His preachings attracted slight attention there, no one - as he later remarked -

**R**being a prophet in his own land.Pop.(

**r**890) 8756; (1900) 9654, of whom 1136 were foreign-born; (1906 estimate) 11,194.Forests cover nearly

**r**z million acres, yielding valuable timber (teak, sandalwood, &c.), and affording grazing-ground for cattle.Sir Robert Peel became

**r**i me minister, and made the member for Newark p vice-president of the Board of Trade.Stefano is another Romanesque church, probably of the

**r**rth century.The early palaces of Verona, before its conquest by Venice, were of noble and simple design, mostly built of fine red brick, with an inner court, surrounded on the ground floor by open arches like a cloister, as, for example, the Palazzo della Ragione, an assize court, begun in the

**r**2th century.A military mutiny at Rastatt on the

**r****r**th of May showed that the army sympathized with the revolution, which was proclaimed two days later at Offenburg amid tumultuous scenes.Armagh for about 2

**r**m., joining the Bann at Whitecoat.The county and the city were named in honour of Edward Dickinson Baker (1811-1861), a political leader, orator and soldier, who was born in London, England, was taken to the United States in 1815, was a representative in Congress from Illinois in 1845-1846and 1849-1851, served in the Mexican War as a colonel (1846-1847), became a prominent lawyer in California and later in Oregon, was a Republican member of the United States Senate in 1860-1861 and was killed at Ball's Bluff, Virginia, on the 21st of October in

**r**861, while serving as a colonel in the Federal army.The calcium salts distilled with calcium formate yield aldehydes

**r**distilled with soda-lime, ketones result.Arcadia, on the other hand, in the heart of Peloponnese, retained till a late date a quite different dialect, akin to the ancient dialect of Cyprus, and more remotely to Aeolic. This distribution makes it clear (

**r**) that the Doric dialects of Peloponnese represent a superstratum, more recent than the speech of Arcadia; (2) that Laconia and its colonies preserve features alike, -n and -w which are common to southern Doric and Aeolic; (3) that those parts of " Dorian " Greece in which tradition makes the pre-Dorian population " Ionic," and in which the political structure shows that the conquered were less completely subjugated, exhibit the Ionic -a and -ov; (4) that as we go north, similar though more barbaric dialects extend far up the western side of central-northern Greece, and survive also locally in the highlands of south Thessaly; (5) that east of the watershed Aeolic has prevailed over the area which has legends of a Boeotian and Thessalian migration, and replaces Doric in the northern Doris.The quantity of electricity which must be given to the sphere to raise it to unit potential is therefore

**R**electrostatic units.Since the potential of a small charge of electricity dQ at a distance

**r**is equal to dQ/**r**, and since the potential of all parts of a conductor is the same in those cases in which the distribution of surface density of electrification is uniform or symmetrical with respect to some point or axis in the conductor, we can calculate the potential by simply summing up terms like rdS/**r**, where dS is an element of surface, o- the surface density of electricity on it, and**r**the distance from the symmetrical centre.Thus the distribution of electricity on a sphere in free space must be uniform, and all parts of the charge are at an equal distance

**R**from the centre.Let

**R**1 be the radius of the inner sphere, R2 the inside radius of the outer sphere, and R2 the outside radius of the outer spherical shell.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).**R**- A, Accordingly var where**R**is the distance of the point in the interspace from the axis, and A is a constant.If then the outer cylinder be at zero potential the potential V of the inner one is V =A log (

**R**2 /**R**1), and its capacity C =1/2 log R2/R1.Let a solid circular sectioned cylinder of radius

**R**1 be enclosed in a coaxial tube of inner radius R2.The two condensers to be compared are connected in the branches of a Wheatstone's Bridge and the other two arms

**R**deter- completed with variable resistance boxes.The electric force due to a point-charge q at a distance

**r**is defined to be q/**r**2, and the total flux or induction through the sphere of radius**r**is therefore 41rq.Applying the above equation to a gas obeying the law pv=RT, for which the work done in isothermal expansion from a volume i to a volume

**r**is W=RT loger, whence dW=**R**log e rdt, he deduced the expression for the heat absorbed by a gas in isothermal expansion H=**R**log er/F'(t).The supernatant liquid is led into settling tanks, where a further amount of "gold is deposited,

**r**and is then filtered through sawdust or sand, the sawdust being afterwards burnt and the gold separated from the ashes and the sand treated in the chloridizing vat.But even here it was impossible that an open rupture Miltiades, 7rEpi 7rpoifr,

**r**At the same time as Miltiades, if not earlier, Apollinaris of Hierapolis also wrote against the Montanists.He inserts " one " in clause

