The conception of the lamina leads immediately to two schemes, according to which a primary wave may be supposed to be broken up. In the first of these the element dS, the effect of which is to be estimated, is supposed to execute its actual motion, while every other element of the plane lamina is maintained at rest.
Now it is evident that the aerial motion in front of the lamina is determined by what happens at the lamina without regard to the cause of the motion there existing.
Imagine a flexible lamina to be introduced so as to coincide with the plane at which resolution is to be effected.
Or the thallus may have a leaf-like form, the branches from the central threads which form the midrib growing out mainly in one plane and forming a lamina, extended right and left of the midrib.
5); or with veins diverging from the base of the lamina in more or less FIG.
Here again, on integration over the entire lamina, the aggregate effect of the secondary waves is necessarily the same as that of the primary.
The,ideal surface of resolution may be there regarded as a flexible lamina; and we know that, if by forces locally applied every element of the lamina be made to move normally to itself exactly as the air at that place does, the external aerial motion is fully determined.
And lateral sides, of a calcareous lamina covered externally by a soft membrane.
Respiration is conducted by the general surface, by the branchial lamina (external branch) of the feet, and the vesicular appendage (when present) at the base of this branch.
When the secondary disturbance thus obtained is integrated with respect to dS over the entire plane of the lamina, the result is necessarily the same as would have been obtained had the primary wave been supposed to pass on without resolution, for this is precisely the motion generated when every element of the lamina vibrates with a common motion, equal to that attributed to dS.
3.1 Palisade Tissue and Spongy Cells 3.2 Cell Formations 3.3 Blade/Lamina and Stalk/Petiole 3.4 Venation
Lateral segmentation affects the lamina, producing indentations, lobings or fissuring of its margins.
Internally they are found to consist of a lamina twisted upon itself, and externally they generally exhibit a tortuous structure, produced, before the cloaca was reached, by the spiral valve of a compressed small intestine (as in skates, sharks and dog-fishes); the surface shows also vascular impressions and corrugations due to the same cause.
(iv.) In the Microporidae and Steganoporellidae the body-cavity becomes partially subdivided by a calcareous lamina ("cryptocyst," Jullien) which grows from the proximal and lateral sides in a plane parallel to the frontal membrane and not far below it.
When the vascular bundles reach the base of the lamina they separate and spread out in various ways, as already described under venation.
The petiole varies in length, being usually shorter than the lamina, but sometimes much longer.
On the same acacia there occur leaves with the petiole and lamina perfect; others having the petiole slightly expanded or winged, and the lamina imperfectly developed; and others in which there is no lamina, and the petiole becomes large and broad.
Ovular characters determine the grouping in the Dicotyledons, van Tieghem supporting the view that the integument, the outer if there be two, is the lamina of a leaf of which the funicle is the petiole, whilst the nucellus is an outgrowth of this leaf, and the inner integument, if present, an indusium.
While the laminated portion of the thallus is being gradually worn off in our latitudes during the autumnal storms, a vigorous new growth appears at the junction of the stipe and the blade, as the result of which a new piece is added to the stipe and the lamina entirely renovated.
In Iridaea the thallus is an entire lamina; in Callophyllis a lobed lamina; in Delesseria it is provided with midrib and veins, simulating the appearance of a leaf of the higher plants; in Constantinea the axis remains cylindrical, and the lateral branches assume the form of leaves.
Laminaria, Padina, Cutleria, Punctaria, Iridaea, Ulva, Porphyra, are leaf-like with a rigidity varying from a fleshy lamina to the thin and pliable.
For the present we confine ourselves to the consideration of displacements in two dimensions, so that the body is adequately represented by a thin lamina or plate.
The position of a lamina movable in its own plane is determinate when we know the positions of any two points A, B of it.
For instance, the lamina FIG.
The lamina when perfectly free to move in its own plane is said to have three degrees of freedom.
Chasles any displacement whatever of the lamina in its own plane is equivalent to a rotation about some finite or infinitely distant point J.
For suppose that in consequence of the displacement a point of the lamina is brought from A to B, whilst the point of the lamina which was originally at B is brought to C. Since AB, BC, are two different positions of the same line in the B C lamina they are equal, and it is evident that the rotation could have been effected by a rotation about J,
As a special case A the three points A, B, C may be in a straight line; J is then at infinity and the displacement is equivalent to FIG 10 a pure translation, since every point of the lamina is now displaced parallel to AB through a space equal to AB.
II); and let J11, Jfs, Jis be the positions in space of the j,~ centres of the rotations by - which the lamina can be brought from the first position to the second, from the second .li_s to the third, and soon.
