# Q sentence example

q

- The existence of earth currents (q.
- Thus 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.
- Cicero and five others (amongst them the famous Q.
- daftoi,me,,t48,Q
- Ann., 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.Advertisement
- 1869 by Giovanni Lanza, with Visconti-Venosta at the foreign office and Q.
- evergreen oaks (Q.
- hex, Q.
- In these islands, we find forests i or woods of oak (Quercus Robur and Q.
- Q.Advertisement
- Laschitzer wrote an introduction to Sir Teuerdank, Q.
- P q P Y?
- Ballota, Q.
- However, 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.
- The large sessile acorns are longer than those of Q.Advertisement
- The Turkey oak in southern England grows twice as fast as Q.
- The pin oak, sometimes called the "burr-oak," Q.
- The over-cup oak, Q.
- In 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.
- alba; it is Q.Advertisement
- The red oak, Q.
- A species nearly allied is the scarlet oak, Q.
- The trunk, though often of considerable size, yields but an indifferent wood, employed for similar purposes to that of Q.
- The wood is coarsely grained, as in all the red-oak group, but harder and more durable than that of Q.
- The cut-leaved oaks are represented in eastern Asia by several species, of which Q.Advertisement
- Evergreen oaks with entire leaves are represented in North America by Q.
- virginiana, also known as Q.
- The evergreen oak of southern Europe is Q.
- The cork oak, Q.
- The valonia of commerce, one of the richest of tanning materials, is the acorn of Q.Advertisement
- The allied Q.
- Q]].
- persica, or according to some Q.
- There 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.
- joined between P and Q.Advertisement
- One very great advantage in this method is that the instrument used between P and Q may be of any ordinary form, i.e.
- By 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.
- The first of the annalists, the father of Roman history, as he has been called, was Q.
- BM- Within quite recent years, however, a special school q Y P has arisen with the main object of treating the processes of evolution quantitatively.
- He has been identified with the author of the four books of Rhetorica dedicated to a certain Q.Advertisement
- Q, Three segments of a pitted vessel of Phanerogam.
- E, epidermis; q, phellogen; 1, cells, and ~1, the pheliogen of the lenticel; k, cortical parenchyma, containing chlorophyll.
- The new capital of Persis was Istakhr on the Pulwar, about q m.
- Several Roman nobles, among them Gnaeus Pompeius (Pompey the Great), Q.
- Palestrina) 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.Advertisement
- q, Quadrate.
- c. 3), especially the senator Q.
- By her he had two sons, Anicius Manlius Severinus Boetius and Q.
- Fernandez Garcia (Q uaracchi, Florence, 1902).
- as St Petersburg and South Finland (Q.Advertisement
- 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.
- In 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.
- The 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.
- q`tal or Pal (" he killed "), which corresponds to Heb.
- The form q`tal illustrates one main peculiarity of Aramaic, as opposed to the other Semitic languages, viz.
- its 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.
- The simple active q`tal makes its passive ethq`tel; the intensive gattel makes.
- q`tal " he has killed," " he killed."
- q`tal wa, " he had killed," " he killed."
- His 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.
- (Lankester.) q, Intestine in transverse section.
- q, Renal organ (nephridium).
- q, Shell.
- Q, Sac containing nutritive mb, Mantle-skirt.
- C. Q.)
- After 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.
- The 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.
- Though Riley was especially interested in the bearings of insect life on agriculture and industry - economic entomology (q.
- q ?' ?'
- ' °° p Q; i r ' Afayette A(l.
- The 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.
- One of the chief objects of Saturninus's hatred was Q.
- Colonies were to be founded in Sicily, Achaea and Macedonia, on the purchase of which the " Tolosan gold," the temple treasures embezzled by Q.
- If 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).
- Q --.
- 'Eav J f9 J Q,cATE EKaUTOS vi.
- HECATO OF RHODES, Greek Stoic philosopher and disciple of Panaetius (Cicero, De q, ficiis, iii.
- q !,: FIG.
