q

The existence of earth currents (q.

40Thus at Karasjok Simpson found for mean values: Temp. less than -20° - Io° to -5° Io° to 15° I + =0.18, I_=0.16 I + =0.36, I_=0.30 I + =0 '45, I_=0'43 Simpson found no clear influence of temperature on Q.

10Cicero and five others (amongst them the famous Q.

10Laschitzer wrote an introduction to Sir Teuerdank, Q.

11P q P Y?

11daftoi,me,,t48,Q

11Ann., 1890, 40, p. 56) employed an arrangement as follows: Four fine platinum or iron wires were joined in lozenge shape, and two sets of these R and S were connected up with two resistances P and Q to form a bridge with a galvanometer G and battery B.

111869 by Giovanni Lanza, with Visconti-Venosta at the foreign office and Q.

11evergreen oaks (Q.

11hex, Q.

11Q.

12Ballota, Q.

12In these islands, we find forests i or woods of oak (Quercus Robur and Q.

12However, when you have such adorable bags to choose from as the Blue Q Happy Camper Shopper, which is patterned with forest and ocean drawings, you might just want to take a chance the bag will work for you.

14It shows on the one hand the labialization of the original velar q(Volscian pis = Latin quis), and on the other hand it palatalizes the guttural c before a following i (Volscian facia=Latin faciat).

00In Britain and in most of its Continental habitats two varieties exist, regarded by many as distinct species: one, Q.

00pedunculata, has the acorns, generally two or more together, on long stalks, and the leaves nearly sessile; while in the other, Q.

00c d, Male flowers of Q.

00e, Female flowers of Q.

00- Q.

00The name of "durmast" oak, originally given to a dark-fruited variety of Q.

00The relative qualities of the two varieties have been the frequent subject of debate, the balance of practical testimony seeming to establish the superiority of Q.

00That obtained from the sessilefruited oak is richer in tannic acid than that yielded by Q.

00In the Saxon period the "mast" seems to have been regarded as the most valuable produce of an oak wood; nor was its use always confined to the support of the herds, for in time of dearth acorns were boiled and eaten by the poor as a substitute for bread both in England and France, as the sweeter produce of Q.

00The British oak grows well in the northern and middle states of America; and, from the superiority of the wood to that of Q.

00This is a fine species, having when young straighter branches than Q.

00The large sessile acorns are longer than those of Q.

00The Turkey oak in southern England grows twice as fast as Q.

00In North America, where the species of oak are very numerous, the most important member of the group is Q.

00The pin oak, sometimes called the "burr-oak," Q.

00The over-cup oak, Q.

00In the woods of Oregon, from the Columbia river southwards, an oak is found bearing some resemblance to the British oak in foliage and in its thick trunk and widely-spreading boughs, but the bark is white as in Q.

00alba; it is Q.

00The red oak, Q.

00A species nearly allied is the scarlet oak, Q.

00The trunk, though often of considerable size, yields but an indifferent wood, employed for similar purposes to that of Q.

00The wood is coarsely grained, as in all the red-oak group, but harder and more durable than that of Q.

00The cut-leaved oaks are represented in eastern Asia by several species, of which Q.

00Evergreen oaks with entire leaves are represented in North America by Q.

00virginiana, also known as Q.

00The evergreen oak of southern Europe is Q.

00The cork oak, Q.

00The valonia of commerce, one of the richest of tanning materials, is the acorn of Q.

00The allied Q.

00Q]].

00persica, or according to some Q.

00There is hardly one of Wagner's orchestral innovations which is not inseparably connected with his adaptation of music to the re q uirements of drama; and modern conductors, in treating Wagner's orchestration, as the normal standard by which all previous and contemporary music must be judged, are doing their best to found a tradition which in another fifty years will be exploded as thoroughly as the tradition of symphonic additional accompaniments is now exploded in the performances of Bach and Handel.

00joined between P and Q.

00One very great advantage in this method is that the instrument used between P and Q may be of any ordinary form, i.e.

00By a modification of the bridge method, applied with excellent results by Dr Muirhead to submarine work, condensers are substituted for a and b, one being also placed in the circuit between P and Q.

00The first of the annalists, the father of Roman history, as he has been called, was Q.

00BM- Within quite recent years, however, a special school q Y P has arisen with the main object of treating the processes of evolution quantitatively.

00He has been identified with the author of the four books of Rhetorica dedicated to a certain Q.

00Q, Three segments of a pitted vessel of Phanerogam.

00E, epidermis; q, phellogen; 1, cells, and ~1, the pheliogen of the lenticel; k, cortical parenchyma, containing chlorophyll.

00The new capital of Persis was Istakhr on the Pulwar, about q m.

00Several Roman nobles, among them Gnaeus Pompeius (Pompey the Great), Q.

00Palestrina) and then marched upon Rome, where again, just before his defeat of Marius, there had been a great massacre of his adherents, in which the learned jurist Q.

00q, Quadrate.

00c. 3), especially the senator Q.

00By her he had two sons, Anicius Manlius Severinus Boetius and Q.

00Fernandez Garcia (Q uaracchi, Florence, 1902).

00as St Petersburg and South Finland (Q.

00Between 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.

00In this war, which, owing to the prominence of the Marsian rebels is often known as the Marsic War, they fought bravely against odds under their leader Q.

00The first dictator is said to have been created in 501 B.C.; the last of the " administrative " dictators belongs to the year 216 B.C. It was an office that was incompatible both with the growing spirit of constitutionalism and with the greater security of the city; and the epoch of the Second Punic War was marked by experiments with the office, such as the election of Q.

00q`tal or Pal (" he killed "), which corresponds to Heb.

00The form q`tal illustrates one main peculiarity of Aramaic, as opposed to the other Semitic languages, viz.

00its paucity of vowels: for where Hebrew has two full vowels - a long and a short - in gatal, and Arabic has three short vowels in qatala, Aramaic has only one short vowel, the sound `` between q and t being merely a half vowel which is not indicated in Syriac writing.

00The simple active q`tal makes its passive ethq`tel; the intensive gattel makes.

00q`tal " he has killed," " he killed."

00q`tal wa, " he had killed," " he killed."

00His family belonged to the clan of the Achaemenidae - in the inscription on the pillars and columns of the palace of Pasargadae (Murghab) he says: "I am Cyrus the king, the Achaemenid" - the principal clan (cbprp'q) of the Persian tribe of the Pasargadae.

00(Lankester.) q, Intestine in transverse section.

00q, Renal organ (nephridium).

00q, Shell.

00Q, Sac containing nutritive mb, Mantle-skirt.

00C. Q.)

00After the subjugation of the Salluvii (Salyes) by the Romans in 123 B.C., having given shelter to their king Tutomotulus and refused to surrender him, the Allobroges were attacked and finally defeated (August 8, 121) at the junction of the Rhodanus and Isara by Q.

00The dates of the various parts of the existing ducal palace are indicated on the plan; the rebuilding was carried on in the following order, P, Q, R, S, T, U, V.

00Though Riley was especially interested in the bearings of insect life on agriculture and industry - economic entomology (q.

00q ?' ?'

00' °° p Q; i r ' Afayette A(l.

00The anomaly AFQ of Q at any moment is called the mean anomaly, and the angle QFP by which the true anomaly exceeds it at that moment is the equation of the centre.

00One of the chief objects of Saturninus's hatred was Q.

00Colonies were to be founded in Sicily, Achaea and Macedonia, on the purchase of which the " Tolosan gold," the temple treasures embezzled by Q.

00If triple bonds, q in number, occur also, and the energy of such a bond be Z, the equation for H becomes H = nE-+-mn -1-p(2X - Y) +q(3X - Z).

00Q --.

00'Eav J f9 J Q,cATE EKaUTOS vi.

00HECATO OF RHODES, Greek Stoic philosopher and disciple of Panaetius (Cicero, De q, ficiis, iii.

00q !,: FIG.

00q Y imam of Sana, necessitated the despatch of large and costly expeditions to Arabia, in which thousands of Turkish .troops have fallen in guerrilla warfare or through the inhospitable climate; in Albania disturbance became almost endemic, owing to the resistance offered by the intractable population to successive attempts of the central authorities to subject the country to regular taxation and the operation of the laws.

00sp," Q.

00Results (Willey), part iii., 1899; see also Q.

