# F Sentence Examples

From the time your period begins until ovulation, your temperature will vary between 97.2 degrees

**F**and 97.6 degrees**F**, but from the time of ovulation until your next period begins, your BBT will typically raise as much as one degree.Unhealthy material should only be composted if you manage your compost pile with strict controls and can be sure that the compost pile will reach a temperature of at least 120

**F**and remain at that temperature for two to three weeks.In practice this subdivision of the segments is so far extended that the intervals of disconnexion become extremely A Line- ----- 2/ --

**f**?Reports to the Postmaster-General upon proposals for transferring to the Post Of

**f**ice the Telegraphs throughout the United Kingdom (1868); Special Reports from Select Committee on the Electric Telegraphs Bills (1868, 1869); Report by Mr Scudamore on the reorganization of the Telegraph system of the United Kingdom (1871); Journ.**F**, Acrecbolic (= pleurembolic) introvert, formed by the snout of the proboscidiferous Gastropod.It is attached to a brass disk E, which is fastened to the centre of the diaphragm

**F**by means of a rivet, and is capable of moving to and fro like a plunger when the diaphragm vibrates.The foot is long, carrying the oblong visceral mass upon it, and projecting (as metapodium) a little beyond it(

**f**).The ciliated band of the left side of the velar area is indicated by a line extending from v to v; the foot

**f**is seen between the pharynx ph and the pedicle of invagination pi.Porphyry says of Origen, Kara Tds rrepi lrpay

**f**caTWV Kai Belot) bo s as `EXX vt cav (Euseb.E is the ear-piece made of ebonite;

**F**is a cap of the same material enclosing the receiver terminals, which are mounted upon the ebonite block G, attached to the distance piece I.AdvertisementFor the boarding schools, or convilli, there are only incomplete reports except

**f**or the institutions directly dependent on the ministry of public instruction, which are comparatively few.The Italians were tired of

**f**,ghting, and the leaders of both factions looked exclusively to their own interests.During the same period the assumption of the Venetian and Roman debts, losses on the issue of loans and the accumulation of annual deficits, had caused public indebtedness to rise from 92,000,000 to 328,000,000, no less than

**f**100,000,000 of the latter sum having been sacrificed in premiums and commissions to bankers and underwriters of loans.**F**, the founder-polyp; I, 2, 3, 4, the succession of polyps budded from the founder-polyp; a', b', c', the succession of polyps budded from 1; a 2, 2 polyps budded from 2; a 3, polyp budded from 3.**F**, foundersecond bud, which usually polyp; I, 2, 3, succession of polyps forms a side branch or pinnule budded from the founder.Advertisement**F**, founder-polyp; 1, 2, 3, 4, 5, 6, succession of polyps budded from the founder; a, b, c, second series of polyps budded from the founder; a 3, b 3, series budded from 3.The next step is illustrated by the female gonophores of Cladocoryne, where the radial and ring-canals

**F**G H Modified from Weismann, Entstehung der Sexualzellen bei den Hydromedusen.A-D are stages common to both; from D arises the hydrotheca (E) or the gonotheca (

**F**); th, theca; st, stomach; 1, tentacles; m, mouth; mb, medusa-buds.Stratford-on-Avon (Stradforde, Straf

**f**ord, Straffordon-Avon) is a place of great antiquity.**F**, Section through the surface tissue of the Brown Alga Cutleria multifida, showing the surface layer of assimilating cells densely packed with phaeoplasts.AdvertisementPhysically wet but physiologically dry ha bit ats,

**f**with the accompanying plant communities of fens, moors, and salt marshes.**F**, Separation of the chromosomes into two groups G, Chromosomes grouped at opposite ends of the spindle to forn the daughter nuclei.Fluorsulphonic acid, SO 2

**F**OH, is a mobile liquid obtained by the action of an excess of hydrofluoric acid on well-cooled sulphur trioxide.He at once took a leading position in the mathematical teaching of the university, and published treatises on the Di

**f**ferential calculus (in 1848) and the Infinitesimal calculus (4 vols., 1852-1860), which for long were the recognized textbooks there.The ordinary revenue of the empire is in excess of the ordinary expenditure, but the extraordinary expenditure not only swallows up this surplus, but necessitates the raising of fresh

**F**loans every year.AdvertisementDuring the reign of Michael (1613-45) the new dynasty came to be accepted by all classes, and the country recovered to some extent from the disorders and exhaustion -4

**f**r om which it had suffered so severely; but it was not 1613-45.**F**o i Notwithstanding the efforts of the Poles and the Military Orders to exclude Russia from the shores of the Baltic and keep her in a state of isolation, she was coming slowly into closer relations with central and western Europe.The points over which a train travels when directed from the main to a branch line are called " facing points " (

**F**P), while those which it passes when running from a branch to a main line are " trailing points " (TP).At many intermediate stations the same arrangements, on a smaller scale, are made; in all of them there is at least accommodation for the passenger and the goods traffic. The stations for

**F**- FIG.The fundamental relation between the applied torque and the tractive force

**F**will be understood from fig.Assuming the wheels to roll along the rail without slipping, this couple will be equivalent to the couple formed by the equal opposite and parallel forces,

**F**1 acting in the direction shown, from the axle-box on to the frame, and**F**1 =µ0, acting along the rail.This force

**F**must not exceed the value.The maximum 1st, 2nd and 3rd class passenger fares are, per kilometre, 067

**f**.A list of horn-players of note during the 18th century is given by C. Gottlieb Murr in Journal

**f**.In the eastern and western portions of this city are situated the residences of the highest dignitaries of the empire; while beyond its confines on the south stand the offices of the six of

**f**icial boards which direct the affairs of the eighteen provinces.He received, however, the province of Languedoc. The peasant revolt of the Tuchins and Coquins, as the insurgents were called, was suppressed with great harshness, and the duke exacted from the states of Languedoc assembled at Lyons a fine of

**f**i 5,000.Quietism, name and thing, became the talk of all the world through the bitter and protracted controversy to which it gave rise between

**F**&.nelon and Bossuet.The eastern boundaries of between

**F**fronti urma er.There is also a corresponding diffusion o

**f**Japanese and Chinese forms along this zone, these being most numer - ous in the eastern Himalaya, and less frequent in the west.The prostomium overhangs the mouth, and is often of considerable size and, as a rule, quite distinct from the segment following, being A„

**f**s / 6/ ' A B I.The "Porisms" quoted are interesting propositions in the theory of numbers, one of which was clearly that the dif

**f**erence between two cubes can be resolved into of two cubes.Let AB be the major axis of the orbit, B the pericentre,

**F**the focus or centre of motion, P the position of the body.It contains the ruined capital of the ancient Hindu kingdom of Vijayanagar, and on the overthrow of that state by the Mahommedans, in

**f**564, the tract now forming the district of Bellary was split up into a number of military holdings, held by chiefs called poligars.B, Section through compound eye (after Miall and Denny); C, organs of smell in cockchafer; (after Kraepelin); D, a, b, sensory pits on cercopods of golden-eye fly; c, sensory pit on palp of stone-fly (after Packard); E, sensory hair (after Miall and Denny);