- q 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.
- sp," Q.
- Results (Willey), part iii., 1899; see also Q.
- Let 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.
- Volusius Saturninus and Q.
- c, 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.
- A, ventral, B, dorsal valves; 1, loop; q, crura; ss, septum; c, cardinal process.
- The quantities a l a, a 2 Q ...
- in 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 ...
- = ePlal, 1 + a i Q 2+ a 2 0 2 +...
- P y q +...
- All 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.
- The 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.
- We 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).
- 1 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.
- +1,q p l !gll p2!g2!
- Recalling 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.
- We may remark the particular result (-) p + p q!
- )- (p+4-1 (p - - q -1)!dpq+ ?l -) 1)!D'1 DT2 p!g!
- an_1 i a n, and in general a n-k a 2 is the symbol for Q k.
- d 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.
- To 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.
- The 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.
- The Hessian in that case is a factor of f, and Q is the third power of u2,...
- For 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?
- retains 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!
- The 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 -}-...
- +aPx2, boxi +qb1 xi -1x2+q(q - 1) b 2 xPx2+...
- The 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.
- 1111 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.
- Q).
- The 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.
- 1 Ze'; Which Preserves Its Expression When 0 And P And 0 And Q Are Separately Or Simultaneously Interchanged.
- Q 1 The Unreduced Generating Function Which Enumerates The Covariants Of Degrees 0, 0' In The Coefficients And Order E In The Variables.
- Here 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.
- Under 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.
- If V is the volume of a ball, H the strength of the field at its centre, and re its apparent susceptibility, the force in the direction x is f= K'VH X dH/dx; and if K',, and are the apparent susceptibilities of the same ball in air and in liquid oxygen, K' Q -K'o is equal to the difference between the susceptibilities of the two media.
- (From Lankester, Q.
- VII, 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.
- (After Lankester and Bourne, Q.
- - Arachnida in which, excluding from consideration the eye-bearing prosthomere, the somites are primarily (that is to say, in the common Q FIG.
- (After Pocock, Q.
- Appendages of 2nd pair folding in a horizontal plane; their basal segments n From Lankester, Q.
- Idem, "Limulus an Arachnid," Q.
- Embryology: - Balfour, " Development of the Araneina," Q.
- gevas, Bahia (S.Salvador) Barcellos rrado Contas Ilheos 0livenca Q ?f19H ostardas rJ°?
- His development of the equation x m +- px = q in an infinite series was extended by Leonhard Euler, and particularly by Joseph Louis Lagrange.
- For 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.
- It should be observed that, by analogy with the definition of a fraction, a P l q mean (al/q)P, not (aP)llq.
- (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.
- (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.
- Proceeding 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 +..
- 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.
- we cut off from Q successive portions each equal to R.
- Suppose we find Q = sR+T, then we repeat the process with R and T; and so on.
- (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.
- Hence u is the greatest common measure of p and q.
- is 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 .
- is 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.
- This 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.
- Similarly the statements P+Q - R - S = T and P+ Q - R= T+ S are the same.
- Thus 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.
- Thus from P+Q - R+S=T we deduce P+(Q - R+S)=P+(T - P).
- Thus, 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.
- The 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.
- Q V, or PV = UQ, as in ï¿½ 38 (vi.).
- Thus 2 x 2 - I - x +x-2 (x _ I) (x+2) is equal to x + 2 q, except when x=1.
- - An equation may involve a fraction of the form Q, where Q involves x.
- we 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.
- We 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.
- The 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, ...
- The generating functions of the two series, mentioned above, for example, are (I +x)-' n and (I+x) P / Q.
- A quaternion is best defined as a symbol of the type q = Za s e s = aoeo + ales = ale, + a3e3, where eo, ...
- a 3 ordinary algebraic quantities, which ma S' g q ?
- may be called the co-ordinates of q.
- Thus e 1 e 2 = - e2ei, and if q, q are any two quaternions, qq is generally different from q'q.
- Putting 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.
- Thus 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.
