Trains coming in contact with projections from other trains or vehicles on parallel lines 7.

In the marine Streptoneura they are ectodermic projections which ultimately fall off; in the Opisthobranchs they are closed pouches; in Paludina and Bithynia they are canals as in Pulmonata.

The appendages of the two maxillary segments arise as treble instead of single projections, thus differing from other appendages.

The appendages of the two maxillary segments arise as treble instead of single projections, thus differing from other appendages.

The cylindrical and modified conical projections of Marinus and Ptolemy were still widely used, the stereographical projection of Hipparchus, was for the first time employed for terrestrial maps in the 16th century, but new projections were introduced in addition to these.

He was he deals with the principles of mathematical geography, map projections, and sources of information with special reference FIG.

Werner (1514) devised three heart-shaped projections, one of which was equivalent.

It will suffice therefore to point out that the ordinary needs of the cartographer can be met by conical projections, and, in the case of maps covering a wide area, by Lambert's equal area projection.

projections of AB, AC on All is equal to the projection of AD.

The gonapophyses are the projections near the extremity of the body that surround the sexual orifices, and vary extremely according to the kind of insect.

In the embryos of many insects there are projections from the segments of the abdomen similar, to a considerable extent, to the rudimentary thoracic legs.

The question whether these projections can be considered an indication of former polypody in insects has been raised.

Map projections were dealt with by two eminent mathematicians, J.

These vascular buds grow out in various directions as little solid projections of cells; they then become channelled and form the new but temporary meshwork.

The first step in this process is that of grinding the surface down until all projections are removed and a close approximation to a perfect plane is obtained.

The gonapophyses are the projections near the extremity of the body that surround the sexual orifices, and vary extremely according to the kind of insect.

Such a plasmodium bears, on its periphery, groups of rounded projections of protoplasm termed end-organs.

A typical graptolite consists of an axis bearing a series of tooth-like projections, like a saw.

The word is also sometimes applied to a heavy timber fitted with iron spikes or projections to be thrown down upon besiegers, and to the large work known as a "cavalier."

The cells not only fuse together in longitudinal and transverse rows, but put out transverse projections, which fuse with others of a similar nature, and thus form an anastomosing network of tubes which extends to all parts of the plant.

It is rich, ornate, yet hardly florid, distinguished by splendid effects of light and shade, obtained by a far bolder use of projections than had hitherto been found in the somewhat fiat design of Venetian façades.

The oldest stage-building was erected in the time of Lycurgus; it consisted of a rectangular hall with square projections (1rapauKs vca) on either side; in As= front of this was built in late Greek or early Roman times a stage with a row of columns which intruded upon the orchestra space; a later and larger stage, dating from the time of Nero, advanced still farther into the orchestra, and this was finally faced (probably in the 3rd century A.D.) by the " bema " of Phaedrus, a platform-wall decorated with earlier reliefs, the slabs of which were cut down to suit their new position.

Ladenburg (Ber., 2, p. 140) devised his prism formula (IV), the six carbon atoms being placed at the six corners of a right equilateral triangular prism, with its plane projections (V, VI).

The linear scale of maps can obviously be used only in the case of maps covering a small area, for in the case of maps of greater extension measurements would be vitiated owing to the distortion or exaggeration inherent in all projections, not to mention the expansion or shrinking of the paper in the process of printing.

- Diagrammatic projections to exhibit the relations of the female genital ducts in Trematodes with those in Cestodes.

BOVIDAE, the name of the family of hollow-horned ruminant mammals typified by the common ox (Bos taurus), and specially characterized by the presence on the skulls of the males or of both sexes of a pair of bony projections, or cores, covered in life with hollow sheaths of horn, which are never branched, and at all events after a very early stage of existence are permanently retained.

- Diagrammatic projections to show the relations of the female reproductive ducts; A, in the Malacocotylea; B, in the Heterocotylea.

It would seem that only the immense weight of the roofs and their heavy projections prevent a collapse of some of these structures in high winds.

During this peculiar locomotion the numerous broad shields of the belly are of great advantage, as by means of their free edges the snake is enabled to catch and use as points of support the slightest projections of the ground.

of the base are the projections of the sides AB, BC, CD,.

It is indeed an image and reflection of the first Being; but the further the line of successive projections is prolonged the smaller is its share in the true existence.

The testes in the pairing-season form projections in the groins, but (except in the Duplicidentata) do not completely leave the cavity of the abdomen.

For the quantitative study of such systems in detail it is convenient to draw plane diagrams which are theoretically projections of the curves of the solid phase rule diagram on one or other of these planes.