00Let x be the number of molecules which dissociate per second when the number of undissociated molecules in unit volume is unity, then in a dilute solution where the molecules do not interfere with each other, xp is the number when the concentration is p. Recombination can only occur when two ions meet, and since the frequency with which this will happen is, in dilute solution, proportional to the square of the ionic concentration, we shall get for the number of molecules re-formed in one second ye where q is the number of dissociated molecules in one cubic centimetre.

00Volusius Saturninus and Q.

00c, c', cardinal process; b', b', hinge-plate; s, dental sockets; 1, loop; q, crura; a, a', adductor impressions; c, accessory divaricator; b, peduncle muscles; ss, septum.

00A, ventral, B, dorsal valves; 1, loop; q, crura; ss, septum; c, cardinal process.

00The quantities a l a, a 2 Q ...

00in terms of x 1, x2, x3,ï¿½ï¿½ The inverse question is the expression of any monomial symmetric function by means of the power functions (r) = sr. Theorem of Reciprocity.-If ï¿½1 P2 "3 01 Q 2 7 3 Al A 2 A3 X m1 X m2 X m3 ...

00= ePlal, 1 + a i Q 2+ a 2 0 2 +...

00P y q +...

00All symmetric functions are expressible in terms of the quantities ap g in a rational integral form; from this property they are termed elementary functions; further they are said to be single-unitary since each part of the partition denoting ap q involves but a single unit.

00The number of partitions of a biweight pq into exactly i biparts is given (after Euler) by the coefficient of a, z xPy Q in the expansion of the generating function 1 - ax.

00We can verify the relations s 30 -a310 -3a 20 a 10 + a30, S 21 - 02100 01 -a 2C a 01 -0 11 0 10 021 The formula actually gives the expression of q) by means of separations of (10P01'), which is one of the partitions of (pq).

001 exp(Adlo + vdol) = (1+/oD10+ v Doi +..ï¿½+ VQ +.ï¿½.)f; now, since the introduction of the new quantities 1.1., v results in the addition to the function (plglp2g2p3g3...) of the new terms A PI Pg1 (p 2q2 p 3g3ï¿½ï¿½ï¿½) +/ AP2Pg2 (p 1 g 1P343 ...)+/ Z3vg3 (p l g i p 2 g 2 ...)+ ï¿½, we find DP141(plqip2q2p3q3ï¿½ï¿½ï¿½) = (p 2 q 2 p 3 q 3ï¿½ï¿½ï¿½), and thence D P141 D P242 D P343 ï¿½ï¿½.

00+1,q p l !gll p2!g2!

00Recalling the formulae above which connect s P4 and a m, we see that dP4 and Dp q are in co-relation with these quantities respectively, and may be said to be operations which correspond to the partitions (pq), (10 P 01 4) respectively.

00We may remark the particular result (-) p + p q!

00)- (p+4-1 (p - - q -1)!dpq+ ?l -) 1)!D'1 DT2 p!g!

00an_1 i a n, and in general a n-k a 2 is the symbol for Q k.

00d x the first evectant; and thence 4cxdi the second evectant; in fact the two evectants are to numerical factors pres, the cubic covariant Q, and the square of the original cubic.

00To prove that this system is complete we have to consider (f, o) 2, 04') 1, (f,Q) 1, (f,Q) 2, (f,Q) 3, 0,Q) 1, (o,Q)2, and each of these can be shown either to be zero or to be a rational integral function of f, 0 Q and R.

00The discriminant of f is equal to the discriminant of 0, and is therefore (0, 0') 2 = R; if it vanishes both f and 0 have two roots equal, 0 is a rational factor of f and Q is a perfect cube; the cube root being equal, to a numerical factor pres, to the square root of A.

00The Hessian in that case is a factor of f, and Q is the third power of u2,...

00For it is easy to establish] the formula (yx) 2 0 4 = 2f.4-2(f y 1) 2 connecting the Hessian with the quartic and its first and second polars; now a, a root of f, is also a root of Ox, and con se uentl the first polar 1 of of q y p f?

00retains the same value, however the suffixes be permuted, we shall obtain a i 7 2 ar a2 a33?Q"l 7r2 rr3 w hich in r a l sum of terms, such as w!

00The general form of perpetuant is (4 K 3 A 2"`) and the generating function 1-z2.1-z3.1-z4 In general when 0 is even and =20, the condition is a l a 2 ...U 24 II(v 1 +a 2)II(a l +a 2 +cr 3)...II(Q 1 +a 2 -}-...

00+aPx2, boxi +qb1 xi -1x2+q(q - 1) b 2 xPx2+...

00The General Term Of A Seminvariant Of Degree 0, 0 And Weight W Will Be A A A Appb°Ob°1B°2...B°4 _ 0 1 2 P 0 1 2 Q P Q P Q Where Ep S =0, Eas=0 And Esp, A Es,=W.

001111 The Number Of Such Terms Is The Number Of Partitions Of W Into 0 0 Parts, The Part Magnitudes, In The Two Portions, Being Limited Not To Exceed P And Q Respectively.

00Q).

00The Number Of Linearly Independent Seminvariants Of The Given Type Will Then Be Denoted By (W; 0, P; 0', Q) (W; 0, P; 0', Q); And Will Be Given By The Coefficient Of A E B E 'Z W In L Z 1 A.

001 Ze'; Which Preserves Its Expression When 0 And P And 0 And Q Are Separately Or Simultaneously Interchanged.

00Q 1 The Unreduced Generating Function Which Enumerates The Covariants Of Degrees 0, 0' In The Coefficients And Order E In The Variables.

00Here compounds of divalent lead have not yet been obtained; by acting with zinc ethide on lead chloride, lead tetraethide, Pb(C 2 IH Q) 4, is obtained, with the separation of metallic lead.

00Under the influence of the transient current, the galvanometer needle undergoes a momentary deflection, or " throw," which is proportional to Q, and therefore to 8B, and thus, if we know the deflection produced by the discharge through the galvanometer of a given quantity of electricity, we have the means of determining the value of 8B.

00If 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.

00(From Lankester, Q.

00VII, Usually considered to be the tergum of the genital somite, but suggested by Pocock to be that of the other [According to the system of numbering explained in the text, if VII is the tergum of the praegenital somite (as is probable) it should be labelled Prg without any number, and the somites VIII to XIII should be lettered 1 to 6, indicating that they are the six normal somites of the mesosoma; whilst XV to XVIII should be replaced by the numbers 7 to 12 - an additional suppressed segment (making up the typical six) being reckoned to the metasomatic fusion.] (From Lankester, Q.

00(After Lankester and Bourne, Q.

00- Arachnida in which, excluding from consideration the eye-bearing prosthomere, the somites are primarily (that is to say, in the common Q FIG.

00(After Pocock, Q.

00Appendages of 2nd pair folding in a horizontal plane; their basal segments n From Lankester, Q.

00Idem, "Limulus an Arachnid," Q.

00Embryology: - Balfour, " Development of the Araneina," Q.

00gevas, Bahia (S.Salvador) Barcellos rrado Contas Ilheos 0livenca Q ?f19H ostardas rJ°?

00His development of the equation x m +- px = q in an infinite series was extended by Leonhard Euler, and particularly by Joseph Louis Lagrange.

00For multiplication, for instance, we have the statement that, if P and Q are two quantities, containing respectively p and q of a particular unit, then p X Q = q X P; or the more abstract statement that p X q= q X p.

00It should be observed that, by analogy with the definition of a fraction, a P l q mean (al/q)P, not (aP)llq.

00(i.) To divide P by Q, we cut off from P successive portions each equal to Q, till we have a piece R left which is less than Q.

00(ii.) To continue the division we may take as our new unit a submultiple of Q, such as Q/r, where r is an integer, and repeat the process.

00Proceeding in this way, we may be able to express P= Q as the sum of a finite number of terms k+m/r+n/r 2 +..

00Having 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.

00we cut off from Q successive portions each equal to R.

00Suppose we find Q = sR+T, then we repeat the process with R and T; and so on.

00(iv.) If P and Q can be expressed in the forms pL and qL, where p and q are integers, R will be equal to (p-kq)L, which is both less than pL and less than qL.

00Hence u is the greatest common measure of p and q.

00is then an expression of the form a p b e c r d s, where p, q, r, s have the greatest possible values consistent with the condition that each of the given expressions shall be divisible by a p b e c r d s .

00is of the form a p b e c r d s, where p, q, r, s have the least possible values consistent with the condition that a P PC'd s shall be divisible by each of the given expressions.