Be the points of the ~ lamina which have become the FIG.
Lamina in fig.
If the origin of rectangular axes fixed in the lamina be shifted through a space whose projections on the original directions of the axes are X, u, and if the axes are simultaneously turned through an angle e, the coordinates of a point of the lamina, relative to the original axes, are changed from x, y to X+x cos ey sin e, u+x sin e+y cos e, or X + x ye, u + Xe + y, ultimately.
In this chain of lovely upland lakes, some fresh, some brackish, some completely closed, others connected by short channels, the chief links in their order from north to south are: - Zwai, communicating southwards with Hara and Lamina, all in the Arusi Galla territory; then Abai with an outlet to a smaller tarn in the romantic Baroda and Gamo districts, skirted on the west sides by grassy slopes and wooded ranges from 6000 to nearly 9000 ft.
Horridus, the lamina is deeply lobed; and in a species of the Australian genus Macrozamia, M.
The young leaves arise on the stem-apex as conical protuberances with winged borders, on which the pinnae appear as rounded humps, usually in basipetal order; the scale-leaves in their young condition resemble fronds, but the lamina remains undeveloped.
10 and 11) have a long, slender petiole terminating in a fanshaped lamina, which may be entire, divided by a median incision into two wedge-shaped lobes, or subdivided into several narrow segments.
Adiantum; the lowest vein in each half of the lamina follows a course parallel to the edge, and gives off numerous branches, which fork repeatedly as they spread in a palmate manner towards the leaf margin.
Each ovule is enclosed at the base by an envelope or collar homologous with the lamina of a leaf; the fleshy and hard coats of the nucellus constitute a single integument.
The long linear leaves of some species of Podocarpus, in which the lamina is traversed by a single vein, recall the pinnae of Cycas; the branches of some Dacrydiums and other forms closely resemble those of lycopods; these superficial resemblances, both between different genera of conifers and between conifers and other plants, coupled with the usual occurrence of fossil coniferous twigs without cones attached to them, render the determination of extinct types a very unsatisfactory and frequently an impossible task.
A pair of small strapshaped leaves succeed the two cotyledons of the seedling, and persist as the only leaves during the life of the plant; they retain the power of growth in their basal portion, which is sunk in a narrow groove near the edge of the crown, and the tough lamina, 6 ft.
The older view was that it was a fertile segment of the leaf; and though its ventral position presents a difficulty, this must be regarded as a possible explanation; the occasional occurrence of sporangia on the lamina in Botrychium has been regarded as supporting it.
The leaves are large and pinnate; their lamina is usually thick, though filmy species of Todea occur.
In Osmunda the region of the leaf which bears the sporangia has its lamina little developed; the leaf thus bears sterile and fertile pinnae, or, as in 0.
A petal often consists of two portions - the lower narrow, resembling the petiole of a leaf, and called the unguis or claw; the upper broader, like the blade of a leaf, and called the lamina or limb.
Some of the feathers of the straw-coloured throat and cheeks partake of the same structure, but in a less degree, while the subterminal part of the lamina is of a lustrous pearly-white.
The pitcher is formed so as to form an in- to the lamina 1.
As an example, any system of forces acting on the lamina in fig.
When prolonged heating is required at very high temperatures it is found necessary to line the furnace-cavity with alternate layers of magnesia and carbon, taking care that the lamina next to the lime is of magnesia; if this were not done the lime in contact with the carbon crucible would form calcium carbide and would slag down, but magnesia does not yield a carbide in this way.
If, instead of supposing the motion at dS to be that of the primary wave, and to be zero elsewhere, we suppose the force operative over the element dS of the lamina to be that corresponding to the primary wave, and to vanish elsewhere, we obtain a secondary wave following quite a different law.
The arrangement of the fibro-vascular system in the lamina constitutes the venation or nervation.
Of a plane lamina bounded by the area, in which the surface density is p. If p is uniform, the C.P. and C.G.
At every point the motion of the lamina will be the same as would have occurred in its absence, the pressure of the waves impinging from behind being just what is required to generate the waves in front.
The only assumption here involved is the evidently legitimate one that, when two systems of variously distributed motion at the lamina are superposed, the corresponding motions in front are superposed also.
In the case of Dionaea muscipula we find a two-lobed lamina, the two lobes being connected by a midrib, which can play the part of a kind of hinge.
In this way two marked forms of leaf are produced - (I) Simple form, in which the segmentation, however deeply it extends into the lamina, does not separate portions of the lamina which become articulated with the midrib or petiole; and (2) Compound form, where portions of the lamina are separated as detached leaflets, which become articulated with the midrib or petiole.