- The equations q'+x = q and y+q' = q are satisfied by the same quaternion, which is denoted by q - q'.
- On the other hand, the equations q'x = q and yq' = q have, in general, different solutions.
- It is the value of y which is generally denoted by q= q'; a special symbol for x is desirable, but has not been established.
- If 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'.
- We imagine a wave-front divided o x Q into elementary rings or zones - often named after Huygens, but better after Fresnelby spheres described round P (the point at which the aggregate effect is to be estimated), the first sphere, touching the plane at 0, with a radius equal to PO, and the succeeding spheres with radii increasing at each step by IX.
- Now 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.
- If 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).
- In 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).
- It is thus sufficient to determine the intensity along the axis of p. Putting q = o, we get C = ffcos pxdxdy=2f+Rcos 'px 1/ (R2 - x2)dx, R being the radius of the aperture.
- The 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.
- Then, 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.
- But 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..
- A 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)').
- If "=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.
- A tie between the middle point of the rod OA and Q can be used if thought desirable.
- 4/2 I = Q Q.
- For a point Q outside the shadow the integration extends over more than half the primary wave.
- The 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?
- With sufficient approximation we may regard BQ and b as rectangular co-ordinates of Q.
- He 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.
- 3; Cicero, Ad Q.
- q.
- The 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.
- S.)/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).
- It 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.).
- ' o P B Sentinel Q A Rutland /, 5 a ssage Paialankw e ?
- 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.
- But the faces bc, ca, over which P and Q act, are also equal, so that the pressure on each face is equal.
- The 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.
- I 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.
- Generally 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.
- In plane motion (4) reduces to dH = 2q"= q /av q?
- In 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.
- Similarly, 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).
- (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).
- 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.
- +a2 522x - b2 + c2121y, P =S21+, Q = 522+ 7 ], R =S23-H".
- Uniplanar 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.
- u - 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.
- The 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.
- (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(?"
- 2n 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?
- `ia a - a u-b sh nf2= i ch log (Q) n =i a-b ?
- m _ c Q du dO dt - rrqu 2r qu AB _ Q du L bq (u -a') +V (b -a')1,l (a -u)11/ndu) L 1,1 (a-a/),,1 (u-b), f u Along the wall Bx, cos n0 =I, sin n0 =o, b >u>o ch nSt = ch log () n=, , fb-a?, ?
- Ja - u ?I a -a b -u' sh nS2=sh log (Q)=?a - b a - a' b - u' At x where = co, u = o, and q= go, (O n b - a ' a + a -b a' cio) - ?a-a'?b a-a' q In crossing to the line of flow x'A'P'J', b changes from o to m, so that with q = Q across JJ', while across xx the velocity is qo, so that i n = go.
- xx' = 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.
- 5, 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'.
- Along 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.
- b a-b (7) cos = a, sin na = 1j a, nd along the free surface APJ, q =Q, 4) =o, u =e-.
- From 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.
- Trans., 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.
- Beginning 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.
- Taking 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.
- But 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.
- 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 =..
- Clebsch 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.
- Now (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.
- Introducing 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.
- (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.
- (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.
- If 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.
- The 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-?
- As 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.
- ZI /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.
- But 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.
- For 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.
- The 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.
- p, 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.
- On the 6th of April 1862 a furious assault on Grant's camps brought on the battle of Shiloh (q.
- Livy, Q.
- Bowker (New York, to vols., 1892-1907); "Index of Periodicals for 1890," &c. (Review of Reviews), by Miss Hetherington (13 vols., 1891-1902); Q.
- &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.
- G, 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.
- In 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.
- As 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.
- It was by Q.
- Aemilius Scaurus, the elder, Q.
- Manlius Torquatus, and like Q.
- Of the other historians, or rather annalists, who belong to this period, such as Q.
- Claudius Quadrigarius, Q.
- The second great poet of the time - Q.
- For two centuries after Juvenal there are no names but those of Q.
- The last pagan prose writer who need be mentioned is Q.
