Q Sentence Examples

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).

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.

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)').

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

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?

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.).

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 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.

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.

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.

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.

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.

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 =..

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 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.

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.

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.

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

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.

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.

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.

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.

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,.

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?

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?'

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.

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.

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.

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

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

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

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

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.

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

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.

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 ?

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.

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.

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).

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

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."

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.

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.

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.

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).

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.

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.

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.

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

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'.

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 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.

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.

Density thgllsh per q.

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.

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.

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.

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.

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.

P Q B R' S R S being the sun.

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."

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'.

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.

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.

It therefore made the aspirates A, E, Q and the semi-vowel I into vowels, and apparently converted the semi-vowel Y = w into the vowel which it placed at the end of the alphabet and substituted for it as the sixth symbol of the alphabet the letter F with the old value of w.

For the Greek digamma Etruscan used both 3 and q, but the former only was borrowed by the other languages.

Q is found on Etruscan inscriptions, but not in the alphabet series preserved; neither Umbrian nor Oscan has this form.

Lobo wrote an account of his travels in Portuguese, which appears never to have been printed, but is deposited in the monastery of St Ro q ue, Lisbon.

It gives shelter not only to vessels plying to its adjoining ports but serves as a harbour of refuge for shipping bound up or down the Atlantic coast, and is fre q uently used for the assembling of naval fleets.

Thus, if the two forces P,Q be represented by the lines OA, OB, they can be replaced by a single force FIG.

Hence if forces P, Q act in OA, OB, the resultant R will pass through C, provided m=P/OA, n=Q/OB;

If we now imagine the point 0 to recede to infinity, the forces P, Q and the resultant R are parallel, and we have R=P+Q, P.AC=Q.CB.

When P, Q have opposite signs the point C divides AB externally on the side of the greater force.

If F, Q, R, be any three forces acting along BC, CA, AB, respectively, the line of action of the resultant is determined by the consideration that the sum of the moments about any point on it must vanish.

Again if PQ be any segment of the beam which is free from load, Q lying to the right of P, we find FPFQ, MPMQ=--F.PQ; (12)

Each extraneous force W acting on a bar may be replaced (in an infinite number of ways) by two components P, Q in lines through the centres of the pins at the extremities.

In practice the forces W are usually vertical, and the components P, Q are then conveniently taken to be vertical also.

We first alter the problem by transferring the forces F, Q to the pins.

The assemblage of parallel forces P can be replaced in general by a single force, and the coplanar system of forces Q by another single force.

The plane in question is called the null-plane of P. If the null-plane of P pass through Q, the null-plane of will pass through P, since PQ is a null-line.

General Motion of a ParticleLet P, Q be the positions of a moving point at times t, t+t respectively.

Let P, Q be the positions of a u-i.aa moving point at times t, t + &, V Q

For consider any two particles at P and Q, acting on one another with equal and opposite forces in the line PQ.

For in time t the mutual action between two particles at P and Q produces equal and opposite momenta in the line PQ, and these will have equal and opposite moments about the fixed axis.

The equation of the latter, referred to its principal axes, being as in II (41), the co-ordinates of the point J where it is met by the instantaneous axis are proportional to p, q, r, and the direction-cosines of the normal at J are therefore proportional to Ap, Bq, Cr, or X, u, v.

The motion of a rigid body in the most general case may be specified by means of the component velocities u, v, w of any point 0 of it which is taken as base, and the component angular velocities p, q, r.

If we eliminate P, Q, R from (22), the resulting equations are integrable with respect to t; thus Moa - M0a.

If 01 be drawn vertically upwards, then in the beginning of the disturbed motion the quantities x, y, p, q, P, Q will all be small.

If p, q, r be the component angular velocities about the principal axes at 0, we have (Ap+B2q+C,2)/r = (Ap+Bq1+Cr2)/2T, (3) each side being in fact equal to unity.

The moving axes Ox, Oy, 01 form a rigid frame of reference whose motion at time t may be specified by the three component angular velocities p, q, r.

When, in any problem, the values of u, v, w, p, q, r have been determined as functions of t, it still remains to connect the moving axes with some fixed frame of reference.

