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The essence of the tax denoted by these names was that the amount was fixed en bloc for a whole group of persons, and afterwards divided among them in various ways.

30Originally it seems to have denoted the coast district between the Oder and the Vistula, a territory which was at first more or less dependent on Poland, but which, towards the end of the 12th century, was ruled by two native princes, who took the title of duke about 1170 and admitted the authority of the German king in 1181.

21The intensity (at any point) of the field due to the magnetization may be denoted by H i, that of the external field by Ho, and that of the resultant field by H.

10The Number Of Linearly Independent Seminvariants Of The Given Type Will Then Be Denoted By (W; 0, P; 0', Q) (W; 0, P; 0', Q); And Will Be Given By The Coefficient Of A E B E 'Z W In L Z 1 A.

11It is quite possible that shabattum and nubattum are from the same root and originally denoted much the same thing - a pause, abstention, from whatever cause or for ceremonial purposes.

00Nevertheless, though the conceptions originally denoted by " evolution " and " development " were shown to be untenable, the words retained their application to the process by which the embryos of living beings gradually make their appearance; and the terms" development," " Entwickelung,"and " evolutio " are now indiscriminately used for the series of genetic changes exhibited by living beings, by writers who would emphatically deny that " development " or " Entwickelung " or " evolutio," in the sense in which these words were usually employed by Bonnet or Haller, ever occurs.

00The Greek form of Gallia was FaXaria, but Galatia in Latin denoted another Celtic region in central Asia Minor, sometimes styled Gallograecia.

00He constructed a map of as many as 576 of these lines, the principal of which he denoted by the letters of the alphabet from A to G; and by ascertaining their refractive indices he determined that their relative positions are constant, whether in spectra produced by the direct rays of the sun, or by the reflected light of the moon and planets.

00As really denoted any integer or whole; whence the English word "ace."

00The words " Asiatic " and " Oriental " are often used as if they denoted a definite and homogeneous type, but Russians resemble Asiatics in many ways, and Turks, Hindus, Chinese, &c., differ in so many important points that the common substratum is small.

00Castor and Pollux), in astronomy, the third sign in the zodiac, denoted by the symbol II.

00In Zeumer's edition of the Leges Wisigothorum the versions of Recceswinth and Erwig, where they differ from each other, are shown in parallel columns, and the laws later than Erwig are denoted by the sign "nov."

00the hypothetical radicals of acids, were denoted by squares enclosing the initial letter of the base; an alkali was denoted by a triangle, and the particular alkali by inserting the initial letter.

00Compounds were denoted by joining the symbols of the components, and by varying the manner of joining compounds of the same elements were distinguished The symbol V was used to denote a liquid, and a vertical line to denote a gas.

00If two compounds combined, the + signs of the free compounds were discarded, and the number of atoms denoted by an Arabic index placed after the elements, and from these modified symbols the symbol of the new compound was derived in the same manner as simple compounds were built up from their elements.

00At a later date Berzelius denoted an oxide by dots, equal in number to the number of oxygen atoms present, placed over the element; this notation survived longest in mineralogy.

00The ringed structure of benzene, C 6 H 61 was first suggested in 1865 by August Kekule, who represented the molecule by six CH groups placed at the six angles of a regular hexagon, the sides of which denoted the valencies saturated by adjacent carbon atoms, the fourth valencies of each carbon atom being represented as saturated along alternate sides.

00A doubly linked pair of atoms is denoted by the sign A with the index corresponding to the side; if there are two pairs of double links, then indices corresponding to both sides are employed.

00The chief of these ministers is denoted 6 E7rl r&o' 7r pay µarwv, and he corresponds to the vizier of the later East.

001 In the early decades of the Christian era the text was current in two forms, which are denoted by H a and H R in this article and in the edition of the text published by the Oxford University Press.

00Such marks had often a religious significance, and denoted that the bearer was a follower of a particular deity.

00But the definition of the cardinal number of a class applies when the class is not finite, and it can be proved that there are different infinite cardinal numbers, and that there is a least infinite cardinal, now usually denoted by o where to is the Hebrew letter aleph.

00The function Zap 1 a 2 P2 ...an n being as above denoted by a partition of the weight, viz.

00The elementary functions are denoted by (1), (12), (13), ...

00The sum of the monomial functions of a given weight is called the homogeneous-product-sum or complete symmetric function of that weight; it is denoted by h.; it is connected with the elementary functions by the formula 1 7r1l7r2!7r3!

00It should be noticed that the real function denoted by (ab) 2 is not the square of a real function denoted by (ab).

00l ax 2 2 ax i l This is called the kth transvectant of f over 4); it may be conveniently denoted by (f, (15)k.

00Let this number be denoted by (w; 0, n).

00The extraordinary advantage of the transformation of S2 to association with non-unitary symmetric functions is now apparent; for we may take, as representative forms, the symmetric functions which are symbolically denoted by the partitions referred to.

00If 0=2, every form is obviously a ground form or perpetuant, and the series of forms is denoted by (2), (22), (23),...(2K+1)....

00Remark, too, that we are in association with non-unitary symmetric functions of two systems of quantities which will be denoted by partitions in brackets ()a, ()b respectively.

00It is not likely, as many scholars have thought, that Akkad was ever used geographically as a distinctive appellation for northern Babylonia, or that the name Sumer denoted the southern part of the land, because kings who ruled only over Southern Babylonia used the double title "king of Sumer and Akkad," which was also employed by northern rulers who never established their sway farther south than Nippur, notably the great Assyrian conqueror Tiglath pileser III.

00When the direction of any vector quantity denoted by a symbol is to be attended to, it is usual to employ for the symbol either a block letter, as H, I, B, or a German capital, as j,, 3?

00The intensity of magnetization, or, more shortly, the magnetization of a uniformly magnetized body is defined as the magnetic moment per unit of volume, and is denoted by I, I, or „a.

00an angle e with the normal, the normal component of the magnetization, I cos e, is called the surface density of the magnetism, and is generally denoted by a.

00A thin sheet of magnetic matter magnetized normally to its surface in such a manner that the magnetization at any place is inversely proportional to the thickness h of the sheet at that place is called a magnetic shell; the constant product hI is the strength of the shell and is generally denoted by 4, or 4.

00Hence if the induction per square centimetre at any point is denoted by B, then in empty space B is numerically equal to H; moreover in isotropic media both have the same direction, and for these reasons it is often said that in empty space (and practically in air and other nonmagnetic substances) B and H are identical.

00- The ratio B/H is called the permeability of the medium in which the induction is taking place, and is denoted byµ.

00The ratio I/H is called the susceptibility of the magnetized substance, and is denoted by «.

00du Bois (Magnetic Circuit, p. 33), the demagnetizing factor, and the ratio of the length of the ellipsoid 2c to its equatorial diameter 2a (=c/a), the dimensional ratio, denoted by the symbol nt.

00r is denoted by I?'

00- The numbers denoted by n (r) in ï¿½ 41 are the binomial coefficients shown in the table in ï¿½ 40; n (r) being the (r+ i) th number in the (n+ i) th row.

00(n+--r-1)lr!=n[r]lr!; this may, by analogy with the notation of ï¿½41, be denoted by n [r 7.

00A point A in space may be associated with a (real, positive, or negative) numerical quantity a, called its weight, and denoted by the symbol aA.

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

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

00This unit is called the supplement of E, and denoted by IE.

00Any linear quantity may be denoted by a symbol (a 1, a2, ...

00The unknown was called yavattavat, and if there were several, the first took this appellation, and the others were designated by the names of colours; for instance, x was denoted by yï¿½nd y by lea (from kalaka, black).

00Stifel introduced the sign (+) for addition or a positive quantity, which was previously denoted by plus, pia, or the letter p. Subtraction, previously written as minus, mene or the letter m, was symbolized by the sign (-) which is still in use.

