## Node Sentence Examples

- B, C, D, E, enlarged.) branched rootstock from which spring slender aerial shoots which are green, ribbed, and bear at each
**node**a whorl of leaves reduced to a toothed sheath. - In other cases the root structure of the stele continues up to the cotyledonary
**node**, though the hypocotyl is still to be distinguished from the primary root by the character of its epidermis. - In many of those ants whose third abdominal segment forms a second "
**node**," the basal dorsal region of the fourth segment is traversed by a large number of very fine transverse striations; over these the sharp hinder edge of the third segment can be scraped to and fro, and the result is a stridulating organ which gives rise to a note of very high pitch. - The motion of the
**node**of this plane is found with great exactness from observaMass, of the g tions of the transits of Venus. - Its weak point is that the apparent motion of the
**node**depends partly upon the motion of the ecliptic, which cannot be determined with equal precision. - From the observed motion of the
**node**of Venus, as shown by the four transits of 1761, 1769, 1874 and 1882, is found Mass of (earth +moon) _Mass of sun 332600 In gravitational units of mass, based on the metre and second as units of length and time, Log. - We may represent the displacement due to one of the trains by y l =a sin 2 i (24) where x is measured as in equation (16) from an ascending
**node**as A in fig. - 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. - It is obvious that the
are alternately in compression and extension, or vice versa, and that for 4X on each side of a**nodes****node**the motion is either to it on both sides or from it on both sides. - He used a tube of variable length and determined the length resounding to a given fork, (1) when the closed end was the first
**node**, (2) when it was the second**node**. - There is a
**node**in the middle. - When the pipe is blown softly the fundamental is very predominant, and there is a
**node**at the middle point. - Each of the first few harmonics may be easily obtained by touching the string at the first
**node**of the harmonic required, and bowing at the first loop, and the presence of theand loops may be verified by putting light paper riders of shape A on the string at the**nodes**and loops.**nodes** - 36, for the fundamental and the first harmonic. When a string is struck or bowed at a point, any harmonic with a
**node**at that point is absent. - The next mode has a
**node**in the middle and two others each 0.132 from the end. - The fundamental mode has that
**node**only. - The next mode has a second
**node**0.226 from the free end; the next,at 0.132 and 0 .**nodes** - The lower end of the jet tube, being open, is a loop, and the
**node**may be regarded as in an imaginary prolongation of the jet tube above the nozzle. - If the jet tube is somewhat longer than half the sounding tube there will be a
**node**in it, and now the condition of equality of pressure requires opposite motions in the two at the nozzle, for theirare situated on opposite sides of that point.**nodes** - The form of the limacon depends on the ratio of the two constants; if a be greater than b, the curve lies entirely outside the circle; if a equals b, it is known as a cardioid; if a is less than b, the curve has a
**node**within the circle; the particular case when b= 2a is known as the trisectrix. - When a single leaf with opposite stem with alteris produced at a
**node**, and leaves. - In the lowest leaf is directly the point of insertion of the pair one leaf is in above the first, leaf in the
**node**, dividing front and the other and commences the leaf into similar halves, at the back; in the the second cycle. - 31, leaf 1 arises from a
**node**n; leaf 2 is separated from it by an internode m, and is placed to the right or left; while leaf 3 is situated directly above leaf 1. - A, The branch with the leaves numbered in their order, n being the
**node**and m the internode; b is a magnified representation of the branch, showing the points of insertion of the leaves and their spiral arrangement, which is expressed by the fraction or one turn of the spiral for two internodes. - Oedogonium sp., oogonium antheridium at a
**node**on at moment of fertilization a lateral appendage. - From the first
**node**arise rhizoids; from the second a lateral bud, which becomes the new plant. - In the higher normal modes there are
or points of rest (y = 0); thus in the second mode there is a**nodes****node**at a distance .1901 from the lower end. - In such cases they are very generally given off from just above each
**node**(often in a circle) of the lower part of the stem or rhizome, perforating the leaf-sheaths. - They are solitary at each
**node**and arranged in two rows, the lower often crowded, forming a basal tuft. - The spike of an inflorescence bears whorls of flowers at each
**node**in the axils of concrescent bracts accompanied by numerous sterile hairs (paraphyses); in a male inflorescence numerous flowers occur at each**node**, while in a female inflorescence the number of flowers at each**node**is much smaller. - Longitude of ascending
**node**(1908.0), 74° 28.6'. - Each
**node**of a trabecula may be simple, i.e. - The double point larities - cusp or spinode; or
**node**; Line-singu5 3. - The
**node**: the point may in the course of its motion come to coincide with a former position of the point, the two positions of the line not in general coinciding. - It may be remarked that we cannot with a real point and line obtain the
**node**with two imaginary tangents (conjugate or isolated point or acnode), nor again the real double tangent with two imaginary points of contact; but this is of little consequence, since in the general theory the distinction between real and imaginary is not attended to. - The singularities (I) and (3) have been termed proper singularities, and (2) and (4) improper; in each of the first-mentioned cases there is a real singularity, or peculiarity in the motion; in the other two cases there is not; in (2) there is not when the point is first at the
**node**, or when it is secondly at the**node**, any peculiarity in the motion; the singularity consists in the point coming twice into the same position; and so in (4) the singularity is in the line coming twice into the same position. - The curve (1 x, y, z) m = o, or general curve of the order m, has double tangents and inflections; (2) presents itself as a singularity, for the equations dx(* x, y, z) m =o, d y (*r x, y, z)m=o, d z(* x, y, z) m =o, implying y, z) m = o, are not in general satisfied by any values (a, b, c) whatever of (x, y, z), but if such values exist, then the point (a, b, c) is a
**node**or double point; and (I) presents itself as a further singularity or sub-case of (2), a cusp being a double point for which the two tangents becomes coincident. - The expression 2 is that of the number of the disposable constants in a curve of the order m with
and cusps (in fact that there shall be a**nodes****node**is I condition, a cusp 2 conditions) and the equation (9) thus expresses that the curve and its reciprocal contain each of them the same number of disposable constants. - But it can be shown, analytically or geometrically, that if the given curve has a
**node**, the first polar passes through this**node**, which therefore counts as two intersections, and that if the curve has a cusp, the first polar passes through the cusp, touching the curve there, and hence the cusp counts as three intersections. - But, as is evident, the
**node**or cusp is not a point of contact of a proper tangent from the arbitrary point; we have, therefore, for a**node**a diminution and for a cusp a diminution 3, in the number of the intersections; and thus, for a curve with 6and K cusps, there is a diminution 26+3K, and the value of n is n= m (m - I)-26-3K.**nodes** - But if the given curve has a
**node**, then not only the Hessian passes through the**node**, but it has there a**node**the two branches at which touch respectively the two branches of the curve; and the**node**thus counts as six intersections; so if the curve has a cusp, then the Hessian not only passes through the cusp, but it has there a cusp through which it again passes, that is, there is a cuspidal branch touching the cuspidal branch of the curve, and besides a simple branch passing through the cusp, and hence the cusp counts as eight intersections. - The
**node**or cusp is not an inflection, and we have thus for a**node**a diminution 6, and for a cusp a diminution 8, in the number of the intersections; hence for a curve with 6and cusps, the diminution is = 66+8K, and the number of inflections is c= 3m(m - 2) - 66 - 8K.**nodes** - Thirdly, for the double tangents; the points of contact of these are obtained as the intersections of the curve by a curve II = o, which has not as yet been geometrically defined, but which is found analytically to be of the order (m-2) (m 2 -9); the number of intersections is thus = m(rn - 2) (m 2 - 9); but if the given curve has a
**node**then there is a diminution =4(m2 - m-6), and if it has a cusp then there is a diminution =6(m2 - m-6), where, however, it is to be noticed that the factor (m2 - m-6) is in the case of a curve having only a**node**or only a cusp the number of the tangents which can be drawn from the**node**or cusp to the curve, and is used as denoting the number of these tangents, and ceases to be the correct expression if the number ofand cusps is greater than unity.**nodes** - Hence, in the case of a curve which has 6
and K cusps, the apparent diminution 2(m 2 - m-6)(26+3K) is too great, and it has in fact to be diminished by 2 1(25(5 - I) +66K+ 2 K(K - I)1, or the half thereof is 4 for each pair of**nodes**, 6 for each combination of a**nodes****node**and cusp, and 9 for each pair of cusps. - The most simple case is when three double points come into coincidence, thereby giving rise to a triple point; and a somewhat more complicated one is when we have a cusp of the second kind, or
**node-cusp**arising from the coincidence of a**node**, a cusp, an inflection, and a double tangent, as shown in the annexed figure, which represents the singularities as on the point of coalescing. - By means of Pliicker's equations we may form a table - The table is arranged according to the value of in; and we have m=o, n= r, the point; m =1, n =o, the line; m=2, n=2, the conic; of m = 3, the cubic, there are three cases, the class being 6, 4 or 3, according as the curve is without singularities, or as it has 1
**node**or r cusp; and so of m =4, the quartic, there are ten cases, where observe that in two of them the class is = 6, - the reduction of class arising from two cusps or else from three.**nodes** - A property independent of the particular axes of co-ordinates used in the representation of the curve by its equation; for instance, the curve may have a
**node**, and in order to this, a relation, say A = o, must exist between the coefficients of the equation; supposing the axes of co-ordinates altered, so that the equation becomes u' = o, and writing A' = o for the relation between the new coefficients, then the relations A = o, A' = o, as two different expressions of the same geometrical property, must each of them imply the other; this can only be the case when A, A' are functions differing only by a constant factor, or say, when A is an invariant of u. - Similarly a cubic through the two circular points is termed a circular cubic; a quartic through the two points is termed a circular quartic, and if it passes twice through each of them, that is, has each of them for a
**node**, it is termed a bicircular quartic. Such a quartic is of course binodal (m = 4, 6= 2, K = o); it has not in general, but it may have, a third**node**or a cusp. Or again, we may have a quartic curve having a cusp at each of the circular points: such a curve is a " Cartesian," it being a complete definition of the Cartesian to say that it is a bicuspidal quartic curve (m= 4, 6 = o, K= 2), having a cusp at each of the circular points. - .,, a given
**node**5. - „
**node**on given line 6.