Since an, = a,r, the coefficient of Q, in the expression for qr is identical with that of Q,- in the expression for q,.

But, p and q being respectively the perpendiculars to the lines of action of the forces, this equation reduces to Pp=Rq, FIG.

Q the letter which immediately succeeds P in the alphabet of Latin and the modern languages of western Europe.

In the Phoenician alphabet a sibilant Zade (Tzaddi) stands between q and p. Hence Q is the nineteenth letter in the Phoenician alphabet, the eighteenth in the Greek numerical alphabet, which alone contains it, the sixteenth (owing to the omission of 8 and E) in the Latin, and (from the addition of J) the seventeenth in the English alphabet.

This is also the earliest form in the Latin alphabet, but forms with the upright turned to the right as in a modern Q are found in the Republican period, while this tail becomes longer and curved in the early Empire.

Many languages find the combination qu, when both sounds are consonantal (qw), difficult; q being the deepest guttural while u (English w) is a lip sound, the points of production are nearly as far separate as they can be.

The Venetians q retained their acquisition for eighty-two years, notwithstanding the neighbourhood of the Turks.

The velar tenuis q, when labialized, became qu, without labialization became k; the velar media g became b or g.

Their numerators are denoted by Pi, P2, their denominators by q,, q2, q3, We have the relations p n = an pn-1 +bn pn-2, qn = angn-1 +bngn-2.

If r be the number of quotients in the recurring cycle, we can by writing down the relations connectin g the successive p's and q's obtain a linear relation connecting p nr +m, t'(n-1)r +m, +m in which the coefficients are all constants.

The functions p n and q n, regarded as functions of a l,..

The Celts represented Indo-European q by p, whilst the Greeks, Illyrians, Thracians, Ligurians, and aborigines of France, Britain and Ireland represented it by k, c or qu.

For if in the triangle abc the side ab is taken so as to represent on a given scale the tension of the surface of contact of the fluids a and b, and if the other sides be and ca are taken so as to represent on the same scale the tensions of the surfaces between b and c and between c and a respectively, then the condition of equilibrium at 0 for the corresponding tensions R, P and Q is that the angle ROP shall be the supplement of abc, POQ of bca, and, therefore, QOR of cab.

If T12 denote the interfacial tension, the energy corresponding to unit of area of the interface b Q FIG.

The second minus the first, or the increase in the sum of tensions, is thus 2 (U n - o' n+l) (o n+ 1 - Q n +2) Hence, if an+1 be intermediate in magnitude between a,, and a71+2, the sum of tensions is increased by the abolition of the stratum; but, if a-n+1 be not intermediate, the sum is decreased.

The degree of instability, as measured by q, is not to be determined from statical considerations only; otherwise there would be no limit to the increasing efficiency of the longer wavelengths.

It appears that the value of q may be expressed in the form q=1,1.

Thus, if d= 1, q -1 -= -115; or for a diameter of one centimetre the disturbance is multiplied 2.7 times in about one-ninth of a second.

Then if p be the density of the upper liquid, and Q that of the lower liquid, and P the original pressure at the surface of separation, then when the surface receives an upward displacement z, the pressure above it will be P - pgz, and that below it will be P - Ogz, so that the surface will be acted on by an upward pressure (p - Q)gz.

In some filamentous forms this " fragmentation " into multicellular pieces of equal length or nearly so is a normal phenomenon, each partial filament repeat s ing the growth, division and q?

C D 0K2, a b c m Q c 6 L -...

The Czech (Cech) alphabet is the same as the English, with the omission of the letters q, w and x.

The arrows m, n, o, p, q, r indicate the direction of travel.

Bay ll c t ' LY Q " yy be Pony.

In the second memoir he reserved for further consideration several ine q ualities of the moon's motion, which he could not determine in his first theory on account of the complicated calculations in which the method he then employed had engaged him.

This upper steelyard is arranged as in fig 9, where A is the point where the pull of the long body lever due to the weight of the goods on the platform comes upon the steelyard; C is the fulcrum of the steelyard, which with the steelyard can be slid to and fro on the frame of the machine; and Q 8 s frl FIG.

