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.Advertisement
If 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.Advertisement
The 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).Advertisement
The " 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.Advertisement
The 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+..Advertisement
To 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.