text: Talk:The School for Scandal

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:The School for Scandal


text: Cartoon portraits and biographical sketches of men of the day/Alfred Tennyson


text: An Australian Parsonage

title: An Australian Parsonage


text:
User:HtnbdResuf/Books/kautilya

Arthashastra

 * Arthashastra
 * Arthashastra/Book I
 * Arthashastra/Book II
 * Arthashastra/Book III
 * Arthashastra/Book IV
 * Arthashastra/Book V
 * Arthashastra/Book VI
 * Arthashastra/Book VII
 * Arthashastra/Book VIII
 * Arthashastra/Book IX
 * Arthashastra/Book X
 * Arthashastra/Book XI
 * Arthashastra/Book XII
 * Arthashastra/Book XIII
 * Arthashastra/Book XIV
 * Arthashastra/Book XV

title: User:HtnbdResuf/Books/kautilya


text:
User:TalBot/soft redirect maintenance/October 2010/redirects

 * Catholic Encyclopedia (1913)/Luis de LeÛn → Catholic Encyclopedia (1913)/Luis de León
 * Index:1960 FBI primer on Nation of Islam.djvu → Index:1965 FBI monograph on Nation of Islam.djvu
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 * The History of the Decline and Fall of the Roman Empire (1897) → The History of the Decline and Fall of the Roman Empire/Volume 1
 * The Story of the Treasure Seekers/Chapter2 → The Story of the Treasure Seekers/Chapter 2


text: Cartoon portraits and biographical sketches of men of the day/Norman Macleod, D.D.


text:
User talk:64.113.185.61

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title: User talk:64.113.185.61


text:
The Encyclopedia Americana (1920)/Volume XX: Naval Observatory - Orleans

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 * ../Newberry, John Strong/
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 * ../Newbery, John/
 * ../Nicolay, John George/
 * ../Nidification/
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 * }


text:
The Encyclopedia Americana (1920)/Volume XXIV: Russia - Silius

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text:
The Encyclopedia Americana (1920)/She Stoops to Conquer

SHE STOOPS TO CONQUER. Though he was thoroughly a child of his time, it was Goldsmith's peculiar genius that he went to life for his influences rather than to books. The central feature of ‘She Stoops to Conquer’ has some resemblances with Farquhar's ‘The Beaux' Stratagem,’ but its veritable source was undoubtedly an episode in the youthful career of Oliver himself.

If in the theatre Goldsmith seems to have been more of a reformer than elsewhere the reason is not far to seek. The refinements of that sentimental comedy which in his day controlled the stage were repugnant to him as an instinctive artist. Before his playwriting days Goldsmith had ridiculed “genteel comedy” and in the “low” passages of ‘The Good-Natured Man’ had resolutely entered the lists against it. ‘She Stoops to Conquer’ is the author's second and more successful play. Less artificial

than the comedy of manners, to which general class it belongs, it has more of Fielding in it than of Congreve. No one but Goldsmith could have given such a view of a country house. And even the London characters are freshly viewed. Their city manners are crossed with the forthrightness of nature. Raillery and repartee dwindle in importance before character and atmosphere. The difference between Goldsmith and Sheridan was that the former knew life whereas the latter knew only the stage. Squire Hardcastle is drawn without a stroke of over-elaboration. Less sportive than Tony he digs as deeply into the memory; but Tony and his mother linger as something more than caricatures. Kate Hardcastle is as much a product of observation as Millamant of ‘The Way of the World’ is a product of thought and Maria of ‘The School for Scandal’ is a product of the stage. It is the veritableness of the atmosphere of the play that saves it from, what the plot would make it, sheer farce. Goldsmith was not fortunate in his relationships with Colman and Garrick, the two monopolists of the theatre of his day. Yet upon its performance by Colman at Covent Garden Theatre, 15 March 1773, ‘She Stoops to Conquer,’ “succeeded prodigiously” (Walpole). It holds the stage in frequent revivals to this day. Editions: Masson, D., Globe edition (1869); Dobson, A., ed., Belles Lettres Series (1905); Temple Dramatists (1900); Everyman's Library (Vol. 415). Consult Forster, ‘Life and Adventures of Oliver Goldsmith’ (1848); Dobson, A., ‘Memoir’ (1899); ‘Cambridge History of English Literature.’