The steelyard is exactly in balance when there is no weight on the platform and Q is at the zero end of its run, at 0.

Let the lower bar of the steel yard be graduated in equal divisions of length, d, each of which represents one penny, so that the distance CA =q X d represents q pence.

Then the number p X q represents the total value of the goods on the platform.

If therefore the upper bar be graduated in divisions, each of which is 4, the indication of the poise Q, viz.

Thus to ascertain the value of goods on the platform of unknown weight at a given price per lb, it is only necessary to slide the steelyard till the weight acts at the division which represents the price per lb, and then to move the poise Q till the steelyard is in balance; the number of the division which defines the position of the poise Q will indicate the sum to be paid for the goods.

Parmenides sought to reduce the variety of nature to a single material element; but he strictly discriminated the inconstant 7retOri from the constant oboia, and, understanding by " existence " universal, invariable, immutable being, refused to attribute to the IraO'q anything more than the semblance of existence.

Similarly, if we divide n P by n q, where q is less than p, the result is n P - q.

The process depends on (ii) of § 45, in the extended form that, if x is a factor of a and b, it is a factor of pa-qb, where p and q are any integers.

If M and N are respectively m and n times a unit, and P and Q are respectively p and q times a unit, then the quantities are in proportion if mq = np; and conversely.

Thus any arithmetical processes which can be applied to the numbers p, q, r, ..

The circuits in which the batterybattery P and and d being galvanometer called the ratio branches placed are called conjugate circuits, and the circuits P, Q, R, and S are called the arms of the bridge, the '44 S arms and S the measuring arm.

To prove this statement, let the conductors P, Q, R, S., be arranged in a lozenge shape, as in fig.

In the practical instrument the three arms of the bridge P, Q, and S are generally composed of coils of wire contained in a box, whilst R is the resistance the value of which is to be determined.

The operation of determining the value of the resistance R therefore consists in altering the ratio of the three resistances P, Q,, and S, until the galvanometer indicates no current through it when the battery circuit is completed or closed by the key.

In one form of Wheatstone's Bridge, known as the series pattern plug-resistance bridge, or Post Office pattern, the two ratio arms, P and Q, each consist of a series of coils of wire, viz.

A and B are the coils to be compared, P and Q are two other L -x FIG.

He considers actions solely in respect of their pleasurable a nd painful consequences ex ected or actual; and he P q, P actual; school.

This circle, projected in Q perspective as an ellipse, is shown in X the figure.

Conceive a perpendicular PQ to be dropped from this point on the fundamental plane, meeting the latter in the point Q; PQ will then be parallel to OZ.

The problem of determining the perturbations of the (2) Q heavenly bodies is perhaps the most complicated with which the mathematical astronomer has to grapple; and the forms under which it has to be studied are so numerous that they cannot be easily arranged under any one head.

Now, consider the values of these same variables expressing the position of the planet at a second point Q, and the speed with which it passes that point.

The point E, being more distant than C, will be attracted with less force, while Q will be attracted with a greater force than will the centre C. Were the force equal on every point of the earth it would have no influence on its rotation, but would simply draw its whole mass toward the attracting body.

It is clear that at Q this residual force as represented by the arrow will be in the same direction as the actual force.

If nothing modified this tendency the result would be to bring the points E and Q into the dotted lines of the attraction.

Let APB be a semicircle, BT the tangent at B, and APT a line cutting the circle in and BT at T; take a point Q on AT so that AQ always equals PT; then the locus of Q is the cissoid.

Padua The school q y g of P adu a.

It is assumed that a flow of heat Q, due to conduction, tends to carry with it a proportional electric current C = aQ.

Quien, the interrogative pronoun which has taken the place of the old qul, seems to come from q u e rn.

This point settled, uniformity is q P y a location.

This involves the expenditure of a quantity of work W, the amount in any particular case being found by the equation W = Q2 - Q I, where W is the work, expressed by its equivalent in British thermal units; Q2 the quantity of heat, also in B.Ther.U., given out at the higher temperature T2; and Q i the heat taken in at the lower temperature T1.