(4) In the Thacher system a flat bar with projections like rivet heads is specially rolled for this purpose.

might be reduced according to the size secure the interior against frost, flow and return hot-water pipe e should pass along beneath the staging, which should be a strong wooden trellis supported by projections in the brickwork.

These projections are termed insertion plates; they are usually slit or notched to form teeth, the edges of which may be smooth and sharp, or may be crenulated.

The anterior margin of each valve except the first is provided with two projections called sutural laminae which underlie the posterior margin of the preceding valve.

Externally, the body of a Sipunculoid presents no projections: its surface is as a rule even, and often glistening, and the colour varies from whitish through yellow to dark brown.

The Delta coast-line, composed of sandhills and, occasionally, limestone rocks, is low, with cape-like projections at the Nile mouths formed by the river silt.

When placed on the stigma, under favourable circumstances, the pollen-grain puts forth a pollen-tube which grows down the tissue of the style to the ovary, and makes its way along the placenta, guided by projections or hairs, to the mouth of an ovule.

Hamilton, still keeping prominently before him as his great object the invention of a method applicable to space of three dimensions, proceeded to study the properties of triplets of the form x+iy+jz, by which he proposed to represent the directed line in space whose projections on the co-ordinate axes are x, y, z.

addition of their several projections agreed with the assumption of Buee and Argand for the case of coplanar lines.

Beneath the Rete, in a hollow, are four thin brass discs, called Tables or Climates, engraved with projections of the sphere for different latitudes.

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.

Regarded as a statement concerning the orthogonal projections -~ ~ -~ -~

It is now evident that in the process of reduction of a coplanar system no change is made at any stage either in the sum of the projections of the forces on any line or in the sum of their moments about any point.

Again it is necessary and sufficient for equilibrium that the sum of the projections of the forces on each of two perpendicular directions should vanish, and (moreover) that the sum of the moments about some one point should be zero.

In words: the sum of the projections of the forces on each of the co-ordinate axes must vanish; and, the sum of the moments of the forces about each of these axes must vanish.

a, /3 be the orthogonal projections of A, B on AB, we have AaB~=ABaf3=AB(I cos~,) =4AB.~2,

The linear scale of maps can obviously be used only in the case of maps covering a small area, for in the case of maps of greater extension measurements would be vitiated owing to the distortion or exaggeration inherent in all projections, not to mention the expansion or shrinking of the paper in the process of printing.

- Diagrammatic projections to exhibit the relations of the female genital ducts in Trematodes with those in Cestodes.

The five fixed webs are attached to the table which is secured to the bottom of the box by the screws p. The three movable webs are attached to the projections XX on the frame aa.

These segments are abundantly supplied with elongate tooth-like projections connected with nerve-endings probably olfactory in function.

Owing to the great extent of Asia, it is not easy to obtain a correct conception of the actual form of its outline from ordinary maps, the distortions which accompany projections of great and misleading.

Map Projections are dealt with separately below.

Map Projections are dealt with separately below.

Vast vertical walls of rock shoot up to a height of 600 ft., cut by their perpendicular joints into quadrangular piers and projections, some of which stand out alone as cathedral-like islets in front of the main cliff.

Vast vertical walls of rock shoot up to a height of 600 ft., cut by their perpendicular joints into quadrangular piers and projections, some of which stand out alone as cathedral-like islets in front of the main cliff.

Organs which respond to the mechanical stimulus of contact are found to possess special contrivances in certain of their cells(I) sensitive spots, consisting of places here and there on the epidermal cells where the wall is thin and in close contact with protoplasmic projections.

Map Projections >>

On the inner surface of both valves several well-defined muscular, vascular and ovarian impressions are observable; they form either indentations of greater or less size and depth, or occur as variously shaped projections.

It may be added that he first examined the conditions of stability of the system formed by Saturn's rings, pointed out the necessity for their rotation, and fixed for it a period (Io h 33 m) virtually identical with that established by the observations of Herschel; that he detected the existence in the solar system of an invariable plane such that the sum of the products of the planetary masses by the projections upon it of the areas described by their radii vectores in a given time is a maximum; and made notable advances in the theory of astronomical refraction (Mec. cel.

The bark, of nearly the same tint as that of the redwood, is extremely thick and is channelled towards the base with vertical furrows; at the root the ridges often stand out in buttress-like projections.

the projections of OP~, OPI,.

Let these projections be denoted algebraically by x1, xi,.

Since the projection of a vector- sum is the sum of the projections of the several vectors, the equation (2) gives if x be the projection of 0G.

