# N Sentence Examples

According to the electromagnetic theory of light K = N2, where

**N**is the refractive index for rays of infinite wave-length.Nitrogen combines with hydrogen to form ammonia, NH 3, hydrazine,

**N**2 H 4, and azoimide,**N**3 H (qq.v.); the other known hydrides,**N**4 H 4 and N5H5, are salts of azoimide, viz.Now if

**n**be any finite cardinal number, it can be proved that the class of those serial relations, which have a field whose cardinal number is**n**, is a relation-number.This relation-number is the ordinal number corresponding to

**n**; let it be symbolized by it.If m and

**n**are finite cardinal numbers, the rational number m/**n**is the relation which any finite cardinal number x bears to any finite cardinal number y when**n**X x = m X y.AdvertisementSuch a number is a "one-many" relation which relates

**n**signed real numbers (or**n**algebraic complex numbers when they are already defined by this procedure) to the**n**cardinal numbers I, 2..Xi to

**n**.This last number exemplifies the fact that one signed real number, such as o, may be correlated to many of the

**n**cardinals, such as 2.The central section, culminating in Tizi

**n**'Tagharat or Tinzar, a peak estimated at 15,000 ft.This last substance may be reduced to mesoporphyrin, C34H3804N4, which by further reduction gives haemopyrrol, C 8 11 13

**N**, possibly methyl-propyl-pyrrol or butyl-pyrrol.AdvertisementChemically they resemble the albumins, being split up by acids or ferments into albumoses, peptones and amino-acids, forming salts, and giving

**N**=C6 1 The pyrimidin ring is numbered 2C "C5.Home died at Merchis* ?

**n**Bank, near Edinburgh, on the 5th of September 1808, in his eighty-sixth year.When the solutions may be taken as effectively dilute, so that the gas laws apply to the osmotic pressure, this relation reduces to E _ nrRT to c1 ey gE c2 where

**n**is the number of ions given by one molecule of the salt, r the transport ratio of the anion, R the gas constant, T the absolute temperature, y the total valency of the anions obtained from one molecule, and c i and c 2 the concentrations of the two solutions.An Orthodox bishop, vested for the holy liturgy, wears over his cassock - (i) the rnxcipcov, or alb (q.v.); the E7nrpay,Acov, or stole (q.v.); (3) the a narrow stuff girdle clasped behind, which holds together the two vestments above named; (4) the E7

**n**, uaviexa, liturgical cuffs, corresponding, possibly, to the pontifical gloves of the West;' (5) the i 7rtyovarcov, a stiff lozengeshaped piece of stuff hanging at the right side by a piece of riband from the girdle or attached to the o-AKKos, the equivalent of the Western maniple (q.v.); (6) the like the Western dalmatic (q.v.), worn instead of the 4acv6Acov, or chasuble; (7) the c?µocp6pcov, the equivalent of the Western pallium (q.v.).Tubes are generally made up around mandrels, and allowed throughout the curing to remain imbedded i

**n**p u lverized French chalk, which affords a useful support for many articles that tend to lose their shape during the process.AdvertisementY ...a

**n**v, the summation being for all permutations of the**n**numbers, is called the determinant of the**n**2 quantities.The matrix consists of

**n**rows and**n**columns.From the value of A we may separate those members which contain a particular element a ik as a factor, and write the portion aik A ik; A k, the cofactor of ar k, is called a minor of order

**n**- i of the determinant.We thus obtain for the product a determinant of order

**n**.The adjoint determinant is the (

**n**- I) th power of the original determinant.AdvertisementAssuming 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.Bezout's method gives the resultant in the form of a determinant of order m or

**n**, according as m is**n**.The function Zap 1 a 2 P2 ...an

**n**being as above denoted by a partition of the weight, viz.Theorem.- The function symbolized by (

**n**), viz.The analogous formula appertaining to

**n**systems of quantities which Vienna Transactions, t.AdvertisementThe similar theorem for

**n**systems of quantities can be at once written down.In the present particular case putting m 10 = 1 2, mot= v and m P4 =o otherwise M10t+M01n+...+Mpot P

**n**4 +...It may be written in the form

**n****n**-1 2 ax 1 +bx1 x2 +cx 1 x 2 + ...; or in the form**n****n****n**=1**n****n**-2 2 +(1)bx x2+ ?If the form, sometimes termed a quantic, be equated to zero the

**n**+I coefficients are equivalent to but**n**, since one can be made unity by division and the equation is to be regarded as one for the determination of the ratio of the variables.If we restrict ourselves to this set of symbols we can uniquely pass from a product of real coefficients to the symbolic representations of such product, but we cannot, uniquely, from the symbols recover the real form, This is clear because we can write

**n**-1**n**-2 2 2n-3 3 a1a2 =a l a 2, a 1 a 2 = a 1 a2 while the same product of umbrae arises from**n****n**-3 3 2n-3 3 aoa 3 = a l .a a 2 = a a 2 .We write;L 22 = a 1 a 2 .b 1

**n**-2 b2s 3**n**- 3 3**n**-3 3**n**-3 3 a 3 = a 1 a 2 .b 1 b 2 .c 1 c2, and so on whenever we require to represent a product of real coefficients symbolically; we then have a one-to-one correspondence between the products of real coefficients and their symbolic forms. If we have a function of degree s in the coefficients, we may select any s sets of umbrae for use, and having made a selection we may when only one quantic is under consideration at any time permute the sets of umbrae in any manner without altering the real significance of the symbolism.In general it will be simultaneous covariant of the different forms

**n**1 rz 2 n3 a, b x, ?Similarly regarding 1 x 2 as additional parameters, we see that every covariant is expressible as a rational function of

**n**fixed covariants.We may write therefore 1 These forms,

**n**in number, are called " associated forms " of f (" Schwesterformen," " formes associbes ").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 .Ternary and Higher Forms.-The ternary form of order

**n**is represented symbolically by (aixl+a2x2+a3x3)' =a'; and, as usual, b, c, d,...For the unipartite ternary quantic of order

**n**he finds that the fundamental system contains a (**n**+4) (**n**-1) individuals.Every 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.Let this number be denoted by (w; 0,

**n**).In order to obtain the seminvari ants we would write down the (w; 0,

**n**) terms each associated with a literal coefficient; if we now operate with 52 we obtain a linear function of (w - I; 8,**n**) products, for the vanishing of which the literal coefficients must satisfy (w-I; 0,**n**) linear equations; hence (w; 8,**n**)-(w-I; 0,**n**) of these coefficients may be assumed arbitrarily, and the number of linearly independent solutions of 52=o, of the given degree and weight, is precisely (w; 8,**n**) - (w - I; 0,**n**).It is shown in the article on Combinatorial Analysis that (w; 0,