**F**, ear of long-horned grasshopper; a, Front shin showing outer opening and air-tube; b, section (after Graber); G, ear of locust from within (after Graber).Twinning is represented only by twinlamellae, which are parallel to the planes m and

**f**and are of secondary origin, having been produced by pressure.The area of the complete curve is 2a 2, and the length of any arc may be expressed in the form

**f**(1 - x 4) - i dx, an elliptic integral sometimes termed the lemniscatic integral.In every direction can be seen luxuriant valleys through which rivers thread their silvery way, wild chasms, magnificent waterfalls - that of Maletsunyane has an unbroken leap of over 600

**f**t.**F**, Fixed coil; D, Movable coil; S, Spiral spring; T, Torsion head; MM, Mercury cups; I, Index needle.Let the curve represent an elliptic orbit, AB being the major axis, DE the minor axis, and

**F**the focus in which the centre of attraction is situated, which centre we shall call the sun.To do this the actual speed in the orbit, and in a yet higher degree the angular speed around

**F**, must be greatest at pericentre, and continually diminish till the apocentre is reached.It follows that p must be greatest at pericentre, where its distance from

**F**is least.By geometrical consideration it can be shown that the angle subtended by p, as seen from

**F**, must be inversely as the square of its distance r.Another curious theorem proposed by Bouilland in 1625 as a substitute for Kepler's second law is that the angular motion of the body as measured around the empty focus

**F**' is (approximately) uniform.That is to an eye at

**F**', the planet would seem to move around the sky with a nearly uniform speed.One of these is the position of the line MN through the sun at

**F**in which the plane of the orbit cuts some fundamental plane of reference, commonly the ecliptic. This is called the line of nodes, and its position is specified by the angle which it makes with some fixed line FX in the fundamental plane.Since the distance of a body from the observer cannot be observed directly, but only the right ascension and declination, calling these a and 6 we conceive ideal equations of the form a =

**f**(a, b, c, e,**f**, g, t) and 5=0 (a, b, c, e,**f**, g, t), the symbols a, b,.Inorganic Chemistry Inorganic chemistry is concerned with the descriptive study o

**f**the elements and their compounds, except those of carbon.The other end is connected with the absorption vessels, which consist of a tube (e) containing calcium chloride, and a set of bulbs (

**f**) containing potash solution.A distinguished philosopher or man of letters would find them bidding

**f**o r his presence, and most of the great names are p ?I I KaTOLKb7ETE E7r ' i%7rt&c t' E

**f**loL »' ye shall dwell securely with me "; for here ir' iXxiSc, as several times in the Septuagint, is a wrong rendering of ni '.To form a roll the several sheets «oXX,

**F**.cara, were joined together with paste (glue being too hard), but not more than twenty sheets in a roll (scapus).The total length, including branches to Adana, Orfa (the ancient Edessa) and other places was to exceed 1550 m.; the kilometric guarantee granted was 15,500 francs (

**f**,;620).The new sultan's reign marked, if not the beginning, at least the high tide Aba-ui-Aziz, o

**f**that course of improvident and unrestrained 1861-1876.The Kurds, the constant oppressors of that people, had received official recognition and almost complete immunity from the control o

**f**the civil law by being formed into a Y g eo Y manry frontier-guard known as the Hamidian cavalry.The east coast of Greenland

**F**is in thii respect highly interesting.In 1758 Home became private secretary to Lord Bute, then secretary of state, and was appointed tutor to the prince of Wales; and in 1760 his patron's influence procured him a pension of 300 per annum and in 1763 a sinecure worth another

**f**Soo.Assuming then 01 to have the coefficients B1, B2,...B,, and

**f**l the coefficients A 1, A21...A,n, we may equate coefficients of like powers of x in the identity, and obtain m+n homogeneous linear equations satisfied by the m+n quantities B1, 2, ...B n, A 1, A 2, ...A m.Forming the resultant of these equations we evidently obtain the resultant of

**f**and 4,.Writing these results Dif = D(1)

**f**, D = D(2)**f**+D(l2)**f**, D3f = D(3)**f**+ (21)**f**+ D(13)**f**, s =1 (J1)11(J3)12(J3)13...If, however,

**F**involve as well the variables, viz.From these formulae we derive two important relations, dp4 = or the function

**F**, on the right which multiplies r, is said to be a simultaneous invariant or covariant of the system of quantics.We may write therefore 1 These forms, n in number, are called " associated forms " of

**f**(" Schwesterformen," " formes associbes ").Every covariant is rationally expressible by means of the forms

**f**, u 2, u3,...To exhibit any covariant as a function of uo, ul, a n = (aiy1+a2y2) n and transform it by the substitution fi y 1+f2 y where

**f**l = aay 1, f2 = a2ay -1, x y - x y = X x thence**f**.The first transvectant, (

**f**,**f**') 1 = (ab) a x b x, vanishes identically.The simultaneous system of two quadratic forms ai, ay, say

**f**and 0, consists of six forms, viz.If (

**f**,4) 1 be not a perfect square, and rx, s x be its linear factors, it is possible to express**f**and 4, in the canonical forms Xi(rx)2+X2(sx)2, 111(rx)2+1.2 (sx) 2 respectively.In fact, if

**f**and 4, have these forms, it is easy to verify that (**f**, 4,)i= (A j z) (rs)r x s x .This method of solution fails when the discriminant R vanishes, for then the Hessian has equal roots, as also the cubic

**f**.The Hessian in that case is a factor of

**f**, and Q is the third power of u2,...If, moreover, 0 vanishes identically

**f**is a perfect cube.The discriminant, whose vanishing is the condition that

**f**may possess two equal roots, has the expression j 2 - 6 i 3; it is nine times the discriminant of the cubic resolvent k 3 - 2 ik- 3j, and has also the expression 4(1, t') 6 .When

**f**= 6xix2 it will be found that 0 = -**f**.We will write the cubic covariant (

**f**, i) 2 =j, and then remark that the result, (**f**,j) 3 = o, can be readily established.The form j is completely defined by the relation (

**f**,j) 3 =o as no other covariant possesses this property.Certain convariants of the quintic involve the same determinant factors as appeared in the system of the quartic; these are

**f**, H, i, T and j, and are of special importance.Now, evidently, the third transvectant of

**f**, expressed in this form, with the cubic pxgxrx is zero, and hence from a property of the covariant j we must have j = pxgxrx; showing that the linear forms involved are the linear factors of j.To determine them notice that R = (a6) and then (

**f**, a 5) 5 = - R 5 (k1 +k2+k3) (**f**, a 4 5) 5 = - 5R5 (m 1 k 1+ m 2 k 2+ m 3 k 3), (**f**, a352) 5 = -10R5 (m21ke +m2k2+m3k3) three equations for determining k 1, k2, k3.When C vanishes j has the form j = pxg x, and (