00The square root he denoted by (j), whereas Paciolus, Cardan and others used the letter R.

00These works possess considerable originality, and contain many new improvements in algebraic notation; the unknown (res) is denoted by a small circle, in which he places an integer corresponding to the power.

00He follows Vieta in assigning the vowels to the unknown quantities and the consonants to the knowns, but instead of using capitals, as with Vieta, he employed the small letters; equality he denoted by Recorde's symbol, and he introduced the signs > and < for greater than and less than.

00His notation is based on that of Vieta, but he introduced the sign X for multiplication, - for continued proportion, :: for proportion, ' and denoted ratio by one dot.

00This last character has since been entirely restricted to multiplication, and ratio is now denoted by two dots (:).

003 By Syriac is denoted the dialect of Aramaic which, during the early centuries of the Christian era, prevailed in Mesopotamia and the adjoining regions.

00The divinity primarily denoted by it is the storm-god who was known also as Ramman, Bir and Dadda.

00Some such idea plainly underlies the familiar phrase "a sweet savour," more literally "a savour of satisfaction," whereby an acceptable offering by fire is so often denoted in the Bible (Gen.

00For instance, in a uniplanar flow, radially inward towards 0, the flow across any circle of radius r being the same and denoted by 27rm, the velocity must be mfr, and 0=m log r,, y=m0, +4,i =m log re ie, w=m log z.

00The components of velocity of the moving origin are denoted by U, V, W, and the components of angular velocity of the frame of reference by P, Q, R; and then if u, v, w denote the components of fluid velocity in space, and u', v', w' the components relative to the axes at a point (x, y, z) fixed to the frame of reference, we have u =U +u' - yR +zQ, v =V +v -zP +xR, w=W +w -xQ +yP.

00the moment of inertia of the body about the axis, denoted by But if is the moment of inertia of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o.

00The rise of Sargon's empire was doubtless the cause of this extension of the name of Akkad; from henceforward, in the imperial title, Sumer and Akkad " denoted the whole of Babylonia.

00When a quantity of heat, H, is supplied to a body, part is expended in raising the temperature of the body, or in expanding the volume against molecular forces, and is represented by an increase in the total quantity of energy contained in the body, which is generally called its Intrinsic Energy, and will be denoted by the symbol E.

00This quotient is called the change of entropy, and may be denoted by (4,"-0').

00Argus with his countless eyes originally denoted the starry heavens (Apollodorus ii.

00Let k denote this height, and let PM be denoted by 1.

00For by transliterating Ka7vap Nepc'ev into Hebrew 1113 10,P and adding together the sums denoted by the Hebrew letters we obtain the number 666.

00and censorious criticism of persons, morals, manners, politics, literature, &c. which the word satire has ever since denoted.

00In the lower margin of the page he inserted a selection of various readings, the relative importance of which he denoted by the first five letters of the Greek alphabet in the following manner: - a was employed to denote the reading which in his judgment was the true one, although he did not venture to place it in the text; 1 3, a reading better than that in the text; y, one equal to the textual reading; S and e, readings inferior to those in the text.

00Moreover, its prefects, since they were two and liable to be disunited, and since they could not be senators, neither combined with the In permanent forts and fortresses, praetorium probably denoted strictly a residence: the official headquarters building (though commonly styled praetorium by moderns) was the principia.

00is held to be compiled with editorial additions from the two ancient documents (90o-700 B.C.) commonly denoted by the symbols J and E.

002 In course of time the exposition of the lesson for the day came more frequently to assume a more elaborate character, and to pass into the category of a Aoyos or even OtXoo-ocNa or OtXoa04nj a; but when it did so the fact was as far as possible denoted by a change of name, the word op. Xla being reserved for the expository or exegetical lecture as distinguished from the pulpit oration or sermon.

00These fossils, which are now in the British Museum, were interpreted by Dr Mantell, who made comparisons with the skeleton of Iguana, on the erroneous supposition that the resemblance in the teeth denoted some relationship to this existing lizard.

00The ordinate of the trapezette will be denoted by u, and the abscissa of this ordinate, i.e.

00the distance of its foot from a certain fixed point or origin 0 on the base (or the base produced), will be denoted by x, so that u is some function of x.

00If the planes of one set divide it into m slabs of thickness h, and those of the other into n slabs of thickness k, so that H =mh, K = nk, then the values of x and of y for any ordinate may be denoted by xo+Oh and yo+Ok, and the length of the ordinate by uo, 0.

00(b) - 49(a), where 4)(x) is any function of x, by [c P(x)]; the area of the trapezette whose bounding ordinates are uo and u m may then be denoted by [Ax.

00In the same way the volume of a briquette between the planes x = xo, y = yo, x= a, y = b may be denoted by [[Vx,y ]y=yo] u 'x' =xo.

00The result of performipg both operations, in order to obtain the volume, is the result of the operation denoted by the product of these two expressions; and in this product the powers of E and of E' may be dealt with according to algebraical laws.

00This is called the trapezoidal or chordal area, and will be denoted by C1.

00This is called the tangential area, and will be denoted by T1.

00+ u m-p + zum), which may be denoted by Cp. With this notation, the area as given by Simpson's rule may be written in the form sC l - 3 C2 or CI+ 1 3 `-(C1C2).

00Hence, if the angle which the tangent at the extremity of the ordinate u 0 makes with the axis of x is denoted by fie, we have area from uo to u1= 2h(uo + ui) - -- i i h 2 (tan y l - tan t u 2 = Wu ' + u2) - 1 Tih 2 (tan 4,2 - tan um-1 t0 26 m, - 2 h(um-1 + um) i h (tan 4, m - and thence, by summation, A =C I - i i h 2 (tan - tan 1,1/o).

00moments, so calculated, before correction are denoted by p 1, P21

00Then, if the true moments are denoted by Pi, v 2, ..., their values are given by vi ?Pl P2 - 11.

00It is usually denoted by X.

00Hence the note produced with any given circle of holes rises in pitch as the disk revolves more rapidly; and if, the revolution of the disk being kept as steady as possible, the tube be passed rapidly across the circles of the first series, a series of notes is heard, which, if the lowest be denoted by C, form the sequence C, C1, El, G1, C2, &c. In like manner, the first circle in which we have two sets of holes dividing the circumference, the one into say 8 parts, and the other into Io,.

00denoted a necklace of twenty-seven pearls; 1 and the fundamental equality of the parts was figured in an ancient legend, by the compulsion laid upon King Soma (the Moon) to share his time impartially between all his wives, the twenty-seven daughters of Prajapati.

00The definition of the coefficients is that if (I-2h cos cp+h 2)-i be expanded in ascending powers of h, and if the general term be denoted by P„h', then P is of the Legendrian coefficient of the nth order.

00The resistance R can thus be divided into two factors, one of which is d 2, where d denotes the diameter of the shot in inches, and the other factor is denoted by p, where p is the resistance in pounds at the same velocity to a similar I-in.

00It is further assumed, as the result of experiment, that the resistance is proportional to the density of the air; so that if the standard density changes from unity to any other relative density denoted by then R= Td 2 p, and is called the coefficient of tenuity.

00If the inclination or change of inclination in degrees is denoted by S or OS, (21) 5/180=i/7r, so that (22) AS 180 _ 180g (Ot and if 5 and i change to D and I for the standard projectile, AT Ov 180g AT (23) DI =g ., = v p, AD = -Tr, and vv or J VQ'V, D(V) -D(v) = 180 [I(V) - i (v)].

00In 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.

0015.6 Tons 15.2 Tons steam-engine, representing graphically by a curve CPD the relation between the volume and pressure of the powder-gas; and in addition the curves AQE of energy e, AvV of velocity v, and AtT of time t can be plotted or derived, the velocity and energy at the muzzle B being denoted by V and E.

00144+x+y years, in all 554 years, + two unknown periods denoted by x and y-in any case considerably more than the 480 years of I Kings vi.