**n**) is the coefficient of a e z w in the ascending expansion of the fraction 1-a.As we have to do only with that part of the expansion which involves positive powers of z, we must try to isolate that portion, say A

**n**(z).Putting

**n**equal to co, in a generating function obtained above, we find that the function, which enumerates the asyzvgetic seminvariants of degree 0, is 1 1-z2.1-z3.1-z4....1-z0 that is to say, of the weight w, we have one form corresponding to each non-unitary partition of w into the parts 2, 3, 4,...0.It may denote a simultaneous orthogonal invariant of forms of orders

**n**i, n2, n3,...; degree 0 of the covariant in the coefficients.The coefficients of the symbols must then present themselves

**n**1,**n**2,**n**3 ...times respectively.Putting a for the mean distance of the earth from the sun, and

**n**for its mean motion in one second, we use the fundamental equation a3 n2 = Mo-1-M', Mo being the sun's mass, and M' the combined masses of the earth and moon, which are, however, too small to affect the result.For the mean motion of the earth in one second in circular measure, we have

**n**8149' l o g.Denoting the two pairs of magnetic poles by

**N**, S and**N**', S', there is attraction between**N**and S', and between S and**N**'; repulsion between**N**and**N**', and between S and S'.The point

**N**, which is the centre of the parallel forces, is called the north or positive pole of the magnet.The field strength in the interior of a long uniformly wound coil containing

**n**turns of wire and having a length of 1 centimetres is (except near the ends) H = 41rin/l.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.The resultant magnetic force at every point of such a surface is in the direction of the normal (

**n**) to the surface; every line of force therefore cuts the equipotential surfaces at right angles.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.Denoting its mean value by Hti, and that of the demagnetizing factor by

**N**, we have H=Ho-Hti=Ho-NI.If the distance of the mirror from the scale is equal to

**n**scale divisions, and if a deflection 0 of the needle causes, the reflected spot of light to move over s scale divisions, we shall have s/**n**= tan 20 exactly, s/2n = tan 0 approximately.If the conductor consists of a coil of wire the ends of which are connected with a suitable galvanometer, the integral electromotive force due to a sudden increase or decrease of the induction through the coil displaces in the circuit a quantity of electricity Q=SBns R, where SB is the increment or decrement of induction per square centimetre, s is the area of the coil,

**n**the number of turns of wire, and R the resistance of the circuit.Let s be the area of a single turn of the standard coil,

**n**the number of its turns, and r the resistance of the circuit of which the coil forms part; and let S,**N**and R be the corresponding constants for a coil which is to be used in an experiment.A primary coil of length 1, having

**n**turns, is wound upon a cylinder made of non-conducting and non-magnetic material, and upon the middle of the primary a secondary or induction coil is closely fitted.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.The rate at which energy is lost being proportional to the frequency, it is obvious that the loss at frequency ioo may be deduced from that at any other frequency

**n**by simply multiplying by too**n**.For simplicity of calculation, the clear length of each rod between the yokes is made 12.56 (=47r) centimetres, while the coil surrounding the standard bar contains 100 turns; hence the magnetizing force due to a current of

**n**amperes will be ion C.G.S.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 strength of the induced current is - HScosO/L, where 0 is the inclination of the axis of the circuit to the direction of the field, and L the coefficient of self-induction; the resolved part of the magnetic moment in the direction of the field is equal to - HS 2 cos 2 6/L, and if there are

**n**molecules in a unit of volume, their axes being distributed indifferently in all directions, the magnetization of the substance will be-3nHS 2 /L, and its susceptibility - 3S 2 /L (Maxwell, Electricity and Magnetism, § 838).By three several protocols signed Germ

**n**at Washington in February 1903, it was agreed that Italy certain claims by Great Britain, Germany and Italy, on Versus behalf of their respective subjects against the Venezuelan government should be referred to three mixed commissions, and that for the purpose of securing the payment of these claims 30% of the customs revenues at the ports of La Guayra and Puerto Caballo should be remitted in monthly instalments to the representative of the Bank of England at Caracas.With ammonia, benzaldehyde does not form an aldehyde ammonia, but condenses to hydrobenzamide, (C 6 H 5 CH) 3

**N**2, with elimination of water.In 1586 Witherington plundered Bahia; E and i

**n**1591 Cavendish made an abortive attack on Santos; French in 1595 Lancaster attacked Olinda.In

**n**= a P, a is the root or base, p is the index or logarithm, and**n**is the power or antilogarithm.Denoting the root by a, and the number 2222222 in this scale by

**N**, we have**N**= 2222222.Thus by adding 2 to aN we can subtract

**N**from aN+2, obtaining 2000-0000, which is =2.Y is represented by the length of the ordinate NP, so that the representation is cardinal; but this ordinate really corresponds to the point

**N**, so that the representation of X is ordinal.The multinomial which is equivalent to (A= a)", and has its terms arranged in ascending powers of a, is called the expansion of (A= a)

**n**.Now suppose that the formula (2) has been established for every power of A+a up to the (

**n**-i)th inclusive, so that (ii_ I) = (**n**- I) (r), (y I) = (**n**-1) (r _ l).Hence it is true for all positive integral powers of

**n**.If we denote

**n**(**n**-i) ..The binomial theorem for positive integral index may then be written (x + y)

**n**= -iyi +.In particular, the number of permutations of the whole stock is

**n**!.If r is greater than m or

**n**(though of course not greater than m+**n**), some of the terms in (22) and (23) will be zero.This is sometimes called the number of homogeneous products of r dimensions formed out of

**n**letters; i.e.If, in this latter case, the proportion of cases in which b is B to cases in which b is not-B is the same for the group of pN individuals in which a is A as for the group of (I-p)

**N**in which a is not-A, then the frequencies of A and of B are said to be independent; if this is not the case they are said to be correlated.Thus we get a formula for the sum of

**n**terms of a series such as 2.4.6+4.6.8+..., or 6.8.10.12+8.10.12.14+...Then, since nr rl is also a rational integral function of

**n**of degree r, we can find a coefficient c r, not containing**n**, and such as to make**N**-c r nr ri contain no power of**n**higher than**n**r - 1.It can be shown by the above reasoning that this can be expressed as a series of terms containing descending powers of