**f**,j) 3 = (ap) 2 (aq)ax = o.The discriminant is the resultant of ax and ax and of degree 8 in the coefficients; since it is a rational and integral function of the fundamental invariants it is expressible as a linear function of A 2 and B; it is independent of C, and is therefore unaltered when C vanishes; we may therefore take

**f**in the canonical form 6R 4**f**= BS5+5BS4p-4A2p5.When R =0, and neither of the expressions AC - B 2, 2AB -3C vanishes, the covariant a x is a linear factor of

**f**; but, when R =AC - B 2 = 2AB -3C =0, a x also vanishes, and then**f**is the product of the form jx and of the Hessian of jx.When a z and the invariants B and C all vanish, either A or j must vanish; in the former case j is a perfect cube, its Hessian vanishing, and further

**f**contains j as a factor; in the latter case, if p x, ax be the linear factors of i,**f**can be expressed as (pa) 5**f**=cip2+c2ay; if both A and j vanish i also vanishes identically, and so also does**f**.They may bear accessory filaments or tentilla (

**f**'), covered thickly with batteries of nematocysts, to which these organisms owe their great powers of -offence and defence.If, however, the condition be the vanishing of i,

**f**contains a linear factor to the fourth power.If m, and m 2 are the strengths of two poles, d the distance between them expressed in centimetres, and

**f**the force in dynes,**f**=ml m2/d2 (I) The force is one of attraction or repulsion, according as the sign of the product m l m 2 is negative or positive.If V denote the potential,

**F**the resultant force, X, Y, Z, its components parallel to the co-ordinate axes and n the line along which the force is directed, then - sn =**F**, b?= X, - Sy = Y, -s Surfaces for which the potential is constant are called equipotential surfaces.If

**F**T is the force along r and**F**t that along t at right angles to r,**F**r =X cos 0+ Y sin 0=M 2 cos 0,**F**t = - X sin 0+ Y cos 0 = - r 3 sin 0.The internal force

**F**is opposite to the direction of the magnetization, and equal to NI, where N is a coefficient depending only on the ratio of the axes.The closed figure a c d e a is variously called a hysteresis curve or diagram or loop. The area

**f**HdB enclosed by it represents the work done in carrying a cubic centimetre of the iron through the corresponding magnetic cycle; expressed in ergs this work is I HdB.The current passes through the rocking key K, which, when thrown over to the right, places a in contact with c and b with d, and when thrown over to the left, places a in contact with e and b with

**f**.In a similar manner, by giving different values to the resistance 4

**F**R, any desired number of points R= between a and c in the curve can FIG.Denoting by W the work in ergs done upon a cubic centimetre of the metal (=_fHdB or

**f**HdI), he finds W =nips approximately, where n 47r is a number, called the hysteretic constant, depending upon the metal, and B is the maximum induction.In the case supposed therefore the total force per square centimetre is H2

**F**=2712-**f**-HI+B ?r (4 7r I +H)2 8?r B2 =87r.The equation

**F**= B 2 /87r is often said to express " Maxwell's law of magnetic traction " (Maxwell, Electricity and Magnetism,, §§ 642-646).He made use of the expression

**F**=Wg=27r12+HI, where W is the weight in grammes per square centimetre of sectional area, and g is the intensity of gravity which was taken as.The weight W is moved along the scale until the yoke just tilts over upon the stop S; the distance of W from its zero position is then, as can easily be shown, proportional to

**F**, and therefore to B 2, and approximately to I 2.It is shown in the paper that the greatest possible force which the isthmus method can apply at a point in the axis of the bobbin is

**F**= 11, 137 I, log i n b/a, I, being the saturation value of the magnet pores, a the radius of the neck on which the cones converge, and b the radius of the bases of the cones.The v, for

**f**, is common in southern English pronunciation; vox, for fox, is found in the Ancren Riwle, c. 1230.The circumstances of his appointment and the erroneous belief that he was receiving a pension of

**f**4 000 per annum for his few days' court work brought Campbell much unmerited obloquy.'The earliest temple in Paestum, the socalled Basilica, must in point of style be associated with the temples D and

**F**at Selinus, and is therefore to be dated about 57 0 -554 B.C.'In Austria the army was now supreme, and the appointment of Prince Felix Schwarzenberg as head of the government was a guarantee that its power would be used in a reactionary

**F**sense without weakness or scruple.If we represent this expression by

**f**(x), the expression obtained by changing x into x-+-h is**f**(x+h); and each term of this may be expanded by the binomial theorem.If we denote these by

**f**i (x),**f**2 (x),..By means of this theorem it can be shown that, whatever the value of n may be,

**f**1 + (plq)(i)x+(p/q)(2)x2+...We cannot, for instance, say that the fraction C _2 I is arithmetically equal to x+I when x= I, as well as for other values of x; but we can say that the limit of the ratio of x 2 - I to x - I when x becomes indefinitely nearly equal to I is the same as the limit of x+ On the other hand, if

**f**(y) has a definite and finite value for y = x, it must not be supposed that this is necessarily the same as the limit which**f**(y) approaches when y approaches the value x, though this is the case with the functions with which we are usually concerned.In the applications with which we are concerned, t, n are very small quantities; and we may take P = x yn - At the same time dS may be identified with dxdy, and in the de nominator p may be treated as constant and equal to

**f**.From the general formula (2), if A be the area of aperture, 102 = A2 / x2

**f**(7) The formation of a sharp image of the radiant point requires that the illumination become insignificant when, n attain small values, and this insignificance can only arise as a consequence of discrepancies of phase among the secondary waves from various parts of the aperture.In the particular case of a rectangular aperture the course of things can be readily followed, especially if we conceive

**f**to be infinite.If A' be the area over which the intensity must be Io in order to give the actual total intensity in accordance with A'102 =ff + 12d4dn, the relation between A and A' is AA' = X 2

**f**2 .Writing for brevity k =p, k =q, (1), we have for the general expression (§ 11) of the intensity X2

**f**212 = S 2 +C 2..The mean brightness varies as .51; and the integral

**f**J02(z)zdz is not convergent.If we suppose the diameter of the lens to be given (2R), and its focal length

**f**gradually to increase, the original differences of phase at the image of an infinitely distant luminous point diminish without limit.The distance

**f**i, which the actual focal length must exceed, is given by d (f1 2 R2) x; so that f1 = 2 R2/X (1) Thus, if X = p j, R= i ?, we find f1= 800 inches.Even for an aperture of 4 in.,

**f**1 would have to be 5 miles.In the case of a single lens of glass with the most favourable curvatures, Sf is about equal to a 2

**f**, so that a 4 must not exceed off.Thus

**f**t2 ds (for A) =**f**A ds (for B)..Accordingly, the optical distance from AoBo to A is represented by

**f**(A +S/c)ds, the integration being along the original path Ao.B) -

**f**S,u ds (along The new wave-surface is formed in such a position that the optical distance is constant; and therefore the dispersion, or the angle through which the wave-surface is turned by the change of refrangibility, is found simply by dividing (5) by the distance AB.If, as in common flint-glass spectroscopes, there is only one dispersing substance,