00The logarithm is also a function of frequent occurrence in analysis, being regarded as a known and recognized function like sin x or tan x; but in mathematical investigations the base generally employed is not 10, but a certain quantity usually denoted by the letter e, of value 2.71828 18284 ...

00The quantity denoted by e is the series, I I I+ I + i.2 +1.2.3+1.2.3.4 + the numerical value of which is, 2.71828 18284 59 0 45 2 353 6 02874.

00usually denoted by e.

00To every geometric mean in the column of numbers there corresponds the arithmetical mean in the column of logarithms. The numbers are denoted by A, B, C, &c., in order to indicate their mode of formation.

00Few traces of private houses have been found within the walls, but as deeds of sale speak of houses in Nineveh, which were bounded on three sides by other houses, there must have been continuous streets within the area denoted by that name.

00This ratio, invariably denoted by 7r, is constant for all circles, but it does not admit of exact arithmetical expression, being of the nature of an incommensurable number.

00For 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.

00instrument, let the solid be placed in the upper scale pan, and let the weight now required to cause the instrument to sink in distilled water at standard temperature to the mark B be denoted by w,.

00The end of this period is generally said to coincide with the loss of the French provinces to Philip Augustus, but literary and political history do not correspond quite so precisely, and the end of the first period would be more accurately denoted by the appearance of the history of 'William the Marshal in 1225 (published for the Societe de l'histoire de France, by Paul Meyer, 3 vols., 1891-1901).

00The significance of the word "mean," i.e., middle, is seen by considering 3 instead of n quantities; these will be denoted by a, b, c. The arithmetic mean b, is seen to be such that the terms a, b, c are in arithmetical progression,.

00It appears to have denoted the territory above Babylonia stretching from Anshan in the southeast north-westwards, across the Tigris-Euphrates district, indefinitely towards Asia Minor.

00The plural is denoted when required by adding one of several words of plurality.

00The most brilliant are situated at the intersections of the inner halo and the parhelic circle; these are known as parhelia (denoted by the letter p in the figures) (from the Gr.

00This Shekinah-glory is several times denoted in the New Testament by & a.

00The following is a select list of genera of miscellaneous decorative plants (orchids, palms and ferns excluded; climbers are denoted by *; bulbous and tuberous plants by f) Stove Plants.

00The following is a select list of genera of stove plants (climbers are denoted by *, bulbous and tuberous plants by f) Acalypha Achimenest Aeschynanthus Allamanda* Alocasiat Amaryllist Anthurium Aphelandra Aralia Ardisia Arisaemaf Aristolochia * Ataccia Begonia Bertolonia Bignonia* Bromeliads Cactus Caladium f Calathea Centropogon Cissus* Clerodendron * Crinumt Codiaeum (Croton) ORcftIDs.

00In ordinary isomers indications of mutual transformation often occur; and among these the predominant fact is that denoted as tautomerism or pseudomerism.

00In algebra it denoted the characters which represented quantities in an equation.

00If the gradient is not uniform, its value may be denoted by dB/dx.

00It would therefore seem that the name Germani originally denoted certain Celtic tribes to the east of the Rhine, and that it was then transferred to the Teutonic tribes which subsequently occupied the same territory.

00Others are the sibilation of consonantal i and the assibilation of -di- to some sound like that of English j (denoted by B in the local variety of Latin alphabet), as in vidadu, " viamdo," i.e.

00Unfortunately Buckle either could not define, or cared not to define, the general conceptions with which he worked, such as those denoted by the terms "civilization," "history," "science," "law," "scepticism," and "protective spirit"; the consequence is that his arguments are often fallacies.

00Thus the name which once denoted the good genius who bestowed the precious gift of water upon man was adopted to this use in vulgar Latin under the form Catamitus.

00Moreover, the solar period (II years) is far outside the limits of the periods of 1 Variable stars (except those sufficiently bright to have received special names) are denoted by the capital letters R to Z followed by the name of the constellation.

00The first nine variables recognized in each constellation are denoted by single letters, after which combinations RR, RS, &c., are used.

00The objects denoted by the other six names - ox, house, valve of a door, water, fish and mark or cross - clearly do not belong to any people in a nomadic state, but to a settled, town-abiding population..

00If we take A as origin and AN as axis of x, the weight of AP may be denoted by wx, where w is the weight per unit length at A.

00Let these projections be denoted algebraically by x1, xi,.

00The squares of the radii of gyration about the principal axes at P may be denoted by k,i+k32, k,f + ki2, k12 + k,2 hence by (32) and (35), they are rfOi, r2Oi, r20s, respectively.

00This acceleration is denoted by g; its value at Greenwich is about 981 centimetre-second units, or 322 feet per second.

00Thus the unit of velocity is that of a point describing the unit of length in the unit of time; it may be denoted by LTi, this symbol indicating that the magnitude of the unit in question varies directly as the unit of length and inversely as the unit of time.

00The unit of acceleration is the acceleration of a point which gains unit velocity in unit time; it is accordingly denoted by LT2.

00unit tinie and is therefore denoted by MLTI.

00The components of angular momentum about Ox, Qy, 01 will be denoted as usual by X, u, v.

00These equations, together with the arbitrary initial values of p, q,r, determine the six constants which we have denoted by po, go, r0, ki, a, ~.

00By an obvious analogy, the expressions OTfO4r may be called the generalized components of momentum; they are usually denoted by Pr, thus = OT/aq,.

00arid if this be denoted by o~1~ we have a second system of equations similar to (23).

00Let the angular velocity of the rotation be denoted by a=dO/dt, then the linear velocity of any point A at the distance r from the axis is or; and the path of that point is a circle of the radius r described about the axis.

00Let the axis Ai carry a wheel of N1 teeth, driving a wheel of ni teeth on the axis Ai, which carries also a wheel of N2 teeth, driving a wheel of 113 teeth on the axis A3, and so on; the numbers of teeth in drivers being denoted by Ns, and in followers by ns, and the axes to which the wheels are fixed being denoted by numbers.

00Then the resulting velocity ratio is denoted by a,, a~ ~3 & a,,, N, - Ni -.

00The symbolical expression of this law is as follows: let efforts be applied to one or any number of points of a machine; let any one of these efforts be represented by P, and the distance traversed by its point of application in a given interval of time by ds; let resistances be overcome at one or any number of points of the same machine; let any one of these resistances be denoted by R, and the distance traversed by its point of application in the gi- en interval of time by ds; then ~.Pds=2~.Rds.

00Let those be denoted by si and s~, so that s=si+si.

00On this a scholiast says that the name "Homeridae " denoted originally descendants of Homer, who sang his poems in succession, but afterwards was applied to rhapsodists who did not claim descent from him.

00Moral feeling, indeed, existed and was denoted by " Aidos "; but the numerous meanings of this word - shame, veneration, pity - show how rudimentary the idea was.

00The fact that the Phoenician Vau was retained in the Greek alphabets, and the vowel v added, shows that when the alphabet was introduced the sound denoted by was still in full vigour.

00It can only have fallen into disuse by degrees, as the sound which it denoted ceased to be pronounced.

00The term " finance," which comes into English through French, in its original meaning denoted a payment (finatio).

00H „ Light and represents a rise of about £I P „ Picked £3 G „ Grey £3 S „ Superior £4 W „ White £4 Z „ Zins Each additional mark means a rise in the price, but it must be understood that it is quite possible for a quality denoted by two letters to be more valuable than one indicated by three or more, since every mark has not the same value.

00Of the Greek there are three forms. One is in the Vatican and Alexandrian MSS.; another is in the Sinaitic. Both these texts are to be found in Swete's Septuagint, the former denoted by B, and the latter by B is the common text, which is followed in the English Apocrypha.

003 The Finns came to apply to the upper gods the term Yumala which originally denoted the living sky; the Samoyedes made the same use of Num, and the Mongols of Tengri.