Obviously OV is parallel to the tangent to the path atP, and its magnitude is ds/dt, where s is the arc. If we project OV on the co-ordinate axes (rectangular or oblique) in the usual manner, the projections u, v, w are called the component velocities parallel to the axes.

If the joint be provided either with projections and recesses, such as murtises and tenons, or with fastenings, such as pins or bolts, so as to resist displacement by sliding, the question of the utmost amount of the tangential resistance CQ which it is capable of exerting depends on the strength of such projections, recesses, or fastenings; and belongs to the subject of strength, and not to that of stability.

Parallel Projections of Figures.If any figure be referred to a system of co-ordinates, rectangular or oblique, and if a second figure be constructed by means of a second system of co-ordinates, rectangular or oblique, and either agreeing with or differing from the first system in rectangularity or obliquity, but so related to the co-ordin.

ates of the first figure that for each point in the first figure there shall be a corresponding point in the second figure, the lengths of whose co-ordinates shall bear respectively to the three corresponding co-ordinates of the corresponding point in the first figure three ratios which are the same for every pair of corresponding points in the two figures, these corresponding figures are called parallel projections of each other.

The properties of parallel projections of most importance to the subject of the present article are the following:

Though not essential for the purposes of the present article, the following consequence will serve to illustrate the principle of parallel projections:

For example, all ellipsoids referred to co-ordinates parallel to any three conjugate diameters are parallel projections of each other and of a sphere referred to rectangular co-ordinates.

Parallel Projections of Systems of Forces.If a balanced system of forces be represented by a system of lines, then will every parallel projection of that system of lines represent a balanced system of forces.

Velocity Ratio of Components of Motion.As the distance between any two points in a rigid body is invariable, the projections of their velocities upon the line joining them must be equal.

Screws.The figure of a screw is that of a convex or concave cylinder, with one or more helical projections, called threads, winding round it.

Twig-like projections, to which the term helictite has been applied by the present writer, are met with in certain portions of the cave, and are interesting by their strange and uncouth contortions.

It is the opinion of almost all who have studied the subject that any natural bed may in time be destroyed by overfishing (perhaps not by removing all the oysters, but by breaking up the colonies, and delivering over the territory which they once occupied to other kinds of animals), by burying the breeding oysters, by covering up the projections suitable for the reception of spat, and by breaking down, through the action of heavy dredges, the ridges which are especially fitted to be seats of the colonies.'

extremities of the coast is only 225 m.; but, on account of projections and indentations, the coast-line measures not less than 2500 m.

The pedicles are always covered with skin well supplied with blood-vessels; and in young deer, or those in which the antlers have been comparatively recently shed, the covering of skin extends over their summits, when they appear as longer or shorter projections on the forehead, according to the species.

The introduction of steel construction has simplified many details of architectural treatment, such as projections for cornices, bay windows and galleries.

These projections and ridges may be homologous with the seminiferous scale of the pines, firs, cedars, &c. The simplest interpretation of the cone of the Abietineae is that which regards it as a flower consisting of an axis bearing several open carpels, which in the adult cone may be very small or large and prominent, the scale bearing the ovules being regarded as a placental outgrowth from the flat and open carpel.

There are always eight tentacles, which are hollow and fringed on their sides, with hollow projections or pinnae; and always eight mesenteries, all of which are complete, i.e.

1774) and Gabriel Cramer; the work also contains the remarkable theorem (to be again referred to), that there are five kinds of cubic curves giving by their projections every cubic curve whatever.

The nature of the two kinds of branches is best understood by considering them as projections, in the same way as we in effect consider the hyperbola and the parabola as projections of the ellipse.

Other epidermic appendages are the horns of ruminants and rhinoceroses - the former being elongated, tapering, hollow caps of hardened epidermis of fibrous structure, fitting on and growing from conical projections of the frontal bones and always arranged in pairs, while the latter are of similar structure, but without any internal bony support, and situated in the middle line.

As the teeth of the upper and the lower jaws work against each other in masticating, there is a general correspondence or harmony between them, the projections of one series, when the mouth is closed, fitting into corresponding depressions of the other.

The five pairs of appendages of the post-oral somites of the head or prosoma thus constituted all primitively carry gnathobasic projections on their coxal joints, which act as hemignaths: in the more specialized forms the mandibular gnathobases cease to develop.

In some places limestones appear as projections from the range; at others conglomerates and Tertiary clay marls form the outermost fold."' On the north versant of the ranges the rainfall increases from the foot of the mountains upwards, and at woo-10,000 ft.

AFRICA, the name of a continent representing the largest of the three great southward projections from the main mass of the earth's surface.

These papillae, which are found everywhere, are the primary papillae; they are covered with small, scale-like projections called secondary papillae, and are specially developed on the dorsal surface, less so on the ventral.