**n**, the first term being nr+1/(r+I).The most important cases are I +2 +3 +...+

**n**= 2n(**n**+I), 12+22+32+...+n2 = sn(**n**+I) (2n+1), I 3 +2 3 +3 3 +...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+...The results in (b) apply also if

**n**is a negative integer.For instance, when

**n**is large,**n**!Taking any number

**n**to be represented by a point on a line at distance nL from a fixed point 0, where L is a unit of length, we start with a series of points representing the integers I, 2, 3,.These values are assumed to be independent, so we have 2n(

**n**- I) derived units of the second species or order.Associated with these new units there is a system of extensive quantities of the second species, represented by symbols of the type = Ei 121 [i=I, 2,...zn(

**n**- I)].He solved quadratic equations both geometrically and algebraically, and also equations of the form x 2 "+ax

**n**+b=o; he also proved certain relations between the sum of the first**n**natural numbers, and the sums of their squares and cubes.The first post-Darwinian systematists naturally and without reflexion accepted of' the idea that existing simpler forms represent stages i

**n**the gradual progress of development - are in fact survivors from past ages which have retained the exact grade of development which their ancestors had reached in past ages.Taking co-ordinates in the plane of the screen with the centre of the wave as origin, let us represent M by,

**n**, and P (where dS is situated) by x, y, z.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.We readily find (with substitution for k of 27r/X) a2b S

**n**J s in fl „2a2E2 „2b2n2 f2X2 f2X2 as representing the distribution of light in the image of a mathematical point when the aperture is rectangular, as is often the case in spectroscopes.Within the rectangle formed by pairs of consecutive dark lines, and not far from its centre, the brightness rises to a maximum; but these subsequent maxima are in all cases much inferior to the brightness at the centre of the entire pattern (=o,

**n**=o).By the principle of energy the illumination over the entire focal plane must be equal to that over the diffracting area; and thus, in accordance with the suppositions by which (3) was obtained, its value when integrated from E= co to = -1-x, and from

**n**= - oo to**n**= -1-oo should be equal to ab.At the focal point (E =o,

**n**= o) all the secondary waves agree in phase, and the intensity is easily expressed, whatever be the form of the aperture.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.If the image of the line be =o, the intensity at any point E,

**n**of the diffraction pattern may be represented by ?2a2t2 S A2f2 the same law as obtains for a luminous point when horizontal directions are alone considered.It has already been suggested that the principle of energy requires that the general expression for I 2 in (2) when integrated over the whole of the plane,

**n**should be equal to A, where A is the area of the aperture.The diffraction pattern is therefore that due to a single aperture, merely brightened

**n**times.We will now consider the important subject of the resolving power of gratings, as dependent upon the number of lines (

**n**) and the order of the spectrum observed (m).It is here of course assumed that the

**n**lines are really utilized.If w now relate to the edge of the grating, on which there are altogether

**n**lines, no- = 2a sin w, and the value of the last term in (I o) becomes no- sin 3w sin O'tan 0', - 1 1 - 6 mnX sin' w tan 0'.If the subject of examination be a luminous line parallel to

**n**, we shall obtain what we require by integrating (4) with respect to 77 from - oo to + oo.By separation of real and imaginary parts, C =M cos 27rv 2 +

**N**sin 27rv2 1 S =M sin 27rv 2 -**N**cos 27rv2 where 35+357.9**N**_ 7rv 3 7r 3 v 7 + 1.3 1.3.5.7 1.3.5.7.9.11 These series are convergent for all values of v, but are practically useful only when v is small .Comparing the expressions for C, S in terms of M,

**N**, and in terms of G, H, we find that G = z (cos u+sin u)-M, H = z (cos u-sin u) +**N**.For example, when u = o, M = o,

**N**=o, and consequently G =H = 2.It was first prepared by C. Scheele and is formed when urea HO C

**N**is treated with water.It is therefore difficult to suppose that the Jewish Church as a whole passed through a stage in which it was felt desirable to substitute o'

**n**'7 H in writing for**n**¦**n**'.Similarly it may be shown that each internal reflection introduces a supplementary deviation of 7r - 2r; hence, if the ray be reflected

**n**times, the total deviation will be D =2(i - r) +**n**(7r - 2r) .Since the value of µ for water is about, it follows that

**n**must be at least unity for a rainbow to be formed; there is obviously no theoretical limit to the value of**n**, and hence rainbows of higher orders are possible.Taking the refractive index of water for the red rays as 0;, and for the violet rays as 1 r, we can calculate the following values for the minimum deviations corresponding to certain assigned values of

**n**.After Rupert's death this was governed by his eldest son, the

**N**elector Louis III.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.Iron, zinc, cadmium, also tin under certain conditions, reduce the dilute acid, partially at least, to nitrous oxide,

**N**2 0, or ammonium nitrate, NH4N03.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').Ignoring temperature effect, and taking the density as a function of the pressure, surfaces of equal pressure are also of equal density, and the fluid is stratified by surfaces orthogonal to the lines of force;

**n**ap, dy, P d z, or X, Y, Z (4) are the partial differential coefficients of some function P, =fdplp, of x, y, z; so that X, Y, Z must be the partial differential coefficients of a potential -V, such that the force in any direction is the downward gradient of V; and then dP dV (5) ax + Tr=0, or P+V =constant, in which P may be called the hydrostatic head and V the head of potential.From the gas-equation in general, in the atmosphere

**n**d dp _ I dp 1 de _ d0 de i de (8) z p dz-edz-p-edz-k-edz' which is positive, and the density p diminishes with the ascent, provided the temperature-gradient de/dz does not exceed elk.I

**n**a straight uniform current of fluid of density p, flowing with velocity q, the flow in units of mass per second across a plane area A, placed in the current with the normal of the plane making an angle 0 with the velocity, is oAq cos 0, the product of the density p, the area A, and q cos 0 the component velocity normal to the plane.Putting (12) a vortex line is defined to be such that the tangent is in the direction of w, the resultant of,

**n**, called the components of molecular rotation.Consider the streaming motion given by w =m =a+si, (5) 4=m ch (

**n**-a)cos(-0), p=m sh(**n**-a)sin(-13).An ellipse interior to

**n**= a will move in a direction opposite to the exterior current; and when**n**= o, U = oo, but V = (m/c) sh a sin 13.Negative values of