00Derived from the verb ma, " to stretch out," her name denoted the ideas of right and rule, and covered the notions of order, law, justice and truth, which remained steadfast and unalterable.

00Let this potential be denoted by V, and let v be the potential of the guard plate and the aluminium flap. This last potential is maintained constant by guard plate and flap being part of the interior coating of a charged Leyden jar.

00Their 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.

00The name Pahlavan, moreover, which denoted the Parthian magnates, passed over into the new empire.

004) at which the surface of contact OP meets the solid is denoted by a, Tbc - T ca - Tab cos a = o, Whence cos a = (Tbc - Tca)/Tab.

00How far it had any similar use in Judaism in Christ's day is uncertain; but in the 4th century A.D., at any rate, it denoted responsible envoys from the central Jewish authority, especially for the collection of religious funds.

00But the altered name of Lombard also denoted henceforth some of the proudest of Italians; and, though the Lombard speech had utterly perished their most common names still kept up the remembrance that their fathers had come from beyond the Alps.

00It denoted the church which included the patriarchates of Antioch, Alexandria, Jerusalem and Constantinople, and their dependencies.

00The alchemists named it Luna or Diana, and denoted it by the crescent moon; the first name has survived in lunar caustic, silver nitrate.

00The already existing worship of Athena Hygieia had nothing to do with Hygieia the goddess of health, but merely denoted the recognition of the power of healing as one of the attributes of Athena, which gradually became crystallized into a concrete personality.

00" twelve shillings " is denoted by 12s.

002, and the points must therefore be denoted by the ordinal numbers 1, 2, 3,.

00may be denoted by s of 4s.

005d., denoted by n X Is.

005d., may also be denoted by - 3 4s.

00According to the definition in § 50 the quantity denoted by 2 of A is made up of a number, 3, and a unit, which is one-sixth of A.

00Under one system, for instance, the continued sum 5 + X 5 + 8 X 7 X 5 would be denoted 7 by 8 I 5; this is somewhat similar in principle to a decimal notation, but with digits taken in the reverse order.

00The number denoted by N will therefore be such that 11 X N X N = N = N; i.e.

00Other units are derived from these by multiplication or division by powers of io, the names being denoted by prefixes.

00In one of these branches is placed a battery B and in another a galvanometer G; the four p Q other resistances are denoted by the letters P, Q, R, S.

00these resistances have values denoted by P, Q, R, and S, then when P: Q :: R: S, the current in the galvanometer circuit will be zero when an electromotive force is applied in the battery circuit.

00As regards moral sentiments generally, the view suggested by Mill is more definitely given by the chief living representative of the associationist school, Alexander Bain; by whom the distinctive characteristics of conscience are traced to " education under government or authority," though prudence, disinterested sympathy and other emotions combine to swell the mass of feeling vaguely denoted by the term moral.

00A second name of the city, which perhaps originally denoted a separate village or quarter, was Su-anna, and in later inscriptions it is often represented ideographically by E-ki, the pronunciation and meaning of which are uncertain.

00Ka-dimirra, the Semitic Bab-ili, probably denoted at first E-Saggila, "the house of the lofty head," the temple dedicated to Bel-Merodach, along with its immediate surroundings.

00That some method of casting lots is denoted by the terms is evident from 1 Sam.

00The civilized men of the Mythopoeic age were not obliged, as Max Muller held, to believe that all phenomena were persons, because the words which denoted the phenomena had genderterminations.

00This ratio is termed the eccentricity, and will be denoted by e.

00The semi-major axis is generally denoted by a, and the semiminor axis by b, and we have the relation b 2 =a 2 (1 - e 2).

00The palatalization of d+ consonant i into some sound denoted merely by i - the central sound of foied, from fo-died; 4.

00Fleeting matter to their mind was not worthy to embody or reflect heavenly supersensuous energies denoted by the names of Christ and the saints.

00A shake of Howie's head denoted no strange encounters of the weird kind.

00The current setting for each option is denoted by an asterisk.

00The sequence of diagrams above shows the stable set, denoted by the blue curve, undergoing a type-2 contact bifurcation.

00The first bifurcation of the vertically upward position is a " reverse " subcritical pitchfork bifurcation denoted by PF2.

00coupling constants are often denoted by the lower case Greek letter alpha, alpha with some specializing subscript.

00Matter was not worthy to embody or reflect spiritual entities denoted by the names of Christ and the saints.

00denoted by this abstract pathname.

00denoted by xsubi the number purchasing.

00denoted by a symbol which specifies its behavior.

00denoted by letters shown in red.

00denoted by [t] .

00All sizes are quoted in cm or inches and are clearly denoted by each applicable product. i. Jewelry items.

00denoted with an asterisk (* ).

00denoted by this abstract pathname.

00Fish farms are represented by the filled rectangular block, with the areas of impacted seabed denoted by the filled ellipses.

00An asterisk denoted that the green banana fritters were vegan - really weird.

00The parameter is usually denoted by l the Greek letter lambda.

00Soil K index 2 is divided into a lower and an upper half denoted by minus and plus signs.

00Poisson's ratio Poisson's ratio is denoted by the Greek letter nu: nu.

00This analysis focuses on networks that serve the operations officers, denoted the Ops desks or ops nets.

00The golden section is normally denoted by the Greek letter phi.

00An inverted term is also denoted by a line drawn above the term, usually pronounced ' bar ' .

00sexagesimal system, with numerals denoted by letters of the Arabic alphabet.

00subcritical pitchfork bifurcation denoted by PF2.

00These should be numbered 1, 2, 3, consecutively in the text and denoted by superscripts.

00The percentage of the charge which is dissipated per minute is usually denoted by a + or a_ according to its sign.

00The mean of and a_ is usually denoted by a± or simply by a, while q is employed for the ratio a_/a+.

00The radioactivity is denoted by A, and A = signifies that the potential of the dissipation apparatus fell I volt in an hour per metre of wire introduced.

00The Latin noun limes denoted generally a path, sometimes a boundary path (possibly its original sense) or boundary, and hence it was utilized by Latin writers occasionally to denote frontiers definitely delimited and marked in some distinct fashion.

00It is quite possible that shabattum and nubattum are from the same root and originally denoted much the same thing - a pause, abstention, from whatever cause or for ceremonial purposes.

00By unity Boole denoted the universe of thinkable objects; literal symbols, such as x, y, z, v, u, &c., were used with the elective meaning attaching to common adjectives and substantives.

00Now, if m represent the mass of the body in grammes its weight will be mg dynes, for it will require a force of mg dynes to produce in it the acceleration denoted by g.

00Nevertheless, though the conceptions originally denoted by " evolution " and " development " were shown to be untenable, the words retained their application to the process by which the embryos of living beings gradually make their appearance; and the terms" development," " Entwickelung,"and " evolutio " are now indiscriminately used for the series of genetic changes exhibited by living beings, by writers who would emphatically deny that " development " or " Entwickelung " or " evolutio," in the sense in which these words were usually employed by Bonnet or Haller, ever occurs.

00Modern inquiry, however, has arrived at other conclusions (see Bible, Old Testament), which may be briefly summarized as follows: the Pentateuch is compiled from various documents, the earliest of which is denoted by J (beginning at Gen.

00The Greek form of Gallia was FaXaria, but Galatia in Latin denoted another Celtic region in central Asia Minor, sometimes styled Gallograecia.

00Sebaoth, or " hosts," attached to the name of Yahweh, denoted the heavenly retinue of stars.

00He constructed a map of as many as 576 of these lines, the principal of which he denoted by the letters of the alphabet from A to G; and by ascertaining their refractive indices he determined that their relative positions are constant, whether in spectra produced by the direct rays of the sun, or by the reflected light of the moon and planets.

00As really denoted any integer or whole; whence the English word "ace."