Since all conics derived from a circular cone appear circular when viewed from the apex, they conceived the treatment of the conic sections as projections of a circle.

This resistance is due to the roughness of the surfaces; the minute projections upon each enter more or less into the minute depressions on the other, and when motion occurs these roughnesses must either be worn off, or continually lifted out of the hollows into which they have fallen, or both, the resistance to motion being in either case quite perceptible and measurable.

Upon these projections the rudiments of the pollen-sacs are then seen, usually four in number, two on each lobe.

It is either smooth, or covered with numerous projections (fig.

The natural vision is such that different central projections of the objects are communicated to both eyes; the difference of the two perspective representations arises from the fact that the projection centres are laterally separated by an interval about equal to the distance between the eyes (the inter-pupillary distance).

Ultimately, somewhere, economic projections resulted.

Thus, the " doomsday " projections by early writers were not entirely baseless.

conic projections.

A future of controlled fertility and rapidly changing roles of women make projections of sex ratios highly conjectural.

cylindrical map projections.

headship rate projections that are 9 years ahead of the last known data point.

We have examined the morphology and longitudinal axon projections of a population of spinal commissural interneurons, in young Xenopus tadpoles.

This bold new production works with puppets, projections, machines and music to weave an irresistible magic.

simple numeration is expanded to " abstract " mathematics by metaphorical projections from our sensory-motor experience.

orthogonal projections with each consisting of sixteen sensors.

population projections show a substantial loss in the city up to the year 2006.

GAD published revised projections for 2004 and later years, based on the revised population estimates, on 30 September 2004.

The cost of the war itself exceed previous public projections from the office of the Secretary of Defense.

A range of intelligence will be used to select the LAs, including evidence from the subnational population projections.

Tool for Stereographic projection - This tools allows you to draw stereographic projections for different crystal types using different poles for the projection axis.

The works are constructed by adapting formal graphic principles, largely based on perspectival and orthographic projections, often parodying GUI layouts.

The 2002-based projections are due to be published in October 2003.

GROS has prepared sub-national projections for the administrative areas of Scotland that are consistent with the Scotland projection.

Each investee company must provide regular reports on business and financial progress - including cashflow projections, management accounts and audited financial statements.

population projections show a substantial loss in the city up to the year 2006.

The household projections were important for Regional Planning Guidance.

The piece involved the use of film and slide projections and an original musical score.

In a manner reminiscent of Feuerbach, Durkheim stated that the deities which men worship together are only projections of the power of society.

Hence all the fancy projections of fabulous economic returns are quite frankly risible.

villusTechie bit: The lining of the small intestine is covered with small finger like projections called villi.

write-off costs have been included in the financial projections.

This theorem has been generalized for any tetrahedron; a sphere can be drawn through the four feet of the perpendiculars, and consequently through the mid-points of the lines from the vertices to the centre of the hyperboloid having these perpendiculars as generators, and through the orthogonal projections of these points on the opposite faces.

The five fixed webs are attached to the table which is secured to the bottom of the box by the screws p. The three movable webs are attached to the projections XX on the frame aa.

The word is also sometimes applied to a heavy timber fitted with iron spikes or projections to be thrown down upon besiegers, and to the large work known as a "cavalier."

Such a plasmodium bears, on its periphery, groups of rounded projections of protoplasm termed end-organs.

A typical graptolite consists of an axis bearing a series of tooth-like projections, like a saw.

Organs which respond to the mechanical stimulus of contact are found to possess special contrivances in certain of their cells(I) sensitive spots, consisting of places here and there on the epidermal cells where the wall is thin and in close contact with protoplasmic projections.

The cells not only fuse together in longitudinal and transverse rows, but put out transverse projections, which fuse with others of a similar nature, and thus form an anastomosing network of tubes which extends to all parts of the plant.

Trains coming in contact with projections from other trains or vehicles on parallel lines 7.

These segments are abundantly supplied with elongate tooth-like projections connected with nerve-endings probably olfactory in function.

Owing to the great extent of Asia, it is not easy to obtain a correct conception of the actual form of its outline from ordinary maps, the distortions which accompany projections of great and misleading.

In the marine Streptoneura they are ectodermic projections which ultimately fall off; in the Opisthobranchs they are closed pouches; in Paludina and Bithynia they are canals as in Pulmonata.

In the embryos of many insects there are projections from the segments of the abdomen similar, to a considerable extent, to the rudimentary thoracic legs.

The question whether these projections can be considered an indication of former polypody in insects has been raised.