- Quite different is the work of "the fierce Tertullian," Q.
- The most distinguished of the early jurists (whose works are lost) were Q.
- If 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.
- If 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.
- In 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.
- We 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.
- Returning 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.
- An 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.
- Let the ball and lid be removed by the silk, and let a charge, say, of positive electricity (-}- Q) be given to the ball.
- The 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).
- Hence 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.
- Thus, consider a sphere uniformly charged with Q units of positive electricity.
- having 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.
- But the charge is Q = 21rra, and therefore the capacity of the thin wire is given by C =1/2 log e llr (2).
- Thus 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.
- This 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.
- 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).
- If 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.
- Let V 1 and V2 be the potentials of the plates, and let a charge Q be given to one of them.
- Then this produces a charge - Q on the inside of the enclosing spherical shell, and a concentric charge +Q on the outside of the shell.
- Then 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).
- For 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.
- Hence Qi /CI =Q2/C2 or Q I /Q 2 =C I /C 2.
- It 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.
- Then 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.
- Accordingly, 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.
- Hence the total electric flux due to a charge Q through an enclosing surface is 41rQ, and therefore is zero through one enclosing no electricity.
- 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.
- Every 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.
- Since 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.
- 4.4), 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.
- If 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).
- If 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.
- d Q - ?
- The history of Belize is inextricably bound up with that of the rest of British Honduras (q.
- Endowed with a handsome face and manly figure, he studied the delivery and gestures of the most distinguished advocates in the Forum, especially Q.
- Pfluger, Cicero's Rede pro Q.
- It took a prominent part in the Social War against Rome, the proconsul Q.
- The brass tube, strengthened at the bearing points by strong truly turned collars, rotates in the cast iron cradle q attached to the declination axis.
- The 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.
- I, 2 5, z8, 3 1, 3 8, 5 1, 9 0, 94) 'IWavvov Tou O€oX6yov; Q and 12, air.
- and Versions.-There are six uncials, N, A, C, P, Q, a, the last of which has not been edited or collated.
- Of the rest, P and Q are imperfect.
- Its area is 999 s q.
- Two equal sprocket wheels Q 1, Q 2, are fastened, the one to the spring pulley, the other to the shaft.
- If a force Q acting at R maintains equilibrium, QR/4 = (P - p)r =T.
- Q 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.
- The force Q, usually measured by a spring, required to maintain the beam in its central position is proportional to (P - p).
- If the angle 0 1 =0 2 =120 0, Q = (P - p) neglecting friction.
- The 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.
- ,?-; g, Q a / I.
- 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,.
- When the initial values of p i, q i
- q,,.
- Pretending to fall in with his views, the ambassadors obtained a written agreement signed by the chief conspirators, and informed Q.
- As 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?
- John Q.
- They held frequent Art of y q war.
- The 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?'
- Blaine (q.
- He did not propose the adoption of free trade, but the administration tariff measure, known as the Mills Bill, from its introducer Congressman Roger Q.
- If 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.
- Then 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.
- from the M N P Q R base MS, and the portions MN, FIG.
- Another 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 ...
- respectively, and a series of tetrahedra having Q as one vertex.
- with 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
- + (-) q -1 gx 4 N1 + (-)4x No; FIG.
- This 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.
- is of the form px + q.
- 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 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.
- The general method of constructing the formulae of § 7 0 for chordal areas is that, if p, q, r, ...
- are k of the factors (including 1) of m, we take A -IPCp+ Q C 4+ RC, .
- ., where P, Q, R, ...
- Pp2 + Q q2 + Rr 2 + ...
- - + Q g2k-2 + 2k The last k - I of these equations give I /P: I /Q 1/R.
- 7.2(y2 - p 2) (r 2 - q 2).
- Combining this with the first equation, we obtain the values of P, Q, R, ..
- provided that p, q, r, ...
- The general expression, if p, q, r,..
- + [(-) kb k h2k d x 2k l 1)k+lbk+1h2k+2 + J x = xo, where P, Q, R,.