00The words " Asiatic " and " Oriental " are often used as if they denoted a definite and homogeneous type, but Russians resemble Asiatics in many ways, and Turks, Hindus, Chinese, &c., differ in so many important points that the common substratum is small.

00Originally it seems to have denoted the coast district between the Oder and the Vistula, a territory which was at first more or less dependent on Poland, but which, towards the end of the 12th century, was ruled by two native princes, who took the title of duke about 1170 and admitted the authority of the German king in 1181.

00Combined in the phrase "populus Romanus Quirites (or Quiritium)" it denoted the individual citizen as contrasted with the community.

00Castor and Pollux), in astronomy, the third sign in the zodiac, denoted by the symbol II.

00In Zeumer's edition of the Leges Wisigothorum the versions of Recceswinth and Erwig, where they differ from each other, are shown in parallel columns, and the laws later than Erwig are denoted by the sign "nov."

00the hypothetical radicals of acids, were denoted by squares enclosing the initial letter of the base; an alkali was denoted by a triangle, and the particular alkali by inserting the initial letter.

00Compounds were denoted by joining the symbols of the components, and by varying the manner of joining compounds of the same elements were distinguished The symbol V was used to denote a liquid, and a vertical line to denote a gas.

00A great advance was made by Dalton, who, besides introducing simpler symbols, regarded the symbol as representing not only the element or compound but also one atom of that element or compound; in other words, his symbol denoted equivalent weights.4 This system, which permitted the correct representation of molecular composition, was adopted by Berzelius in 1814, who, having replaced the geometric signs of Dalton by the initial letter (or letters) of the Latin names of the elements, represented a compound by placing a plus sign between the symbols of its components, and the number of atoms of each component (except in the case of only one atom) by placing Arabic numerals before the symbols; for example, copper oxide was Cu +0, sulphur trioxide S+30.

00If two compounds combined, the + signs of the free compounds were discarded, and the number of atoms denoted by an Arabic index placed after the elements, and from these modified symbols the symbol of the new compound was derived in the same manner as simple compounds were built up from their elements.

00At a later date Berzelius denoted an oxide by dots, equal in number to the number of oxygen atoms present, placed over the element; this notation survived longest in mineralogy.

00The ringed structure of benzene, C 6 H 61 was first suggested in 1865 by August Kekule, who represented the molecule by six CH groups placed at the six angles of a regular hexagon, the sides of which denoted the valencies saturated by adjacent carbon atoms, the fourth valencies of each carbon atom being represented as saturated along alternate sides.

00A doubly linked pair of atoms is denoted by the sign A with the index corresponding to the side; if there are two pairs of double links, then indices corresponding to both sides are employed.

00Another form of isomerism is occasioned by spatial arrangements, many of the reduced terephthalic acids existing in two stereo-isomeric forms. Baeyer explains this by analogy with fumaric and maleic acids: he assumes the reduced benzene ring to lie in a plane; when both carboxyl groups are on the same side of this plane, the acids, in general, resemble maleic acids, these forms he denotes by rcis-cis, or shortly cis-; when the carboxyl groups are on opposite sides, the acids correspond to fumaric acid, these forms are denoted by rcis-trans, or shortly trans-.

00A gas, therefore, has two specific heats, generally denoted by C p and C„, when the quantity of gas taken as a unit is one gramme molecular weight, the range of temperature being IÃ‚° C. It may be shown that Cp C„ = R, where R is the gas- constant, i.e.

00If twelve grammes of amorphous carbon be burnt to carbon dioxide under constant volume, the heat evolved (96.96 cal.) does not measure the entire thermal effect, but the difference between this and the heat required to break down the carbon molecule into atoms. If the number of atoms in the carbon molecule be denoted by n, and the heat required to split off each atom from the molecule by d, then the total heat required to break down a carbon molecule completely into atoms is nd.

00The chief of these ministers is denoted 6 E7rl r&o' 7r pay µarwv, and he corresponds to the vizier of the later East.

001 In the early decades of the Christian era the text was current in two forms, which are denoted by H a and H R in this article and in the edition of the text published by the Oxford University Press.

00Such marks had often a religious significance, and denoted that the bearer was a follower of a particular deity.

00But the definition of the cardinal number of a class applies when the class is not finite, and it can be proved that there are different infinite cardinal numbers, and that there is a least infinite cardinal, now usually denoted by o where to is the Hebrew letter aleph.

00The essence of the tax denoted by these names was that the amount was fixed en bloc for a whole group of persons, and afterwards divided among them in various ways.

00The function Zap 1 a 2 P2 ...an n being as above denoted by a partition of the weight, viz.

00The elementary functions are denoted by (1), (12), (13), ...

00The sum of the monomial functions of a given weight is called the homogeneous-product-sum or complete symmetric function of that weight; it is denoted by h.; it is connected with the elementary functions by the formula 1 7r1l7r2!7r3!

00It should be noticed that the real function denoted by (ab) 2 is not the square of a real function denoted by (ab).

00l ax 2 2 ax i l This is called the kth transvectant of f over 4); it may be conveniently denoted by (f, (15)k.

00Every symmetric function denoted by partitions, not involving the figure unity (say a non-unitary symmetric function), which remains unchanged by any increase of n, is also a seminvariant, and we may take if we please another fundamental system, viz.

00Let this number be denoted by (w; 0, n).

00The extraordinary advantage of the transformation of S2 to association with non-unitary symmetric functions is now apparent; for we may take, as representative forms, the symmetric functions which are symbolically denoted by the partitions referred to.

00If 0=2, every form is obviously a ground form or perpetuant, and the series of forms is denoted by (2), (22), (23),...(2K+1)....

00Remark, too, that we are in association with non-unitary symmetric functions of two systems of quantities which will be denoted by partitions in brackets ()a, ()b respectively.

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

00It is not likely, as many scholars have thought, that Akkad was ever used geographically as a distinctive appellation for northern Babylonia, or that the name Sumer denoted the southern part of the land, because kings who ruled only over Southern Babylonia used the double title "king of Sumer and Akkad," which was also employed by northern rulers who never established their sway farther south than Nippur, notably the great Assyrian conqueror Tiglath pileser III.

00When the direction of any vector quantity denoted by a symbol is to be attended to, it is usual to employ for the symbol either a block letter, as H, I, B, or a German capital, as j,, 3?

00The field-strength at any point is also called the magnetic force at that point; it is denoted by H, or, when it is desired to draw attention to the fact that it is a vector quantity, by the block letter H, or the German character, C. Magnetic force is sometimes, and perhaps more suitably, termed magnetic intensity; it corresponds to the intensity of gravity g in the theory of heavy bodies (see Maxwell, Electricity and Magnetism, § 12 and § 68, footnote).

00The intensity of magnetization, or, more shortly, the magnetization of a uniformly magnetized body is defined as the magnetic moment per unit of volume, and is denoted by I, I, or „a.

00an angle e with the normal, the normal component of the magnetization, I cos e, is called the surface density of the magnetism, and is generally denoted by a.

00A thin sheet of magnetic matter magnetized normally to its surface in such a manner that the magnetization at any place is inversely proportional to the thickness h of the sheet at that place is called a magnetic shell; the constant product hI is the strength of the shell and is generally denoted by 4, or 4.

00Hence if the induction per square centimetre at any point is denoted by B, then in empty space B is numerically equal to H; moreover in isotropic media both have the same direction, and for these reasons it is often said that in empty space (and practically in air and other nonmagnetic substances) B and H are identical.

00The intensity (at any point) of the field due to the magnetization may be denoted by H i, that of the external field by Ho, and that of the resultant field by H.

00- The ratio B/H is called the permeability of the medium in which the induction is taking place, and is denoted byµ.

00The ratio I/H is called the susceptibility of the magnetized substance, and is denoted by «.

00du Bois (Magnetic Circuit, p. 33), the demagnetizing factor, and the ratio of the length of the ellipsoid 2c to its equatorial diameter 2a (=c/a), the dimensional ratio, denoted by the symbol nt.