**n**must be interpreted by a streaming motion on a parallel plane at a level slightly different, as on a double Riemann sheet, the stream passing from one sheet to the other across a cut SS' joining the foci S, S'.The velocity of a liquid particle is thus (a 2 - b 2)/(a 2 +b 2) of what it would be if the liquid was frozen and rotating bodily with the ellipse; and so the effective angular inertia of the liquid is (a 2 -b 2) 2 /(a 2 +b 2) 2 of the solid; and the effective radius of gyration, solid and liquid, is given by k 2 = 4 (a 2 2), and 4 (a 2 For the liquid in the interspace between a and

**n**, m ch 2(0-a) sin 2E 4) 1 4Rc 2 sh 2n sin 2E (a2_ b2)I(a2+ b2) = I/th 2 (na)th 2n; (8) and the effective k 2 of the liquid is reduced to 4c 2 /th 2 (**n**-a)sh 2n, (9) which becomes 4c 2 /sh 2n = s (a 2 - b 2)/ab, when a =00, and the liquid surrounds the ellipse**n**to infinity.For instance, with

**n**= I in equation (9), the relative stream function is obtained for a sphere of radius a, by making it, y' =1y+2Uy 2 = 2U(r 2 -a 3 /r) sin?If there are more B corners than one, either on xA or x'A', the expression for i is the product of corresponding factors, such as in (5) Restricting the attention to a single corner B, a =

**n**(cos no +i sin 110) _ (b-a'.0-a) +1!Ja - u ?I a -a b -u' sh nS2=sh log (Q)=?a - b a - a' b - u' At x where = co, u = o, and q= go, (O

**n**b - a ' a + a -b a' cio) - ?a-a'?b a-a' q In crossing to the line of flow x'A'P'J', b changes from o to m, so that with q = Q across JJ', while across xx the velocity is qo, so that i**n**= go.Helmholtz, of the efflux of a jet between two edges A and A 1 in an infinite wall, is obtained by the symmetrical duplication of the above, with

**n**= 1, b = o, a' = - oo, as in fig.Generally, by making a' = -oo, the line x'A' may be taken as a straight stream line of infinite length, forming an axis of symmetry; and then by duplica tion the result can be ob A tained, with assigned

**n**, a, and b, of the efflux from a symmetrical converging FIG.Thus with a' =o, a stream is split symmetrically by a wedge of angle ' zr/

**n**as in Bobyleff's problem; and, by making a = oo, the wedge extends to infinity; then chnS2= u, sh nS2= b**n**u.This is a closed Sumner line for

**n**=I, when the boundary consists of two parallel walls; and**n**= z gives an Elastica.Over the ellipsoid, p denoting the length of the perpendicular from the centre on a tangent plane, px _ pv _ _ pz 1= a2+X' b +A'

**n**c2+A p2x2 + p2y2 p2z2 I (a2 - + X)2 (b 2 +x)2 + (0+X)2, p 2 = (a2+A)12+(b2+X)m2+(c2+X)n2, = a 2 1 2 +b 2 m 2 +c 2**n**2 +X, 2p d = ds; (8) Thence d?A card will show the influence of the couple

**N**if projected with a spin in its plane, when it will be found to change its aspect in the air.An elongated body like a ship has c 2 -c 1 positive, and the couple

**N**tends to disturb the axial movement and makes it unstable, so that a steamer requires to be steered by constant attention at the helm.Table of Rifling for Stability of an Elongated Projectile, x Calibres long, giving S the Angle of Rifling, and

**n**the Pitch of Rifling in Calibres.I +W a W a), ' (k) 4 (I I) I+ w- R For a shot in air the ratio W'/W is so small that the square may be neglected, and formula (II) can be replaced for practical purpose in artillery by tan26= n2 = W i (0 - a) (k ð)7()4, (12) if then we can calculate /3, a, or (3-a for the external shape of the shot, this equation will give the value of 6 and

**n**required for stability of flight in the air.The components of force, X, Y, and

**N**, acting on the liquid at 0, and reacting on the body, are then X=It.The third division would consist of the collections of the so-called Pseudo-leges Canuti, the laws of Edward the Confessor, of Henry I., and the great compilation of the Quadripartitus, then of a number of short notices and extracts like the fragments on the "wedding of a wife," on oaths, on ordeals, on the king's peace, on rural customs (Rectitudines singularum personarum), the treatises on the reeve (gerefa) and on the judge (dema), formulae of oaths, notions as to wergeld, &c. A fourth group might be made of the charters,

**n**as they are based on Old English private and public law and supply us with most important materials in regard to it.After his death, the Assyrians, who were still nominally the vassals of Babylonia, threw off neser L - g

**n**a ll disguise, and Shalmaneser I.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.The asym ptotes are x= = 2na,

**n**being an integer.Outline of the ventral surface to show the external apertures and nervous system; a, rosette-organ; b, uterine pore; c, terminal sucker; e, vaginal pore; g, male gonopore;

**n**, o, p, nervous system.Ti 3

**N**4 is a copper-coloured powder obtained by heating the ammonio-chloride TiC1 4.4NH 3 in ammonia.Tetramethylammonium iodide,

**N**(CH 3) 4 I, is the chief product obtained by the action of methyl iodide on ammonia (Hofmann).By warming its aqueous solution with an excess of silver oxide it is converted into tetramethylammonium hydroxide,

**N**(CH3)40H, which crystallizes in hygroscopic needles, and has a very alkaline reaction.A, Fasciola hepatica, from the ventral surface (X 2); the alimentary and nervous systems only shown on the left side of the figure, the excretory only on the right; a, right main branch of the intestine; c, a diverticulum; g, lateral ganglion;

**n**, lateral nerve; o, mouth; p, pharynx; s, ventral sucker; cs, cirrus sac; d, left anterior dorsal excretory vessel; m, main vessel; v, left anterior ventral trunk; x, excretory pore.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.By the end of the 15th century

**n**he mountain had resumed much the same general aspect as it is resented before the eruption described by Pliny.The only branch of the lacquerers art that can be said to have shown any marked development in the Meiji era is that in which parts of the decorative scheme consist of objects in gold, silver, shakudo, shibuichi, iron, or, above all, ivory or mother-

**N**One, headed by Namikawa Yasuyuki of KiOto, took for its objects

**N**the utmost delicacy and perfection of technique, rich ness of decoration, purity of design and harmony of color.In its modern form the theorem, which is true for all values of

**n**, is written as (x +a)**n**-1+ I.The hyperbolic or Gudermannian amplitude of the quantity x is ta

**n**(sinh x).Methane and its homologues give origin to the " paraffin " or " fatty series " of the general formula C,H 2, ,+ 1 000H, ethylene gives origin to the acrylic acid series, C

