Archimedes concluded from his measurements that the sun's diameter was greater than 27' and less than 32'; and even Tycho Brahe was so misled by his measures of the apparent diameters of the sun and moon as to conclude that a total eclipse of the sun was impossible.'
(1773), p. 190) also gives results of measurements by Gascoigne of the diameters of the moon, Jupiter, Mars and Venus with his micrometer.
A, The youngest stage, is magnified 22 diameters; b, older, is magnified 8 diameters; c, .the adult medusa, is magnified 6 diameters.
In the middle part of a rod which has a length of 400 or 500 diameters the effect of the ends is insensible; but for many experiments the condition of endlessness may be best secured by giving the metal the shape of a ring of uniform section, the magnetic field being produced by an electric current through a coil of wire evenly wound round the ring.
When the length of the wire exceeds 400 diameters, or thereabouts, Ho may generally be considered as equivalent to H, 10.
With these arrangements there is no demagnetizing force to be considered, for the ring has not any ends to produce one, and the force due to the ends of a rod 400 or 500 diameters in length is quite insensible at the middle portion; H therefore is equal to Ho.
Webs serve not only for pointing on stars to determine their coordinates (in manner afterwards described), but also for estimating the diameters of the star-images in terms of these 4" intervals.
Hence, if p is the maximum value of the mean effective pressure corresponding to about 85% of the boiler pressure,, uW = pd 2 le /D (26) is an expression giving a relation between the total weight on the coupled wheels, their diameters and the size of the cylinder.
Four strings of iron casing are usually employed, having the following diameters: to in., 84 in., 64 in.
In another respect the observations of Fraunhofer appear at first sight to be in disaccord with theory; for his measures of the diameters of the red rings, visible when white light was employed, correspond with the law applicable to dark rings, and not to the different law applicable to the luminous maxima.
The error thus arising may be compensated by a rotation of the object-glass about one of the diameters y= =x.
The typical Egyptian obelisk is an upright monolith of nearly square section, generally to diameters in height, the sides slightly convex, tapering upwards very gradually and evenly, and terminated by a pyramidion whose faces are inclined at an angle of 60°.
The spurious bows he showed to consist of a series of dark and bright bands, whose distances from the principal bows vary with the diameters of the raindrops.
Taking advantage of these results, Henri Pitot (1695-1771) afterwards showed that the retardations arising from friction are inversely as the diameters of the pipes in which the fluid moves.
He was the first to describe an instrument fitted with a sight and paper screen for observing the diameters of the sun and moon in a dark room.
Forged and annealed, magnified r000 diameters, showing pearlite.
In Byzantine times five columns, of various diameters, with no two bases of the same size, bearing Corinthian capitals, were set up about 6 ft.
Sca, through,, u rpov, measure), in geometry, a line passing through the centre of a circle or conic section and terminated by the curve; the "principal diameters of the ellipse and hyperbola coincide with the "axes" and are at right angles; " conjugate diameters " are such that each bisects chords parallel to the other.
2) to determine the height of a column, which should vary from eight to ten diameters according to the intercolumniation: and it is generally the custom to fix the lower diameter of the shaft by the height required and the Order employed.
He, however, successfully employed the instrument in measuring double stars, so close as I" or 2", and using a power of 300 diameters, with results that agreed satisfactorily amongst themselves and with those obtained with the filar micrometer.
Arago made many measures of the diameters of the planets with such a micrometer.
By making very thin sections and employing high magnification (1000-1200 diameters), Renault has been enabled to detect numerous forms of bacilli in the woody parts preserved in coal, one of which, Micrococcus carbo, bears a strong resemblance to the living Cladothrix found in trees buried in peat bogs.
It has therefore been proposed, for greater depths, to put four columns of tubbings of smaller diameters, 82 and 52 ft., in the shaft, and fill up the remainder of the boring with concrete, so that with thinner and lighter castings a greater depth may be reached.
The same thing can be effected in a more perfect manner by the use of spiral or scroll drums, in which the rope is made to coil in a spiral groove upon the surface of the drum, which is formed by the frusta of two obtuse cones placed with their smaller diameters outwards.
In the following table are given the values of the diameters of the molecules of six substances with which it is easy to experiment in the gaseous state, these values being calculated in different ways from formulae supplied by the kinetic theory.
It is an erecting telescope with a field of view of 10° and a magnification of 3 diameters, and admits plenty of light.
In the memoir cited above Regnault gives an account of determinations of the velocity in air in pipes of great length and of diameters ranging from o 108 metres to i i metres.
But with the sole exception of proving that the volumes of spheres are in the triplicate ratio of their diameters, a theorem probably due to Eudoxus, no mention is made of its mensuration.
That " circles are to one another as the squares on their diameters " and that " in the greater of two concentric circles a regular 2n-gon can be inscribed which shall not meet the circumference of the less," however nearly equal the circles may be.
