By supposing the retardation to vary uniformly and continuously we, fall upon the case of an ordinary prism: but there;, is then no diffraction spectrum in the usual sense.
The rate of diminution of amplitude expressed by the coefficient a in the index of the exponential is here greater than the coefficient b expressing the retardation of phase by a small term depending on the emissivity h.
After a very short interval of time, the length of which depends on the inductive retardation of the cable, the condensers corresponding to C 1 and C3 at the other end begin to be charged from the cable, and since the charge of C3 passes through the receiving instrument I or G the signal is recorded.
When the secondary wave of least retardation is unobstructed, or when a ray passes through the point under consideration.
Mag., 1837, 10, p. 364) was that any ray which suffered in traversing the plate a retardation of an odd number of half wave-lengths would be extinguished, and that thus the spectrum would be seen interrupted by a number of dark bars.
Such a conclusion would be in the face of the principle of energy, which teaches plainly that the retardation in question leaves the aggregate brightness unaltered.
The expression (5) gives the illumination at due to that part of the complete image whose geometrical focus is at =o, the retardation for this component being R.
E is then the co-ordinate relatively to 0 of any focal point 0' for which the retardation is R; and the required result is obtained by simply integrating (5) with respect to from - cc to +oo.
The formation of black bands is thus explained, and it requires that the plate be introduced upon one particular side, and that the amount of the retardation be adjusted to a particular value.
Taking as the standard phase that of the secondary wave from A, we may represent the effect of PQ by cos 27r (_) .ds, where, l = BP - AP is the retardation at B of the wave from P relatively to that from A.
Some phenomena of retardation in the production of the effect had led Sir G.
Also in air for very low velocities, but, where the velocities are high, the retardation is great, the projectile takes longer to traverse each succeeding space, and consequently the time of flight for any range is longer; the axis must therefore be directed still higher above the point to be struck.
The position of these fringes will depend on the total retardation in time of the one beam with respect to the other; and thus it might be expected to vary with the direction of the earth's motion,.
For a time the retardation of the normal rate of increase among the native population was concealed from view by the extraordinary immigration.
The superintendent of the Ninth Census, 1870, presented a computation 01 the effects of this causefirst, through direct losses, by wounds or disease, either in actual service of the army or navy, or in a brief term following discharge; secondly, through the retardation of the rate of increase in the colored element, due to the privations, exposures and excesses attendant upon emancipation; thirdly, through the check given to immigration by the existence of war, the fear of conscription, and the apprehension abroad of results prejudicial to the national welfare.
The glochidium is formed by the precocious development of the anterior adductor and the retardation of all the other organs except the shell.
Tyndall's own summary of the course of research on the subject was as follows: The idea of semi-fluid motion belongs entirely to Rendu; the proof of the quicker central flow belongs in part to Rendu, but almost wholly to Agassiz and Forbes; the proof of the retardation of the bed belongs to Forbes alone; while the discovery of the locus of the point of maximum motion belongs, I suppose, to me.
The heat evolved by this process of solidification retards the fall of temperature; but after this the rate of cooling remains regular until T (750°) on the line Sa (Ar 3) is reached, when a second retardation occurs, due to the heat liberated by the passage within the pasty mass of part of the iron and carbon from a state of mere solution to that of definite combination in the ratio Fe 3 C, forming microscopic particles of cementite, while the remainder of the iron and carbon continue dissolved in each other as austenite.
At the second retardation, K" (Ar2, about 770°) this ferrite changes to the normal magnetic a-ferrite, so that the mass as a whole becomes magnetic. Moreover, the envelopes of ferrite which began forming at Ar 3 continue to broaden by the accession of more and more ferrite born from the austenite progressively as the temperature sinks, till, by the time when Ar t (about 690°) is reached, so much free ferrite has been formed that the remaining mother-metal has been enriched to the composition of hardenite, i.e.
One necessary effect of the tidal retardation of the earth's rotation is gradually to increase this length.
On the voyage he noticed the retardation of the pendulum in approaching the equator; and during his stay on the island he observed, on the 7th of November 1677, a transit of Mercury, which suggested to him the important idea of employing similar phenomena for determining the sun's distance.
Of e~~ the variation of each co-ordinate is simple-harmonic, with the prescribed period, but there is a retardation of phase as compared with the force.
An excess of resistance above effort involves an excess of work performed above energy expended; that excess of work is performed by means of the retardation of the machinery.
When a machine undergoes alternate acceleration and retardation, so that at certain instants of time, occurring at the end of intervals called periods or cycles, it returns to its original speed, then in each of those periods or cycles the alternate excesses of energy and of work neutralize each other; and at the end of each cycle the principle of the equality of energy and work stated in 87, with all, its consequences, is verified exactly as in the case of machines of uniform speed.
Energy of Acceleration and Work of Retardation for a Shifting Body.Let w be the weight of a body which has a motion of translation in any path, and in the course of the interval of time ~t let its velocity be increased at a uniform rate of acceleration from v1 to v2.