It is rich, ornate, yet hardly florid, distinguished by splendid effects of light and shade, obtained by a far bolder use of projections than had hitherto been found in the somewhat fiat design of Venetian façades.

The oldest stage-building was erected in the time of Lycurgus; it consisted of a rectangular hall with square projections (1rapauKs vca) on either side; in As= front of this was built in late Greek or early Roman times a stage with a row of columns which intruded upon the orchestra space; a later and larger stage, dating from the time of Nero, advanced still farther into the orchestra, and this was finally faced (probably in the 3rd century A.D.) by the " bema " of Phaedrus, a platform-wall decorated with earlier reliefs, the slabs of which were cut down to suit their new position.

Ladenburg (Ber., 2, p. 140) devised his prism formula (IV), the six carbon atoms being placed at the six corners of a right equilateral triangular prism, with its plane projections (V, VI).

Soc. Trans., p. 1013) considered in detail an octahedral form, and showed how by means of certain simple rotations of his system the formulae of Kekule and Claus could be obtained as projections.

It will suffice therefore to point out that the ordinary needs of the cartographer can be met by conical projections, and, in the case of maps covering a wide area, by Lambert's equal area projection.

He was he deals with the principles of mathematical geography, map projections, and sources of information with special reference FIG.

Of the two projections proposed by him one is a modified conical projection with curved parallels and straight meridians; in the second projection (see fig.

The cylindrical and modified conical projections of Marinus and Ptolemy were still widely used, the stereographical projection of Hipparchus, was for the first time employed for terrestrial maps in the 16th century, but new projections were introduced in addition to these.

Werner (1514) devised three heart-shaped projections, one of which was equivalent.

Map projections were dealt with by two eminent mathematicians, J.

Map Projections >>

Other forms show no indication of ever having been attached, while some that had been moored by means of a peduncle during the early portion of their existence have become detached at a more advanced stage of life, the opening becoming gradually cicatrized, as is so often seen in Leptaena rhomboidalis, Orthisina anomala, &c. Lastly, some species adhere to submarine objects by a larger or smaller portion of their ventral valve, as is the case with many forms of Crania, Thecidium, Davidsonia, &c. Some Cranias are always attached by the whole surface of their lower or ventral valve, which models itself and fills up all the projections or depressions existing on either the rock, shell or coral to which it adhered.

On the inner surface of both valves several well-defined muscular, vascular and ovarian impressions are observable; they form either indentations of greater or less size and depth, or occur as variously shaped projections.

It may be added that he first examined the conditions of stability of the system formed by Saturn's rings, pointed out the necessity for their rotation, and fixed for it a period (Io h 33 m) virtually identical with that established by the observations of Herschel; that he detected the existence in the solar system of an invariable plane such that the sum of the products of the planetary masses by the projections upon it of the areas described by their radii vectores in a given time is a maximum; and made notable advances in the theory of astronomical refraction (Mec. cel.

These vascular buds grow out in various directions as little solid projections of cells; they then become channelled and form the new but temporary meshwork.

The first step in this process is that of grinding the surface down until all projections are removed and a close approximation to a perfect plane is obtained.

Since the circulation round any triangular area of given aspect is the sum of the circulation round the projections of the area on the coordinate planes, the composition of the components of spin,, 7,, is according to the vector law.

BOVIDAE, the name of the family of hollow-horned ruminant mammals typified by the common ox (Bos taurus), and specially characterized by the presence on the skulls of the males or of both sexes of a pair of bony projections, or cores, covered in life with hollow sheaths of horn, which are never branched, and at all events after a very early stage of existence are permanently retained.

- Diagrammatic projections to show the relations of the female reproductive ducts; A, in the Malacocotylea; B, in the Heterocotylea.

Now the granite, continuing for long distances, forms the prevailing rock; then, again, it forms the foundation for thick strata of schist and sandstone, itself only appearing in valleys of erosion and river boulders, in rocky projections on the coasts or in the ridges of the mountains....

It would seem that only the immense weight of the roofs and their heavy projections prevent a collapse of some of these structures in high winds.

During this peculiar locomotion the numerous broad shields of the belly are of great advantage, as by means of their free edges the snake is enabled to catch and use as points of support the slightest projections of the ground.

The region PbEeE' contains all the alloys that commence their solidification by the crystallization of lead; similarly, the other two regions correspond to the initial crystallization of bismuth and tin respectively; these areas are the projections of the three sheets of the freezing-point surface.

Construct a small cylinder inside the gas, having dS as base and edges such that the projections of each on the coordinate axes are udt, vdt, wdt.

of the base are the projections of the sides AB, BC, CD,.

