# Ordinate Sentence Examples

The hourly values are derived from smoothed curves, the object being to get the mean

**ordinate**for a 60-minute period.Two sections can be distinguished, the Rhizophysina, with long tubular coenosarc-bearing

**ordinate**cormidia, and Physalina, with compact coenosarc-bearing scattered cormidia.We take a fixed line OX, usually drawn horizontally; for each value of X we measure a length or abscissa ON equal to x.L, and draw an

**ordinate**NP at right angles to OX and equal to the corresponding value of y .In mechanics, the amplitude of a wave is the maximum

**ordinate**.This implies the treatment of a plane or solid figure as being wholly comprised between two parallel lines or planes, regarded by convention as being vertical; the figure being generated by an

**ordinate**or section moving at right angles to itself through a distance which is called the breadth of the figure.AdvertisementIf now we wish to represent the variations in some property, such as fusibility, we determine the freezing-points of a number of alloys distributed fairly uniformly over the area of the triangle, and, at each point corresponding to an alloy, we erect an

**ordinate**at right angles to the plane of the paper and proportional in length to the freezing temperature of that alloy.The rectangle, for instance, has so far been regarded as a plane figure bounded by one pair of parallel straight lines and another pair at right angles to them, so that the conception of " rectangularity " has had reference to boundary rather than to content; analytically, the rectangle must be regarded as the figure generated by an

**ordinate**of constant length moving parallel to itself with one extremity on a straight line perpendicular to it.This is the simplest case of generation of a plane figure by a moving

**ordinate**; the corresponding figure for generation by rotation of a radius vector is a circle.A briquette may therefore be defined as a solid figure bounded by a pair of parallel planes, another pair of parallel planes at right angles to these, a base at right angles to these four planes (and therefore rectangular), and a top which is a surface of any form, but such that every

**ordinate**from the base cuts it in one point and one point only.It may be regarded as generated either by a trapezette moving in a direction at right angles to itself and changing its top but keeping its breadth unaltered, or by an

**ordinate**moving so that its foot has every possible position within a rectangular base.AdvertisementThe

**ordinate**of the trapezette will be denoted by u, and the abscissa of this**ordinate**, i.e.The " mid-

**ordinate**" is the**ordinate**from the middle point of the base, i.e.The " mean

**ordinate**" or average**ordinate**is an**ordinate**of length 1 such that Hl is equal to the area of the trapezette.It therefore appears as a calculated length rather than as a definite line in the figure; except that, if there is only one

**ordinate**of this length, a line drawn through its extremity is so placed that the area of the trapezette lying above it is equal to a corresponding area below it and outside the trapezette.Formulae giving the area of a trapezette should in general also be expressed so as to state the value of the mean

**ordinate**(§§ 12 (v), 15, 19).AdvertisementThe " median

**ordinate**" is the**ordinate**which divides the area of the trapezette into two equal portions.The " central

**ordinate**" is the**ordinate**through the centroid of the trapezette (§ 32).In the case of the briquette the position of the foot of the

**ordinate**u is expressed by co-ordinates x, y, referred to a pair of axes parallel to a pair of sides of the base of the briquette.The

**ordinate**through the centroid of the figure is the ' ` central**ordinate**."The area of the trapezette, measured from the lower bounding

**ordinate**up to the**ordinate**corresponding to any value of x, is some function of x.AdvertisementThe statement that the

**ordinate**u of a trapezette is a function of the abscissa x, or that u=f(x), must be distinguished from u =f(x) as the equation to the top of the trapezette.Similarly, analytical plane geometry deals with the curve described by a point moving in a particular way, while analytical plane mensuration deals with the figure generated by an

**ordinate**moving so that its length varies in a particular manner depending on its position.The result of treating this area as if it were the

**ordinate**of a trapezette leads to special formulae, when the data are of the kind mentioned in § 44.This will be seen by taking the mid-

**ordinate**as the**ordinate**for which x = o, and noticing that the odd powers of x introduce positive and negative terms which balance one another when the whole area is taken into account.If u is an algebraical function of x of degree not exceeding p, and if the area of a trapezette, for which the

**ordinate**v is of degree not exceeding p+q, may be expressed by a formula Aovo-1--yivi+..AdvertisementTo extend these methods to a briquette, where the

**ordinate**u is an algebraical function of x and y, the axes of x and of y being parallel to the sides of the base, we consider that the area of a section at distance x from the plane x = o is expressed in terms of the ordinates in which it intersects the series of planes, parallel to y=o, through the given ordinates of the briquette (§ 44); and that the area of the section is then represented by the**ordinate**of a trapezette.This

**ordinate**will be an algebraical function of x, and we can again apply a suitable formula.The methods of §§ 59 and 60 can similarly be extended to finding the position of the central

**ordinate**of a briquette, or the mean q th of elements of the briquette from a principal plane.If, as is usually the case, the

**ordinate**throughout each strip of the trapezette can be expressed approximately as an algebraical function of the abscissa, the application of the integral calculus gives the area of the figure.The first, which is the best known but is of limited application, consists in replacing each successive portion of the figure by another figure whose

**ordinate**is an algebraical function of x or of x and y, and expressing the area or volume of this latter figure (exactly or approximately) in terms of the given ordinates.The position of the central

**ordinate**is given by x = v 1 /po, and therefore is given approximately by pl/po.To find the moments with regard to the central

**ordinate**, we must use this approximate value, and transform by means of the formulae given in § 32.If the transformation is made first, and if the resulting raw moments with regard to the (approximate) central