**n**H 27, - 1 000H, and so on.Dibasic acids of the paraffin series of hydrocarbons have the general formula C

**n**H 2 (000H) 2 "; malonic and succinic acids are important members.If a condenser of capacity C is charged to potential V, and discharged

**n**times per second through a galvanometer, this series of intermittent discharges is equivalent to a current nCV.If all the plates on one side are connected together and also those on the other, the condensers are j oined i

**n**parallel.If the difference

**N**Isopies `som et7„,l8 FIG.The value of the index,

**n**, appears to be different for different types of molecule.In the modified Joule-Thomson equation (17), both c and

**n**have simple theoretical interpretations, and it is possible to express the thermodynamical properties of the substance in terms of them by means of reasonably simple formulae.If two diatomic molecules, having each 5 degrees of freedom, combine to form a molecule with 6 degrees of freedom, we should have

**n**= 2, or the energy lost would be 2pc per unit mass.In the Church of England and its sister and daughter churches the position of the archbishop is defined by the medieval in the Roman Catholic Church, save as modified on the

**n**one hand by the substitution of the supremacy of the crown for that of the Holy See, and on the other by the restrictions imposed by the council of Trent.This creed may be the form which Jerome mentions in one of his letters 17,

**n**.But even if we date the rise of heresies in the reign of Domitian instead of Trajan, 2 the attributing of this epistle against 2 O

**n**this point (date of the outbreak of heresy) there is some inconsistency in the reported fragments of Hegesippus.On the other hand in the Diplarthra, the tcl group to which the vast majority of modern Ungulates A i

**n**belong, the second or lower row has been shifted altogether towards the inner side of the limb, so that the magnum is brought considerably into relation with the scaphoid, and is entirely removed from the cuneiform, as in most existing mammals.The scales are at

**n**,**n**; they are fastened only at the middle, and are kept down by the brass pieces t, t.If p" is the refracting angle of the prism, and

**n**the magnifying power of the eye-piece, then p"ln will be the distance observed.The rate at which the motor is transmitting work is then 550 H.P., where

**n**is the revolutions per second of the armature.If we take the sum of

**n**terms of the series '±'H-'±..The numbers obtained by giving

**n**any value in these expressions are of the first, second, third,.The equation of energy is dQ=dE+pdv, (17) expressing that the total energy dQ is used partly in increasing the internal energy of the gas, and partly in expanding the gas against the pressure p. If we take p = RNT/v from equation (14) and substitute for E from equation (16), this last equation becomes dQ 2 (

**n**+3)RNdT +RNTdv (18) which may be taken as the general equation of calorimetry, for a gas which accurately obeys equation (14).We obtain Cv = z (

**n**+3) R /J m.To examine what is meant by a zero value of

**n**we refer to formula (15).The value of

**n**is the number of terms in the energy of the molecule beyond that due to translation.The molecules of gases for which

**n**= o must accordingly be spherical in shape and in internal structure, or at least must behave at collisions as though they were spherical, for they would otherwise be set into rotation by the forces experienced at collisions.The next value which occurs is

**n**=2.The value

**n**= 2 is appropriate to bodies of which the shape is that of a solid of revolution, so that there is no rotation about the axis of symmetry.We must accordingly suppose that the molecules of gases for which

**n**=2 are of this shape.No molecule could possibly be imagined for which

**n**had a negative value or the value**n**=1.The theory therefore passes a crucial test when it is discovered that no gases exist for which

**n**is either negative or unity.There are many thousands of lines in the mercury spectrum, so that from this evidence it would appear that for mercury vapour

**n**ought to be very great, and y almost equal to unity.Instead of this we have

**n**= o, and -y = I I.After vaguely looking at it a long time, "Il

**n**'y a que moi qui pouvais concevoir la tete de Leonidas," he whispered, and died.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.Then, if we take ordinates Kb, Lg, Mc, Nd, Pf, equal to B'B, GG', C'C, D'D, FF', the figure abgcdfe will be the equivalent trapezoid, and any ordinate drawn from the base to the a LM

**N**P e X top of this trapezoid will be equal to the portion of this ordinate (produced) which falls within the original figure.B where x = the distance between the two lines =

**N**/No.On any line OX take a length ON equal to xG, and from

**N**draw NP at right angles to OX and equal to uH; G and H being convenient units of length.If 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.Although the acid is monobasic, salts of polymeric forms exist of the types (MP0 3)

**n**, where**n**may be 1, 2, 3, 4, 6.It shortened fitfully by eight seconds between 1790 and 1879; soon afterwards, restoration set in, and its exact length in 1903 was 2 d 20h 48'

**n**568, being only two seconds short of its original value.Rr; t Maplt 9?

**n**Mauryl., ' v.?Let

**N**be displaced forward to**n**.If the source makes

**n**vibrations in one second it is said to have " frequency "**n**.It sends out

**n**waves in each second.If each wave travels out from the source with velocity U the

**n**waves emitted in one second must occupy a length U and therefore U = nX.At

**N**the displacement is away from C and there is extension.At M, as at J, there is no change, and at

**N**it is easily seen that the motion is backward.To find the relation of the velocity to displacement and pressure we shall express the fact that the wave travels on carrying all its conditions with it, so that the displacement now at M will arrive at

**N**while the wave travels over MN.In the time dt which the wave takes to travel over MN the particle displacement at

**N**changes by QR, and QR= - udt, so that QR/MN = - u/U.The maximum particle velocity is 21rna (where

**n**is the frequency and a the amplitude), or 27raU/X.Immediately above this fixed plate, and almost in contact with it, is another of the same dimensions, and furnished with the same number,

**n**, of openings similarly placed, but passing obliquely through in an opposite direction from those in the fixed plate, the one set being inclined to the left, the other to the right.Now, it is evident that each coincidence of the perforations in the two plates is followed by a non-coincidence, during which the air-current is shut off, and that consequently, during each revolution of the upper plate, there occur

**n**alternate passages and interceptions of the current.If, then, we can determine the number m of revolutions performed by the plate in every second, we shall at once have the number of vibrations per second corresponding to the audible note by multiplying m by

**n**.Suppose that in

**N**beats of the clock the flashes have moved exactly one place back.Then the first flash in the new position is viewed by the 8Nth passage of the opening, and the second flash in the original position of the first is viewed when the pendulum has made exactly

**N**beats and by the (8**N**+ i)th passage of the hole.Then the wheel makes 8

**N**+ 1 revolutions in**N**clock beats, and the fork makes 32**N**+ 4 vibrations in the same time.If the frequency of o is