Insect-pollinated, Entomophilae, a very large class characterized by sticky pollen grains, the surface of which bears spines, warts or other projections (fig.

It is indeed an image and reflection of the first Being; but the further the line of successive projections is prolonged the smaller is its share in the true existence.

The bark, of nearly the same tint as that of the redwood, is extremely thick and is channelled towards the base with vertical furrows; at the root the ridges often stand out in buttress-like projections.

The testes in the pairing-season form projections in the groins, but (except in the Duplicidentata) do not completely leave the cavity of the abdomen.

For the quantitative study of such systems in detail it is convenient to draw plane diagrams which are theoretically projections of the curves of the solid phase rule diagram on one or other of these planes.

(4) In the Thacher system a flat bar with projections like rivet heads is specially rolled for this purpose.

might be reduced according to the size secure the interior against frost, flow and return hot-water pipe e should pass along beneath the staging, which should be a strong wooden trellis supported by projections in the brickwork.

These projections are termed insertion plates; they are usually slit or notched to form teeth, the edges of which may be smooth and sharp, or may be crenulated.

The anterior margin of each valve except the first is provided with two projections called sutural laminae which underlie the posterior margin of the preceding valve.

7); if there are slight projections which are more or less pointed, the leaf is dentate or toothed; when the projections lie regularly over each other, like the teeth of a saw, the leaf is serrate (fig.

Externally, the body of a Sipunculoid presents no projections: its surface is as a rule even, and often glistening, and the colour varies from whitish through yellow to dark brown.

The Delta coast-line, composed of sandhills and, occasionally, limestone rocks, is low, with cape-like projections at the Nile mouths formed by the river silt.

When placed on the stigma, under favourable circumstances, the pollen-grain puts forth a pollen-tube which grows down the tissue of the style to the ovary, and makes its way along the placenta, guided by projections or hairs, to the mouth of an ovule.

Hamilton, still keeping prominently before him as his great object the invention of a method applicable to space of three dimensions, proceeded to study the properties of triplets of the form x+iy+jz, by which he proposed to represent the directed line in space whose projections on the co-ordinate axes are x, y, z.

addition of their several projections agreed with the assumption of Buee and Argand for the case of coplanar lines.

Beneath the Rete, in a hollow, are four thin brass discs, called Tables or Climates, engraved with projections of the sphere for different latitudes.

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.

Regarded as a statement concerning the orthogonal projections -~ ~ -~ -~

It is now evident that in the process of reduction of a coplanar system no change is made at any stage either in the sum of the projections of the forces on any line or in the sum of their moments about any point.

Again it is necessary and sufficient for equilibrium that the sum of the projections of the forces on each of two perpendicular directions should vanish, and (moreover) that the sum of the moments about some one point should be zero.

In words: the sum of the projections of the forces on each of the co-ordinate axes must vanish; and, the sum of the moments of the forces about each of these axes must vanish.

Again, since the shortest distance between any two conjugate lines cuts the central axis at right angles, the orthogonal projections of two conjugate lines on a plane perpendicular to the central axis will be parallel (fig.

a, /3 be the orthogonal projections of A, B on AB, we have AaB~=ABaf3=AB(I cos~,) =4AB.~2,

projections of AB, AC on All is equal to the projection of AD.

the projections of OP~, OPI,.

Let these projections be denoted algebraically by x1, xi,.

Since the projection of a vector- sum is the sum of the projections of the several vectors, the equation (2) gives if x be the projection of 0G.

Obviously OV is parallel to the tangent to the path atP, and its magnitude is ds/dt, where s is the arc. If we project OV on the co-ordinate axes (rectangular or oblique) in the usual manner, the projections u, v, w are called the component velocities parallel to the axes.

If the joint be provided either with projections and recesses, such as murtises and tenons, or with fastenings, such as pins or bolts, so as to resist displacement by sliding, the question of the utmost amount of the tangential resistance CQ which it is capable of exerting depends on the strength of such projections, recesses, or fastenings; and belongs to the subject of strength, and not to that of stability.

Parallel Projections of Figures.If any figure be referred to a system of co-ordinates, rectangular or oblique, and if a second figure be constructed by means of a second system of co-ordinates, rectangular or oblique, and either agreeing with or differing from the first system in rectangularity or obliquity, but so related to the co-ordin.

ates of the first figure that for each point in the first figure there shall be a corresponding point in the second figure, the lengths of whose co-ordinates shall bear respectively to the three corresponding co-ordinates of the corresponding point in the first figure three ratios which are the same for every pair of corresponding points in the two figures, these corresponding figures are called parallel projections of each other.