00This may be written (P+ Q - R) +S = T; and this statement, by definition of the sign -, is the same as the statement that (P+Q - R) = T - S.

00Similarly the statements P+Q - R - S = T and P+ Q - R= T+ S are the same.

00Thus from the equation P+Q - R+S=T and the identity P+Q - R+S= P - R +S+Q we have the equation P - R +S+Q=T, which is the same statement as P - R +S=T - Q.

00Thus from P+Q - R+S=T we deduce P+(Q - R+S)=P+(T - P).

00Thus, if we have an equation P=Q, where P and Q are numbers involving fractions, we can clear of fractions, not by multiplying P and Q by a number m, but by applying the equal multiples P and Q to a number m as unit.

00The standard form is usually taken to be ax2+bx+c =0, from which we find, by transformation, (2 ax+b) 2 =b 2 - 4ac, 4 (}b 2 -4ac} -b and thence x = 2a (ii.) In an equation of the form Q=V, the expressions P, Q, U, V are usually numerical.

00Q V, or PV = UQ, as in ï¿½ 38 (vi.).

00Thus 2 x 2 - I - x +x-2 (x _ I) (x+2) is equal to x + 2 q, except when x=1.

00- An equation may involve a fraction of the form Q, where Q involves x.

00we can replace pr or -pr by (+p)r or (- p)r, subject to the conditions that (+p) (+q) = (-p) (- q) = (+pq), (+p) (-q) = (- p) (+ q) = (-pq), and that + (-s) means that s is to be subtracted.

00We therefore define algebraical division by means of algebraical multiplication, and say that, if P and M are multinomials, the statement " P/M = Q " means that Q is a multinomial such that MQ (or QM) and P are identical.

00The application of the method to the calculation of (I +x) n, when n= p/q, q being a positive integer and p a positive or negative integer, involves, as in the case where n is a negative integer, the separate consideration of the form of the coefficients b 1, b 2, ...

00The generating functions of the two series, mentioned above, for example, are (I +x)-' n and (I+x) P / Q.

00A quaternion is best defined as a symbol of the type q = Za s e s = aoeo + ales = ale, + a3e3, where eo, ...

00a 3 ordinary algebraic quantities, which ma S' g q ?

00may be called the co-ordinates of q.

00Thus e 1 e 2 = - e2ei, and if q, q are any two quaternions, qq is generally different from q'q.

00Putting q=a+,61+yj+bk, Hamilton calls a the scalar part of q, and denotes it by Sq; he also writes Vq for 01+yj+b ï¿½, which is called the vector part of q.

00Thus every quaternion may be written in the form q = Sq+Vq, where either Sq or Vq may separately vanish; so that ordinary algebraic quantities (or scalars, as we shall call them) and pure vectors may each be regarded as special cases of quaternions.

00The equations q'+x = q and y+q' = q are satisfied by the same quaternion, which is denoted by q - q'.

00On the other hand, the equations q'x = q and yq' = q have, in general, different solutions.

00It is the value of y which is generally denoted by q= q'; a special symbol for x is desirable, but has not been established.

00If we put qo= Sq' - Vq', then qo is called the conjugate of q', and the scalar q'qo = qoq' is called the norm of q' and written Nq'.

00We 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.

00Now as to the phase of the secondary wave, it might appear natural to suppose that it starts from any point Q with the phase of the primary wave, so that on arrival at P, it is retarded by the amount corresponding to QP. But a little consideration will prove that in that case the series of secondary waves could not reconstitute the primary wave.

00If the primary wave at 0 be cos kat, the effect of the secondary wave proceeding from the element dS at Q is dS 1 dS - p cos k(at - p+ 4 A) = - -- sin k(at - p).

00In the case of the circular aperture the distribution of light is of course symmetrical with respect to the focal point p=o, q=o; and C is a function of p and q only through 11 (p 2 -}-q 2).

00It 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.

00The limiting efficiency of the microscope is attained when the angular aperture amounts to 180°; and it is evident that a lateral displacement of the point under observation through -IX entails (at the old image) a phase-discrepancy B Q' of a whole period, one extreme ray FIG.

00Then, if Q be any radiant point and Q' its image (primary focus) in the spherical mirror AP, we have 1 1 2cos4) v l + u 'a ' ' where v 1 = AQ', u =AQ, a =OA, =angle of incidence QAO, equal to the angle of reflection Q'AO.

00But if we now suppose that Q lies on the circle u= a cos 0, the middle term vanishes, and we get, correct as far as w4, QP= (u+a sin 4) sin w) 1 ' 3 1 {- a sin2c?sin4w V 4u so that QP - u=asin0sinw -Ft asin¢tanOsin 4 w..

00A similar expression can be found for Q'P - Q"A; and thus, if Q' A =v, Q' AO = where v =a cos (0", we get - - -AQ' = a sin w (sin 4 -sink") - - 8a sin 4 w(sin cktan 4 + sin 'tan cl)').

00If "=4), the term of the first order vanishes, and the reduction of the difference of path via P and via A to a term of the fourth order proves not only that Q and Q' are conjugate foci, but also that the foci are exempt from the most important term in the aberration.

00A tie between the middle point of the rod OA and Q can be used if thought desirable.

004/2 I = Q Q.

00For a point Q outside the shadow the integration extends over more than half the primary wave.

00The position of Q corresponding to a given value of V, that is, to a band of given order, is by (19) BQ= aa b AD=V?

00With sufficient approximation we may regard BQ and b as rectangular co-ordinates of Q.

00He is probably identical with the Bestia who encouraged the Italians in their revolt, and went into exile (90) to avoid punishment under the law of Q.

003; Cicero, Ad Q.

00q.

00The prologues to the comedies were among the original sources of Suetonius; but he quotes or refers to the works of various grammarians and antiquaries - Porcius Licinus, Volcacius Sedigitus, Q.

00S.)/n==Authorities== - The two most ancient manuscripts of Lucretius, O and Q, are both at Leiden, one being a folio (oblongus) and the other a quarto (quadrates).

00It is not probable that the sweet-smelling gums and resins of the countries of the Indian Ocean began to be introduced into Greece before the 8th or 7th century B.C., and doubtless XiOavos or X q /3avw-rOs first became an article of extensive commerce only after the Mediterranean trade with the East had been opened up by the Egyptian king Psammetichus (c. 664-610 B.C.).

00' o P B Sentinel Q A Rutland /, 5 a ssage Paialankw e ?

00Let P, Q denote the normal thrust across the sides bc, ca, and R the normal thrust across the base ab.

00Then, since these three forces maintain equilibrium, and R makes equal angles with P and Q, therefore P and Q must be equal.

00But the faces bc, ca, over which P and Q act, are also equal, so that the pressure on each face is equal.

00The varying direction of the inclining couple Pc may be realized by swinging the weight P from a crane on the ship, in a circle of radius c. But if the weight P was lowered on the ship from a crane on shore, the vessel would sink bodily a distance P/wA if P was deposited over F; but deposited anywhere else, say over Q on the water-line area, the ship would turn about a line the antipolar of Q with respect to the confocal ellipse, parallel to FF', at a distance FK from F FK= (k2-hV/A)/FQ sin QFF' (2) through an angle 0 or a slope of one in m, given by P sin B= m wA FK - W'Ak 2V hV FQ sin QFF', (3) where k denotes the radius of gyration about FF' of the water-line area.

00I n a straight uniform current of fluid of density p, flowing with velocity q, the flow in units of mass per second across a plane area A, placed in the current with the normal of the plane making an angle 0 with the velocity, is oAq cos 0, the product of the density p, the area A, and q cos 0 the component velocity normal to the plane.

00Generally if S denotes any closed surface, fixed in the fluid, M the mass of the fluid inside it at any time t, and 0 the angle which the outward-drawn normal makes with the velocity q at that point, dM/dt = rate of increase of fluid inside the surface, (I) =flux across the surface into the interior _ - f f pq cos OdS, the integral equation of continuity.

00In plane motion (4) reduces to dH = 2q"= q /av q?

00In particular, for a jet issuing into the atmosphere, where p=P, q 2 /2g = h - z, (9) or the velocity of the jet is due to the head k-z of the still free surface above the orifice; this is Torricelli's theorem (1643), the foundation of the science of hydrodynamics.