**f**Sy ds = Sµ.s, where s is simply the thickness traversed by the ray.If we put for shortness 7 for the quantity under the last circular function in (I), the expressions (i), (2) may be put under the forms u sin T, v sin (T - a) respectively; and, if I be the intensity, I will be measured by the sum of the squares of the coefficients of sin T and cos T in the expression u sin T +v sin (T - a), so that I =u 2 +v 2 +2uv cos a, which becomes on putting for u, v, and a their values, and putting

**f**=Q .If we write p = 27rR/A (6), we must regard p as a function of

**f**, and we may take with sufficient approximation under any ordinary circumstances where p' denotes the value of p at 0, and is a constant, which is positive when the retarding plate is held at the side on which the blue of the spectrum is seen.Only in this case can cos {p' +(m- -27th/Af)

**f**} retain the constant value - I throughout the integration, and then only when and a = 27Th/A**f**(8) cos p'=- 1 ..Then the displacement at 0 will take place in a direction perpendicular to 0 1 0, and lying in the plane Z0 1 0; and, if 1' be the displacement at 0, reckoned positive in the direction nearest to that in which the incident vibrations are reckoned positive, = 4?y (1 +cos 0) sin 4

**f**' (bt - r).Claudius Ptolemy (130) rectified this error, and in the so-called syntonous or intense diatonic scale reduced the proportions of his tetrachord to s, iii,

**f**, -i.Apart from this movement the most notable events in the Transvaal at this period were the development of agriculture,' the gradual revival of trade (the output of the gold mines in 1909 totalled

**f**30,925,000, and at the end of the year 156,000 native labourers were employed), and the continued difficulty with regard to British Indians.Praagh, The 1 The government expended over

**f**r,000,000 on a land and agriculture bank and in 1910 made a grant of**f**roo,000 towards the establishment of a college of agriculture at Pretoria.Other important contributors to this sphere of literature were Isho' bar Nan (t827/8), John bar Zo`bi (beginning of the 13th century), Jacob bar Shakko (f1241), and the great Nestorian scholar `Abadisho' (

**f**1318).There are other isolated sermons and treatises by

**f**lfric, printed in vol.Specialists may here and there improve on a statement or a theory, but it will always remain a great authority, a monument of patient and exhaustive research of intellectual power, and

**f**ripe and disciplined judgment.The fruit is edible and its juice is made into beer; the sap of the tree is made into wine, and its pith into bread; the leaves furnish an excellent thatch, and the fibre extracted from their midribs is used

**f**or fish lines, cordage, hammocks, nets, &c.; and the wood is hard and makes good building' material.The position of the river is highly

**f**vourable for the development of its trade.On raising the piston, the valve

**F**remains closed and a vacuum tends to be created in the cylinder, but the pressure of the atmosphere forces the liquid up the tube D and it raises the valve E and passes into the cylinder.On reversing the motion the valve E closes and the liquid is forced through the valve

**F**to the upper part of the cylinder.In this case the piston is solid, and the outlet pipe, G which is placed at the bottom of the cylinder, has a valve

**F**opening outwards, the inlet pipe and valve are the same as before.On raising the piston the liquid rises in the cylinder, the valve E opening and

**F**remaining shut.On again

**F**J J raising the piston the valve E opens ?g G admitting more liquid whilst**F**re- mains closed.Popa, a detached peak in the Myingyan district, belongs to this system and rises to a height of nearly 5000

**f**t., but it is interesting mainly as an extinct volcano, a landmark and an object of superstitious folklore, throughout the whole of Central Burma.In this table n is the refractive index of the glass for sodium light (the D line of the solar spectrum), while the letters C,

**F**and G' refer to lines in the hydrogen spectrum by which dispersion is now generally specified.It is used to determine the density of a body experimentally; for if W is the weight of a body weighed in a balance in air (strictly in vacuo), and if W' is the weight required to balance when the body is suspended in water, then the upward thrust of the liquid (I) (2) "

**F**r an Minim ' 'i n or weight of liquid displaced is W-W, so that the specific gravity (S.G.), defined as the ratio of the weight of a body to the weight of an equal volume of water, is W/(W-W').But by Green's transformation

**f**flpdS =**f****f**PPdxdydz, (2) thus leading to the differential relation at every point = dy dp The three equations of equilibrium obtained by taking moments round the axes are then found to be satisfied identically.Thus if the plane is normal to Or, the resultant thrust R =

**f**fpdxdy, (r) and the co-ordinates x, y of the C.P. are given by xR =**f****f**xpdxdy, yR =**f****f**ypdxdy.Suppose the ship turns about an axis through

**F**in the water-line area, perpendicular to the plane of the paper; denoting by y the distance of an element dA if the water-line area from the axis of rotation, the change of displacement is EydA tan 8, so that there is no change of displacement if EydA = o, that is, if the axis passes through the C.G.The 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.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.As an application of moving axes, consider the motion of liquid filling the ellipsoidal case 2 y 2 z2 Ti + b1 +- 2 = I; (1) and first suppose the liquid be frozen, and the ellipsoid l3 (4) (I) (6) (9) (I o) (II) (12) (14) = 2 U ¢ 2, (15) rotating about the centre with components of angular velocity, 7 7,

**f**'; then u= - y i +z'i, v = w = -x7 7 +y (2) Now suppose the liquid to be melted, and additional components of angular velocity S21, 522, S23 communicated to the ellipsoidal case; the additional velocity communicated to the liquid will be due to a velocity-function 2224_ - S2 b c 6 a 5 x b2xy, as may be verified by considering one term at a time.Thus for m =2, the spheres are orthogonal, and it can be verified that a13 a2 3 aY3 i

**f**/' = ZU (I - 13 - 7.2 3 + 3) ' (8) where a l, a2, a =a l a 2 /J (a 1 2 +a 2 2) is the radius of the spheres and their circle of intersection, and r 1, r 2, r the distances of a point from their centres.In the absence of a medium the inertia of the body to transtion is the same in all directions, and is measured by the (3) But the change of the resultant momentum

**F**of the medium as.In his valiant attempt to fill these gaps Rad„ u was obliged to invent kings and even dynasties, 13 the existence

**f**which is now definitely disproved.Extraction of cane juice by diffusion (a process more fully described under the head of beetroot sugar manufacture) is adopted in a few plantations in Java and Cuba, in Louisiana Etr cti o n and the Hawaiian Islands, and in one or two factories y

**f**i in Egypt; b u t hitherto, except under exceptional conditions (as at Aska, in the Madras Presidency, where the local price for sugar is three or four times the London price), it would not seem to offer any substantial advantage over double or triple crushing.These cells are

**f**- - imbedded in the peri pheral parenchyma, E"- and lead into convo luted excretory tubes _ that form an anasto- - mosis opening to the exterior by a pore at the " hinder " end of the body.The ancient Tanais lay some