The properties of parallel projections of most importance to the subject of the present article are the following:

Though not essential for the purposes of the present article, the following consequence will serve to illustrate the principle of parallel projections:

For example, all ellipsoids referred to co-ordinates parallel to any three conjugate diameters are parallel projections of each other and of a sphere referred to rectangular co-ordinates.

Parallel Projections of Systems of Forces.If a balanced system of forces be represented by a system of lines, then will every parallel projection of that system of lines represent a balanced system of forces.

Velocity Ratio of Components of Motion.As the distance between any two points in a rigid body is invariable, the projections of their velocities upon the line joining them must be equal.

Screws.The figure of a screw is that of a convex or concave cylinder, with one or more helical projections, called threads, winding round it.

Twig-like projections, to which the term helictite has been applied by the present writer, are met with in certain portions of the cave, and are interesting by their strange and uncouth contortions.

It is the opinion of almost all who have studied the subject that any natural bed may in time be destroyed by overfishing (perhaps not by removing all the oysters, but by breaking up the colonies, and delivering over the territory which they once occupied to other kinds of animals), by burying the breeding oysters, by covering up the projections suitable for the reception of spat, and by breaking down, through the action of heavy dredges, the ridges which are especially fitted to be seats of the colonies.'

extremities of the coast is only 225 m.; but, on account of projections and indentations, the coast-line measures not less than 2500 m.

The pedicles are always covered with skin well supplied with blood-vessels; and in young deer, or those in which the antlers have been comparatively recently shed, the covering of skin extends over their summits, when they appear as longer or shorter projections on the forehead, according to the species.

The introduction of steel construction has simplified many details of architectural treatment, such as projections for cornices, bay windows and galleries.

These projections and ridges may be homologous with the seminiferous scale of the pines, firs, cedars, &c. The simplest interpretation of the cone of the Abietineae is that which regards it as a flower consisting of an axis bearing several open carpels, which in the adult cone may be very small or large and prominent, the scale bearing the ovules being regarded as a placental outgrowth from the flat and open carpel.

There are always eight tentacles, which are hollow and fringed on their sides, with hollow projections or pinnae; and always eight mesenteries, all of which are complete, i.e.

1774) and Gabriel Cramer; the work also contains the remarkable theorem (to be again referred to), that there are five kinds of cubic curves giving by their projections every cubic curve whatever.

The nature of the two kinds of branches is best understood by considering them as projections, in the same way as we in effect consider the hyperbola and the parabola as projections of the ellipse.

Other epidermic appendages are the horns of ruminants and rhinoceroses - the former being elongated, tapering, hollow caps of hardened epidermis of fibrous structure, fitting on and growing from conical projections of the frontal bones and always arranged in pairs, while the latter are of similar structure, but without any internal bony support, and situated in the middle line.

As the teeth of the upper and the lower jaws work against each other in masticating, there is a general correspondence or harmony between them, the projections of one series, when the mouth is closed, fitting into corresponding depressions of the other.

The five pairs of appendages of the post-oral somites of the head or prosoma thus constituted all primitively carry gnathobasic projections on their coxal joints, which act as hemignaths: in the more specialized forms the mandibular gnathobases cease to develop.

In some places limestones appear as projections from the range; at others conglomerates and Tertiary clay marls form the outermost fold."' On the north versant of the ranges the rainfall increases from the foot of the mountains upwards, and at woo-10,000 ft.

AFRICA, the name of a continent representing the largest of the three great southward projections from the main mass of the earth's surface.

Mag., 1859, 17, p. 123 seq.), considering them by means of their projections on the circumscribing sphere and not, as Cauchy, in solido.

Poinsot gave the formula E 2k = eV + F, in which k is the number of times the projections of the faces from the centre on to the surface of the circumscribing sphere make up the spherical surface, the area of a stellated face being reckoned once, and e is the ratio " angles at a vertex /21r" as projected on the sphere, E, V, F being the same as before.

These papillae, which are found everywhere, are the primary papillae; they are covered with small, scale-like projections called secondary papillae, and are specially developed on the dorsal surface, less so on the ventral.

Since all conics derived from a circular cone appear circular when viewed from the apex, they conceived the treatment of the conic sections as projections of a circle.

This resistance is due to the roughness of the surfaces; the minute projections upon each enter more or less into the minute depressions on the other, and when motion occurs these roughnesses must either be worn off, or continually lifted out of the hollows into which they have fallen, or both, the resistance to motion being in either case quite perceptible and measurable.

These divisions either are simple projections in the form of acute or obtuse teeth (fig.

When a tubular corolla is split in such a way as to form a strap-like process on one side with several tooth-like projections at its apex, it becomes ligulate or strap-shaped (fig.