It is evident that the discharged heat Qz is equal to the abstracted heat Q ', plus the work expended, seeing that the work W, which causes the rise in temperature from T 1 to Tz, is the thermal equivalent of the energy actually expended in raising the temperature to the level at which it is rejected.

The relation then between the work expended and the actual cooling work performed denotes the efficiency of the process, and this is expressed by Qt/(Q2-Q1); but as in a perfect refrigerating machine it is understood that the whole of the heat Q i is taken in at the absolute temperature T 11 and the whole of the heat Q2, is rejected at the absolute temperature T2, the heat quantities are proportional to the temperatures, and the expression T,/(T 2 -T,) gives the ideal coefficient of performance for any stated temperature range, whatever working substance is used.

If r represents the latent heat of the vapour, and q 2 and q1 the amounts of heat contained in the liquid at the respective temperatures of T2 and T11 then the loss from the heat carried from the condenser into the refrigerator is shown by (q2-q1)/r and the useful refrigerating effect produced in the refrigerator is r-(q 2 -q i).

This is shown by the curve AB, and is the useless work represented by the expression (q 2 -q 1)/r.

After some work, they found there were nineteen different letters used, with "E, I, L, O, U, Q, and W" missing.

This was the location of a Q site decoy aerodrome for Methwold.

Genu valgum, external tibial torsion and femoral anteversion increase the Q angle.

A Uruguay Q In which year did Fat Les sing Vindaloo, Englands unofficial anthem that year?

Q. How many qualified archivists does the Museum employ?

Q Should I be seeking similar assurances from my suppliers?

Q Why are there sometimes issues about stock availability?

Regards, Lawrence Chard Q Hello there, My inquiry is I have a gold bangle.

Q. My mother aged 71 has recently been taking barbiturate sleeping pills.

Q. What temperature should I wash my baby bed linen in to kill bacteria?

There's a big pair of double gates here, much beloved by Network Q spectators.

Q. Do you still use hot bitumen (tar )?

More... Q. Can your explain the grading of carbon blanks?

Q I would very much like to cheer myself up and go blond.

Send this article to a friend Q. Why has my skin gone blotchy?

Campus Q. Can I come and visit the campus Q. Can I come and visit the campus at any time?

Q Hi Alan, We have a beautiful coffered ceiling in our master bedroom.

Q To be an atheist in his time was likely to attract public censure.

Q. What can be done to prevent cleft lip?

Q. Can I use coinage from the Channel Islands or the Isle of Man?

Of all the would-be competitors to the Palm Treo 650 we've seen, the Motorola Q seems best poised to surpass it.

Q Why does the CIA need an exemption from rules that would govern the conduct of our military in interrogation practices?

Q. What is the current view on combined oral contraceptives for people with lupus?

Q. As to the cause of death one cause is given, namely coronary thrombosis?

Using our estimate of 0.9m for leg-length, this leads to the estimate v q crit = Ö 10.

I tiled the shower cubical in the same way, with cork adhesive, from B&Q.

This information was conveyed to Mr Q in a letter dated 21 August.

Q. Can the detail of our final declaration be different from the draft declaration that we submitted in October?

Thus it was that the Q lay exposed on the table, while declarer played A and ruffed a diamond.

Q - I have heard of laser diffusers what are these?

A. To warn the driver that the level crossing gates were shut against the railroad Q What building is in the left background?

Q. Can a student Nurse act as an approved witness when administering a controlled drug?

Q. Do you now have your own version of the girl with the pearl earring hanging up at home?

Q 1. 1 For whom has this e-book been written?

Q. How are we to use the word, if we would have it made effectual to salvation?

Q. We received a letter from Barclays Bank offering compensation for a mis-sold endowment.

Q 4-4 Do I need permission to show a copyright image using an epidiascope or similar device?

Q. Could recent mercury exposure affect the developing fetus?

Q. Water constantly runs or drips through the group head itself or into the drip tray from behind the stainless steel facia plate.

Q Quickfencer Faster, lighter, easier and safer Lamma show 2004/2005 winner Models available for equestrian fencing.

Q Hi, I believe it is bad feng shui for the end of the bed to face a door.