**f**m.In German, however, V is used with the same value as

**F**, while W takes the value that V has in English.The rivers forming this system are the Maranon from Puerto Limon to Tabatinga on the Brazilian frontier (484 m.), the Japura, Putumayo, Javary, Napo, Tigre, Huallaga, Ucayali, Pachitea, Jurua, Purus, Acre, Curaray and Aguarico all navigable over parts of their courses for steamers of 4 to 8

**f**t.A, Dorsal view showing the nervous system and digestive system; a, mouth; b, pharynx; c, d, e, gut; E, post-genital union of two limbs of gut;

**f**, excretory pore; g, vaginal pore; h, j, k, brain and nerves; 1, dorsal nerves; m, ventral nerves; n, adoral sucker; o, posterior sucker; p, hooks on posterior sucker; r, vitello-intestinal duct.**F**intestine and so gets rid of the excess of yolk.Henri de Tourville, in his Histoire de la formation particulariste (1903), basing his argument on the Ynglinga Saga, interpreted in the light of " Social Science," reveals Odin, " the traveller," as a great " caravan-leader " and warrior, who, driven

**f**rem Asgard - a trading city on the borders of the steppes east of the Don - by " the blows that Pompey aimed at Mithridates," brought to the north the arts and industries of the East.There was some talk of inducing d J Y Th

**f**i $ g Glad stone to join the Tory government, and on the 29th of November Lord Malmesbury dubiously remarked, " I cannot make out Gladstone, who seems to me a dark horse."Men and women of all ranks began to visit it; the emperor himself consented (

**f**887) to witness a performance by the great stars of the stage at the private residence of Marquis Inouye; a dramatic reform association was organized by a number of prominent noblemen and scholars; drastic efforts were made to purge the old historical dramas of anachronisms and inconsistencies, and at length a theatre (the Yurabu-za) was built on purely European lines, where instead of sitting from morning to night witnessing one long-drawn-out drama with interludes of whole farces, a visitor may devote only a few evening-hours to the pastime.The present head, however, isa later substitute

**f**or the original, which was destroyed by fire.In 1692 he failed for

**f**17,000.According to the Canon Law, which "was the ecclesi- Pers

**f**- astical law of medieval Europe, and is still the law of heretics.The lining of these pits is amply supplied with branches from the trigeminal nerves, but the

**f**unction is still quite unknown.Let a charge +Q be

**f**t the ellipsoid a similar and slightly larger one, that distribution will be in equilibrium and will produce a constant potential throughout the interior.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).Then bearing in mind that a= (I/4x1-)dV/dn, and p =-(1/4xr)VV, we have finally E 2 c/v=2

**f****f**v.-dS+ 2J J J Vp dv.He therefore employed the corresponding expression for a cycle of infinitesimal range dt at the temperature t in which the work dW obtainable from a quantity of heat H would be represented by the equation dW =HF'(t)dt, where

**F**'(t) is the derived function of**F**(t), or dF(t)/dt, and represents the work obtainable per unit of heat per degree fall of temperature at a temperature t.It simply asserts that the efficiency function

**F**'(t), which is known as Carnot's function, is the same for all substances at the same temperature.Holtzmann (1845) by the same assumption deduced the value J/T for the function

**F**'(t), but obtained erroneous results by combining this assumption with the caloric theory.Clausius (1850), applying the same assumption, deduced the same value of

**F**'(t), and showed that it was consistent with the mechanical theory and Joule's experiments, but required that a vapour like steam should deviate more considerably from the gaseous laws than was at that time generally admitted.This most fundamental point was finally settled by a more delicate test, devised by Lord Kelvin, and carried out in conjunction with Joule (1854), which showed that the fundamental assumption W =H in isothermal expansion was very nearly true for permanent gases, and that

**F**'(t) must therefore vary very nearly as J/T.Kelvin had previously proposed to define an absolute scale of temperature independent of the properties of any particular substance in terms of Carnot's function by making

**F**'(t) constant.If, starting from E, the same amount of heat h is restored at constant pressure, we should arrive at the point

**F**on the adiabatic through B, since the substance has been transformed from B to**F**by a reversible path without loss or gain of heat on the whole.Since the amounts of heat supplied at constant pressure from E to

**F**and from E to C are in the limit proportional to the expansions EF and EC which they produce, the ratio S/s is equal to the ratio ECÃ†**F**.Observing that

**F**is a function of the co-ordinates expressing the state of the substance, we obtain for the variation of S with pressure at constant temperature, dS/dp (0 const) '=' 2**F**/dedp =-0d 2 v/d0 2 (p const) (12) If the heat supplied to a substance which is expanding reversibly and doing external work, pdv, is equal to the external work done, the intrinsic energy, E, remains constant.The energy E and the total heat

**F**are functions of the temperature only, by equations (9) and (I I), and their variations take the form dE = sdO, d**F**= Sd0.If we also assume that they are constant with respect to temperature (which does not necessarily follow from the characteristic equation, but is generally assumed, and appears from Regnault's experiments to be approximately the case for simple gases), the expressions for the change of energy or total heat from 00 to 0 may be written E - Eo = s(0 - 0 0),

**F**- Fo = S(0-00).But this procedure in itself is not sufficient, because, although it would be highly probable that a gas obeying Boyle's law at all temperatures was practically an ideal gas, it is evident that Boyle's law would be satisfied by any substance having the characteristic equation pv =

**f**(0), where**f**(0) is any arbitrary function of 0, and that the scale of temperatures given by such a substance would not necessarily coincide with the absolute scale.This gives by equation (9) the condition Odp/d0 =p, which is satisfied by any substance possessing the characteristic equation p/0=

**f**(v), where**f**(v) is any arbitrary function of v.The characteristic equation of the fluid must then be of the form v/0=

**f**(p), where**f**(p) is any arbitrary function of p. If the fluid is a gas also obeying Boyle's law, pv =**f**(0), then it must be an ideal gas.Putting d0/dp=A/0 2 in equation (15), and integrating on the assumption that the small variations of S could be neglected over the range of the experiment, they found a solution of the type, v/0 =

**f**(p) - SA /30 3, in which**f**(p) is an arbitrary function of p. Assuming that the gas should approximate indefinitely to the ideal state pv = R0 at high temperatures, they put**f**(p)=Rip, which gives a characteristic equation of the form v= Re/p - SA /30 2 .The value of B is determined by observing the latent heat, Lo =

**F**"o -**F**'0, which gives B =B" - B' =L0+(s' - So)00+(n+r)copo - bpo+dho (45) This constant may be called the absolute latent heat, as it expresses the thermal value of the change of state in a manner independent of temperature.Aramdisch, 2nd ed., p. 9

**f**.I

**f**.Rose the third day, A, B, D, E (

**F**omits " the third day " being a theological creed; the translation of C is uncertain).Estimated revenue X22,000; tribute