**n**, that of**N**is 2n.Since U=

**n**X where U is the velocity of sound, X the wave-length, and**n**the frequency, it follows that the forward frequency is greater than the backward frequency.Then the

**n**waves occupy a space U + w - u.Since there are

**n**waves in distance U + w - u the number he actually receives is**n**(U + w - v)/(U + w - u).In this case AK = 4X 2 =l, and the frequency

**n**2 = U/X 2 = 3U/4l.In this case HK = 2X 1 =1, and the frequency is

**n**i = U/X 1 = U/2l.In the next mode H and L represent the ends and HL =2.2 =1 and

**n**2 = U/X 2 =2U/2l.In the third mode HM =X 3 =l and

**n**3 =U/X 3 =3U/2l, and so on.If U is the velocity of sound in a gas at pressure P with density p, and if waves of length X and frequency

**N**are propagated through it, then the distanc?e l between the dust-heaps is 2 =**N**- zN Vyp' where y is the ratio of the two specific heats.If d is measured for two gases in succession for the same frequency

**N**, we have 72 p 2P1 d22 71 p i p s d12' where the suffixes denote the gases to which the quantities relate.The middle of the string is a loop. In the next mode A and C represent the ends and AC = X = and

**n**2 = U/A 2 = 2U/2/ = (2/21) A / (T/m).In the third mode A and D represent the ends and AD = P. 3 =1 and

**n**3 = U/A3 = 3U/2l = (3/21)¦(Tim) and so on.Keeping the same tension, it may be shown that nl is constant by finding

**n**for various lengths.The law that, caeteris paribus,

**n**varies inversely as the thickness may be tested by forming a string of four lengths of the single thread used before, and consequently of double the thickness of the latter, when, for the same length and tension, the compound thread will exhibit double the number of ventral segments presented by the single thread.If r is of the order of A,

**n**is of the order of y; and the kinetic energy of the radial motion is of the same order as that of the longitudinal motion.The formation of beats may be illustrated by considering the disturbance at any point due to two trains of waves of equal amplitude a and of nearly equal frequencies

**n**, n2.If we measure the time from an instant at which the two are in the same phase the resultant disturbance is y=a sin i t+a sin 27rn2t =2a cos ir(

**n**i -**n**2)t sin ir(nl-t-n2)t, which may be regarded as a harmonic disturbance of frequency (ni+n2)/2 but with amplitude 2a cos 7r(**n**i -**n**2)t slowly varying with the time.Taking the squares of the amplitude to represent the intensity or loudness of the sound which would be heard by an ear at the point, this is 4a 2 cos t ir(ni - n2)t =2a 2 {1 -cos 27r(

**n**l - n2)t}, a value which ranges between o and 4a 2 with frequency .n1 - n2.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.C A W W 3 j ?..a... ? ?-- -- -

**n**--- --y ?If X ---- r - i the scales are so chosen i that a inch represents 1 x '

**n**- "--, in.The loads at D', E, due to unit weight on the rail girder are (p-

**n**)/p and**n**/p. The reaction at B' is {(p-**n**)xi+**n**(xi+p)}' /pi.But if the load is distributed to the bracing intersections by rail and cross girders, then the shear at C' will be greatest when the load extends to

**N**, and will have the values wXADN and -wXNEB.Let P be the cost of one pier; G the cost of the main girders for one span, erected;

**n**the number of spans; 1 the length of one span, and L the length of the bridge between abutments.Divide the span L into any convenient number

**n**of equal parts of length 1, so that nl = L; compute the radii of curvature R 1, R2, R3 for the several sections.The large loans raised in Europe, the first instalment of which Byron had himself brought over, while providing the Greeks with the sinews of war, provided seco

**n**d civil w them also with fresh material for strife.The Greeks, who had been squandering the money provided by the loans in every sort of senseless extravagance, affected to despise the Egyptian invaders, but they

**n**h l`**n**were soon undeceived.A hard-and-fast rule of pronunciation is that only vowel or diphthong sounds, or the letters" m,"

**n**," ng," k," t "and" p "are permissible at the end of words, and hence the final letter of all words ending in anything else is simply suppressed or is pronounced as though it were a letter naturally producing one or other of those sounds.It combines directly with most elements, including nitrogen; this can be taken advantage of in forming almost a perfect vacuum, the oxygen combining to form the oxide, CaO, and the nitrogen to form the nitride, Ca 3

**N**2.As regards its constitution, it has been given at different times the formulae NI 3, NHI 2, NH 2 I,

**N**2 H 3 I 3, &c., these varying results being due to the impurities in the substance, owing to the different investigators working under unsuitable conditions, and also to the decomposing action of light.Chattaway determined its composition as

**N**2 H 3 I 3, by the addition of excess of standard sodium sulphite solution, in the dark, and subsequent titration of the excess of the sulphite with standard iodine.Compounds are known which may be looked upon as derived from ammonia by the replacement of its hydrogen by the sulpho-group (HS0 3); thus potassium ammon-trisulphonate,

**N**(SO 3 K) 3.2H20,is obtained as a crystalline precipitate on the addition of excess of potassium sulphite to a solution of potassium nitrite, KN02+3K2S03+2H20=**N**(S03K) 3 +4KHO.Thus the path of the ray when the aether is at rest is the curve which makes fds/V least; but when it is in motion it is the curve which makes fds/(V+lug-m y -I-nw) least, where (l,m,

**n**) is the direction vector of Ss.I

**n**respect of civic rights no privileges of sex, birth or vocation are recognized.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.By means of a well-chosen value of

**n**, determined by a few experiments, it is possible, pending further experiment, with the most recent design, to utilize Bashforth's experimental results carried out with old-fashioned projectiles fired from muzzle-loading guns.Also the velocity v at the end of the arc is given by (87) ve = u e sec 0 cos

**n**.Pressures Observed In A Closed Vessel With Various Explosives 20 15 s

**n**05 10 -15 20 25 30 35 40.45 50.We have for the number of partitions an analytical theory depending on generating functions; thus for the partitions of a number

**n**with the parts I, 2, 3, 4, 5, &c., without repetitions, writing down the product I +x.The formula shows that except for numbers of the form (3n 2

**n**) the number of partitions without repetitions into an odd number of parts is equal to the number of partitions without repetitions into an even number of parts, whereas for the excepted numbers these numbers differ by unity.Mehler, who proved that a simple relation existed between the function of zero order and the zonal harmonic of order

