Areas of Plane Rectilinear Figures.
To the eye the contrast between the wide winding irregular passages of the sand-pit, calculated for the admission of a horse and cart, and the narrow rectilinear accurately-defined galleries of the catacomb.
The species of Linnaeus were supposed to represent a series of steps in a scale of ascending complexity, and it was thought possible thus to arrange the animal kingdom in a single series - the orders within the classes succeeding one another in regular gradation, and the classes succeeding one another in a similar rectilinear progression.
2), which has two parallel sides MA and SF, a base MS at right angles to these, and G H the remainder of its boundary from A to F rectilinear, no part of the figure being outside the space between MA (produced) and SF (produced).
Another question to which he devoted much attention was that of obtaining rectilinear motion by linkage.
Associated with these irregular escarpments are occasional rectilinear ridges, the work of extensive erosion on monoclinal structures, of whick Echo Cliffs, east of the Painted Desert (so called from its manycoloured sandstones and clays), is a good example.
With the renewal of uplift by which the earlier cycle of erosion was interrupted and the present cycle introduced, inequalities of surface due to renewed faulting were again introduced; these still appear as cliffs, of more nearly rectilinear front than the retreating escarpments formed in the previous cycle.
(v) Pyramid with rectilinear base.
It imitates the motions made in polishing a speculum by hand by giving both a rectilinear and a lateral motion to the polisher, while the speculum revolves slowly; by shifting two eccentric pins the course of the polisher can be varied at will from a straight line to an ellipse of very small eccentricity, and a true parabolic figure can thus be obtained.
The new rectilinear mole, sanctioned in 1881, has been built out into the sea for a distance of 600 yds.
The circles in the centre indicate a rectilinear series of indicate the five turns of the spiral, scales and two lateral secondand show the insertion of each of the ary spirals, one turning from leaves.
One of the simplest illustrations of the rectilinear flow of heat is the steady outflow through the upper strata of the earth's crust, which may be considered practically plane in this connexion.
- This method endeavours to realize the conditions of equation (I), namely, uniform rectilinear flow.
Atwood's published works, exclusive of papers contributed to the Philosophical Transactions, for one of which he obtained the Copley medal, are as follows: - Analysis of a Course of Lectures on the Principles of Natural Philosophy (Cambridge, 1784); Treatise on the Rectilinear Motion and Rotation of Bodies (Cambridge, 1784), which gives some interesting experiments, by means of which mechanical truths can be ocularly exhibited and demonstrated, and describes the machine, since called by Atwood's name, for verifying experimentally the laws of simple acceleration of motion; Review of the Statutes and Ordinances of Assize which have been established in England from the 4th year of King John, 1202, to the 37th of his present Majesty (London, 1801), a work of some historical research; Dissertation on the Construction and Properties of Arches (London, 1801), with supplement, pt.
These are no longer cast but hammered into shape, and decoration is elaborate curvilixear rather than simple rectilinear, the forms and character of the ornamentation of the northern European weapons resembling in some respects Roman arms, while in others they are peculiar and evidently representative of northern art.
On the Newtonian system the motion of a particle entirely uninfluenced by other bodies, when referred to a suitable base, would be rectilinear, with constant velocity.
This may be compared with the equation of rectilinear motion of a particle, viz.
Again, the primary substance has rectilinear motion in two directions, backwards and forwards, at once a condensation, which produces cohesion and substance, and a dilatation, the cause of extension and qualities.
In the field, armies lived as a rule in camp (q.v.), and when the provision of canvas shelter was impossible in bivouac. At the present time, however, it is unusual, in Europe at any rate, for troops on active service to hamper themselves with the enormous trains of tent wagons that would be required, and cantonments or bivouacs, or a combination of the two have therefore taken the place, in modern warfare, of the old long rectilinear lines of tents that marked the restingplace and generally, too, the order of battle of an 18th-century army.
The investigation of caustics, being based on the assumption of the rectilinear propagation of light, and the validity of the experimental laws of reflection and refraction, is essentially of a geometrical nature, and as such it attracted the attention of the mathematicians of the 17th and succeeding centuries, more notably John Bernoulli, G.
In the article Refraction it is shown that a ray of light traversing a homogeneous medium is deviated from its rectilinear path when it enters a medium of different refractive index; it is therefore readily seen that the path of a ray through continuously varying media is necessarily curvilinear, being compounded of an infinite number of infinitesimally small rectilinear deviations.
This we can only do by conceiving them as originally moving through intelligible space in rectilinear paths and with uniform velocities.
The next stage is geometrical mensuration, where geometrical methods are applied to determine the areas of plane rectilinear figures and the volumes of solids with plane faces.
To find the area of any rectilinear figure, various methods are available.
The rectilinear rays, which we have considered above, but which have no real existence, are nothing but the paths in which the light waves are transmitted.
It has been found useful in some cases to examine microscopically the thin film of coal that often covers the pinnae of fossil fronds, in order to determine the form of the epidermal cells which may be preserved in the carbonized cuticle; rectilinear epidermal cell-walls are usually considered characteristic of Cycads, while cells with undulating walls are more likely to belong to Ferns.
That this is actually the case is proved by experiments on the interference of polarized light, from which it may be deduced that the polarization-vector of a train of plane waves of plane polarized light executes rectilinear vibrations in the plane of the waves.