- q) a J O l x f o udxdy (1619(X q) dx 4 P u dx dy d 4)(b, y) dy dy +.
- The molten metal is poured into the moulds N, which are carried on wheels running on rails Q.
- The 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.
- (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.
- G, 7P aq ?Q.
- At every point R N Q FIG.
- At 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.
- Take a point P in the disturbed part, and a point Q which the disturbance has not yet reached.
- Since 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.
- The component of T A Q FIG 30.
- He 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.
- The 2nd Army then turned northward (3rd, q th, 5th and 6th divisions).
- +' 7.11 1!?I/II?I?:i?q??!'ii -_- ......
- Draw a vertical at D, intersecting fh, kg, in s and q.
- 58, 5 q and 60 show an independent girder, a cantilever, and a cantilever and suspended girder bridge.
- dX Q ?..
- Varius 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.
- Although 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.
- It was the scene of the defeat of C. Papirius Carbo and C. Norbanus by Q.
- The 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.
- Now 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.
- If 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.
- For 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.
- noix de Galle), are produced on Quercus fectoria, a variety of Q.
- The 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.
- In 304, however, Q.
- It never had a chance contedera- q tion of Bar.
- About twentythree years after the destruction of Carthage the Romans accused the islanders of piracy, and sent against them Q.
- i 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.
- so 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.
- Now, 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.
- f (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).
- Replacing 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.
- His distinguished friend, Q.
- 8 1Kantur, Q s a i Za_hwa ?
- It 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.
- Monacensis (q) of the 7th century, and cod.
- Monacensis (q) of the 7th century, and by the quotations in Ambrosiaster, to which cod.
- BÃ¶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.
- The 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.
- Since 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 ?
- Q 49 + 3 (49) 3 + 6 (49)5 +&c.
- By 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.
- q).
- It 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.
- land 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.
- Thus 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.
- 3) refracts upwards, while the prism Q, which has its refracting edge perpendicular to that of P, refracts towards the right.
- WIVELISCOMBE (pronounced Wilscomb), a market town in the western parliamentary division of Somersetshire, England, q z m.
- 26, note q).
- Q uaternary.
- PUBLIUS 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.
- Subsequently, he went as legate to Q.
- One of these diminutive convents is appropriated to the "oblati" or novices (Q), the other to the sick monks as an "infirmary" (R).
- As 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).
- Comparing 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.
- The 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.
- 2, we obtain lap, bq, cr} 2 2= 2 t(lp+mq+nr)/(l-1-m+n)} 2, the accents being dropped, and p, q, r regarded as current co-ordinates.
- q, Left external gill-plate.
- This page gives an overview of all articles in the 1911 Brittanica which are alphabetized under Q to Quo.
- We know also of Q.
- Among 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.
- A 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.
- But 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."
- 0 e l e1Q ° Q ° V ee ?d e °?
- q to p. Not less clear is the well attested tradition (e.g.
- On 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.
- We 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.
- Omitting 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.
- The value of the constants P and Q can be obtained by making deflexion experiments at three distances.
- It is, however, possible by suitably choosing the proportions of the two magnets to cause either P or Q to be very small.
- Thus 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.
- 't o +u^ u ` D roriva" Q F3`?ste?
- Q ?,?
- '? !-.*1 - DldSau Q.
- He had a number of distinguished Romans as pupils, amongst them Q.
- Mucius Scaevola the augur and Q.
- They 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.
- when Q, Iridium pivct.
- It 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.
- At 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.
- This 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).
- ULVERSTON, a market town in the North Lonsdale parliamentary division of Lancashire, England, in the Furness district, q a m.
- The other images on the parhelic circle are the paranthelia (q) and the anthelion (a) (from the Greek av-ri, opposite, and iXcos, the sun).
- The paranthelia (q) may be due to two internal or two external reflections.
- q, Opening of vas deferens.
- Let 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.
- A 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.
