Cycloid

“ The intrinsic equation is s = 4a sin ψ, and the equation to the evolute is s = 4a cos ψ, which proves the evolute to be a similar cycloid placed as in fig. 2, in which the curve QOP is the evolute and QPR the original cycloid. The radius of curvature at any point is readily deduced from the intrinsic equation and has the value ρ = 4 cos 1/2θ, and is equal to twice the normal which is 2a cos 1/2θ. ”

“ Evangelista Torricelli, in the first regular dissertation on the cycloid (De dimensione cycloidis, an appendix to his De dimensione parabolae, 1644) , states that his friend and tutor Galileo discovered the curve about 1599. John Wallis discussed both the history and properties of the curve in a tract De cycloide published at Oxford in 1659. He there shows that the cycloid was investigated by Carolus Bovillus about 1500, and by Cardinal Cusanus (Nicolaus de Cusa) as early as 1451. Honoré Fabri (Synopsis geometrica, 1669) treated of the curve and enumerated many theorems concerning it. ”

“ Suppose now that we have a number of ions starting from the plane x = 0, and moving towards the plane x = a. The particles starting from x = 0 describe cycloids, and the greatest distance they can get from the plane is equal to the diameter of the generating circle of the cycloid, i.e. to 2Xm/eH2. (After reaching this distance they begin to approach the plane.) ”

“ They usually cover the body more or less evenly and are imbricated like shingles on a roof, the free edge being turned backward. Such normal scales are of two types, ctenoid or cycloid. Ctenoid scales have a comb-edge of fine prickles or cilia; cycloid scales have the edges smooth. These two types are not very different, and the one readily passes into the other, both being sometimes seen on different parts of the same fish. In general, however, the more primitive representatives of the typical fishes, those with abdominal ventrals and without spines in the fins, have cycloid or smooth scales. ”

“ Modern practice has accepted the curve known in general terms as the cycloid, as that best filling all the requirements of wheel teeth, and this curve is employed to produce two distinct forms of teeth, epicycloidal and involute. ”

“ The Dipnoi have overlapping cycloid scales. The rounded scales of Amia and of many fossil ganoids such as Holoptychius are shaped like cycloid scales, but differ from them in being more or less coated with enamel. In Eels and some other Teleosteans the scales are completely degenerate and have almost disappeared. Some Teleosteans, like Diodon hystrix, have scales with triradiate roots from which arise long sharp spines directed backwards. These scales, which resemble teeth, contain no enamel; they become erect when the fish inflates its body into a globular form. ”

“ Lips. an. 1695,—to these a lead weight is an eternal ballance, and keeps watch as well as a couple of centinels, inasmuch as the construction of them was a curve-line approximating to a cycloid,—if not a cycloid itself. ”

“ If a circle PMB roll upon another circle SPT (fig. 23) any point M on it will generate an epicycloid MN. The radius of curvature of the curve at M will always be MP, for the part at M is being produced by rotation round the point P. It follows that a line from B to M will always be tangential to the epicycloid. If the epicycloid be a cam moving as a centre round the centre R (not shown in the figure) of the circle SPT, the leverage it will exert upon a plane surface BM moving round a parallel axis at B, will always be as BP to PR, that is, a constant ”

“ It is found during the winter months in several parts of the Continent that as the temperature falls the pressure rises, producing anti-cyclones over the cold area; whereas, when the temperature begins to rise, the pressure falls, and cyclones are attracted to the warming area.
Small natural cyclones are often seen on dusty roads, the whirling column having a core of dusty air, and the centre of the vortex travelling along the road, tossing up the dust in a very disagreeable way to pedestrians. Sometimes such a cyclone will toss up dry leaves to a height of four or five feet. ”

“ An anticyclone of good energy lies to the east of it, with its isobars extending well to the north and contracting the width of the tongue in the north; another anticyclone lies to the west, and this also seems to be pressing on the narrow monsoonal tongue and helping to contract its diameter, at the same time the energy in both high pressures is adding force to the circulation of the wind, and so aiding in the development of the cyclonic circulation. A modified Λ depression exists to the south-east of the Australian Bight, and there is another over New Zealand. ”

“ But cyclones are not all alike—far from it. Some are well developed, with strong gradients, high winds, extended cloud areas, heavy precipitation, and decided temperature contrasts. Others are but poorly developed, with weak gradients, light winds, small temperature differences, and it may be without any precipitation whatever. Some cover immense districts of country; others are small and affect only a limited area. It therefore becomes necessary to examine the characteristics of each approaching cyclone, as shown on the daily weather map, very carefully. ”

“ The ascension of air with a higher sensible temperature would not alone suffice to supply the tremendous power of the cyclone. The difference of temperature, even in extreme eases between lower and higher strata, is wholly insufficient to account for the enormous energy developed by our cyclones of hundreds of miles in diameter. We therefore require another source of power. Nor have we far to seek it. The sun's rays falling upon dry earth heat it, and thus raise the temperature of the air in contact with it. ”

“ The anti-cyclone simply reverses the conditions of the cyclone. Its centre is an area of high pressure, and the air rushes out from it in all directions towards surrounding regions of low pressure. As before, all parts of the current will be deflected towards the right, and the result, clearly, is a whirl opposite in direction to that of the cyclone. But here there is a tendency to dissipation rather than to concentration of energy, hence, considered as a storm-generator, the anti-cyclone is of relative insignificance. ”

“ Suppose a large area on the earth over which the air is still in bright sunshine. After a time, when the air gets heated and charged with vapour, columns of air would begin to ascend in a disorderly fashion. But suppose an anti-cyclone is blowing at one side of this area. When the upper air descends to the earth, it spreads outwards in all directions; but the earth’s rotation interferes and changes the radial into a spiral motion. The anti-cyclonic winds will prevent the formation of local cyclones, and drive all the moist, hot air to its circumference, just above the earth. ”