00The curve showing the circumferential (or longitudinal) changes was also plotted, and from the two curves thus obtained it was easy, on the assumption that the metal was isotropic in directions at right angles to the magnetization, to calculate changes of volume; for if circumferential elongation be denoted by 1 1, and transverse elongation by 1 2, then the cubical dilatation (40r -) = l l 2/ 2 approximately.

00r is denoted by I?'

00- The numbers denoted by n (r) in Ã¯¿½ 41 are the binomial coefficients shown in the table in Ã¯¿½ 40; n (r) being the (r+ i) th number in the (n+ i) th row.

00(n+--r-1)lr!=n[r]lr!; this may, by analogy with the notation of Ã¯¿½41, be denoted by n [r 7.

00A point A in space may be associated with a (real, positive, or negative) numerical quantity a, called its weight, and denoted by the symbol aA.

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

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

00This unit is called the supplement of E, and denoted by IE.

00Any linear quantity may be denoted by a symbol (a 1, a2, ...

00The deficiencies of the Greek symbolism were partially remedied; subtraction was denoted by placing a dot over the subtrahend; multiplication, by placing bha (an abbreviation of bhavita, the product ") after the factors; division, by placing the divisor under the dividend; and square root, by inserting ka (an abbreviation of karana, irrational) before the quantity.

00The unknown was called yavattavat, and if there were several, the first took this appellation, and the others were designated by the names of colours; for instance, x was denoted by yÃ¯¿½nd y by lea (from kalaka, black).

00Stifel introduced the sign (+) for addition or a positive quantity, which was previously denoted by plus, pia, or the letter p. Subtraction, previously written as minus, mene or the letter m, was symbolized by the sign (-) which is still in use.

00The square root he denoted by (j), whereas Paciolus, Cardan and others used the letter R.

00These works possess considerable originality, and contain many new improvements in algebraic notation; the unknown (res) is denoted by a small circle, in which he places an integer corresponding to the power.

00He follows Vieta in assigning the vowels to the unknown quantities and the consonants to the knowns, but instead of using capitals, as with Vieta, he employed the small letters; equality he denoted by Recorde's symbol, and he introduced the signs > and < for greater than and less than.

00His notation is based on that of Vieta, but he introduced the sign X for multiplication, - for continued proportion, :: for proportion, ' and denoted ratio by one dot.

00This last character has since been entirely restricted to multiplication, and ratio is now denoted by two dots (:).

003 By Syriac is denoted the dialect of Aramaic which, during the early centuries of the Christian era, prevailed in Mesopotamia and the adjoining regions.

00The divinity primarily denoted by it is the storm-god who was known also as Ramman, Bir and Dadda.

00Some such idea plainly underlies the familiar phrase "a sweet savour," more literally "a savour of satisfaction," whereby an acceptable offering by fire is so often denoted in the Bible (Gen.

00For instance, in a uniplanar flow, radially inward towards 0, the flow across any circle of radius r being the same and denoted by 27rm, the velocity must be mfr, and 0=m log r,, y=m0, +4,i =m log re ie, w=m log z.

00The components of velocity of the moving origin are denoted by U, V, W, and the components of angular velocity of the frame of reference by P, Q, R; and then if u, v, w denote the components of fluid velocity in space, and u', v', w' the components relative to the axes at a point (x, y, z) fixed to the frame of reference, we have u =U +u' - yR +zQ, v =V +v -zP +xR, w=W +w -xQ +yP.

00the moment of inertia of the body about the axis, denoted by But if is the moment of inertia of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o.

00The rise of Sargon's empire was doubtless the cause of this extension of the name of Akkad; from henceforward, in the imperial title, Sumer and Akkad " denoted the whole of Babylonia.

00When a quantity of heat, H, is supplied to a body, part is expended in raising the temperature of the body, or in expanding the volume against molecular forces, and is represented by an increase in the total quantity of energy contained in the body, which is generally called its Intrinsic Energy, and will be denoted by the symbol E.

00This quotient is called the change of entropy, and may be denoted by (4,"-0').

00Argus with his countless eyes originally denoted the starry heavens (Apollodorus ii.

00Let k denote this height, and let PM be denoted by 1.

00For by transliterating Ka7vap Nepc'ev into Hebrew 1113 10,P and adding together the sums denoted by the Hebrew letters we obtain the number 666.

00and censorious criticism of persons, morals, manners, politics, literature, &c. which the word satire has ever since denoted.

00In the lower margin of the page he inserted a selection of various readings, the relative importance of which he denoted by the first five letters of the Greek alphabet in the following manner: - a was employed to denote the reading which in his judgment was the true one, although he did not venture to place it in the text; 1 3, a reading better than that in the text; y, one equal to the textual reading; S and e, readings inferior to those in the text.

00Moreover, its prefects, since they were two and liable to be disunited, and since they could not be senators, neither combined with the In permanent forts and fortresses, praetorium probably denoted strictly a residence: the official headquarters building (though commonly styled praetorium by moderns) was the principia.

00is held to be compiled with editorial additions from the two ancient documents (90o-700 B.C.) commonly denoted by the symbols J and E.

002 In course of time the exposition of the lesson for the day came more frequently to assume a more elaborate character, and to pass into the category of a Aoyos or even OtXoo-ocNa or OtXoa04nj a; but when it did so the fact was as far as possible denoted by a change of name, the word op. Xla being reserved for the expository or exegetical lecture as distinguished from the pulpit oration or sermon.

00These fossils, which are now in the British Museum, were interpreted by Dr Mantell, who made comparisons with the skeleton of Iguana, on the erroneous supposition that the resemblance in the teeth denoted some relationship to this existing lizard.

00The ordinate of the trapezette will be denoted by u, and the abscissa of this ordinate, i.e.

00the distance of its foot from a certain fixed point or origin 0 on the base (or the base produced), will be denoted by x, so that u is some function of x.

00If the planes of one set divide it into m slabs of thickness h, and those of the other into n slabs of thickness k, so that H =mh, K = nk, then the values of x and of y for any ordinate may be denoted by xo+Oh and yo+Ok, and the length of the ordinate by uo, 0.

00(b) - 49(a), where 4)(x) is any function of x, by [c P(x)]; the area of the trapezette whose bounding ordinates are uo and u m may then be denoted by [Ax.

00In the same way the volume of a briquette between the planes x = xo, y = yo, x= a, y = b may be denoted by [[Vx,y ]y=yo] u 'x' =xo.

00The result of performipg both operations, in order to obtain the volume, is the result of the operation denoted by the product of these two expressions; and in this product the powers of E and of E' may be dealt with according to algebraical laws.

00This is called the trapezoidal or chordal area, and will be denoted by C1.

00This is called the tangential area, and will be denoted by T1.

00+ u m-p + zum), which may be denoted by Cp. With this notation, the area as given by Simpson's rule may be written in the form sC l - 3 C2 or CI+ 1 3 `-(C1C2).

00Hence, if the angle which the tangent at the extremity of the ordinate u 0 makes with the axis of x is denoted by fie, we have area from uo to u1= 2h(uo + ui) - -- i i h 2 (tan y l - tan t u 2 = Wu ' + u2) - 1 Tih 2 (tan 4,2 - tan um-1 t0 26 m, - 2 h(um-1 + um) i h (tan 4, m - and thence, by summation, A =C I - i i h 2 (tan - tan 1,1/o).

00moments, so calculated, before correction are denoted by p 1, P21

00Then, if the true moments are denoted by Pi, v 2, ..., their values are given by vi ?Pl P2 - 11.

00It is usually denoted by X.