- B is now uninsulated and brought to face C, which is uninsulated; the charge on C will be (q/p) 2 Q.
- It 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.
- Q' Penan?h g Prov.Welleley 3 s 0 -.._ .,.0 1=Higher 2 = Longitude East too ore Arch.
- x-` Q ..o(rlg el Vo n a 4 ', E tdhoven.r _ A ` '/; gi.
- Before the teleutospore reaches maturity the nuclei fuse, and the uninucleate condition Q C then continues again until aeci dium formation.
- When 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.
- In 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'.
- 16) 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.
- Q, Tuyeres.
- e of public humiliation, the king and the queen mother p g q in Ashanti and Jaman, by R.
- Reicher 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.
- H:r ° Huy', Theu?c„ ?, ' r,Grchieso encienne Catelet Le y ubeuge iGppevil e e Q ?
- To 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".
- If 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.
- The areas of successive surfaces vary as their radii, hence the rate of transmission Q/AT varies inversely as the radius r, and is Q/2lrrlT, if 1 is the length of the cylinder, and Q the total heat, calculated from the condensation of steam observed in a time T.
- The heat Q transmitted in a given time T may be deduced from an observation of the rise of temperature of the water, and the amount which passes in the interval.
- Q?u 32 3 4 ?
- The heat per second gained by conduction by an element dx of the bar, of conductivity k and cross section q, at a point where the gradient is dB/dx, may be written gk(d 2 6/dx 2)dx.
- The last expression in terms of k/k' is very simple, but the first is more useful in practice, as the quantities actually measured are E, C, 1, q, and the difference of temperature.
- Morrison, and Roger Q.
- On the south side and Q.
- The German slaves under Crixus were defeated at Mt Garganus in Apulia by the praetor Q.
- The great size of leaf when fully developed (4 to q ins.
- About a year after Johnson had begun to reside in London he was fortunate enough to obtain regular employment from Edward Cave (q.
- Density thgllsh per q.
- See Recueil des opinions de Stanislas de Clermont-Tonnerre (q vols., Paris, 1791), the text of his speeches as published by himself; A.
- We also have an inscription of 117 B.C. (now preserved in the Palazzo Municipale at Genoa) giving the text of the decision given by the patroni, Q.
- q }' 4 Their land was afterwards included in the provinces of Pannonia and Noricum, and under Roman rule, Vindobona, the modern Vienna, became a place of some importance.
- Wars and con conquests between Greeks and Greeks, especially on the q p y part of Syracuse, though not wanting, have been on the whole less constant than in old Greece.
- In Rome, in 1844, his eldest da q ghter, Julia Romana (afterwards the wife of Michael Anagnos, Dr Howe's assistant and successor), was born, and in September the travellers returned to America, and Dr Howe resumed his activities.
- p. 324 and " The Mystery of Seisin," Law Q.
- El Sayed Pasha Shokrt% Scale, English Miles I 2 Railways ' Cn Canals Reference Pa/Ace Q.
- Girga (q,v.), pop. 19,893, iS 22 m.
- slope of earth value q;, , ~N ~ q,, slope, or brickwork, ~ ~ height.
- Q; of flesh.
- q =1 from ~ f, dem.
- This stone-work was usually formed on the outside with rotary motion, but sometimes the vase was rotated upon the grinder (Q.
- 24), but more usually grinders blocks of quartzite sandstone (26-34), and occasionally Df diorite (Q.
- high, hollowed so as to be marvellously light and highly polished (Q.
- The lines are generally of standard gauge (q.
- The loss of Norway necessitated considerable reductions of expenditure, but the economies actually practised fell far short of the requirements of y P q after 1815.
- These offices, however, are purely minis q > P Y terial, are not necessarily limited to students, and give no place in the hierarchy and no particular consideration or social status.
- (A, B, C, D, E, H, L, M, P, from Engler and Prantl, by permission of Wilhelm Engelmann; F, G, K, 0, from Oltmanns, by permission of Gustav Fischer; Q, from by permission of the Clarendon Press; N 1, N 2, from Hauck, by permission of Eduard Kummer.) the brown colouring matter which is added to chlorophyll is identical with phycophaein; two varieties of it have been termed phycopyrrin and peridinine.