“ A glance at a number of the charts shows that there is nearly always present either an area of low pressure, called a cyclone, usually having an approximately circular form, and, as a rule, moving in an easterly or northeasterly direction; or an area of high pressure, called an anticyclone, also nearly circular in form, but almost stationary in position. The wind in all cases also blows in a direction nearly parallel with the isobars, having the region of lowest pressure on the left hand. ”

“ Calibrate each personal sampling pump with a representative sampler in line. Sample at 1.7 ± 5% L/min with a nylon cyclone or 2.2 ± 5% L/min with an HD cyclone for a total sample size of 200 to 1000 L. Do not exceed 2 mg dust loading on the filter. NOTE: Do not allow the sampler assembly to be inverted at any time. Turning the cyclone to more than 90 °C from vertical may deposit over-sized material from the cyclone body onto the filter. Obtain an area high-volume bulk sample in the vicinity of the personal sampling area. ”

“ The chief objection to the theory of cyclosis appears to be that the resultant motion is so greatly in excess of the rotation of protoplasm in the cell. More or less motion is observed in various kinds of free cells, but the movement of diatoms is not evident in those without either a raphe or a keel upon which and apparently by which the phenomena are produced. ”

“ The effect of each.—Hence it appears that in a storm the wind may shift from any one of three causes, and we are not entitled to call it a cyclone unless the wind shift more than 180°. If the change of direction be less than 90°, the shifting may be due to diurnal rotation alone; if it be less than 180°, the shifting may be, and is probably, due to (1) and (2) . The sailor has therefore no proof to show that he has been in a cyclone unless the wind during the storm changed its directions more than 180°. Cyclones, there is reason to believe, are often whirlwinds in a storm. ”

“ So also in an anticyclone the descending current of air is warmer than it is under normal conditions, and its downward motion must be due to some other cause than an increase of density resulting from a lowering of its temperature. The decrease of pressure in the one case, and its increase in the other, thus can not be caused by differences of heating or cooling of the lower strata; and both cyclones and anticyclones must be considered as parts of the general circulation of the atmosphere, such as it was conceived by Ferrel. ”

“ As the weather changes, the affected patients increase with a rush.
He is of opinion that the supposed rapid spread of influenza on the establishment of anti-cyclonic conditions may be explained in this way. The air in the cyclonic vortex, drawn chiefly from the atmosphere over the ocean, is moist, and contains none of [Pg 110] the contagion; the air of the anti-cyclone, derived from the higher strata, and thus from distant cyclones, descending, blows gently over the land to the nearest cyclone, and, being drier, is more able to carry suspended particles with it. ”

“ Professor Douglas, of Ann Arbor University, entertains his friends now and then by manufacturing miniature cyclones. He first suspends a large copper plate by silken cords. The plate is heavily charged with electricity, which hangs below in a bag-like mass. He uses arsenious acid gas, which gives the electricity a greenish tint. That mass of electricity becomes a perfect little cyclone. It is funnel-shaped and spins around like a top. When he moves the plate over a table, his cyclone catches up pennies, pens, pith balls and other small articles, and scatters them in every direction. ”

“ The availability of a pre-selector such as the GK2.69 cyclone sampler, which is designed to conform to the respirable dust sampling criteria at a flow rate nearly two and a half times that of the nylon cyclone, offers the field industrial hygienist the ability to collect a quantifiable sample mass during tasks of short duration or of low dustiness, conditions which may not have yielded a quantifiable mass using the nylon cyclone. ”

“ The velocity of the cyclonic currents will depend largely upon the difference in barometric pressure between the storm-centre and the confines of the cyclone system. And the velocity of the currents will determine to some extent the degree of deflection, and hence the exact path of the descending spiral in which the wind approaches the centre. But in every case and in every part of the cyclone system it is true, as Buys Ballot's famous rule first pointed out, that a person standing with his back to the wind has the storm-centre at his left. ”

“ If it moves along a line south of any given place, the locality is affected by its easterly and northeasterly to northerly and northwesterly winds, which make up the coldest and stormiest side of the cyclone. As the barometer at its center is always low, the cyclone is called a 'low area,' or 'low,' for short, and as such appears in Weather Bureau reports. Storm intensity in a cyclone is in due relation to the minima of its own barometric pressures and to the maxima of the anti-cyclone nearest it. ”

“ Cyclomyces is from two Greek words, meaning a circle and fungus. This genus is very distinct from other tube-bearing genera. The pileus is fleshy, leathery or membranaceous, and usually cushion-formed. Upon the lower surface are the plate-like bodies resembling the gills of Agarics but which are composed of minute pores. These pore bodies are arranged in concentric circles around the stem.
Cyclomyces Greenii. Berk.
Figure 360.—Cyclomyces Greenii
Figure 361.—Cyclomyces Greenii. ”

“ The gyrating disc of a cyclone can never, I apprehend, exceed a few miles in diameter. On shore we seldom find it exceeding in breadth as many rods, in most cases not of as many fathoms, as its advocates give it miles at sea. I think the dust-whirl in the street is a true type of the tornado (cyclone) at sea.
800. The three forces.—There are in the various parts of the storm at least three forces at work in effecting a change of wind, as observed on board ship at sea. (1.) One is diurnal rotation: it alone can never work a change of direction exceeding 90° ”

“ The better developed the cyclone, the higher its velocity of progression, and the nearer its track lies to the station, the more emphatic and the more rapid are the weather changes it causes. On the other hand, the weaker the cyclone, the slower its rate of progression, and the further away its track, the less marked and the slower the weather changes. The probable track of a coming storm, and its probable rate of movement, therefore, need careful study if our forecasts are to be reliable. ”