00Hence the note produced with any given circle of holes rises in pitch as the disk revolves more rapidly; and if, the revolution of the disk being kept as steady as possible, the tube be passed rapidly across the circles of the first series, a series of notes is heard, which, if the lowest be denoted by C, form the sequence C, C1, El, G1, C2, &c. In like manner, the first circle in which we have two sets of holes dividing the circumference, the one into say 8 parts, and the other into Io,.

00denoted a necklace of twenty-seven pearls; 1 and the fundamental equality of the parts was figured in an ancient legend, by the compulsion laid upon King Soma (the Moon) to share his time impartially between all his wives, the twenty-seven daughters of Prajapati.

00The definition of the coefficients is that if (I-2h cos cp+h 2)-i be expanded in ascending powers of h, and if the general term be denoted by P„h', then P is of the Legendrian coefficient of the nth order.

00The resistance R can thus be divided into two factors, one of which is d 2, where d denotes the diameter of the shot in inches, and the other factor is denoted by p, where p is the resistance in pounds at the same velocity to a similar I-in.

00It is further assumed, as the result of experiment, that the resistance is proportional to the density of the air; so that if the standard density changes from unity to any other relative density denoted by then R= Td 2 p, and is called the coefficient of tenuity.

00If the inclination or change of inclination in degrees is denoted by S or OS, (21) 5/180=i/7r, so that (22) AS 180 _ 180g (Ot and if 5 and i change to D and I for the standard projectile, AT Ov 180g AT (23) DI =g ., = v p, AD = -Tr, and vv or J VQ'V, D(V) -D(v) = 180 [I(V) - i (v)].

00In 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.

0015.6 Tons 15.2 Tons steam-engine, representing graphically by a curve CPD the relation between the volume and pressure of the powder-gas; and in addition the curves AQE of energy e, AvV of velocity v, and AtT of time t can be plotted or derived, the velocity and energy at the muzzle B being denoted by V and E.

00In the Septuagint column he drew attention to those passages for which there was no Hebrew equivalent by prefixing an obelus; but where the Septuagint had nothing corresponding to the Hebrew text he supplied the omissions, chiefly but not entirely from the translation of Theodotion, placing an asterisk at the beginning of the interpolation; the close of the passage to which the obelus or the asterisk was prefixed was denoted by the metobelus.

00144+x+y years, in all 554 years, + two unknown periods denoted by x and y-in any case considerably more than the 480 years of I Kings vi.

00The logarithm is also a function of frequent occurrence in analysis, being regarded as a known and recognized function like sin x or tan x; but in mathematical investigations the base generally employed is not 10, but a certain quantity usually denoted by the letter e, of value 2.71828 18284 ...

00The quantity denoted by e is the series, I I I+ I + i.2 +1.2.3+1.2.3.4 + the numerical value of which is, 2.71828 18284 59 0 45 2 353 6 02874.

00usually denoted by e.

00To every geometric mean in the column of numbers there corresponds the arithmetical mean in the column of logarithms. The numbers are denoted by A, B, C, &c., in order to indicate their mode of formation.

00Few traces of private houses have been found within the walls, but as deeds of sale speak of houses in Nineveh, which were bounded on three sides by other houses, there must have been continuous streets within the area denoted by that name.

00This ratio, invariably denoted by 7r, is constant for all circles, but it does not admit of exact arithmetical expression, being of the nature of an incommensurable number.

00For 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.

00instrument, let the solid be placed in the upper scale pan, and let the weight now required to cause the instrument to sink in distilled water at standard temperature to the mark B be denoted by w,.

00The end of this period is generally said to coincide with the loss of the French provinces to Philip Augustus, but literary and political history do not correspond quite so precisely, and the end of the first period would be more accurately denoted by the appearance of the history of 'William the Marshal in 1225 (published for the Societe de l'histoire de France, by Paul Meyer, 3 vols., 1891-1901).

00The significance of the word "mean," i.e., middle, is seen by considering 3 instead of n quantities; these will be denoted by a, b, c. The arithmetic mean b, is seen to be such that the terms a, b, c are in arithmetical progression,.

00It appears to have denoted the territory above Babylonia stretching from Anshan in the southeast north-westwards, across the Tigris-Euphrates district, indefinitely towards Asia Minor.

00The plural is denoted when required by adding one of several words of plurality.

00The most brilliant are situated at the intersections of the inner halo and the parhelic circle; these are known as parhelia (denoted by the letter p in the figures) (from the Gr.

00This Shekinah-glory is several times denoted in the New Testament by & a.

00The following is a select list of genera of miscellaneous decorative plants (orchids, palms and ferns excluded; climbers are denoted by *; bulbous and tuberous plants by f) Stove Plants.

00The following is a select list of genera of stove plants (climbers are denoted by *, bulbous and tuberous plants by f) Acalypha Achimenest Aeschynanthus Allamanda* Alocasiat Amaryllist Anthurium Aphelandra Aralia Ardisia Arisaemaf Aristolochia * Ataccia Begonia Bertolonia Bignonia* Bromeliads Cactus Caladium f Calathea Centropogon Cissus* Clerodendron * Crinumt Codiaeum (Croton) ORcftIDs.

00It thus denoted the whole country from the Tiber to the mouth of the Savo, and just included the Mons Massicus, though the boundary was not very precisely fixed (see below).

00In ordinary isomers indications of mutual transformation often occur; and among these the predominant fact is that denoted as tautomerism or pseudomerism.

00In algebra it denoted the characters which represented quantities in an equation.

00If the gradient is not uniform, its value may be denoted by dB/dx.

00It would therefore seem that the name Germani originally denoted certain Celtic tribes to the east of the Rhine, and that it was then transferred to the Teutonic tribes which subsequently occupied the same territory.

00Others are the sibilation of consonantal i and the assibilation of -di- to some sound like that of English j (denoted by B in the local variety of Latin alphabet), as in vidadu, " viamdo," i.e.

00Unfortunately Buckle either could not define, or cared not to define, the general conceptions with which he worked, such as those denoted by the terms "civilization," "history," "science," "law," "scepticism," and "protective spirit"; the consequence is that his arguments are often fallacies.

00Thus the name which once denoted the good genius who bestowed the precious gift of water upon man was adopted to this use in vulgar Latin under the form Catamitus.

00Moreover, the solar period (II years) is far outside the limits of the periods of 1 Variable stars (except those sufficiently bright to have received special names) are denoted by the capital letters R to Z followed by the name of the constellation.

00The first nine variables recognized in each constellation are denoted by single letters, after which combinations RR, RS, &c., are used.

00The objects denoted by the other six names - ox, house, valve of a door, water, fish and mark or cross - clearly do not belong to any people in a nomadic state, but to a settled, town-abiding population..

00If we take A as origin and AN as axis of x, the weight of AP may be denoted by wx, where w is the weight per unit length at A.

00Let these projections be denoted algebraically by x1, xi,.

00The squares of the radii of gyration about the principal axes at P may be denoted by k,i+k32, k,f + ki2, k12 + k,2 hence by (32) and (35), they are rfOi, r2Oi, r20s, respectively.

00This acceleration is denoted by g; its value at Greenwich is about 981 centimetre-second units, or 322 feet per second.

00Thus the unit of velocity is that of a point describing the unit of length in the unit of time; it may be denoted by LTi, this symbol indicating that the magnitude of the unit in question varies directly as the unit of length and inversely as the unit of time.

00The unit of acceleration is the acceleration of a point which gains unit velocity in unit time; it is accordingly denoted by LT2.

00unit tinie and is therefore denoted by MLTI.

00The components of angular momentum about Ox, Qy, 01 will be denoted as usual by X, u, v.

00These equations, together with the arbitrary initial values of p, q,r, determine the six constants which we have denoted by po, go, r0, ki, a, ~.

00By an obvious analogy, the expressions OTfO4r may be called the generalized components of momentum; they are usually denoted by Pr, thus = OT/aq,.

00arid if this be denoted by o~1~ we have a second system of equations similar to (23).