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User:TalBot/soft redirect maintenance/October 2010/references

 * Index:1960 FBI primer on Nation of Islam
 * Index:The Cambridge History of American Literature 3.djvu
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 * Scriptorium/Archives/2009-12


text: User:TalBot/soft redirect maintenance/October 2010/changes


title: Index:BraceRefraction1904.djvu


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 THE FitzGerald-Lorentz "Contraction" Hypothesis to explain the negative results of the Michelson-Morley experiment of interference between two rays, at right angles and parallel to the earth's motion, has been tested by Rayleigh in his experiments on the double refraction of liquids and of glass. He assumes the contraction to be $$\left(10^{-4}\right)^{2}$$, and also the excess of the index above unity to be proportional to the density. The first assumption is apparently in error by a half and should be 0.5 × 10-8. The second assumption does not seem to be entirely valid for glass, at least, when compared with the double refraction produced by a given strain. The first correction reduces his margin down to 50 times for a liquid and 1.5 times for glass. The second will reduce the margin to considerably less than unity for glass, which would thus leave us only the observations on liquids upon which to base our conclusion.

While the method of Rayleigh cannot be regarded by any means as a conclusive test of the hypothesis, it is the only experimental one attempted and can be extended so as to give a safe margin for a solid like glass.

This suggestion of the "contraction" hypothesis by Lorentz, from considerations in regard to intermolecular forces analogous to the interaction, through the mediation ''Phil. Mag.'' S. 6. Vol. 7. No. 40. April 1904.

title: Page:BraceRefraction1904.djvu/1


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Page:BraceRefraction1904.djvu/2

318 of the æther, of electric and magnetic forces, is certainly plausible enough to warrant further examinations and extension experimentally. That the intermolecular forces are not altered by factors many times less than those obtained by Rayleigh, is found to be the case in the media used.

Two arrangements suggest themselves: the one, a system rotating about a vertical axis, the other a similar system rotating about a horizontal axis so as to shift the plane of polarization from a position at 45° to the earth's orbital motion through an angle of 90°. In the matter of simplicity, sensibility, and stability the latter method would be preferable. However, the first arrangement was selected for the purpose of utilizing the same mounting for other experiments. A heavy beam was pivoted between the floor and ceiling so as to carry a trough with its horizontal axis intersecting the pivotal axis. This system could be rotated continuously so as to bring it into any desired position. This trough was 413 cms. long, 15 cms. wide, and 27 cms. deep on the inside, and built up of 5 cms. planking in order to give sufficient stability to the polarizing and mirror systems which it carried.

In order to obtain sufficient intensity through the total column, the 2856 cms. of water used, sunlight was so thrown into the trough as to keep its path the same whatever its position. The lens 1 (fig. 1) of about 2 m focus converged the sun's rays, from a carefully adjusted heliostat, within the nicol 4, after reflexion from 2 and 3. The diverging beam was then successively reflected from mirrors 5, 6, and 7 upon the concave mirror 8. The radius of curvature of this latter was about 15 m., and it was mounted, as were the other mirrors, upon brass plates containing adjusting-screws fastened to the ends of the trough. The axis of the reflected cone was displaced in a horizontal plane, so that the return ray passed through the analysing system 9-11 placed to one side of the polarizer. The lens 12 converged the light, which would otherwise have come to a focus at a distance of about 2 m. beyond, to the eye 15 at a distance of 25 cms. from 9. Thus the eye could observe 9 directly or by means of the telescope 14. Both the heliostat-mirror and the lens 1 were diaphragmed down so that the aperture of the cone of rays was slightly less than that of the mirror 8 whose aperture was about 15 cms. This prevented diffused light from the mirror and the water reaching the nicol 11 to any serious extent, and also aided in the adjustments of the mirrors so as to keep the rays fixed when the trough was rotated.

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320 The total-reflecting prism 2 was carried by a universal mounting parsing through a rod forming the prolongation of the axis about which the system rotated. By properly shifting 1 and 2 the ray 2-3 could be brought exactly in the axis of rotation, so that when the trough was rotated the return ray at 9 remained at a definite point in the field of view. 3 and 4 were then shifted until the ray passed through them symmetrically. Any change in the direction of the incident ray at 1 would of course cause a shift, but Improperly regulating the heliostat this could be avoided. However, with such a long optical lever slight irregularities might occur after a rotation, but these were always compensated for before observing the field of view by adjusting 2 until the beam of light occupied the exact position it did previous to rotation.

The polarizing nicol was either one with ends normal to the ray, or, if of the ordinary type, mounted in a cell with thin cover-glass ends so as not to affect the ray when the system was under water. The analysing nicol was a Glan-Thompson of 15 mms. aperture. The analysing and polarizing systems together with the prisms and lens were mounted within tubes to prevent access of the water and upon a common cross-piece fastened to the trough. By adjusting 8 the cone of rays could be sent into the analyser symmetrically so as to fill completely the field of view. The principal planes of the nicols were crossed and at 45° to the vertical plane. A metal diaphragm was placed lengthwise between the entering and the emerging rays and between the mirror 5 and the polarizing system so as to prevent scattered light reaching the analyser.

