From the Adoption of Parabolic Teaching to the End of the Ministry in Galilee.
Could be reflected and converged by cylindrical parabolic mirrors.
Let the length of half the parabolic chain be called s, then 4.
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.
A A is a concave parabolic mirror, whose axis a c is inclined to the axis of the tube a b so that the image of an object in the focus of the mirror may be viewed by an eye-piece at E, the angle b a c being tier equal to the angle c a E.
12039 of 1896) brought forward the idea of focusing a beam of electric radiation for telegraphic purposes on a distant station by means of parabolic mirrors, and tried this method successfully on Salisbury Plain up to a distance of about a couple of miles.
Elliptic orbits, and a parabolic orbit considered as the special case when the eccentricity of the ellipse is 1, are almost the only ones the astronomer has to consider, and our attention will therefore be confined to them in the present article.
In a letter, Del movimento della cometa apparsa it mese di decembre 1664, published in 1665 under the pseudonym Pier Maria Mutoli, he was the first to suggest the idea of a parabolic path; and another of his astronomical works was Theorica mediceorum planetarum ex causis physicis deducta (Florence, 1666), in which he considered the influence of attraction on the satellites of Jupiter.
These doctrinal interpretations introduce the economy of blinding the Jews into the parabolic teaching; the declaration as to the redemptive character of the Passion into the sayings; the sacramental, institutional words into the account of the Last Supper, originally, a solemnly simple Messianic meal; and the formal night-trial before Caiaphas into the original Passion-story with its informal, morning decision by Caiaphas, and its one solemn condemnation of Jesus, by Pilate.
Example 4.- Parabolic cylinder, axial advance, and liquid streaming past.
The great variety in the apparent motions of meteors proves that they are not directed from the plane of the ecliptic; hence their orbits are not like the orbits of planets and short-period comets, which are little inclined, but like the orbits of parabolic comets, which often have great inclinations.
It follows that, by taking two ordinates in a certain position with regard to the bounding ordinates, the area of any parabolic trapezette whose top passes through their extremities can be expressed in terms of these ordinates and of the breadth of the trapezette.
In the case of the parabolic trapezette, for instance, xu is of degree 3 in x, and therefore the first moment is lh(xouo+4xlui-+x2u2).
Then we can take the strips in pairs, and treat each pair as a parabolic trapezette.
The above formulae apply only to a parabolic trapezette.
Here Jesus' teaching contains no parables and but three allegories, the Synoptists present it as parabolic through and through.
Scott (Comptes rendus, 1861, 53, p. 108) any sound whatever may be made to record its trace on the paper by means of a large parabolic cavity resembling a speaking-trumpet, which is freely open at the wider extremity, but is closed at the other end by a thin stretched membrane.
'The centre span is a two-hinged parabolic braced rib arch, and there are side spans of 190 and 210 ft.
Follows nearly the parabolic line of pressures.
For parabolic or bowstring girders, when r =8, the limiting span is 1280 ft.
In this case it is found that the body falls relatively to the ship as if the latter were at rest, and alights at the foot of the mast, having consequently pursued a parabolic path relatively to the earth.
If the dimensions of the bar are suitably chosen, the distribution of temperature is always very nearly parabolic, so that it is not necessary to determine the value of the critical current C 2 = hpllaRo very accurately, as the correction for external loss is a small percentage in any case.
It consists of two parabolic branches tending in opposite directions.
If two roots are imaginary the equation is y 2 =(x 2 +a 2) (x - b) and the curve resembles the parabolic branch, as in the preceding case.
Chap. 21) of Leonard Digges 1 (originally published by his son Thomas in 1571, and again in 1591): - "Marvellous are the conclusions that may be performed by glasses concave and convex, of circular and parabolic forms, using for multiplication of beams sometime the aid of glasses transparent, which, by fraction, should unite or dissipate the images or figures presented by the reflection of other."
He did not attempt the formation of a parabolic figure on account of the probable mechanical difficulties, and he had besides satisfied himself that the chromatic and not the spherical aberration formed the chief faults of previous telescopes.