00Let the angular velocity of the rotation be denoted by a=dO/dt, then the linear velocity of any point A at the distance r from the axis is or; and the path of that point is a circle of the radius r described about the axis.

00Let the axis Ai carry a wheel of N1 teeth, driving a wheel of ni teeth on the axis Ai, which carries also a wheel of N2 teeth, driving a wheel of 113 teeth on the axis A3, and so on; the numbers of teeth in drivers being denoted by Ns, and in followers by ns, and the axes to which the wheels are fixed being denoted by numbers.

00Then the resulting velocity ratio is denoted by a,, a~ ~3 & a,,, N, - Ni -.

00The symbolical expression of this law is as follows: let efforts be applied to one or any number of points of a machine; let any one of these efforts be represented by P, and the distance traversed by its point of application in a given interval of time by ds; let resistances be overcome at one or any number of points of the same machine; let any one of these resistances be denoted by R, and the distance traversed by its point of application in the gi- en interval of time by ds; then ~.Pds=2~.Rds.

00Let those be denoted by si and s~, so that s=si+si.

00On this a scholiast says that the name "Homeridae " denoted originally descendants of Homer, who sang his poems in succession, but afterwards was applied to rhapsodists who did not claim descent from him.

00Moral feeling, indeed, existed and was denoted by " Aidos "; but the numerous meanings of this word - shame, veneration, pity - show how rudimentary the idea was.

00The fact that the Phoenician Vau was retained in the Greek alphabets, and the vowel v added, shows that when the alphabet was introduced the sound denoted by was still in full vigour.

00It can only have fallen into disuse by degrees, as the sound which it denoted ceased to be pronounced.

00The term " finance," which comes into English through French, in its original meaning denoted a payment (finatio).

00H „ Light and represents a rise of about £I P „ Picked £3 G „ Grey £3 S „ Superior £4 W „ White £4 Z „ Zins Each additional mark means a rise in the price, but it must be understood that it is quite possible for a quality denoted by two letters to be more valuable than one indicated by three or more, since every mark has not the same value.

00Of the Greek there are three forms. One is in the Vatican and Alexandrian MSS.; another is in the Sinaitic. Both these texts are to be found in Swete's Septuagint, the former denoted by B, and the latter by B is the common text, which is followed in the English Apocrypha.

003 The Finns came to apply to the upper gods the term Yumala which originally denoted the living sky; the Samoyedes made the same use of Num, and the Mongols of Tengri.

00Derived from the verb ma, " to stretch out," her name denoted the ideas of right and rule, and covered the notions of order, law, justice and truth, which remained steadfast and unalterable.

00Let this potential be denoted by V, and let v be the potential of the guard plate and the aluminium flap. This last potential is maintained constant by guard plate and flap being part of the interior coating of a charged Leyden jar.

00Their 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.

00The name Pahlavan, moreover, which denoted the Parthian magnates, passed over into the new empire.

00The same Chrysippus fixed upon a certain characteristic of true presentations, which he denoted by the much disputed term " apprehensive " (KaTaX717rTLK7 4avraQEa).

004) at which the surface of contact OP meets the solid is denoted by a, Tbc - T ca - Tab cos a = o, Whence cos a = (Tbc - Tca)/Tab.

00How far it had any similar use in Judaism in Christ's day is uncertain; but in the 4th century A.D., at any rate, it denoted responsible envoys from the central Jewish authority, especially for the collection of religious funds.

00But the altered name of Lombard also denoted henceforth some of the proudest of Italians; and, though the Lombard speech had utterly perished their most common names still kept up the remembrance that their fathers had come from beyond the Alps.

00It denoted the church which included the patriarchates of Antioch, Alexandria, Jerusalem and Constantinople, and their dependencies.

00The alchemists named it Luna or Diana, and denoted it by the crescent moon; the first name has survived in lunar caustic, silver nitrate.

00The already existing worship of Athena Hygieia had nothing to do with Hygieia the goddess of health, but merely denoted the recognition of the power of healing as one of the attributes of Athena, which gradually became crystallized into a concrete personality.

00" twelve shillings " is denoted by 12s.

002, and the points must therefore be denoted by the ordinal numbers 1, 2, 3,.

00may be denoted by s of 4s.

005d., denoted by n X Is.

005d., may also be denoted by - 3 4s.

00According to the definition in § 50 the quantity denoted by 2 of A is made up of a number, 3, and a unit, which is one-sixth of A.

00Under one system, for instance, the continued sum 5 + X 5 + 8 X 7 X 5 would be denoted 7 by 8 I 5; this is somewhat similar in principle to a decimal notation, but with digits taken in the reverse order.

00The number denoted by N will therefore be such that 11 X N X N = N = N; i.e.

00Other units are derived from these by multiplication or division by powers of io, the names being denoted by prefixes.

00In one of these branches is placed a battery B and in another a galvanometer G; the four p Q other resistances are denoted by the letters P, Q, R, S.

00these resistances have values denoted by P, Q, R, and S, then when P: Q :: R: S, the current in the galvanometer circuit will be zero when an electromotive force is applied in the battery circuit.

00As regards moral sentiments generally, the view suggested by Mill is more definitely given by the chief living representative of the associationist school, Alexander Bain; by whom the distinctive characteristics of conscience are traced to " education under government or authority," though prudence, disinterested sympathy and other emotions combine to swell the mass of feeling vaguely denoted by the term moral.

00A second name of the city, which perhaps originally denoted a separate village or quarter, was Su-anna, and in later inscriptions it is often represented ideographically by E-ki, the pronunciation and meaning of which are uncertain.

00Ka-dimirra, the Semitic Bab-ili, probably denoted at first E-Saggila, "the house of the lofty head," the temple dedicated to Bel-Merodach, along with its immediate surroundings.

00That some method of casting lots is denoted by the terms is evident from 1 Sam.

00The civilized men of the Mythopoeic age were not obliged, as Max Muller held, to believe that all phenomena were persons, because the words which denoted the phenomena had genderterminations.

00This ratio is termed the eccentricity, and will be denoted by e.

00The semi-major axis is generally denoted by a, and the semiminor axis by b, and we have the relation b 2 =a 2 (1 - e 2).

00The palatalization of d+ consonant i into some sound denoted merely by i - the central sound of foied, from fo-died; 4.

00Fleeting matter to their mind was not worthy to embody or reflect heavenly supersensuous energies denoted by the names of Christ and the saints.

00The second of the three systems was the sexagesimal system, with numerals denoted by letters of the Arabic alphabet.

00These should be numbered 1, 2, 3, consecutively in the text and denoted by superscripts.

00Generally, these foundations are denoted with hue suggestions.

00Like the nobles, however, different materials and articles would denote a man's occupation: a blue robe denoted a servant, a flat cap an apprentice, or a retainer would wear his lord's coat of arms on a badge sewn to their left sleeve.

00Also on the left side is the left trigger button (usually denoted as "L") and this is activated with your left index finger.

00Braids often denoted warriors in Africa and Native Americans in the Plains wore long braids adorned with feathers.

00The original slash pairing was Kirk and Spock, denoted Kirk/Spock or K/S.

00Ranks were denoted using the epaulets, with stripes and chevrons showing the various ranks.

00They are denoted with a hash tag (such as "#info") and designated on the web page in this format: "<P id="info">".

00The percentage of the charge which is dissipated per minute is usually denoted by a + or a_ according to its sign.

01The radioactivity is denoted by A, and A = signifies that the potential of the dissipation apparatus fell I volt in an hour per metre of wire introduced.

01Sebaoth, or " hosts," attached to the name of Yahweh, denoted the heavenly retinue of stars.

01Every symmetric function denoted by partitions, not involving the figure unity (say a non-unitary symmetric function), which remains unchanged by any increase of n, is also a seminvariant, and we may take if we please another fundamental system, viz.

01A shake of Howie's head denoted no strange encounters of the weird kind.

02

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.