The following delicate method, a detailed description of which I give elsewhere, was used for observing the slightest trace 1/100 or 0.0012 mm. thick, cemented with Canada balsam between two thin cover-glasses without double refraction, the latter being cemented to a brass ring carried by an arm extending from a collar slipping over the brass containing-tube of the nicol. This collar carried an arm with the scale divided into some 60 divisions representing half degrees. 10 was a similar thin section of mica of order $$\tfrac{1}{75}$$ approx., cemented similarly and covering nearly the entire aperture of the nicol 11. This system, which I will designate as tho "compensator," was mounted on a collar slipping over the nicol between the collar and the strip of the first system. This

title: Page:BraceRefraction1904.djvu/4


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Page:BraceRefraction1904.djvu/5

 had an arm for rotating and also a pointer passing over the scale referred to.

In the adjustments 2 was moved until, when the trough was turned completely round, the ray as seen on a white mark did not shift. Water which had been heated to drive out air and prevent minute bubbles forming in it and upon the mirrors and thus causing diffused light was then flowed into the trough until it covered the analysing and polarizing systems. This usually caused a shift of the rays, and 2 was again adjusted until the spot of light remained fixed when the trough was rotated. 8 was then adjusted until the return rays passed through the analyser so as to give a uniform field of view when examined directly with the eye through a small circular aperture or by means of the telescope 14. The light after its passage through this 30 metres of water appeared of a beautiful light-green tint. With the mica sections removed the nicols were adjusted for extinction, which was fairly complete. The sensitive strip 9 was then thrown in and rotated to extinction, and then turned through 45° so as to bring its principal axes at 45° to the principal plane of the analyser. 10 was then placed in position and turned until the field on each side was of the same intensity as that of the sensitive strip. The eye thus saw the field of view illuminated uniformly with green light in the neighbourhood of this strip. The slightest trace of double refraction in the direction desired would at once make itself evident in the relative increase or diminution of the light from the strip.

The conditions of maximum sensibility in photometric comparisons, namely a vanishing line and a uniform field, were thus attained. A small piece of glass compressed vertically to the slightest degree with the fingers placed after the polarizer 4 showed a sharp change of intensity at this bounding line. A match could be immediately obtained by rotating the compensator 10. By noting the position of the pointer for a match and then shifting the same until such a change could just be detected, a measure of the sensibility of the system could be obtained. This angle was found to be 0°.2 under favourable conditions. At each observation the sensibility was determined. A match was obtained with, say, the trough in the meridian at noon, this was then turned through 90° into the direction of the earth's orbital motion. The position of the return image at the polarizer was noted, and if it had shifted in any way it was brought back by the adjustment of 2 into its initial position and then the field of view examined. In no case could a change be observed, i.e.

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Page:BraceRefraction1904.djvu/6

 there was still a match indicating no double refraction. Various positions were taken in and at right angles to the meridian with the same result. Hence, we may conclude that to this order of sensibility there is no double refraction in the water due to its motion through the æther. These observations were taken during the latter part of July 1903. It is evident that a rotation of the plane of polarization due to the earth's field of force would not affect this match, as both portions of the field would vary in intensity by the same amount. To make sure of this the trough was rotated through 180° into the meridian so as to reverse the direction: but no effect could be observed. It is evident that since the rotation due to a magnetic field is always in a definite direction and independent of the direction of the ray, such a rotation of the plane of polarization would be reversed with respect to an observer moving with the trough. Hence this could not mask any effect due to double refraction.

A second check was made with a cell of turpentine 1.6 mm. thick, whose ends were made with thin cover-glasses without double refraction, which would give a rotation of about 0°.5, while if we take 0°.015 as Verdet's constant for water and 0.2 as the earth's field and a length of 30 m. we find about 0°.15 for the rotation. On inserting this cell after the polarizer, no effect could be detected.