Quark (q) A fundamental fermion that has strong interactions.

Q 9. 21 How can we assess male fertility?

Q Do your house signs come with wall fixings?

Q / Are there any restrictions on using the flumes in the leisure pool?

A. Specialist foreign language teachers; primary generalists; Native speaker etc. etc. Q. Who are the pupils?

Q. Why ca n't gripe water be given to babies under a month old?

Q. A man in the audience said, " If ministers stop preaching hellfire, they will have no control over their people.

Q. Is it true that rheumatism can be helped by Ayurvedic herbs?

No definitive answers from Q or Mojo so far, but the fat lady ai n't hollered yet.

This should only take a few days. Q I am taking hydrocortisone.

So that means that the value of x is given by cos( q) multiplied by the hypotenuse.

Mrs Q had suffered a myocardial infarction whilst in the unit.

In that case the general, tho not invariable, superiority of the Q version remains to be accounted for.

Q, the eccentric inventor of British spy gadgets in the James Bond movies, would be proud of that Moscow rock.

Q If ITV merges, is it not invidious that two sales houses will report to one Plc?

Q Horror movies- especially those that feature deranged killers are very prone to getting future installments.

Q. Can I make any money from this plot of land A. No Q. can children become lairds?

Q. My horse has acute laminitis now, is Formula 4 Feet safe to feed?

Q What advice should a solicitor give to a client commencing litigation on a pro bono basis about costs?

Ministers will announce that they see no reason to bow to the demands of a vociferous lobby led by Asda, B&Q and Ikea.

Q A I have had lupus for about four years.

Q What should I do when I have active lupus and get a bad cold or flu?

Q What one piece of advice would you give to someone trying macrobiotics for the first time?

That one night changed my outlook on many things, including my future life's work Q How has macrobiotics helped you?

Q - I became partially deaf as a result of the german measles at the age of eleven.

On the other hand there, R is the completion of Q under the Euclidean metric.

During Bond's tour of Q's laboratory, a boom mic is briefly visible at the top of the screen.

Q I used to use the minus sign - to play my blank tile.

Q. What has caused the extreme motion sickness throughout my pregnancy?

Chapter One Q. Where is the home of the Russian navy 's Baltic Fleet?

High resolution at low Q is handy for indexing, and is essential for tackling moderately complex magnetic structures with powder neutron data.

Q. What do you call a nun with a washing machine on her head?

Were there such grounds the of formal logic would require distinct semantic accounts for the wffs p q and p q and p p.

Q. Can I labor with a low lying placenta?

Stages of labor Q. What causes a retained placenta?

Q. Can a competent plumber install a heat pump to run my central heating system?

Back to top Q - Were any of the cast puppeteers before they joined AVENUE Q?

On the five first four hands would net q want to be.

Therefore, that interval contains a rational q x and all those rationals are distinct.

There are numerous good restaurants in the Citadelle end of town. q Night 3.

A calling station would net q throwing darts shooting you a sense.

Thus the body m n is surrounded by a larger amount of light than the body p q, as is shown above.

Indeed, this is a norm on f q (t ).

The Poisson approximation would be acceptable (q small and k q small ).

Figure 2 shows the dependence of bending stiffness on test angle q.

A unit quaternion has m = 1. det( Q R )= m 4.

The project must be within a 20-mile radius of a B&Q store.

Question & Answers Q My partner occasionally hits me, the last time was 8 months ago, but he was very remorseful afterward.

In many cases the high Q element can be realized by using a dielectric resonator.

This is shown by the mean reversion of q relative to its average.

Q Surely the huge success of the BBC's Blue Planet series could herald a revival?

Q. There are a number of very romantic moments in the film - are you a romantic at heart?

He won with the J, cashed A, crossed to Q and scored a diamond ruff.

Q - How do I report someone else breaking a rule?

Book online for Avenue Q The quirky, silly and splendidly salacious Broadway hit arrives in the West End at last.

The people who founded Q, meanwhile, have all scarpered off to Word magazine.

Q Could you please send me an immunization schedule for Derbyshire?

Q Do you inevitably develop scleroderma if you have severe Raynaud's?