00Similarly, the streaming velocity V reversed will give rise to a thrust 27rpmV in the direction xC. Now if the cylinder is released, and the components U and V are reversed so as to become the velocity of the cylinder with respect +m /a) 2 - U2 The components of the liquid velocity q, in the direction of the normal of the ellipse n and hyperbola t, are -mJi sh(n--a)cos(r-a),mJ2 ch(n-a) sin (E-a).

00(io) The velocity q is zero in a corner where the hyperbola a cuts the ellipse a; and round the ellipse a the velocity q reaches a maximum when the tangent has turned through a right angle, and then q _ (Ch 2a-C0s 2(3).

00The 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.

00+a2 522x - b2 + c2121y, P =S21+, Q = 522+ 7 ], R =S23-H".

00Uniplanar motion alone is so far amenable to analysis; the velocity function 4 and stream function 1G are given as conjugate functions of the coordinates x, y by w=f(z), where z= x +yi, w=4-Plg, and then dw dod,y az = dx + i ax - -u+vi; so that, with u = q cos B, v = q sin B, the function - Q dw u_vi=g22(u-}-vi) = Q(cos 8+i sin 8), gives f' as a vector representing the reciprocal of the velocity in direction and magnitude, in terms of some standard velocity Q.

00u - b), u =ae ?, (5) where u =a, a' at the edge A, A l.; u at a corner B; u=o across xx' where 4 = oo; and u = oo, 43-= co across the end J J' of the jet, bounded by the curved lines APJ, A'P'J', over which the skin velocity is Q.

00The stream lines xBAJ, xA'J' are given by = 0, m; so that if c denotes the ultimate breadth JJ' of the jet, where the velocity may be supposed uniform and equal to the skin velocity Q, m=Qc, c=m/Q.

00(b-a.0-a) (6) (Q) AI (a-a .0b) ch n2= ch log (Q) n cos 114+i sh log (9) re sin n9 = 2(r+ fi n) = b - a ' ju -a (7) a-a' l u-b nf2 = sh log (cos nO +1 ch log (" sin 110 =2(?"

002n u (a -b.b -a')' not requiring the integration of (II) and (12) If 0=a across the end J J' of the jet, where u = oo, q= Q, b-a' a-b ch 7/2,=cos na = I, , sh 162 = i sin na = i,, a - a a-a Then a-a'+(a+a) cos 2na-[a+a'+(a-a) cos 2najcos 2110 (a-a') sin' 2na X cos 211a - cos 2110 Along the wall AB, cos nO =o, sin n0= I, a> u> b, ch n2= i sh log (q) n= i?

00`ia a - a u-b sh nf2= i ch log (Q) n =i a-b ?

00m _ c Q du dO dt - rrqu 2r qu AB _ Q du L bq (u -a') +V (b -a')1,l (a -u)11/ndu) L 1,1 (a-a/),,1 (u-b), f u Along the wall Bx, cos n0 =I, sin n0 =o, b >u>o ch nSt = ch log () n=, , fb-a?, ?

00Ja - 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.

00xx' = Q.JJ' (31) JJ _ g o _ lb-a' la_I a-b a' 11n xx' Q L Va - a' b Va-a' b j ' (32) giving the contraction of the jet compared with the initial breadth of the stream.

005, I ch S2 = u a, sh C2= ' u (I) (I and along the jet APJ, oo > u=aerslc>a, sh S2=i sin 0 =iu=ie zrs/o, (2) PM sin 0 ds = f e ds = 1 = 1 sin 0, (3) cos 272a - cos 2n0 = 2Q - ?ib L a b2 s i n' 27ta u-b A (a- (u -a.u -b') sin 2110 - 2 a-a .u-b ?l (u -a.u -a') = s in 2na u-b 2n b) A (ab.ba') p l u -bJ (u -a.u -a') sh nS2=i sin 110=i then the radius sin 2170 (30) A', cos nO= i, sin n0=o, n 1 ' b-a' ch nS2= ch log (9) = Va -a' n shnS2= shlog (Q) q _ o> u>a'.

00Along the jet surface A'J', q = Q, b-a' ch nSl= cos 110= a-a la - b sh nft=i sin nO=i a'>u=a'erl"> -oo, giving the intrinsic equation.

00b a-b (7) cos = a, sin na = 1j a, nd along the free surface APJ, q =Q, 4) =o, u =e-.

00From A to B, a>u >b, 0=0, ch S2= ch log Q=cos a-i sin 2a a-b I sh S2= sh log Q= I (a u-b-a/) s i n a Q = (u-b) cos a-2(a-a') sin 2 a+1,/ (a-u.u- a')sin a (8) u-b ds _ ds d4 _ Q dw Q du - Q d 4) du q du (u-b) cos a-2(a- a') sin 2 a (a-u.0 - a') sin a (9) it j- -j' AB _f a(2b - a - a')(u-b)-2(a-b)(b-a')+2V (a - b.

00Trans., 1890); the solution is given by ch nS2=sn w, shnS2=i cn w (II) so that, round the boundary of the polygon, ik = K', sin n8 =o; and on the surface of the vortex 1P= o, q = Q, and cos n8=sn4p,nB= Zit -am sic, (12) the intrinsic equation of the curve.

00Beginning with a single body in liquid extending to infinity, and denoting by U, V, W, P, Q, R the components of linear and angular velocity with respect to axes fixed in the body, the velocity function takes the form = Ucb1+V42+W43+ P xi+Qx2+Rx3, (I) where the 0's and x's are functions of x, y, z depending on the shape of the body; interpreted dynamically, C -p0 represents the impulsive pressure required to stop the motion, or C +p4) to start it again from rest.

00Taking Ox along OS, the Stokes' function at P for the source S is p cos PSx, and of the source H and line sink OH is p(a/f) cos PHx and - (p/a) (PO - PH); so that = p (cos PSx+f cos PHx PO a PH), (q) and Ili = -p, a constant, over the surface of the sphere, so that there is no flow across.

00But supposing them determined for the motion of a body through a liquid, the kinetic energy T of the system, liquid and body, is expressible as a quadratic function of the components U, V, W, P, Q, R.

00Thus 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 =..

00Clebsch to take the form T= 2p(x12 +x22)+2p'x32 + q (xiyi +x2y2) +q'x3y3 +2r(y12+y22)+2r'y32 so that a fourth integral is given by dy 3 /dt = o, y = constant; dx3 (4 y) (q + y) _ (y y) dt - xl 'x2 xl Y Y x l 2 - 1, y2 () = (x12 +x22) (y12 + y22) = (X 1 2 + X 2) +y22)-(FG-x3y3)2 = (x 1 y32-G2)-(Gx3-Fy3) 2, in which 2 = F 2 -x3 2, x l y l +x2y2 = FG-x3y3, Y(y1 2 +y2 2) = T -p(x12 +x22) -p'x32 -2q(xiyi 'x2y2)- 2 q ' x = (p -p') x 2 + 2 (- q ') x 3 y 3+ m 1, (6) m1 = T 2 i y 3 2 (7) so that dt3) 2 =X3, (8) where X3 is a quartic function of x3, and thus t is given by an elliptic (8) (6) (I) integral of the first kind; and by inversion x 3 is in elliptic function of the time t.

00Now (x1 - x21) (y 1 +y21) = xl l +x2y2 + - (' r 1 2 - x2y1) = FG-x3y3+iV X3, yi+3 7 21_FG-x3y3+2V X3 xl+x21 X12 +X22 (x 1 +x 2 i) = - i{(q' - q)x3+r'y3]+irx3(y1+y21), = FG - x3y3 +ZJ X3 dt2log(x1+x22) - - (q g) x 3- r y3+rx3 F2x32 (12) d dl2 log V x1 ± x2 2 (q'-q)x3-(r'-r) y3FrFF2-x 2 3 ' (13) requiring the elliptic integral of the third kind; thence the expression of x1-f -x21 and yl-}-y21.

00Introducing Euler's angles 0, c15, x1= F sin 0 sin 0, x 2 =F sin 0 cos 0, xl+x 2 i =iF sin 0e_, x 3 = F cos 0; sin o t=P sin 4+Q cos 0, dT F sin 2 0d l - dy l + dy 2x = (qx1+ryi)xl +(qx2+ry2)x2 = q (x1 2 +x2 2) +r (xiyi +x2y2) = qF 2 sin 2 0-Fr (FG - x 3 y 3), (16) _Ft (FG _x 323 Frdx3 (17) F x3 X3 elliptic integrals of the third kind.