**r**and 2.Doubtless the framer of Jude

**r**would have preferred the aegis of " James the Lord's brother," if this, like that of Paul, had not been already appropriated.Thus, about noon on the

**r**6th he reached the high ground between St Privat and Amanvillers, and still without instructions he determined to direct his corps on Bruville and Doncourt, whence he could judge from the drift of the smokeclouds whether he could fall on the Prussian left.By this means the latter, who were to make the main attack, were brought opposite a portion of the Canal du Nord, which was dry along a front of

**r**a miles.None of them, in point of fact, has held its ground, and even his proposal to denote unknown quantities by the vowels A, E, I, 0, u, Y - the consonants B, c, &c., being reserved for general known quantities - has not been taken up. In this denotation he followed, perhaps, some older contemporaries, as Ramus, who designated the points in geometrical figures by vowels, making use of consonants,

**R**, S, T, &c., only when these were exhausted.At the opening of the congress which assembled in that city on the

**r**5th February 1819 he submitted an elaborate exposition of his views on government, and concluded by surrendering his authority into the hands of congress.The average size of farms, as in the other states, has declined, falling from 124.6 acres in 1880 to i io

**r**acres in 1900.The slides are kept firmly down to their bearings by the rollers

**r**,**r**,**r**,**r**, attached to axes which are, in the middle, very strong springs.The depression is distinguished according to form and slope as (

**r**) a basin when of a roughly round outline, (2) a trough when wide and elongated, or (3) a trench when narrow and elongated lying along the edge of a continent.According to the investigations of Svante Arrhenius the osmotic pressure in atmospheres may be obtained by simply multiplying the temp rature of freezing (

**r**) by the factor -12.08, and it varies with temperature (t) according to the law which holds good for gaseous pressure.In the tropical and subtropical belts of the Atlantic and Indian Oceans south of the equator the salinity diminishes rapidly from the surface downwards, and at 500 fathoms reaches a minimum of 34.3 or 34.4 p e

**r**mille; after that it increases again to 800 fathoms, where it is almost 34.7 or 34.8, and this salinity holds good to the bottom, even to the greatest depths, as was first shown by the " Gauss " and afterwards by the " Planet " between Durban and Ceylon.The cathedral has a fine polygonal apse of the

**r**6th century.The first indication is a dull hollow sound heard when treading on the pavement or floor, probably occasioned

**r**FIG.In the working of thick seams inclined at a high angle, such as those in the south of France, and in the lignite mines of Styria and Bohemia, the method of working in horizontal slices, about i 2 or

**r**5 ft.In a large colliery where the shafts are situated near the centre of the field, and the workings extend on all sides, both to the dip and rise, the drawing roads for the coal may be of three different kinds - (

**r**) levels driven at right angles to the dip, suitable for horse roads, (2) rise ways, known as jinny roads, jig-brows, or up-brows, which, when of sufficient slope, may be used as self-acting planes, i.e.A road maybe used as a self-acting or gravitating incline when the gradient is

**r**in 30 or steeper, in which case the train is lowered by a rope passing over a pulley or brake drum at the upper end, the return empty train being attached to the opposite end of the rope and hauled up by the descending load.The different elements making up the drawing arrangements of a colliery are - (

**r**) the cage, (2) the shaft or pit fittings, (3) the drawing-rope, (4) the engine and (5) the surface arrangements.He was appointed secretary of the Labour party in 1900 and held the position for

**r****r**years; and editor of the " Socialist Library " in 1905.The external forces holding the brake from turning are W, distant

**R**from the axis, and the reaction, W 1 say, of the lever against the fixed pin P, distant R1 from the axis.Both these forces usually act at the same radius

**R**, the distance from the axis to the centre line of the rope, in which case the torque T is (W-p)**R**, and consequently the brake horse-power is (W - p)RX21rN, When µ 33,000 changes the weight W rises or falls against the action of the spring balance until a stable condition of running is obtained.This device consists of a roller of radius

**r**, pressed into contact with a disk.The block A carries the disk D, B carries the roller

**R**and counting gear.If a force Q acting at

**R**maintains equilibrium, QR/4 = (P - p)**r**=T.It is to be noticed that each number is the sum of the numbers immediately 35 above and to the left of it; and 35 that the numbers along a line, termed a base, which cuts off an equal number of units along the top row and column are the co efficients in the binomial expansion of (I+x)

**r**- 1, where**r**represents the number of units cut off.If the system is supposed to obey the conservation of energy and to move solely under its own internal forces, the changes in the co-ordinates and momenta can be found from the Hamiltonian equations aE aE qr = 49 - 1 57., gr where q