**f**,iioo.The reading micrometers e,

**f**also serve to measure, independently, the separation of the segments, by scales attached to the slides; such measurements can be employed as a check on those made by the screws.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.A second commission, which was appointed in 1901 and issued its final report in 1905, taking 4000

**f**t.The maintenance of the conditions of steadiness implied in equation (I) depends upon the constancy of

**F**, and therefore of the coefficient of friction µ between the rubbing surfaces.Poncelet (1788-1867) invented a form of Prony brake which automatically adjusted its grip as µ changed, thereby maintaining

**F**constant.Within any one year the precipitation is in general usually less in the western part of the state than in the eastern, the mean difference for all the years of record up to the close of 1903 being 2.5 in.; the western part also is marked by having a

**f**Aricetyn ?'Administration, Revenue,

**f**&c. - For administrative purposes the country is divided into districts (Bezirkscimter), and stations (Stationsbezirke).The fragment beginning TfOva

**F**t 'ac -yap xaaov has been translated by Thomas Campbell, the poet.Between

**F**and A A Virtual Virtual, erect, diminished Erect, same size CO Between oc and A A a superficial account of the traffic in indulgences, and a rough and ready assumption, which even Kostlin makes, that the darkness was greatest just before the dawn.It is generally accurate in

**f**acts but written in an unsatisfactorily eulogistic vein.Art was limited most of all by poverty

**F**in technical appliances.Now if the notch of the tan gent sight be carried to H' in order to lay on T, the fore-sight, and with it the axis, H will be moved to

**F**', the line of fire will be HF'D', and the shot will strike T since D'T = DT.The rocking-bar consists of a carrier a fixed to the cradle, a rockingbar d pivoted to the carrier at e, a sight bar

**f**carrying the sights and sighting telescope.In addition to this Guido is generally credited with the introduction of the

**F**clef.But he did not permit his political enterprise to stay his military preparations; and, by constant attention to the minutest details, by June 1 he had got together an army of 360,000 for the defence of France, one half

**f**of which was available for field service.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.The right trapezium so constructed,

**F**' may be called the equivalent right trapezium.Then the figure is (usually) the sum of two trapezoids

**F**on base AE, and its area can be calculated as in § 24.Let E and

**F**be two magnitudes so related that whenever**F**has any value (within certain limits) E has a definite corresponding value.The corresponding solid figure, in its most general form, is such as would be constructed to represent the relation of a magnitude E to two magnitudes

**F**and G of which it is a function; it would stand on a plane base, and be comprised within a cylindrical boundary whose cross-section might be of any shape.In the notation of the integral calculus, this area is equal to

**f**x o udx; but the notation is inconvenient, since it implies a division into infinitesimal elements, which is not essential to the idea of an area.Simpson's (first) formula, for instance, holds for

**f**= I, and is obtained by taking p = i and ignoring differences after 52up.If we write -fxo

**f**yox s yiu dx dy, we first calculate the raw values coo., ai,o, 0.1,1,If the data of the briquette are, as in § 86, the volumes of the minor briquettes, but the condition as to close contact is not satisfied, we have y "`x P u dx dy = K + L + R - X111010-0,0

**f**xo yo i'?Either or both of the expressions K and L will have to be calculated by means of the formula of § 84; if this is applied to both expressions, we have a formula which may be written in a more general form

**f****f**4 u4(x, y) dx dy = u dx dy.Even where u is an explicit function of x, so that

**f**x udx may be expressed in terms of x, it is often more convenient, for construction of a table of values of such an integral, to use finite-difference formulae.Among the incidental operations are (a) the valuation of the bullion by weighing and assaying it; (b) " rating" the bullion, or calculating the amount of copper to be added to make up the standard alloy; (c) recovering the values from ground-up crucibles, ashes and floor sweepings (the Mint " sweep "); (d) assaying the melted bars; (e) " pyxing " the finished coin or selecting specimens to be weighed and assayed; (

**f**) " telling " or counting the coin.The first fruits of his work were a comic opera, Der neue krumme Teufel, and a Mass in

**F**major (both written in 1751), the former of which was produced with success.I

**f**?.As AB returns from EF towards CD the layer of air next to it follows it as if it D E

**F**were pulled back by AB.But

**f**o 2dx=0 since the sum of the displacements = o.At the instant that the original wave reaches

**F**the wave from E has travelled to a circle of radius very nearly equal to EF-not quite, as S is not quite in the plane of the rails.But the interval between 4 and -4-`56 4-14 is quite perceptible, and on the piano, for instance, a separate string must be provided above

**f**.This note is

**f**sharp, and the interval t is termed a sharp.Taking the successive key-notes D, A, E, B, it is found that besides small and negligible differences, each introduces a new sharp, and so we get the five sharps, C, D,

**F**, G, A, represented nearly by the black keys.If we start with

**F**as key-note, besides a small difference at we have as the fourth from it 3 X 4 = y, making with B = I R 5 an interval and requiring a new note, B flat.In works on sound it is usual to adopt Helmholtz's notation, in which the octave from bass to middle C is written c d e

**f**g a b c'.The octave above is c' d'e'

**f**' g' a' b' c".Let an external force

**F**act on the system, and for simplicity suppose its period is so great compared with that of the mechanism that we may take it as practically in equilibrium with the restoring force.Suppose now that

**F**=a sin 22rn i t+b sin 21rn 2 t, the second term will evidently produce a series of combination tones of periodicities 2n 1, 2772, n, - n2, and n 1 -1-n 2, as in the first method.Peaceful overtures from Pretorius were declined, and some of his partisans in the Free State were accused %

**f**treason (February 1857).The latest change in the material of bridges has been the introduction of

**f**erro-concrete, armoured concrete, or concrete strengthened with steel bars for arched bridges.Launhardt found that, for stresses always of the same kind,

**F**= (t-u)/(t-fmax.) approximately agreed with experiment.For stresses of different kinds Weyrauch found

**F**In some recent masonry arched bridges of spans up to ' so

**f**t.Let A be the dead load and B the live load, producing stress in a bar; p =B / A the ratio of live to dead load;

**f**i the safe working limit of stress for a bar subjected to a dead load only and**f**the safe working stress in any other case.If a bar is subjected to alternations of stress having the range A =

**f**max .-**f**min ., then, by Wchler's law, the bar will ultimately break, if**f**maxPutting the values of

**F**in (1) and solving for**f**max ., we get for the breaking stress of a bar subjected to repetition of varying stress,**f**max.If A t A, are the cross sections of the tension and compression flanges or chords, and h the distance between their mass centres, then on the assumption that they resist all the direct horizontal forces the total stress on each flange is Ht=H,=M/h and the intensity of stress of tension or compression is

**f**t = M/Ath,**f**c = M/Ach.As the load travels, the shear at the head of the train will be given by the ordinates of a parabola having its vertex at A, and a maximum

**F**max.Till W 1 has advanced a distance a only one load is on the girder, and the curve A"

**F**gives bending moments due to W 1 only; as W1 advances to a distance a+b, two loads are on the girder, and the curve FG gives moments due to W 1 and W2.When the load is at