There is a double covering of the anther - the outer, or exothecium, resembles the epidermis,and often presents stomata and projections of different kinds (fig.

Upon these projections the rudiments of the pollen-sacs are then seen, usually four in number, two on each lobe.

It is either smooth, or covered with numerous projections (fig.

When the carpels in a syncarpous pistil do not fold inwards so that the placentas appear as projections on the walls of the ovary, then the ovary is unilocular (fig.

The natural vision is such that different central projections of the objects are communicated to both eyes; the difference of the two perspective representations arises from the fact that the projection centres are laterally separated by an interval about equal to the distance between the eyes (the inter-pupillary distance).

In a manner reminiscent of Feuerbach, Durkheim stated that the deities which men worship together are only projections of the power of society.

Hence all the fancy projections of fabulous economic returns are quite frankly risible.

The Techie bit: The lining of the small intestine is covered with small finger like projections called villi.

I hope that these write-off costs have been included in the financial projections.

Projections and estimates indicate that in the year 2020 the United States will need approximately 730,000 more affordable housing units to fill the needs of its low-income seniors.

In 2004, it generated over $304 million in sales revenue for game publishers and projections for 2005 are even larger with some analysts expecting over $1.3 billion in revenue.

Take Two has indicated that the ban will not have a dramatic impact on their current sales projections.

In October 2005, The New York Times said that the companies' first post-merger report was barely above Wall Street's projections.

Tiny hair-like projections on the surface of these passageways slowly sweep the mucus along, out of the lungs and up the trachea to the back of the throat, where it may be swallowed or coughed up.

Mucociliary escalator-The coordinated action of tiny projections on the surfaces of cells lining the respiratory tract, which moves mucus up and out of the lungs.

The central part of these cells is located in the spine, and they send threadlike projections to every part of the body.

Villi-Tiny, finger-like projections that enable the small intestine to absorb nutrients from food.

Tiny hair like projections (cilia) from cells lining the respiratory tract beat constantly to move debris trapped by mucus upwards and out of the respiratory tract.

Cilia-Tiny hairlike projections on certain cells within the body.

Cilia-Tiny hairlike projections on certain cells within the body.

Cilia are small, hair-like projections that beat continuously and serve to constantly sweep the respiratory tract clean of such debris as mucus, bacteria, viruses, and dead cells.

Cilia-Tiny hairlike projections on certain cells within the body.

Mucociliary escalator-The coordinated action of tiny projections on the surfaces of cells lining the respiratory tract, which moves mucus up and out of the lungs.

Bone age is useful in projecting final stature; research has shown that it is more meaningful in making such projections than chronological age alone.

Families can tune in to Santa radar online via NORADSanta.org beginning in early December for projections and updates.

The villi are small, hair like projections that come off the walls of the small intestine.

Villi are small projections from the walls of your small intestine which increase the surface area and hence, your body's ability to absorb vitamins and minerals.

Upon closer examination, this velvet texture is comprised of millions of small projections known as villi.

These minuscule projections play a number of roles, but when it comes to digestion and absorption of nutrients, the villi increase the small intestine's absorptive area.

Another role played by these tiny hair-like projections is that they actually aid in the digestion of food.

In order to interact and mine unobtanium (source of the main interest in the planet), humans use genetically engineered bodies that are controlled by human projections.

Do you want software to help you make future financial projections?

They have projections for Fall 2006 and Winter 2007.

Lugs: The projections on the top and bottom of a watch face where the bands are attached.

Additionally, the owner explains the company's target market, projections for future demand for their product and analyzes their competition.

PC numbers passed the 820 million mark in 2004 with projections topping the one billion mark in 2007.

Projections of $54 billion a year to be invested, means that the personal financial advisor field is wide open to innovation and growth.

You'll need a proforma profit and loss statement with income and profit projections forecasted out three years.

You'll need three-year projections of assets and cash-flow.

With an established corporation,the Financial Projections portion of the business plan should include sales figures for the previous three-five years.

Financial projections (monthly and quarterly), a forecast for the next five years, and a break even analysis will also be found here.

Cost Projections The new marketing program is estimated to cost the same as the existing marketing program.

Cost Projections The new marketing program is estimated to cost the same as the existing marketing program.

This will include spreadsheets, balance sheets, cash flow projections, and income statements.

These requests include a complete business proposal that includes predicted product or service growth, current sales, and financial projections.

Sam does his best to accomplish the task, with Al returning with new projections, such as "Okay, you've done something wrong, because now Ziggy says there's a ninety percent probability that both Susie and Joe are going to die tomorrow."