On the westward slopes, especially of the Selkirks and Coast Ranges, vegetation is almost tropical in its density and luxuriance, the giant cedar and the Douglas fir sometimes having diameters of 10 ft.
He was also a diligent and skilful observer, and busied himself not only with astronomical subjects, such as the double stars, the satellites of Jupiter and the measurement of the polar and equatorial diameters of the sun, but also with biological studies of the circulation of the sap in plants, the fructification of plants, infusoria, &c.
Proposition 14 shows how to draw an ellipse through five given points, and Prop. 15 gives a simple construction for the axes of an ellipse when a pair of conjugate diameters are given.
Diameters are mostly used, the 4 in.
Moreover, a single pair of rolls suffices for armour plates of any width or thickness, whereas if shafts of different diameters were to be rolled, a special final groove would be needed for each different diameter, and, as there is room for only a few large grooves in a single set of rolls, this would imply not only providing but installing a separate .set of rolls for almost every diameter of shaft.
Crossed out, the circle being crossed by diameters to show the degrees; others have found in it a corruption of "the alidade" (q.v.).
The movement of S is obtained by means of a relay engine, in which there are two rams of different diameters; a constant pressure is always acting on the smaller of these when the motor is at work, while the governor (or handpower if desired) admits or exhausts pressurewater from the face of the other, and the movements to and fro thus given to the two rams alter the position of the stud S, and thus change the stroke of the plungers of the main engine.
The external diameters of the amphitheatre are 410 and 348 ft., while the corresponding diameters of the arena are 233 and 167 ft.
His first telescope magnified three diameters; but he soon made instruments which magnified eight diameters, and finally one that magnified thirty-three diameters.'
Focal length, with a magnifying power of 38 diameters, which he presented to the Royal Society of London in December 1671.
Succeeded in mounting them with all necessary rigidity free from flexure but have given them optically true plane surfaces, notwithH standing their large diameters, viz., II and 15.7 in.
When the eclipse is total, there is a real geometrical shadow - very small compared with the penumbra (for the apparent diameters of the sun and moon are nearly equal, but their distances are as 370: I); when the eclipse is annular, the shadow is all penumbra.
Some arcades of the amphitheatre (the diameters of which are 282 ft.
It may further be shown that if Binets ellipsoid be referred to any system of conjugate diameters as co-ordinate axes, its equation will be ~2+~2+~-2I, (27)
The path is therefore an ellipse of which a, b are conjugate semi-diameters, and is described in the period 24 Ju; moreover, the velocity at any point P is equal to ~ OD, where OD is the semi-diameter conjugate to OP. ~,This type of motion;,s called elliptic harmonic. If the co-ordinate axes are the principal axes of the ellipse, the angle ft in (I o) is identical with the excentric angle.
The problem is identical with that of finding the common conjugate diameters of the ellipsoids T(x, y, I) =const., V(x, y, 1) =const.
If in (21) we imagine that x, y, I denote infinitesimal rotations of a solid free to turn about a fixed point in a given field of force, it appears that the three normal modes consist each of a rotation about one of the three diameters aforesaid, and that the values of in are proportional to the ratios of the lengths of corresponding diameters of the two quadrics.
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.
Hookes wheels with oblique or helical teeth are in fact screws of many threads, and of large diameters as compared with their lengths.
The letters A B show a vertical section through a fragment of a potato leaf, enlarged 1_00 diameters; A is the upper surface line, and B the lower; the lower surface of the leaf is shown at the top, A Fin.
One is shown more highly magnified (400 diameters) at F; the contained protoplasm breaks up into a definite number of parts as at G, forming eight minute mobile bodies called "zoospores," each zoospore being furnished with two extremely attentuated vibrating hairs termed "cilia," as shown at H.
The distance between the planes is supposed to be very small compared with their ultimate diameters, but at the same time large enough to exceed the range of the attractive forces.
Similarly, the diameters of flat or spheroidal colonies may vary from a few times to many hundred times that of the individual cells, the divisions of which have produced the colony.
The diameters range from 400 m.
Huygens, in his Systema saturnium (1659), describes a micrometer with which he determined the apparent diameters of the principal planets.
Auditory ment in the crocodile, and with the ", chain " of Chicken, X 6 processus folii of the mammalian diameters; lateral and basal malleus, it follows that the whole views.
In order to meet the objection that the phenomenon might be due to electromagnetic action between the coil and the rod, Bidwell made some experiments with iron rings, and found that the length of their diameters varied under magnetization in precisely the same manner as the length of a straight rod.
In his experiments upon this subject Fraunhofer employed plates of glass dusted over with lycopodium, or studded with small metallic disks of uniform size; and he found that the diameters of the rings were proportional to the length of the waves and inversely as the diameter of the disks.
Such a rule of the two diameters not only guides us toward the sun in the system and the heart in man, but draws lines through the length and breadth of the aggregate of a man's particular daily behaviors and waves of life into his coves and inlets, and where they intersect will be the height or depth of his character.