**F**', the reaction at B' is m/l and the moment at C' is m(l-x)ll, which will be reckoned positive, when it resists a tendency of the right-hand part of the girder to turn counter-clockwise.I c Is I

**f**l ?The point

**F**is.Consider any other point

**F**of the curve, fig.This page gives an overview of all articles in the 1911 Brittanica which are alphabetized under

**F**to Far.Only one compound of hydrogen and fluorine is known, namely hydrofluoric acid, HF or H 2

**F**2, which was first obtained by C. Scheele in 1771 by decomposing fluor-spar with concentrated sulphuric acid, a method still used for the commercial preparation of the aqueous solution of the acid, the mixture being distilled from leaden retorts and the acid stored in leaden or gutta-percha bottles.The latter integral becomes, on expanding in a series, fds/V

**f**(udx+vdy+wdz)/V2-1-**f**(udx+vdy+wdz)2/V3ds+..., since ids = dx.Moreover, this is precisely the condition for the absence of interference between the component of a split beam; because, the time of passage being to the first order fds/V

**f**(udx+vdy+wdz)V2, the second term will then be independent of the path (43 being a single valued function) and therefore the same for the paths of both the interfering beams. If therefore the aether can be put into motion, we conclude (with Stokes) that such motion, in free space, must be of strictly irrotational type.On the political and administrative side the struggle of the Poles was weakened by the faults which had been the ruin of their kingdom -

**f**action pushed to the point of anarchy, want.Collecting all the coefficients, into one, we put (I) R = nd 2 p = nd 2

**f**(v), where and n is called the coefficient of reduction.In any region of velocity where it is possible to represent p with sufficient accuracy by an empirical formula composed of a single power of v, say v m, the integration can be effected which replaces the summation in (to), (16), and (24); and from an analysis of the Krupp experiments Colonel Zabudski found the most appropriate index m in a region of velocity as given in the following table, and the corresponding value of gp, denoted by

**f**(v)or v m lk or its equivalent Cr, where r is the retardation.Now these integrations are quite intractable, even for a very simple mathematical assumption of the function

**f**(v), say the quadratic or cubic law,**f**(v) = v 2 /k or v3/k.If the pressure falls off uniformly, so that the pressure-curve is a straight line PDF sloping downwards and cutting AM in

**F**, then the energy-curve will be a parabola curving downwards, and the velocity-curve can be represented by an ellipse, or circle with centre**F**and radius FA; while the time-curve will be a sinusoid.But if the pressure-curve is a straight line

**F**'CP sloping upwards, cutting AM behind A in**F**', the energy-curve will be a parabola curving upwards, and the velocity-curve a hyperbola with center at**F**'.This muzzle velocity is about 5% greater than the 2150

**f**/s of the range table, so on these considerations we may suppose about 10% of work is lost by friction in the bore; this is expressed by saying that the factor of effect is**f**=0.9.A, B, C, D, E,

**F**, Terminals to which standard cell or voltages to be tested are attached.**F**, Projecting ungues of the furca.For these Tigqune Sopherim or " corrections of the scribes " see Geiger, Urschrift, pp. 308

**f**.; Strack, Prolegomena Critica, p. 87; Buhl, Canon and Text of the Old Testament, pp. 103**f**.Brixianus (

**f**) of the 6th century would be added if it were not probable that it is merely a Vulgate MS. with intrusive elements.This i

**f**the post-prophetic problem which occupies the more profound of the later Old-Testament books, but first received its true solution in the gospel, when the last shreds of the old nationalism disappeared and the spiritual kingdom found its centre in the person of Christ.Even when seen in minute features only he recognized them as constant progressive characters or " chronologic varieties " in 3b --i C D E

**F**G H I -14-21 -I-31 1 - I - 41 contrast with contemporaneous or " geographic varieties," which he considered inconstant and of slight systematic value.A pair of coiled nephridial tubes (n) formed of a file of perforated `' drain-pipe "cells, with ciliated tag-like" flame "cells (

**f**), open into a contractile bladder (bl), FIG.From these are given off at irregular intervals short lateral branches, each of which terminates in a flame-cell (

**f**) precisely similar in structure to the flame-cells found in Planarians, Trematodes and Cestodes; here as there the question whether they are open to the body cavity or not must probably be answered in the negative.G, enlarged view of the antenna

**f**.The extraing to foot of rotifers; at, median blastoporic opening of antenna, united by a nerve to br, brain the cloaca leads us to a (letter omitted in B); bl, bladder, re ver y different view, which ceiving ramified kidney in B, C, D; finds negative support

**f**, foot, and**f**.g, its cement-gland;.From a note in the manuscript we learn that two men,

**F**rman and Owun, made the version.For this purpose the C and

**F**lines in the spark-spectrum of hydrogen, situated in the red and blue respectively, are usually employed.If 6

**F**and Sc are the angular deviations of these rays, then S**F**- Sc is called the mean dispersion of the prism.This quantity may readily be expressed in terms of the refractive indices for the three colours, for if A is the angle of the prism (supposed small) bc=(/1c - I)A, bD =(/ AD - OA,

**F**- I)A, where µc, A n, µ**F**are the respective indices of refraction.In front of the church stands a marble fountain (

**F**), covered by a dome supported on columns.Facing the west are the stables (e), ox-sheds (

**f**), goatstables (g), piggeries (h), sheep-folds (i), together with the servants' and labourers' quarters (h).The choir terminated in a semicircular apse (

**F**), surrounded by five chapels, also semicircular.Immediately on the right of entrance was the abbot's house (G), in close proximity to the guest-house (

**F**).With a distinct entrance from the outer court was the kitchen court (

**F**), with its buttery, scullery and larder, and the important adjunct of a stream of running water.The hall was a very spacious apartment, measuring 83

**f**t.Obviously these equations show that the curves intersect in four points, two of which lie on the intersection of the line, 2 (g - g')x +2 (

**f**-**f**')y+c - c'=o, the radical axis, with the circles, and the other two where the lines x2+y2= (x+iy) (x - iy) =o (where i = - - I) intersect the circles.The St Lawrence varies only a few feet in the year and always has pellucid bluish-green water, while the Mississippi, whose tributaries begin only a short distance south of the Great Lakes, varies 40

**f**t.At the mouth of the White, the Arkansas and the Mississippi the level of recurrent floods is 6 or 8

**f**t.The gill axis d is seen lying in the sub-pallial chamber between the foot b and the mantle c. From it depend the gillfilaments or lamellae - formed by united filaments - drawn as black lines

**f**.In this region the inner lamellae of the inner gill-plates are no longer !

**f****f****f**fi**f****f**, I' .i!` FIG.Lankester suggested that

**f**, Foot.Thus the Roman letters E and

**F**are liable to be confused in capital script, but not in cursive (e,**f**), C, G, in capitals, c, e in the cursive writing called Caroline minuscule, c, t, in the angular cursive of the 13th century and later.On either alternative, however, " the first discourses " mentioned may have originally been a separate discourse; for Book