**ordinate**are o, 72, 71-3, ..., the true moments µ1, u2, /13, ...with regard to the central**ordinate**are given by Lo=o 1 i / h2,3 83.If QD is the bounding

**ordinate**of one of the component strips, we can calculate the area of Qdbl in the ordinary way.Since the curve represents a longitudinal disturbance in air it is always continuous, at a finite distance from the axis, and with only one

**ordinate**for each abscissa.The

**ordinate**of the curve changes sign as we pass through a node, so that successive sections are moving always in opposite directions and have opposite displacements.The dotted curve represents the superposition, which simply doubles each

**ordinate**.Experience shows that (a) a parabola having the same

**ordinate**at the centre of the span, or (b) a parabola having 15 ons FIG.Such a line has for abscissa the distance of a load from one end of a girder, and for

**ordinate**the bending moment or shear at any given section, or on any member, due to that load.These ideas are further developed in various papers in the Bulletin and in his L'Anthropometrie, ou mesure des differentes facultes de l'homme (18'ji), in which he lays great stress on the universal applicability of the binomial law, - according to which the number of cases in which, for instance, a certain height occurs among a large number of individuals is represented by an

**ordinate**of a curve (the binomial) symmetrically situated with regard to the**ordinate**representing the mean result (average height).The

**ordinate**of the dotted curve which contains its "centre of gravity" has, of course, for its abscissa the "mean" number of glands; the maximum**ordinate**of the curve is, however, at 2.98, or sensibly at 3 glands, showing what Pearson has called the "modal" number of glands, or the number occurring most frequently.The force at A1 may be replaced by its components Xi, Yi, parallei to the co

**ordinate**axes; that at A1 by V1 its components X2, Yf, and so on.The relation between x and t in any particular case may be illustrated by means of a curve constructed with I as abscissa and x as

**ordinate**.A curve with I as abscissa and u as

**ordinate**is called the curve of velocities or velocity-time curve.Let r1 be the radiusvector of a point of contact on the wheel, Xi the

**ordinate**from the straight line before mentioned to the corresponding point of contact on the rack.Also, since the axis is a tangent to the rolling curve, the

**ordinate**PR is the perpendicular from the tracing point P on the tangent.Hence the relation between the radius vector and the perpendicular on the tangent of the rolling curve must be identical with the relation between the normal PN and the

**ordinate**PR of the traced curve.The

**ordinate**to any point upon this curved line then represents on the left-hand scale the maximum continuous yield per day for each acre of drainage area, from a reservoir whose capacity is equal to the corresponding abscissa.We find on the left-hand scale of yield that the height of the

**ordinate**drawn to the 50-inch mean rainfall curve from 200,000 on the capacity scale, is 1457 gallons per day per acre; and the straight radial line, which cuts the point of intersection of the curved line and the co-ordinates, tells us that this reservoir will equalize the flow of the two driest consecutive years.At any point on the latus transversum erect an

**ordinate**.Then the square of the

**ordinate**intercepted between the diameter and the curve is equal to the rectangle contained by the portion of the diameter between the first vertex and the foot of the**ordinate**, and the segment of the**ordinate**intercepted between the diameter and the line joining the extremity of the latus rectum to the second vertex.The conics are distinguished by the ratio between the latus rectum (which was originally called the latus erectum, and now often referred to as the parameter) and the segment of the

**ordinate**intercepted between the diameter and the line joining the second vertex with the extremity of the latus rectum.When the cutting plane is inclined to the base of the cone at an angle less than that made by the sides of the cone, the latus rectum is greater than the intercept on the

**ordinate**, and we obtain the ellipse; if the plane is inclined at an equal angle as the side, the latus rectum equals the intercept, and we obtain the parabola; if the inclination of the plane be greater than that of the side, we obtain the hyperbola.In modern notation, if we denote the

**ordinate**by y, the distance of the foot of the**ordinate**from the vertex (the abscissa) by x, and the latus rectum by p, these relations may be expressed as 31 2 for the hyperbola.To co

**ordinate**the opening of all new outlets.Has Carey lost the ability to co-

**ordinate**his feet now he is in goal?The schemes aim to co

**ordinate**, not compete with existing services.In forms in which, on the other hand, the coenosarc forms an elongated, tubular axis or stem, the appendages are arranged as regularly recurrent cormidia along it, and the cormidia are then said to be "

**ordinate**."A trapezette may therefore be defined as a plane figure bounded by two straight lines, a base at right angles to them, and a top which may be of any shape but is such that every

**ordinate**from the base cuts it in one point and one point only; or, alternatively, it may be defined as the figure generated by an**ordinate**which moves in a plane so that its foot is always on a straight base to which the**ordinate**is at right angles, the length of the**ordinate**varying in any manner as it moves.Starting from any

**ordinate**ue,o, the result of integrating with regard to x through a distance 2h is (in the example considered in § 61) the same as the result of the operation 3h(I + 4E + E 2), where E r denotes the operation of changing x into x+h (see Differences, Calculus oF).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.Let PQ be the

**ordinate**of the point P FIG.The length or area obtained by dividing the area or the volume of the figure by its breadth is the mean

**ordinate**(mean height) or mean section (mean sectional area) of the figure.Quadrature-formulae or cubature-formulae may sometimes be conveniently replaced by formulae giving the mean

**ordinate**or mean section.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.It arises mainly in statistics, when the

**ordinate**of the trapezette represents the relative frequency of occurrence of the magnitude represented by the abscissa x; the magnitude of the abscissa corresponding to the median**ordinate**is then the " median value of x."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.