(4) On Spirals (Peri helikon) is a book of twenty-eight propositions.
When the directive force is constant, the curve is a cycloid; under other conditions, spirals and other curves are described (see Mechanics) .
When an engineer has to construct a railway up a hill having a still steeper slope, he must secure practicable gradients by laying out the line in ascending spirals, if necessary tunnelling into the hill, as on the St Gothard railway, or in a series of zigzags, or he must resort to a rack or a cable railway.
The tree is tapped either in the same manner as the Hevea, or by encircling the tree with a simple spiral cut at an inclination of 45°, or by two parallel spirals if the tree be large.
The horns are long, ringed, and form spirals with from three to five turns.
The have been identified by Helbig with small spirals of gold wire, such as are found in early Etruscan tombs lying near the head of the skeleton.
Such spirals were used in early Athens to confine the back hair, and this fashion may therefore be identified as the Kpc f3vXos.
In his investigations respecting cycloidal lines and various spiral curves, his attention was directed to the loxodromic and logarithmic spirals, in the last of which he took particular interest from its remarkable property of reproducing itself under a variety of conditions.
This work included the "Logometria," the trigonometrical theorem known as "Cotes' Theorem on the Circle" (see TRIGONOMETRY), his theorem on harmonic means, subsequently developed by Colin Maclaurin, and a discussion of the curves known as "Cotes' Spirals," which occur as the path of a particle described under the influence of a central force varying inversely as the cube of the distance.
Among the ammonites the loss of power to coil the shell is one feature of racial old age, and in others old age is accompanied by closer coiling and loss of surface ornamentation, such as spines, ribs, spirals; while in other forms an arresting of variability precedes extinction.
Uredospores, septa of Basidiomycetes), spirals, reticulations, rings, &c. (capillitium fibres of Podaxon, Calostoma, Battarrea), occur as in the vessels of higher plants, while sculptured networks, pittings and so forth are as common on fungus-spores as they are on pollen grains.
But in such cases a series of secondary spirals or parastichies are seen running parallel with each other both right and left, which to a certain FIG.
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.
Later we find two periods of zigzag designs in south Germany with an intermediate stage of spirals and wavy lines, while in north and east Germany the so-called string-ornamentation predominates.
They introduced a special style of ornament ("geometric") instead of that of the Bronze Age, characterized by spirals and marine animals and plants.
They are unusually interesting from the fact that many of the exposed slabs in the walls of the chambers are ornamented with spirals and other devices, rudely incised.
The latter are formed of two spirals of wire, sometimes four such spirals being used, whilst there were also brooches in animal forms, one of the latter being found with a bronze sword.
Divisions perpendicular to the long axis: - Vibrio (Muller-Ldffler), commashaped, motile, monotrichous; Spirillum (Ehrenb.), more strongly curved in open spirals, motile, lopho trichous; Spirochaete (Ehrenb.), spirally coiled in numerous close turns, motile, but apparently owing to flexile movements, as no cilia are found.
The ornamentation of the period is as a rule confined to spirals, bosses and concentric circles.
It may be well to explain here that a claim has been set up by his admirers for the celebrated artist, architect and engineer, Leonardo da Vinci, to be regarded as the discoverer of the principles and practice of flight (see Theodore Andrea Cook, Spirals in Nature and Art, 1903).
Superimposed sections of rightand left-handed quartz, as may sometimes be present in sections of twinned crystals, exhibit Airy's spirals in the polariscope.