**F**begins quite fresh with the definition of the science of being, long afterwards called " Metaphysics," and Book Z begins Aristotle's fundamental doctrine of substance.Finally the group (0, Z), the book (E) and the group (II, 0), though unconnected with one another, are all connected though imperfectly with " the first discourses " (A,B,

**F**).**F**1), and investigates the axioms or common principles of things as things (ib.He especially owed his celebrity and fortune to his idea of crossing Niagara Falls on a tight-rope, i ioo

**f**t.For The Sake Of Greater Generality, The Days Of The Week Are Denoted By The First Seven Letters Of The Alphabet, A, B, C, D, E,

**F**, G, Which Are Placed In The Calendar Beside The Days Of The Year, So That A Stands Opposite The First Day Of January, B Opposite The Second, And So On To G, Which Stands Opposite The Seventh; After Which A Returns To The Eighth, And So On Through The 365 Days Of The Year.Now If One Of The Days Of The Week, Sunday For Example, Is Represented By E, Monday Will Be Represented By

**F**, Tuesday By G, Wednesday By A, And So On; And Every Sunday Through The Year Will Have The Same Character E, Every Monday**F**, And So With Regard To The Rest.The Fourth Year Was Bissextile, And The Dominical Letters Were

**F**, E; The Following Year D, And So On.In This Case X= 18, Therefore () R = 2; And In The Second Column Of Letters, Opposite 39, In The Table We Find

**F**, Which Is The Letter Of The Proposed Year.There Are Also Eight Lines In Which 25 And 26 Occur, Namely, C,

**F**, 1, P, S, C,**F**, P. In The Other 14 Lines, 25 Either Does Not Occur At All, Or It Occurs In A Line In Which Neither 24 Nor 26 Is Found.Revard (Paris, 1816); Delambre, Traite de l'astronomie theorique et pratique, tome iii.; Histoire de l'astronomie moderne; Methodus technica brevis, perfacilis, ac perpetua construendi Calendarium Ecclesiasticum, Stylo tam novo quam vetere, pro cunctis Christianis Europae populis,

**F**&c., auctore Paulo Tittel (GÃ¶ttingen, 1816); Formole analitsche pel 1 If Saturday, substitute Sunday immediately following.His charities were without limit; thus he contributed £300,000 for the relief of the sufferers from the Bengal famine of 1873-1874, and it is computed that during his possession of the raj he expended at least

**f**2,000,000 on charities, works of public utility, and charitable remissions of rent.If the mercury in the thermometer stand above this zero the spirit must be reckoned weaker than the hydrometer indicates by the number on the thermometer scale level with the top of the mercury, while C

**f**if the thermometer indicate a temperature a? ?!A small supernumerary weight

**F**is added, which can be placed upon the top of the stem.**F**is so adjusted that when the 60 weight is placed on the lower stem the instrument sinks to the same point in distilled water when**F**is attached as in proof spirit when**F**is removed.Although excelled by Alabama in th County Seats County Boundaries; ' -i

**f**y?See C.

**F**Adams, Jr., "Wessagusset and Weymouth" in No.D, E,

**F**, Trochosphere stage, D fp, Pore in the foot (belonging mf, The mantle-flap or limbus to the pedal gland?).Assuming for a moment the change to be one of density and leaving out of account the pressure shift, the cases (e) and (

**f**) point to the fact that it is the closeness of packing of similar molecules which is effective, e.g.The city lies about 7000

**f**t.**F**His point was that there are no things in themselves different from minds or acting on them; that man is no product of things; nor does his thinking arise from passive sensations caused by things; nor is the end of his existence attainable in a world of things; but that he is the absolute free activity constructing his own world, which is only his own determination, his self-imposed limit, and means to his duty which allies him with God.Further, Wundt declares that the psychical compound of sensations, with which, according to him, we actually start, is not a complex sensation, but a compound idea; so that I am expected to believe that, when I hear the chord of D, I am not conscious of single sensations of D,

**F**, A, and have only a compound idea of the chord - as if the hearing of music were merely a series of ideas!It is free from Moorish idioms, and, like Galician and Portuguese, it often retains the original Latin

**f**which Castilian changes into h.**F**, Wooden columns on existing stone bases, forming a porticus or covered walk along the top of the wall.The mica card is generally mounted on a brass framework,

**F****F**, with a brass cap, C, fitted with a sapphire centre and carrying four magnetized needles, N, N, N, N, as in fig.It can be divided into three regions - (i.) head,

**f**(ii.) trunk, and (iii.) tail, separated from one another by two transverse septa.Similarly if we have

**F**more unknowns than we have equations to determine them, we must fix arbitrarily**F**coordinates before we fix the state of the whole system.The number

**F**is called the number of degrees of freedom of the system, and is measured by the excess of the number of unknowns over the number of variables.The temperature may then rise and the concentration of B increase in the liquid in a manner represented by some such line as b

**f**.The conditions may then remain those of equilibrium along the curve

**f**E, but before reaching**f**the solution may become supersaturated with B and deposit B crystals spontaneously.The latent heat L at any temperature is given by L=Lo -

**f**0 64 0 (s - s')dT, where Lo is value at To and s--s' is the difference in the specific heats of water and ice.The resistance offered by the liquid, and therefore the force

**F**, required to drive one grammemolecule through the liquid with unit velocity is the sum of the corresponding quantities for the individual ions.Thus

**F**, which is equal to I/U-1-1/V, is known.**F**is a covered walk, with the necessary at the end.The shields of arms are for the dukes of

**f**iilich and Berg, counts of Ravensberg, and for the electors of Bavaria.The money they cost her was a small sum in comparison to the

**f**12,000,000 she lavished on her long series of lovers, who began with Soltykov and Stanislaus Poniatowski before she came to the throne, and ended with the youthful Platon Zubov, who was tenant of the post at her death.He obtained a high reputation, but his work was impaired by his controversial temper, which frequently developed into an irritated

**f**anaticism, though he was always entirely sincere.The badge is a white cross surmounted by the royal crown, in the centre the initial

**F**surrounded by a crimson fillet on which is the motto Furchtlos and Treu; in the angles of the cross are four golden leopards; the ribbon is crimson with two black stripes.In Scotland Robert Haldane sold his estate and devoted

**f**, 25,000 to the cause; with others he would have gone to India himself but for the prohibition of the East India Company, one of whose directors said he would rather see a band of devils in India than a band of missionaries.The rays, rendered parallel by the collimator objective, meet a plane mirror (

**f**) of silvered glass, which reflects them to the prisms (g, g').In order to bring a spectral line upon the camera slit, the slit is widely opened and the plane mirror (

**f**) rotated until the line is seen.A hot-water pipe

**f**should run along both sides of the pathway, close to the front ledge of the lowest beds.Fig 36, b and c, are examples of the former, and d, e,

**f**of the latter.