In Short's first telescopes the specula were of glass, as suggested by Gregory, but he afterwards used metallic specula only, and succeeded in giving to them true parabolic and elliptic figures.
The reflecting surface is first ground to a spherical form, the parabolic figure being given in the final process by regulating the size of the pitch squares and the stroke of the polishing machine.
Assoc. Report, 1899, with a slight modification Specific Heat Of Water In Terms Of Unit At 20° C. 4.180 Joules to allow for the increase in the specific heat below 20° C. This was estimated in 1899 as being equivalent to the addition of the constant quantity 0.020 to the values of the total heat h of the liquid as reckoned by the parabolic formula (5).
The result might of course have been inferred from the theory of the parabolic funicular in 2.
This applies to an elliptic or hyperbolic orbit; the case of the parabolic orbit may be examired separately or treated as a limiting case.
Even when the resolution is regularized by the action of external vibrations of suitable frequency, as in the beautiful experiments of Savart and Plateau, the drops must still come into contact before they reach the summit of their parabolic path.
Names may also be used for the different forms of infinite branches, but we have first to consider the distinction of hyperbolic and parabolic. The leg of an infinite branch may have at the extremity a tangent; this is an asymptote of the curve, and the leg is then hyperbolic; or the leg may tend to a fixed direction, but so that the tangent goes further and further off to infinity, and the leg is then parabolic; a branch may thus be hyperbolic or parabolic as to its two legs; or it may be hyperbolic as to one leg and parabolic as to the other.
The epithets hyperbolic and parabolic are of course derived from the conic hyperbola and parabola respectively.
Next, if the line S2 touch at b the arc aa so that the two portions ab, ba lie on the same side of the line Sl, then projecting the figure as before, the tangent at b, that is, the line S2 itself, is projected to infinity; the arc ab is projected into a parabolic leg, and at the same time the arc ba is projected into a parabolic leg, having at infinity the same direction as the other leg, but so that the two legs may or may not belong to the same branch.
And we thus see that the two parabolic legs represent a contact of the line infinity with the curve, - the point of contact being of course the point at infinity determined by the common direction of the two legs.
The two legs of a parabolic branch may converge to ultimate parallelism, as in the conic parabola, or diverge to ultimate parallelism, as in the semi-cubical parabola y 2 = x 3, and the branch is said to be convergent, or divergent, accordingly; or they may tend to parallelism in opposite senses, as in the cubical parabola y = x 3 .
Secondly, if two of the intersections coincide, say if the line infinity meets the curve in a onefold point and a twofold point, both of them real, then there is always one asymptote: the line infinity may at the twofold point touch the curve, and we have the parabolic hyperbolas; or the twofold point may be a singular point, - viz., a crunode giving the hyperbolisms of the hyperbola; an acnode, giving the hyperbolisms of the ellipse; or a cusp, giving the hyperbolisms of the parabola.
Another corollary is that in the case of a body moving in a parabolic orbit the velocity at any moment is that which would be acquired by the body in falling from an infinite distance to the place it occupies at the moment.
He, moreover, threw out the suggestion (in his Cometographia, 1668) that comets move round the sun in orbits of a parabolic form.
The values of d 2 E/dt 2 agree as well as can be expected, considering the difference of the ranges of temperature and the great variety in the methods of observation adopted; they are calculated assuming the parabolic formula, which is certainly in many cases inadequate.
2 illustrate the differences from the parabolic formula, measured in degrees of temperature, as observed by H.
In this particular case the parabolic formula appears to be undoubtedly inadequate.
It consists in half of a short focused parabolic mirror, which concentrates all the light coming from the one side on to the object.
Elec. Eng., 1898, 2 7, p. 99) very successfully produced true parabolic reflectors for projectors, by depositing copper upon carefully ground and polished glass surfaces rendered conductive by a film of deposited silver.
His chief works, beside the above, are: The Chief End of Revelation (Lond., 1881); The Parabolic Teaching of Christ (Lond., 1882); F.
Much more easily manipulated is the parabolic side-illuminator invented by R.