**n**.Hence arose i

**n**the 2nd century A.D.At present, both in

**N**and B, Hebrews is placed after 2 Thess., but in B there is also a continuous numeration of sections throughout the epistles, according to which I to 58 cover Romans to Galatians, but Ephesians, the next epistle, begins with 70 instead of 59, and the omitted section numbers are found in Hebrews.In the first place it is certainly identical with the MS. called

**n**which is quoted in the margin of the 1550 edition of Robert Stephanus' Greek Testament; this MS. according to Stephanus' preface was collated for him by friends in Italy.The principal properties of logarithms are given by the equations log (mn) = log m --Flogs

**n**, loga(m/**n**) = toga m -logo.Thus in arithmetical calculations if the base is not expressed it is understood to be io, so that log m denotes log

**n**m; but in analytical formulae it is understood to be e.Napier's logarithms are not the logarithms now termed Napierian or hyperbolic, that is to say, logarithms to the base e where e= 2.7182818 ...; the relation between

**N**(a sine) and L its logarithm, as defined in the Canonis Descriptio, being**N**=10 7 e L/Ip7, so that (ignoring the factors re, the effect of which is to render sines and logarithms integral to 7 figures), the base is C".The best general method of calculating logarithms consists, in its simplest form, in resolving the number whose logarithm is required into factors of the form I - i r

**n**, where**n**is one of the nine digits, and making use of subsidiary tables of logarithms of factors of this form.All that is required therefore in order to obtain the logarithm of any number is a table of logarithms, to the required number of places, of

**n**, 9n, 99**n**, 999**n**, &c., for**n**= I, 2, 3,In 1846 Peter Gray constructed a new table to 12 places, in which the factors were of the form I - (oi) r

**n**, so that**n**had the values I, 2,.Although the method is usually known by the names of Weddle and Hearn, it is really, in its essential features, due to Briggs, who gave in the Arithmetica logarithmica of 1624 a table of the logarithms of I + i r

**n**up to r =9 to 15 places of decimals.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.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.The equations finally arrived at are DX2(A2_ 2) (x2_ A2m)2+g2A2 ' DgA3 (A A l m) 2 +g 2 A2 ' where is the wave-length in free ether of light whose refractive index is

**n**, and A m the wave-length of light of the same period as the electron, is a coefficient of absorption, and D and g are constants.As A m is a wave-length corresponding to an absorption band, this formula can be used to find values of A m which satisfy the observed values of

**n**within the region of transparency, and so to determine where the absorption bands are situated.And,, secondly, with a laborious zeal then less common than now among,

**n**2 (I - K 2) = 2**n**2 =**n**2 = I historians, he sought to bring to light fresh historical material by patient search for letters, diaries and other manuscripts of value which had escaped the notice of previous students.Nencki has shown that alloxan combines with thiourea in alcoholic solution, in the presence of sulphur dioxide to form pseudothiouric acid, C 5 H 6

**N**4 S0 3.Nothing definite is yet known with regard to the transmission of the parasites by an alternate invertebrate host, although there is presumptive evidence in favour of this supposition.2 A word or two must be said in conclusion with reference to the supposed connexion of the Spirochaetae with the

**n**Trypanosomes.On the western side of the cloister is another two-story building (

**N**).At the south-east corner we find the hen and duck house, and poultry-yard (m), and the dwelling of the keeper (

**n**).We are unhappily unable to identify any other of the principal buildings (

**N**).Detached from the great mass of the monastic edifices was the original abbot's house (

**N**),with its dining-hall (P).If this be applied to the right-hand side of the identity m m m 2 m2 tan-=- -

**n****n**-3n-5n" it follows that the tangent of every arc commensurable with the radius is irrational, so that, as a particular case, an arc of 45 having its tangent rational, must be incommensurable with the radius; that is to say, 3r/4 is an incommensurable number."In the following stemma M and

**N**are "mixed" or "conflated" MSS., being formed by the blending of readings from the "pure" or "unmixed" codices A, B and D, E respectively.M

**N**Intermixture may take place to any extent, and the more of it there has been the more difficult does it become to trace the transmission of a text.It is well known in England for its graceful habit, the slender, grey - or white - barked stem, the delicate, drooping branches and the quivering leaves, a bright, clear green in s p r i

**n**g, becoming duller in the summer, but often keeping their greenness rather late into the 5 autumn.Equating The Above Two Values Of X, We Have 15

**N**' 3 =19 M' 16; Whence**N**' =M' 4'N1 13.The Epact J Depends On The Golden Number

**N**, And Must Be Determined From The Fact That In 1582, The First Year Of The Reformed Calendar,**N**Was 6, And J 26.In Like Manner, When The Number Of Centuries Is 24 25=49, We Must Have 2 =2; When 5 The Number Of Centuries Is 24 2 X25 =74, Then 25=3; And, Generally, When The Number Of Centuries Is 24

**N**X25, Then 25 =**N**1.Now This Is A Condition Which Will Evidently Be Expressed In General By The Formula

**N**(**N**1).For The Golden Number We Have

**N**= (401 $ 1) R; Therefore L = Before Easter.If V =

**N**/A then**N**expresses the ratio of the volume of the instrument up to the zero of the scale to that of one of the scale-divisions.If we suppose the lower part of the instrument replaced by a uniform bar of the same sectional area as the stem and of volume V, the indications of the instrument will be in no respect altered, and the bottom of the bar will be at a distance of

**N**scale-divisions below the zero of the scale.Methyl orange (helianthin, gold orange, Mandarin orange), (CH 3) 2

**N**C 6 H 4**N**2 C 6 H 4 SO 3 Na, is the sodium salt of paradimethylaminobenzene-azo-benzene sulphonic acid.The constitution of the oxyazo compounds has attracted much attention, some chemists holding that they are true azophenols of the type R

**N**2 R l OH, while others look upon them as having a quinonoid structure, i.e.Diazoimino benzene, C 6 H 5

**N**3, is also known.Azoxy Compounds, R

**N**O**N**R', are usually yellow or red crystalline solids which result from the reduction of nitro or nitroso compounds by heating them with alcoholic potash (preferably using methyl alcohol).Benzene-azoethane, C 6 H 5

**N**2 C 2 H 5, is a yellow oil which boils at about 180 C. with more or less decomposition.**N**2 COOH, may also be considered as mixed azo derivatives.Diazobenzenecyanide, C 6 H 5

**N**2 CN, is an unstable oil, formed when potassium cyanide is added to a solution of a diazonium salt.The single existing

**N**genus comprises the European beaver, Castor fiber, of Europe and orthern Asia, and the North American C. canadensis.Let somehow or other retardations be introduced so that the optical length of the successive parts increases by the same quantity nX,