00(22) Y (F2 x2) Suppose x 3 -F is a repeated factor of X3, then y 3 = G, and X 3 = (x 3 -F)2 [P' _ P(X3+F)2+2' _ G(X +F) -G 2 ], (23) nd putting x3-F=y, (y) 2= 7'3'2- [41' r 1' F 2 -{-4 g r qFG - G2 +2 (2P'r 19F+9 r q G) y+ r y (24) o that the stability of this axial movement is secured if A = 4 P' r ?'F 2 + 4 Y q FG - G 2 (25) s negative, and then the axis makes r J l (-A)/7r nutations per second.

00(9) c 2 Ci If the shot is moving as if fired from a gun of calibre d inches, in which the rifling makes one turn in a pitch of n calibres or nd inches, so that the angle S of the rifling is given by tan S = ird/nd = 2 d p/u, (10) '°If a denotes the density of the metal, and if the shell has a cavity homothetic with the external ellipsoidal shape, a fraction f of the linear scale; then the volume of a round shot being sird 3, and sird 3 x of a shot x calibres long W =*ird 3 x(I -f 3)v, (20) 2 Wki 2= 61rd 3 xo(I-f 5)Q, (21) Wk22=67rd3x 2 2+0 2(I - f5)Q.

00If p denotes the density of the air or medium W' = sird 3 xp, (23) W' I p __ W I -1 3 k12 I k22 x2 ±i a 2= 101-1 3 '111 2= 2 tan g S = Q (l - a) x 2+ I (26) in which a/p may be replaced by 800 times the S.G.

00The ellipsoid is the only shape for which a and (3 have so far been determined analytically, as shown already in § 44, so we must restrict our calculation to an egg-shaped bullet, bounded by a prolate ellipsoid of revolution, in which, with b =c, Ao= fo (a2 + X)V [4(a2+X)(b +X)2]-J0 2(a2 +X)3/2(b2+X), (13) Ao+2Bo = I, (t4) _ B 0 t - A 0 I a?I-A0' Q I - Bo I-{- A o I-?

00As the ring is moved from 0 to 0' in time t, with velocity Q, and angular velocity R, the components of liquid momentum change from aM'U +E and SM'V along Ox and Oy to aM'U'+ and /3M'V' along O'x' and O'y', (I) the axis of the ring changing from Ox to O'x'; and U = Q cos 0, V = Q sin 0, U' =Q cos (o - Rt), V' =Q sin (0 - Rt), (2) so that the increase of the components of momentum, X 1, Y 1, and N1, linear and angular, are X 1 = (aM'U'+ 0 cos Rt - aM'U - - 1 3M'V' sin Rt =(a - (3)M'Q sin_(0 - Rt) sin Rt - ver Rt (3) Y 1 = (aM'U'+) sin Rt-[-13M'V' cos Rt - (3M'V = (a - (3) M'Q cos (0 - Rt) sin Rt +t sin RT, N1=[ - (aM'U'+E) sin (0 - Rt)+ 1 3M'V' cos (o - Rt)]OO' = [- (a - 1 3) M'Q cos (o - Rt) sin (o - Rt) - sin (o - Rt) ]Qt.

00ZI /t = - (a - s) M'Q 2 sine cos ° - EQ sin() =[ - (a - (3)M'U+E]V (8) Now suppose the cylinder is free; the additional forces acting on the body are the components of kinetic reaction of the liquid - aM' (Ç_vR), - (3M' (-- E -FUR), - EC' dR, (9) so that its equations of motion are M (Ç - vR) _ - aM' (_vR) - (a - $) M'VR, (io) M (Ç+uR) = - OM' (dV+U R) - (a - ()M'UR - R, '(II) C dR = dR + (a - Q)M'UV+0V; (12) and putting as before M+aM'=ci, M+13M' = c2, C+EC'=C3, ci dU - c2VR=o, dV +(c1U+E)R=o, c 3 dR - (c 1 U+ - c 2 U)V =o; showing the modification of the equations of plane motion, due to the component E of the circulation.

00But in the Majerda Mountains there are dense primeval forests lingering to the present day, and consisting chiefly of the cork oak (Quercus ruber), and two other species of oak (Quercus mirbeckii and Q.

00For immiscible liquids the vapour pressure curve is the horizontal line ab, described so that aP = QB and bQ=AP. For partially miscible liquids the curve is Pa i b i Q.

00The curves Pa4Q, having a minimum at a4, Pa3Q, having a maximum at a 31 and Pa 5 Q, with neither a maximum nor minimum, correspond to the types i., ii., iii.

00p, Lips of redia; q, collar; r, processes serving as rudimentary feet; s, embryos; 1, trabecula crossing body-cavity of redia; u, glandular cells; v, birth-opening; w, w', morulae; y, oral sucker; y', ventral sucker; z, pharynx.

00On the 6th of April 1862 a furious assault on Grant's camps brought on the battle of Shiloh (q.

00Livy, Q.

00Bowker (New York, to vols., 1892-1907); "Index of Periodicals for 1890," &c. (Review of Reviews), by Miss Hetherington (13 vols., 1891-1902); Q.

00&c., where p+pq is the quantity whoseTi power or root is required, p the first term of that quantity, and q the quotient of the rest divided by p, m the power, which may be a positive or negative integer or a fraction, and a, b, c, &c., the several terms in order, In a second letter, dated the 24th of October 1676, to Oldenburg, Newton gave the train of reasoning by which he devised the theorem.

00G, prefrontal; M, maxilla; J, poison-fang; Tr, transpalatine; Pt, pterygoid; p, palatine; Q, quadrate; Sq, squamosal; Pm, premaxilla; T.a, articular; Pe and Di, muscles.

00In such a diagram, a point P defines a particular mixture, both as to percentage, composition and temperature; a vertical line through P corresponds to the mixture at all possible temperatures, the point Q being its freezing-point.

00As it cools from P to Q the mixture remains wholly liquid, but when 200 the temperature Q is reached there is a halt in the cooling, due to the formation of crystals loo° of A.

00It was by Q.

00Aemilius Scaurus, the elder, Q.

00Manlius Torquatus, and like Q.

00Of the other historians, or rather annalists, who belong to this period, such as Q.

00Claudius Quadrigarius, Q.

00The second great poet of the time - Q.

00For two centuries after Juvenal there are no names but those of Q.

00The last pagan prose writer who need be mentioned is Q.

00Quite different is the work of "the fierce Tertullian," Q.

00The most distinguished of the early jurists (whose works are lost) were Q.

00If the two small conducting spheres are placed with centres at a distance d centimetres, and immersed in an insulator of dielectric constant K, and carry charges of Q and Q' electrostatic units respectively, measured as above described, then the mechanical force between them is equal to QQ'/Kd 2 dynes.

00If a small conducting body is charged with Q electrostatic units of electricity, and placed in any electric field at a point where the electric force has a value E, it will be subject to a mechanical force equal to QE dynes, tending to move it in the direction of the resultant electric force.

00In the same manner, if an electrified body carries a positive charge Q electrostatic units and is placed in an electric field at a place where the electric force or electromotive intensity has a value E units, it is urged in the direction of the electric force with a mechanical force equal to QE dynes.

00We must, however, assume that the charge Q is so small that it does not sensibly disturb the original electric field, and that the dielectric constant of the insulator is unity.

00Returning to the case of the charged body with the space around it cut up into electric cells by the tubes of force and shells of potential, it is obvious that the number of these cells is represented by the product QV, where Q is the charge and V the potential of the body in electrostatic units.

00An electrified conductor is a store of energy, and from the definition of potential it is clear that the work done in increasing the charge q of a conductor whose potential is v by a small amount dq, is vdq, and since this added charge increases in turn the potential, it is easy to prove that the work done in charging a conductor with Q units to a potential V units is z QV units of work.

00Let the ball and lid be removed by the silk, and let a charge, say, of positive electricity (-}- Q) be given to the ball.

00The explanation is as follows: the charge (-}- Q) of positive electricity on the ball creates by induction an equal charge (- Q) on the inside of the canister when placed in it, and repels to the exterior surface of the canister an equal charge (+ Q).

00Hence when the ball is touched against the inside of the canister before withdrawing it a second time, the fact that the system is found subsequently to be completely discharged proves that the charge - Q induced on the inside of the canister must be exactly equal to the charge +Q on the ball, and also that the inducing action of the charge -{-Q on the ball created equal quantities of electricity of opposite sign, one drawn to the inside and the other repelled to the outside of the canister.