**r**denotes dg**r**ldt, &c., and E is the total energy expressed as a function of pi, qi,.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.T =273, we obtain

**R**=1.35 X Io -16 and this enables us to determine the mean velocities produced by heat motion in molecules of any given mass.We obtain Cv = z (n +3)

**R**/J m.Henceforth Logrono became the home of the most prominent of the Spanish political generals of the

**r**9th century.The crystals are orthorhombic, with angles similar to those of marcasite; they are often prismatic in habit, and the prism M is usually terminated by the deeply striated faces of an obtuse dome

**r**.The curse of Ernulphus or Arnulphus of Rochester (c.

**r**loo), often quoted by students of English literature, is a very fair specimen of that class of composition.Even before the beginning of the agitation led by Ronge, another movement fundamentally distinct, though in some respects similar, had been originated at Schneiderriihl, Posen, under the guidance of Johann Czerski (1813-1893), also a priest, who had come into collision with the church authorities on the then much discussed question of mixed marriages, and also on that PRO

**r**.This may have been Amos's Gilgal and was almost certainly that of

**r**Mace.Revenue is chiefly derived from hut and poll taxes,

**R**customs, wharfage dues, game licences and land tax.He now became bishop of Autun, with a stipend of 22,000 livres, and was installed on the

**r**5th of March.He continued quietly to observe the course of events during the disastrous years

**r**8r 2-13; and even at the beginning of the Moscow campaign he summed up the situation in the words, "It is the beginning of the end."Stolp, mentioned in the

**r**1 th century, received town rights in 1273.In terms of a treaty concluded in 1867 for ten years, renewed in 1877 for a similar period, and continued in 1887 with the proviso that it should be terminable on two years' notice, the finances and the entire government of Waldeck-Pyrmont are managed by Prussia, the little country having found itself unable to support unassisted the military and other burdens involved by its share in the North German Confederation of 1867-187

**r**and subsequently as a constituent state of the German empire.Peter Lombard (c.

**r****r**50) added as a seventh that of ordination, and to this number the Latin Church adhered at the councils of Florence and Trent.After the Irish the leading foreign elements are Canadian English (18.7%), Canadian French (

**r**5.8%) and English (9.7%), these four constituting threefourths of the foreign population.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.It was found that projectiles fired from a rifled gun deviated laterally from the line of Sights for fire owing to the axial spin of the projectile, and that if the

**r**i fled spin were right-handed, as in the British service, the deviation was to the right.Its name is derived from the "Teat" or conduit which conveyed water from Horningsham, about

**r**m.Also Zeller, Socrates and the Socratic Schools; Dyeck, De Megaricorum doctrines (Bonn, 1827); Mallet, Histoire de l'ecole de Megare (Paris, 1845); Ritter, Ober die Philosophie der

**r**meg.But on the

**r**5th the critical nature of the situation dawned on them, and naturally on Blucher first, as his headquarters were nearer to the frontier than Wellington's, and Blucher had had previous experience of Napoleon's powers.Blucher wisely shifted his own headquarters to Sombreffe on the afternoon of the

**r**5th.During the night of the

**r**5th orders were sent for the divisions to move eastwards towards Nivelles, and at dawn the Reserve marched for Mt.But if the intelligence which the duke rightly relied on had come to hand on the

**r**5th, it cannot be doubted that he would have effected a more expeditious concentration on his inner flank.Then, keeping Lobau provisionally at Charleroi, Napoleon hastened to Fleurus, arriving about

**r****r**.He and his son-in-law, Jacob Milborne, were charged with treason for refusing to submit to Ingoldsby, were convicted, and on the

**r**6th of May 1691 were executed.The difficulties to which reference has been made in § i

**r**are largely due to the abstract nature of the process involved in the second of the above steps.If

**R**and S are the ends of a prismoid, A and B their areas, h the perpendicular distance between them, and C the area of a section by a plane parallel to**R**and S and midway between them, the volume of the prismoid is *h(A+4C+B).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.By drawing Ac and Ad parallel to BC and BD, so as to meet the plane through CD in c and d, and producing QP and RS to meet Ac and Ad in q and

**r**, we see that the area of Pqrs is (x/h - x 2 /h 2) X area of cCDd; this also is a quadratic function of x.The centroid of a hemisphere of radius

**R**, for instance, is the same as the centroid of particles of masses 0, 7rR 2, and 4.A -n- (64C1 - 20C2+C4) '

**R**C 1+9 (C 1 - C2) ?1(C l - C4).Combining this with the first equation, we obtain the values of P, Q,

**R**, ..