In order to produce a retardation from the greater velocity~ v2 to the less velocity Vf, it is necessary to apply to the body a resistance connected with the retardation and the time by an equation identical in every respect with equation (71), except by the substitution of a resistance for an effort; and in overcoming that resistance the body performs work to an amount determined by equation (72), putting Rds for Pas..
Energy Stored and Restored by Deviations of Velocity.Thus a body alternately accelerated and retarded, so as to be brought back to its original speed, performs work during its retardation exactly equal in amount to the energy exerted upon it during its acceleration; so that that energy may be considered as stored during the acceleration, and restored during the retardation, in a manner analogous to the operation of a reciprocating force (~ 108).
Let e denote the quantity by which the energy exerted in each cycle of the working of the machine alternately exceeds and falls short of the work performed, and which has consequently to be alternately stored by acceleration and restored by retardation of the flywheel.
That, in spite of retardation and retrogression, the old order of ideas should have yielded to the new all over Europe, - that science should have won firm standing-ground, and political liberty should have struggled through those birth-throes of its origin, - was in the nature of things.
Before his death, however, the retardation of light in denser media was demonstrated by the experiments of H.
At the same time, the tendency to a retardation in the development of the posterior thoracic somites is very general in Malacostracan larvae, and may perhaps be correlated with the f
The equation of light is the time taken by light to traverse the sun's mean distance from the earth; it can be found by the acceleration or retardation of the eclipses of Jupiter's satellites according as Jupiter is approaching opposition or conjunction with the sun; a recent analysis shows that its value is 498.6", which leads to the same value of the parallax as above, but the internal discrepancies of the material put its authority upon a much lower level.
The term "perfect gas" is applied to an imaginary substance in which there is no frictional retardation of molecular motion; or, in other words, the time during which any molecule is influenced by other molecules is infinitesimally small compared with the time during which it traverses its mean free path.
The actual number of sets of apparatus it was possible to work multiplex depended upon the length of the line, for if the latter were long, retardation effects modified the working conditions.
The only element of uncertainty was caused by the retardation of the current, which between Potsdam and Teheran (3000 m.) took 0 8.20 to travel; but it is probable that the final value can be accepted as correct to within os 05.
This retardation was still more pronounced in the case of tungsten-steel, which lost its magnetism at 910° and remained nonmagnetic till it was cooled to 570°, a difference of 240°.
The extreme discrepancy is that between the waves which travel through the outermost parts of the object-glass at L and L'; so that if we adopt the above standard of resolution, the question is where must P be situated in order that the relative retardation of the rays PL and PL' may on their arrival at B amount to a wave-length (X).
The directions of the lateral spectra are such that the passage from one element of the grating to the corresponding point of the next implies a retardation of an integral number of wave-lengths.
These directions, in which the retardation between A and B is exactly mnX, may be called the principal directions.
On either side of any one of them the illumination is distributed according to the same law as for the central image (m = o), vanishing, for example, when the retardation amounts to (mn t 1)X.
In an engraved glass grating there is no opaque material present by which light could be absorbed, and the effect depends upon a difference of retardation in passing the alternate parts.
For if the alternate parts were equal and alike transparent, but so constituted as to give a relative retardation of :IX, it is evident that the central image would be entirely extinguished, while the first spectrum would be four times as bright as if the alternate parts were opaque.
If it were possible to introduce at every part of the aperture of the grating an arbitrary retardation, all the light might be concentrated in any desired spectrum.
6), and the diffracted rays make an angle ¢ (upon the same side), the relative retardation from each element of width (a+d) to the next is (a+d) (sin 9 +sin op); and this is the quantity which is to be equated to mX.
Then the relative retardation of the extreme rays (corresponding to the edges A, B of the grating) is mnX.
If BQ be the direction for the first minimum (the darkness between the central and first lateral band), the relative retardation of the extreme rays is (mn+1)X.
If the retardation be too little, the overlapping of the processions is incomplete, so that besides the procession of half period there are residues of the original processions of full period.
The same thing occurs if the retardation be too great.
It is easy to see that the length of the chord (which passes in all cases through 0) increases to a maximum near the place where the phase-retardation is s of a period, then diminishes to a minimum when the retardation is about a of a period, and so on.
After a rough estimate of the perturbations it must sustain from the attraction of the planets, he predicted its return for 1757,-a bold prediction at that time, but justified by the event, for the comet again made its appearance as was expected, though it did not pass through its perihelion till the month of March 1759, the attraction of Jupiter and Saturn having caused, as was computed by Clairault previously to its return, a retardation of 618 days.
For the alteration of wave-length entails, at the two limits of a diffracted wave-front, a relative retardation equal to mndX.
This expresses the retardation of the extreme relatively to the central ray, and is to be reckoned positive, whatever may be the signs of w, and 0 .