00Thus, consider a sphere uniformly charged with Q units of positive electricity.

00having a charge Q repels a unit charge placed at a distance x from its centre with a force Q/x 2 dynes, and therefore the work W in ergs expended in bringing the unit up to that point from an infinite distance is given by the integral W = Q x 2 dx = Hence the potential at the surface of the sphere, and therefore the potential of the sphere, is Q/R, where R is the radius of the sphere in centimetres.

00But the charge is Q = 21rra, and therefore the capacity of the thin wire is given by C =1/2 log e llr (2).

00Thus if Q is the surface density, S the thickness of the shell at any point, and p the assumed volume density of the matter of the shell, we have v =Abp. Then the quantity of electricity on any element of surface dS is A times the mass of the corresponding element of the shell; and if Q is the whole quantity of electricity on the ellipsoid, Q =A times the whole mass of the shell.

00This mass is equal to 47rabcp,u; therefore Q = A47rabcp s and b =pp, where p is the length of the perpendicular let fall from the centre of the ellipsoid on the tangent plane.

00Hence 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).

00If we consider a length l of the cylinder, the charge Q on the inner cylinder is Q=27rR l ly, where v is the surface density, and by Coulomb's law v = E i /47r, where E 1 = A/R 1 is the force at the surface of the inner Ai cylinder.

00Let V 1 and V2 be the potentials of the plates, and let a charge Q be given to one of them.

00Then this produces a charge - Q on the inside of the enclosing spherical shell, and a concentric charge +Q on the outside of the shell.

00Then when the inner cylinder is at potential V 1 and the outer one kept at of two potential V 2 the lines of electric force between the cylinders Q (4).

00For if C l and C2 are the capacities and Q i and Q2 are the charges after contact, then Qi/CI and Q2/C2 are the potential differences of the coatings and must be equal.

00Hence Qi /CI =Q2/C2 or Q I /Q 2 =C I /C 2.

00It has been shown above that the potential due to a charge of q units placed on a very small sphere, commonly called a point-charge, at any distance x is q/x.

00Then the electric force due to the point s' charge q at distance x is q/x, and the resolved part normal to the element of surface dS is q cos0/x 2.

00Accordingly, since the total solid angle round a point is 47r, it follows that the total flux through the closed surface due to the single point charge q is 41rq, and what is true for one point charge is true for any collection forming a total charge Q of any form.

00Hence the total electric flux due to a charge Q through an enclosing surface is 41rQ, and therefore is zero through one enclosing no electricity.

00The 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.

00Every tube of electric force must therefore begin and end on electrified surfaces of opposite sign, and the quantities of positive and negative electricity on its two ends are equal, since the force E just outside an electrified surface is normal to it and equal to a/41r, where a is the surface density; and since we have just proved that for the ends of a tube of force EdS = E 1 dS', it follows that adS = a'dS', or Q = Q', where Q and Q' are the quantities of electricity on the ends of the tube of force.

00Since the potential rises proportionately to the quantity in the conductor, the ends of these ordinates will lie on a straight line and define a triangle whose base line is a length equal to the total quantity Q and V height a length equal to the final potential V.

004.4), and hence the work done in charging the conductor with quantity Q to final potential V is zQV, or since Q=CV, where C is its capacity, the work done is represented by 1CV 2 or by 2Q2/C.

00If then we put a negative point-charge -qr/d at B, it follows that the spherical surface will be a zero potential surface, for q rq 1 (24).

00If we make a distribution of negative electricity over it, which has a density a varying according to the law a = -(d 2 -r 2) q /42rr AP3.

00d Q - ?

00The history of Belize is inextricably bound up with that of the rest of British Honduras (q.

00Endowed with a handsome face and manly figure, he studied the delivery and gestures of the most distinguished advocates in the Forum, especially Q.

00Pfluger, Cicero's Rede pro Q.

00It took a prominent part in the Social War against Rome, the proconsul Q.

00The brass tube, strengthened at the bearing points by strong truly turned collars, rotates in the cast iron cradle q attached to the declination axis.

00The tube V, on the contrary, is attached to the cradle, and merely forms a support for the finder Q, the handles at f and p, and the moving ring P. The latter gives quick motion in position angle; the handles at p clamp and give slow motion in position angle, those at f clamp and give slow motion in right ascension and declination.

00I, 2 5, z8, 3 1, 3 8, 5 1, 9 0, 94) 'IWavvov Tou O€oX6yov; Q and 12, air.

00and Versions.-There are six uncials, N, A, C, P, Q, a, the last of which has not been edited or collated.

00Of the rest, P and Q are imperfect.

00Its area is 999 s q.

00Two equal sprocket wheels Q 1, Q 2, are fastened, the one to the spring pulley, the other to the shaft.

00If a force Q acting at R maintains equilibrium, QR/4 = (P - p)r =T.

00Q is supplied by a spring, the extensions of which are recorded on a drum driven proportionally to the angular displacement of the driving pulley; thus a work diagram is obtained.

00The force Q, usually measured by a spring, required to maintain the beam in its central position is proportional to (P - p).

00If the angle 0 1 =0 2 =120 0, Q = (P - p) neglecting friction.

00The victory of the Radicals resulted in the establishment of a railway rate commission, based upon a constitutional amendment of 1890 and a statute of 1891, the passage of an alien land law in 1891, which was declared unconstitutional and amended in 1892, the adoption of the Australiaw ballot system for cities and towns of more than io,000 inhabitants (1892), the retirement of Roger Q.

00,?-; g, Q a / I.

00If 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,.

00When the initial values of p i, q i

00q,,.

00Pretending to fall in with his views, the ambassadors obtained a written agreement signed by the chief conspirators, and informed Q.

00As might have been anticipated, this caused no break in the policy of the English king and his parliament, and a series of famous acts passed in the year 1534 completed and confirmed the independence of the Church of England, which, except during five years under Queen Mary, p g Y Q Y?

00John Q.

00They held frequent Art of y q war.

00The introduction of trunnionless guns recoiling axially through a fixed cradle enabled sights to be attached to the non-recoil parts of the mounting, so that the necessity of removing a delicate telescopic sight every round disappeared, and Q?'

00Blaine (q.

00He did not propose the adoption of free trade, but the administration tariff measure, known as the Mills Bill, from its introducer Congressman Roger Q.

00If a .JP solid circle be fixed in any one position and a tube be pivoted on its centre so as to move; and if the line C D be drawn upon the circle pointing towards any object Q in the heavens which lies in the plane of the circle, by turn ing the tube A B towards any other object P in the plane of the circle, the angle B 0 D will be the angle subtended by the two objects P and Q at the eye.

00Then MA'B'N is a right trapezium, whose area is equal to that of Cabd; and it is related to the latter in such a way that, if any two lines parallel to AC and BD meet AB, CD, MN, A'B', in E, G, P, E', and F, H, Q, F', respectively, the area of the piece PE'F'Q of the right trapezium 'B.

00from the M N P Q R base MS, and the portions MN, FIG.

00Another method of verifying the formula is to take a point Q in the mid-section, and divide up the prismoid into two pyramids with vertex Q and bases ABCD ...

00respectively, and a series of tetrahedra having Q as one vertex.

00with regard to a parallel line through the centroid are given by Mi=N1 - xNo=o, M2 = N 2 - 2xN i -{- x 2 No = N2 - x2No, M Q = N Q - g _ 1 q(q 2, I) x 2 Ns -2

00+ (-) q -1 gx 4 N1 + (-)4x No; FIG.

00This would involve p and q; but, for our purposes, the data are the sides pa+q and pb+q and the base b - a, and the expression of the integral in terms of these data would require certain eliminations.

00is of the form px + q.

00By 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.

00The methods of §§ 59 and 60 can similarly be extended to finding the position of the central ordinate of a briquette, or the mean q th of elements of the briquette from a principal plane.

00The general method of constructing the formulae of § 7 0 for chordal areas is that, if p, q, r, ...

00are k of the factors (including 1) of m, we take A -IPCp+ Q C 4+ RC, .

00., where P, Q, R, ...

00Pp2 + Q q2 + Rr 2 + ...

00- + Q g2k-2 + 2k The last k - I of these equations give I /P: I /Q 1/R.

007.2(y2 - p 2) (r 2 - q 2).