- (A, C, D, E, F, G, H, K, L, M, P, Q, from Oltmanns, by permission of Gustav Fischer; B, N, 0, R, from Engler and Prantl, by permission of Wilhelm Engelman,) mass and from it all the nuclei of the carpospores are thus derived.
- There is a central region, roughly triangular in shape, with its base resting upon the Quaternary K Triassic Tertiary Carboniferous q & Metamorphic 7 Jurassic Aegean Sea and its apex in Servia.
- ARCTURUS, the brightest star in the northern hemisphere, situated in the constellation Bootes in an almost direct line with the tail Q' and rt) of the constellation Ursa Major (Great Bear); hence its derivation from the Gr.
- The second covered Q uito 3 ft.
- Adams (ed.), Memoirs of John Q uincy Adams, comprising portions of his diary from 1795 to 1848 (12 vols., Philadelphia, 1874-1877).
- The mixture is fed in continuously to the central pan (e), whence it overflows into the compartments (c'), (c 2), (c 3) successively until it reaches the circumference, where it is discharged continously by o and into the collecting-box (q), being now converted into salt-cake.
- In the war of 306 B.C. it was conquered by Q.
- 17) be a section of the polar axis; it is then easy to adjust the weight P attached to its lower end so that the centre of gravity X of the whole moving parts of the instrument shall be in the vertical (V V) of a line passing through the apex of the hollowed flange p q at q, which flange forms part of the polar axis.
- If now a wheel W is forced up against q with a pressure equal to the weight of the moving part of the instrument, the whole weight of the moving part would rest upon W in unstable equilibrium; or if a pressure R, less than W, is employed, we have the end friction on the lower bearing removed to an extent = R sin 4),4), and the friction on the bearings of the upper pivot removed to the extent of F cos 4), - where 4 is the latitude of the place.
- The current is supplied by accumulators, and the switch-board is ^ q attached to the platform in a position convenient for use by the astronome his assistant.
- A small graduated circle p concentric with A is attached to the circular base b and read by the microscopes q r, attached to a.
- li., Q.
- A Steady Current Of Liquid, Q Grammes Per Second, Of Specific Heat, Js Joules Per Degree, Flowing Through A Fine Tube, A B, Fig.
- He studied rhetoric under Molo (Molon) of Rhodes, and law under the guidance of Q.
- After the death of the augur, he transferred himself to the care of Q.
- 1-28) draws the libellous statements which he inserts into the speech of Q.
- Beltrami, De Commentariolo Petitionis Q.
- P Q B R' S R S being the sun.
- Q is M.
- Every E, which is common to S, Q, R, is M.
- As we see from Lotze's own defence, the conclusion cannot be drawn without another premise or premises to the effect that " S, Q, R, are /, and is the one real subject of M."
- Servois says, with reference to the general representation of a directed line in space: " L'analogie semblerait exiger que le trineme filt de la forme p cos a+q cos a+r cos y; a, 1 3, y etant les angles d'une droite avec trois axes rectangulaires; et qu'on eut (p cos a+ g cos /3+ r cos y)(p' cos a+ q cos /3 + r cos y) =cos 2 a+cos 2) 3+cos 2 y = 1.
- Les valeurs de p, q, r, p', q,' r', qui satisferaient a cette condition seraient absurdes; mais seraient-elles imaginaires, reductibles a la forme generale A+B - 1 ?
- Any quaternion may now be expressed in numerous simple forms. Thus we may regard it as the sum of a number and a line, a+a, or as the product, fly, or the quotient, be-', of two directed lines, &c., while, in many cases, we may represent it, so far as it is required, by a single letter such as q, r, &c.
- And one of Hamilton's earliest advances in the study of his system (an advance independently made, only a few months later, by Arthur Cayley) was the interpretation of the singular operator q()q1, where q is a quaternion.