**n**being some number and X the wave-length.The optical effect as regards resolving power is the same as with a grating of

**N**lines in the nth order, but, nearly all the light not absorbed by the glass may be concentrated in one or two orders.'Lord Rayleigh, to whom we owe the first general discussion of the theory of the spectroscope, found by observation that if two spectroscopic lines of frequencies n1 and

**n**, are observed in an instrument, they are just seen as two separate lines when the centre of the central diffraction band of one coincides with the first minimum intensity of the other.We may say therefore that if the difference between the frequencies

**n**1 and**n**, of the two waves is such that in the combined image of the slit the intensity at the minimum between -the two maxima falls to 0.81, the lines are just resolved and**n**l /(**n**l**n**2) may then be called the resolving power.As purity and resolving power are essentially positive quantities,

**n**i in the above expression must be the greater of the two frequencies.The resolving power in the case of gratings is simply mn, where m is the order of spectrum used, and

**n**the total number of lines ruled on the grating.A homogeneous oscillation is one which for all time is described by a circular function such as sin(nt+ a), t being the time and

**n**and a constants.If

**N**be the frequency of a homogeneous vibration sent out by a molecule at rest, the apparent frequency will be**N**(1 v/ V), where V is the velocity of light and v is the velocity of the line of sight, taken as positive if the distance from the observer increases.Balmer, who showed that the four hydrogen lines in the visible part of the spectrum may be represented by the equation

**n**= A(i - 4/s2), where**n**is the reciprocal of the wave-length and therefore proportional to the wave frequency, and s successively takes the values 3, 4, 5, 6.The most complete hydrogen spectrum is that measured by Evershed 8 in the flash spectrum observed during a total solar eclipse, and contains thirty-one lines, all of which agree with considerable accuracy with the formula, if the frequency number

**n**is calculated correctly by reducing the wave-length to vacuo.9 It is a characteristic of Balmer's formula that the frequency approaches a definite limit as s is increased, and it was soon discovered that in several other spectra besides hydrogen, series of lines could be found, which gradually come nearer and nearer to each other as they become fainter, and approach a definite limit.The second form contains two or three constants according as

**N**is taken to have the same value for all elements or not.C. Pickering' used in a special case, presently to be referred to, was put into a more general form by Thiele, who, however, assumes

**N**to have the same value for all spectra, and not obtaining sufficient agreement, rejects the formula.Halm subsequently showed that if

**N**may differ in different cases, the equation is a considerable improvement on Rydberg's.As he takes

**N**to be strictly the same for all elements the equation has only three disposable constants A, a and b.For the trunk series write

**n**s**N**= (I +U) (s +12)' and for the main branch series.The quantity

**N**may serve to fix the third fundamental unit.If we wish to be more general, while still adhering to Deslandres' law as a correct representation of the frequencies when s is small, we may write

**n**- A (s+ 1 1) 2 - - a Po+Pi(s + c) -F +pr(s+ c)r' where s as before represents the integer numbers and the other quantities involved are constants.If we only assign positive values to

**n**and a, the band fades away from the head, the lines at first increasing in distance.A discussion of band spectra on a very broad basis was given by Thiele,' who recommends a formula - q +qi(s+c)+ +qr(s+c)r

**n**in the discharge, except within the region of the kathode glow.The change of frequency (dn) for a series of lines which behave similarly is approximately proportional to the frequency (

**n**) so that we can take the fraction do/**n**as a measure of the shift.Here

**n**represents an integer which is 3 if the vibration is a simple doublet, but may have a higher integer value.Close to and on either side of the absorptive band µ 2 has large positive and negative values, and if the above expression remains correct the change of frequency would, close to the centre of absorption, be 2 k-2"+3, which for

**n**=3 and k= Io is 1/2000, or 500 times greater than the observed shifts, but this represents now the maximum displacement and not the displacement of the most intense portion of the radiation.The arithmetical mean of

**n**quantities is the sum of the quantities divided by their number**n**.The geometrical mean of

**n**quantities is the nth root of their product.The harmonic mean of

**n**quantities is the arithmetical mean of their reciprocals.The 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,.The quadratic mean of

**n**quantities is the square root of the arithmetical mean of their squares.Heated with anhydrous sodium acetate and acetic anhydride it gives cinnamic acid; with ethyl bromide and sodium it forms triphenyl-carbinol (C 6 H 5) 3 C OH; with dimethylaniline and anhydrous zinc chloride it forms leuco-malachite green C6H5CH[C6H4N(CH3)2]2; and with dimethylaniline and concentrated hydrochloric acid it gives dimethylaminobenzhydrol, C 6 H 5 CH(OH)C 6 H 4

**N**(CH 3) 2.The only consonants are k,1, m,

**n**and p, which with the gently aspirated h, the five vowels, and the vocalic w, make up all the letters in use.That category is probably the invention of '

**N**? ??kOUTERGORRIDOR ` " ???????? ? ?? ? ?By the time of Ine, however, pending, pen(

**n**)ing (" penny "), had already come into use for the latter, while, owing to the temporary disappearance of a gold coinage, scilling had come to denote a mere unit of account.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.To direct the card eight short light needles,

**N****N**, are suspended by silk threads from the outer ring.**N**, Hole for filling, with screw plug.Not only was its very existence an obstacle to .the T he Parcy a

**n**d the spread of their temporal power in the peninsula, Norman but it frequently acted in concert with the pope 's Kingdom enemies and thwarted the papal policy.As early therefore as the late 16th century B.C. the name Naharin (

**N**'h'ryn) was in use.The Sea of the Great Bend would seem to be the sea fed by the north-to-south waters of Naharin, just as the Mediterranean, fed by the south-to-north waters of the Nile, is called the Great Circle (š

**n**wr).They all obeyed except Hyperm(

**n**)estra, who spared Lynceus.The vowel sounds ai, oi, ui have become e, o, u; and a, o, u before the finals d and

**n**are now et, o, ii.If in unit mass of any phase we have

**n**components instead of one we must know the amount of**n**- I components present in that unit mass before we know the exact composition of it.If, instead of one phase, we have r phases, we must find out the values of r(

**n**- I) quantities before we know the composition of the whole system.With r phases we can form r - I equations for each component, and with

**n**components and r phases we obtain**n**(r - 1) equations.Here

**n**is the number of gramme-molecules of solute, T the absolute temperature, R the gas constant with its usual "gas" value, p the vapour pressure of the solvent and v1 the volume in which one gramme-molecule of the vapour is confined.