00Combining this with the first equation, we obtain the values of P, Q, R, ..

00provided that p, q, r, ...

00The general expression, if p, q, r,..

00+ [(-) kb k h2k d x 2k l 1)k+lbk+1h2k+2 + J x = xo, where P, Q, R,.

00q) a J O l x f o udxdy (1619(X q) dx 4 P u dx dy d 4)(b, y) dy dy +.

00The molten metal is poured into the moulds N, which are carried on wheels running on rails Q.

00The extension of 0 holds down the right-hand end of the rod S which is also pivoted at P, and enables its end to fit into one of the three inverted steps on the bottom of the shoot Q.

00(q) Jesus carries His cross to Golgotha, and is crucified there between two others; the cross's title and Pilate's refusal to alter it (xix.

00G, 7P aq ?Q.

00At every point R N Q FIG.

00At J the displacement is forward, but since the curve at Q is parallel to the axis the displacement is approximately the same for all the points close to J, and the air is neither extended nor compressed, but merely displaced bodily a distance represented by JQ.

00Take a point P in the disturbed part, and a point Q which the disturbance has not yet reached.

00Since the conditions in the region PQ remain always the same, the momentum perpendicular to AB entering the region at Q is equal to the momentum perpendicular to AB leaving the region at P. But, since the motion at Q is along AB, there is no momentum there perpendicular to AB.

00The component of T A Q FIG 30.

00He found that if two tones of frequencies p and q are sounded, and if q lies between Np and (N-Fop, then a tone of frequency either (N + I) p - q, or of frequency q - Np, is heard.

00The 2nd Army then turned northward (3rd, q th, 5th and 6th divisions).

00+' 7.11 1!?I/II?I?:i?q??!'ii -_- ......

00Draw a vertical at D, intersecting fh, kg, in s and q.

0058, 5 q and 60 show an independent girder, a cantilever, and a cantilever and suspended girder bridge.

00dX Q ?..

00Varius Rufus published his famous tragedy Thyestes from an MS. which he found amongst the papers of Cassius after his death, is due to a confusion of Cassius's murderer, Q.

00Although Caesar had freed him from paying tribute to the Aduatuci, he joined Catuvolcus (winter, 54 B.C.) in a rising against the Roman forces under Q.

00It was the scene of the defeat of C. Papirius Carbo and C. Norbanus by Q.

00The polarization itself is determined from the electric force (P,Q,R) by the usual statical formula of linear type which becomes tor an isotropic medium (.f',g',h') = c2(P,Q,R), because any change of the dielectric constant K arising from the convection of the material through the aether must be independent of the sign of v and therefore be of the second order.

00Now the electric force (P,Q,R) is the force acting on the electrons of the medium moving with velocity v; consequently by Faraday's electrodynamic law (P,Q,R) = (P',Q' - vc, R'+vb) where (P',Q',R') is the force that would act on electrons at rest, and (a,b,c) is the magnetic induction.

00If v varies with respect to locality, or if there is a velocity of convection (p,q,r) variable with respect to direction and position, and analytical expression of the relation (ii) assumes a more complex form; we thus derive the most general equations of electrodynamic propagation for matter treated as continuous, anyhow distributed and moving in any manner.

00For the simplest case of polarized waves travelling parallel to the axis of x, with the magnetic oscillation y along z and the electric oscillation Q along y, all the quantities are functions of x and t alone; the total current is along y and given with respect to our moving axes by __ (d_ d Q+vy d K-1 Q, dt dx) 47rc 2 + dt (4?rc 2) ' also the circuital relations here reduce to _ dydQ _dy _ dx 47rv ' _ dt ' d 2 Q dv dx 2 -417t giving, on substitution for v, d 2 Q d 2 Q d2Q (c2-v2)(7372 = K dt 2 2u dxdt ' For a simple wave-train, Q varies as sin m(x-Vt), leading on substitution to the velocity of propagation V relative to the moving material, by means of the equation KV 2 + 2 uV = c 2 v2; this gives, to the first order of v/c, V = c/K i - v/K, which is in accordance with Fresnel's law.

00noix de Galle), are produced on Quercus fectoria, a variety of Q.

00The ectoderm loses entirely the ciliation which it had in the planula and actinula stages and commonly secretes on its external surface a protective or supporting investment, the perisarc. Contrasting with this, the anthopolyp is generally of s q uat form, the diameter often exceeding the height; the peristome is wide, a hypostome is lacking, and the ectoderm, or so much of it as is exposed, i.e.

00In 304, however, Q.

00It never had a chance contedera- q tion of Bar.

00About twentythree years after the destruction of Carthage the Romans accused the islanders of piracy, and sent against them Q.

00i passes into a, as genus, generis, generatum; into o, as sari, saxosus; q passes into s, as torqueo, torsi, &c. (3) The resolution of a word into root or stem and inflexional or derivative affixes was an idea wholly unknown, and the rules of formation are often based on unimportant phenomena; e.g.

00so that Denoting dx/dt, the horizontal component of the velocity, by q, (49) v cos i =q, equation (43) becomes (50) dq/dt= -r cos i, and therefore by !(48) (51) dq _dq dt ry di - dt di-g' It is convenient to express r as a function of v in the previous notation (52) Cr = f(v), dq _vf(v) di - Cg ' an equation connecting q and i.

00Now, since v sec i (54) di sec i dq C f(q sec i)' and multiplying by /dt or q, (55) dx C q sec i dq - f (q sec i)' and multiplying by dy/dx or tan i, (56) dy C q sec i tan dq - f (q sec i) ' also (57) di Cg dq g sec i .f (g sec i)' (58) d tan i C g sec i dq - q.

00f (q sec i)' from which the values of t, x, y, i, and tan i are given by integration with respect to q, when sec i is given as a function of q by means of (51).

00Replacing then the angle i on the right-hand side of equations (54) - (56) by some mean value, t, we introduce Siacci's pseudovelocity u defined by (59) u = q sec, t, so that u is a quasi-component parallel to the mean direction of the tangent, say the direction of the chord of the arc.

00His distinguished friend, Q.

008 1Kantur, Q s a i Za_hwa ?

00It is probable that these requirements suggested the form of the first Christian Gospel, which the writer believes to be rightly identified with the so-called Logia of St Matthew, now often designated by the symbol Q.

00Monacensis (q) of the 7th century, and cod.

00Monacensis (q) of the 7th century, and by the quotations in Ambrosiaster, to which cod.

00BÃ¶ckh has remarked the great diversity between weights of the same age -- those marked "Ad Augusti Temp" ranging 4971 to 5535, those tested by the fussy praefect Q.

00The dogmas of the Basilidians, as given by Hippolytus, read almost like passages from Neoplatonic works: g ird oWv v, obx 6N n, OLO"Ga, OLK Q,vo u nov, obx Q.7f abvOErop, OLK av671r011, OLK ava(o-Oi j rov, OLK twOpw'ros ()UK Oeos avwi]TWS, ava60Oi i rw,, ?L7rpoatp g TWS, loraOWS, ?a/en-Ow/iron KOOµov 7)O %7] oE 7ro ijo-aL.

00Since loge(I +x) =x-2x 2 -3x 3 - 4x4+&c., we have, by changing the sign of x, log e (I - x) _ - x - zx 2 - 3x 3 - x 4 - &c.; whence g 1 +x to=2(x+ix'+1x5+&c.), e l - x and, therefore, replacing x by p +q, log e q =2 p +q +3 () 3T ?

00Q 49 + 3 (49) 3 + 6 (49)5 +&c.

00By these means, and by the lavishness of his expenditure on public entertainments as aedile, he acquired such popularity with the plebs that he was elected pontifex maximus in 63 B.C. against such distinguished rivals as Q.

00q).

00It was, however, a consequence of his work that in q 1786 the provinces and kingdoms were replaced by twelve intendencias (Guadalajara, Zacatecas, Durango, Sonora, Puebla, Vera Cruz, Merida, Oaxaca, Valladolid, Guanajato, San Luis Potosi, Mexico), whose governors and minor officials were directly dependent on the viceroy, the former alcaldes, mayores and corregidores, who were very corrupt, being abolished.

00land grant given by the Spanish viceroy to Stephen Q Austin in 1820, and had been estranged from Mexico partly by the abolition of slavery under a decree of President Guerrero, and partly by the prospect of the Centralist constitution of 1836.