- Clifford makes use of a quasi-scalar w, commutative with quaternions, and such that if p, q, &c., are quaternions, when p-I-wq= p'+wq', then necessarily p= p', q = q'.
- Then the biquaternion n q + wr suffices.
- q ']/Sq), and its expression is nSq+wVr.
- The axis of the member xQ+x'Q' of the second-order complex Q, Q' (where Q=nq+wr, Q'=nq'+wr' and x, x' are scalars) is parallel to a fixed plane and intersects a fixed transversal, viz.
- the line parallel to q' q-- 1 which intersects the axes of Q and Q'; the plane of the member contains a fixed line; the centre is on a fixed ellipse which intersects the transversal; the axis is on a fixed ruled surface to which the plane of the ellipse is a tangent plane, the ellipse being the section of the ruled surface by the plane; the ruled surface is a cylindroid deformed by a simple shear parallel to the transversal.
- This has a reciprocal Q -1= p-r = qq-1 - wp1 rq1, and a conjugate KQ (such that K[QQ'] = KQ'KQ, K[KQ] = Q) given by KQ = Kq-}-rlKp+wKr; the product QQ' of Q and Q' is app'+nqq'+w(pr'+rq'); the quasi-vector RI - K) Q is Combebiac's linear element and may be regarded as a point on a line; the quasi-scalar (in a different sense from the rest of this article) 2(1+K)Q is Combebiac's scalar (Sp+Sq)+Combebiac's plane.
- If Q= Ep+nq+wr and we put Q= (I +Zwt)(Ep-i-nq)X (1 Zwt) -1 we find that the quaternion t must be 2f (r) /f (q - p), where f(r)=rq - Kpr.
- The point p=Vt may be called the centre of Q and the length St may be called the radius.
- If Q and Q' are commutative, that is, if QQ' = Q'Q, then Q and Q' have the same centre and the same radius.
- Thus Q-1, Q 2, Q',.
- Q and KQ have a common centre and equal and opposite radii; that is, the t of KQ is the negative conjugate of that of Q.
- Assuming dH/do = 0.305 for saturated steam, he found that S was nearly independent of the pressure at constant temperature, but that it varied with the temperature from o 387 at 100° C. to o 665 at 160° C. Writing Q for the Joule-Thomson " cooling effect," dO/dp, or the slope BC/AC of the line of constant total heat, he found that Q was nearly independent of the pressure at constant temperature, a result which agrees with that of Joule and Thomson for air and COs; but that it varied with the temperature as (1/0) 3.8 instead of (i/0) 2.
- These results for the variation of Q are independent of any assumption with regard to the variation of H.
- The experimental results of Grindley with regard to the mode of variation of Q have been independently confirmed by Callendar (Proc. R.S.
- (is) The index n in the above formula, representing the rate of variation of c with temperature, is approximately the same as that expressing the rate of variation of the cooling effect Q, which is nearly proportional to c, and is given by the formula SQ= (n+i)c - b..
- Callendar's experiments on the cooling effect for steam by the throttling calorimeter method gave n =3-33 and c =26.3 c.c. at 100° C. Grindley's experiments gave nearly the same average value of Q over his experimental range, but a rather larger value for n, namely, 3.8.
- Regnault's formula for the total heat is here again seen to be inadmissible, as it would make the latent heat of steam vanish at about 870° C. instead of at 365° C. It should be observed, however, that the assumptions made in deducing the above formulae apply only for moderate pressures, and that the formulae cannot be employed up to the critical point owing to the uncertainty of the variation of the specific heats and the cooling effect Q at high pressures beyond the experimental range.
- Q, Cooling effects in adiathermal expansion.
- I ancaste r ?r y q 1 4N ?U N „?;?'
- The law passed by him and his colleague Q.
- In the 4th and 5th centuries it was frequently used in the West of any q y }' bishop (Du Cange, s.v.); but it gradually came to be reserved to the bishop of Rome, becoming his official title.