00Thus we regard Rotifers as an independent stem branching off at the outset of the rise from the Platode type to higher Invertebrata The Polyzoa (q v), which in many ways recall Rotifers, appear to be equally independent.

003) refracts upwards, while the prism Q, which has its refracting edge perpendicular to that of P, refracts towards the right.

00WIVELISCOMBE (pronounced Wilscomb), a market town in the western parliamentary division of Somersetshire, England, q z m.

0026, note q).

00Q uaternary.

00PUBLIUS RUTILIUS RUFUS, Roman statesman, orator and historian, born c. 158 B.C. He was on intimate terms with the younger Scipio, under whom he served in the Numantine War (134), and he also accompanied Q.

00Subsequently, he went as legate to Q.

00One of these diminutive convents is appropriated to the "oblati" or novices (Q), the other to the sick monks as an "infirmary" (R).

00As peculiarities of arrangement may be noticed the position of the kitchen (Q), between the refectory and calefactory, and of the infirmary (W) (unless there is some error in its designation) above the river to the west, adjoining the guest-houses (XX).

00Comparing this equation with ux 2 +vy 2 +w2 2 +22G'y2+2v'zx+2W'xy=0, we obtain as the condition for the general equation of the second degree to represent a circle :- (v+w-2u')Ia 2 = (w +u -2v')/b2 = (u+v-2w')lc2 In tangential q, r) co-ordinates the inscribed circle has for its equation(s - a)qr+ (s - b)rp+ (s - c) pq = o, s being equal to 1(a +b +c); an alternative form is qr cot zA+rp cot ZB +pq cot2C =o; Tangential the centre is ap+bq+cr = o, or sinA +q sin B+rsinC =o.

00The general equation to a circle in this system of co-ordinates is deduced as follows: If p be the radius and 1p+mg+nr=o the centre, we have p= (lpl+mgi+nri)/(l+m+n), in which i, q i, r i is a line distant p from the point 1p+mq+nr= o.

002, we obtain lap, bq, cr} 2 2= 2 t(lp+mq+nr)/(l-1-m+n)} 2, the accents being dropped, and p, q, r regarded as current co-ordinates.

00q, Left external gill-plate.

00This page gives an overview of all articles in the 1911 Brittanica which are alphabetized under Q to Quo.

00We know also of Q.

00Among the Chinese the name of the silkworm is " si, " Korean " soi "; to the ancient Greeks it became known as Q?p, the nation whence it came was to them ?r?pE S and the fibre itself o ptKc v, whence the Latin sericum, the French soie, the German Seide and the English silk.

00A discussion of band spectra on a very broad basis was given by Thiele,' who recommends a formula - q +qi(s+c)+ +qr(s+c)r n in the discharge, except within the region of the kathode glow.

00But some have maintained that the source in question also contained a good many narratives, and in order to avoid any premature assumption as to its contents and character several recent critics have named it " Q."

000 e l e1Q ° Q ° V ee ?d e °?

00q to p. Not less clear is the well attested tradition (e.g.

00On the other hand there are two or three forms called Sabine by Latin writers which do appear to show the sound q unchanged, especially the name of the Sabine god Quirinus, which seems to be at least indirectly connected with the name of the Sabine town Cures.

00We do not, however, know that the initial sound of this word was originally a Velar q, and Professor Ridgeway (" Who were the Romans," London, 1908,1908, in Proceedings of the British Academy, iii.

00Omitting correction terms depending on the temperature and on the inductive effect of the earth's magnetism on the moment of the deflecting magnet, if 0 is the angle which the axis of the deflected magnet makes with the meridian when the centre of the deflecting magnet is at a distance r, then zM sin B=I+P+y2 &c., in which P and Q are constants depending on the dimensions and magnetic states of the two magnets.

00The value of the constants P and Q can be obtained by making deflexion experiments at three distances.

00It is, however, possible by suitably choosing the proportions of the two magnets to cause either P or Q to be very small.

00Thus it is usual, if the magnets are of similar shape, to make the deflected magnet 0.467 of the length of the deflecting magnet, in which case Q is negligible, and thus by means of deflexion experiments at two distances the value of P can be obtained.

00't o +u^ u ` D roriva" Q F3`?ste?

00Q ?,?

00'? !-.*1 - DldSau Q.

00He had a number of distinguished Romans as pupils, amongst them Q.

00Mucius Scaevola the augur and Q.

00They are as follow: HEpi Tov KatvKovTos (On Duty), in three books, the original of the first two books of Cicero's De oficiis; HEpi lrpovoias (On Providence), used by Cicero in his De divinatione (ii.) and probably in part of the second book of the De Deorum natura; a political treatise (perhaps called HEpi 1roXCTG6S), used by Cicero in his De republica; HEpi €bOvµias (On Cheerfulness); Hcpi aipEVECwv (On Philosophical Schools); a letter to Q.

00when Q, Iridium pivct.

00It was by its constant reliance on monachism that the papacy of the 12th century had attained this result, and the popes of that period were especially fortunate in having for their champion the monk St Bernard, whose admirable qualities enabled him to dominate public q P opinion.

00At C a new o° A C liquid phase appears - the B solution of water in liquid ' r q Ivater 50 Phenol phenol, the solubility of which FIG.

00This outer court also contains the guest-chambers (P), the stables and lodgings of the lay brothers (N), the barns and granaries (Q), the dovecot (H) and the bakehouse (T).

00ULVERSTON, a market town in the North Lonsdale parliamentary division of Lancashire, England, in the Furness district, q a m.

00The other images on the parhelic circle are the paranthelia (q) and the anthelion (a) (from the Greek av-ri, opposite, and iXcos, the sun).

00The paranthelia (q) may be due to two internal or two external reflections.

00q, Opening of vas deferens.

00Let A and C be two fixed disks, and B a disk which can be brought at will within a very short distance of either A or C. Let us suppose all the plates to be equal, and let the capacities of A and C in presence of B be each equal to p, and the coefficient of induction between A and B, or C and B, be q.

00A small charge Q is communicated to A, and A is insulated, and B, uninsulated, is brought up to it; the charge on B will be - (q/p)Q.

00B is now uninsulated and brought to face C, which is uninsulated; the charge on C will be (q/p) 2 Q.

00It is obvious that at the end of n such operations the charge on A will be r n Q, so that the charge goes on increasing in geometrical progression.

00Q' Penan?h g Prov.Welleley 3 s 0 -.._ .,.0 1=Higher 2 = Longitude East too ore Arch.

00x-` Q ..o(rlg el Vo n a 4 ', E tdhoven.r _ A ` '/; gi.

00Before the teleutospore reaches maturity the nuclei fuse, and the uninucleate condition Q C then continues again until aeci dium formation.

00When the gradually falling temperature reaches 1430° (q), the mass begins to freeze as -y-iron or austenite, called " primary " to distinguish it from that which forms part of the eutectic. But the freezing, instead of completing itself at a fixed temperature as that of pure water does, continues until the temperature sinks to r on the line Aa.

00In other words, the composition of the frozen part and that of the mother-metal respectively are p and q at the beginning of the freezing, and r and t' at the end; and during freezing they slide along Aa and AB from p to r and from q to t'.

0016) in which this wonderful process is carried out is a huge retort, lined with clay, dolomite or other refractory material, hung aloft and turned on trunnions, DD, through the right-hand one of which the blast is carried to the gooseneck E, which in turn delivers it to the tuyeres Q at the bottom.

00Q, Tuyeres.

00e of public humiliation, the king and the queen mother p g q in Ashanti and Jaman, by R.

00Reicher proved with sulphur: aT /aP = AvT/q, v being the change in volume which accompanies the change from rhombic to prismatic sulphur, and q the heat absorbed.

00H:r ° Huy', Theu?c„ ?, ' r,Grchieso encienne Catelet Le y ubeuge iGppevil e e Q ?

00To take the simple case of the " wall " or flat plate considered by Fourier for the definition of thermal conductivity, suppose that a quantity of heat Q passes in the time T through an area A of a plate of conductivity k and thickness x, the sides of which are constantly maintained at temperatures B' and 8".

00If Q is expressed in terms of this unit in equation (I), it is necessary to divide by c, or to replace k on the right-hand side by the ratio k/c. This ratio determines the rate of diffusion of temperature, and is called the thermometric conductivity or, more shortly, the diffusivity.

00The areas of successive surfaces vary as their radii, hence the rate of tr