In order to determine the relative retardation which corresponds to a given rotation of the compensator, the polarizing and analysing systems were dismounted and placed on a support with their optic axes in line. The system was illuminated by an acetylene flame, the light from which passed through green glass or celluloid of about the same tint as that obtained after passage through the water. The sensitive strip, compensator, a quarter-wave plate mounted on a vertical circle, and a vertical strip of glass capable of carrying a weight, and, in addition, a micrometer-screw carrying two horizontal cross-wires in front of a horizontal strip of glass held within a clamp so as to produce a flexure, were arranged to be placed in the path of the light. The order of the mica quarter-wave plate was found to be approximately ¼ for green light, λ=0.00005 cm., by comparison in the usual way with a quartz or selenite wedge. With the nicols crossed and the plane of polarization at 45° to the vertical, the circle carrying the quarter-wave plate was adjusted until the light was extinguished and the mean of its positions for a number of settings noted. The sensitive strip was then thrown in with its axes at 45° to the plane of polarization, and after that the compensator which was set for a match. By rotating

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 the quarter-wave plate this match was destroyed, but by rotating the compensator this could again be obtained. In this way the retardation of the compensator could be at once determined in terms of that of the quarter-wave plate. Thus, a rotation of 5° of the compensator corresponds to 16' of that of the quarter-wave plate. It was found that the rotation of the compensator was proportional to that of the quarter-wave plate approximately for these small angles.

A further comparison was made with the vertical crown-glass strip. This was 13 mms. wide and 2 mms. thick. The quarter-wave plate was removed and this strip inserted instead and a setting made with the compensator. On adding 200 gms. a match was obtained on rotating the compensator through 2°.5. From this can be calculated the relative retardation produced in glass per unit weight and unit width. Another comparison was made with white light from the acetylene flame direct by removing both strip and compensator and inserting the micrometer and horizontal glass strip in addition to the vertical glass strip. When the clamp for producing flexure was screwed up a horizontal black band appeared between the two cross-wires. For one flexure, where the band was quite distinct, 500 gms. on the vertical glass strip gave a reading of 36 on the micrometer-screw and 200 gms. gave 14, thus showing the proportionality. A movement of the cross-wires, just sufficient to observe a shift, gave a reading of 12, which was the sensibility of the system for that flexure. On releasing the screw until the flexure was so far reduced that the band was barely visible, 200 gms. gave a shift of 23 divisions and 100 gms. gave 11 divisions as near as could be observed, and this was the smallest weight which could be observed to produce any double refraction. A direct shift of the cross-wires gave 13 divisions as the sensibility. Using direct white light and the sensitive strip and compensator 0°.1 rotation of the latter could be detected, thus giving it a sensibility of $$\tfrac{200}{2.5}$$×0.1=8 gms., or 12.5 times that of the band under similar conditions of light intensity and adjustment. With greater intensity and more careful adjustment higher sensibility could be obtained by both methods. In fact, Rayleigh, using lime-light and a black band, has been able to detect a weight of 25 gms. on a vertical glass strip 15 mms. wide, or a sensibility over four times as great as that obtained above with the acetylene flame and a black band.

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 From the above data we may calculate the least change in the index which could be observed if the water had become doubly refracting. If θ is the angle which the plane of polarization makes with one of the principal axes of the mica then the component vibrations or the principal axes of the resultant ellipse in the quarter-wave plate are in the ratio of tan θ to 1. For small angles then the ratio of the change of phase to the total or $$\tfrac{\lambda}{4}$$ is proportional to the angle θ. Thus 1° rotation of the mica gives

$\frac{1}{45}\times\frac{\lambda}{4}=\frac{\lambda}{180}$,

but 16' of the quarterwave plate was equivalent to 5° of the compensator, and as 0°.2 rotation of the latter could be detected, this reduces to

$\frac{16}{60}\div5\times0.2\times\frac{\lambda}{180}=\frac{\lambda}{17,000}=6\times10^{-5}\lambda$

approx. for green. The total path of the light in the water was 2856 cms. Taking its index as 1.33, the number of waves is

$\frac{2856\times1\frac{1}{3}}{.00005}=7.6\times10^{7}$.|undefined

As $$6\times10^{-5}$$ of a single wave could be detected, the fraction of the total would be

$6\times10^{-5}\times\frac{1}{7.6}\times10^{-7}=7.8\times10^{-13}$.

This represents the greatest difference in velocity or in index between the two components which could exist referred to that of water for green light, λ = .00005 cm.

Mascart has shown that in the case of water under compression the increment in the excess of the index above unity is nearly proportional to the increment of its density. If in the movement of matter through æther an increase in density in this direction took place, producing a change in the natural frequency of the molecular systems similar to that which occurs in glass, say, then, to determine how great it might be from these results, it is necessary to measure the

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Rh increment in phase which represents the sensibility of the experiment in terms of the excess of the index above unity. This excess of index is $$\tfrac{1}{3}$$ while the index is $$\tfrac{4}{3}$$, hence our limit should be four times larger or $$3.1\times10^{-12}$$. The greatest change which could be expected is the difference between unity and $$\sqrt{1-\tfrac{v^{2}}{V^{2}}}$$ where $${v}$$ is orbital velocity and $${V}$$ light-velocity or

$\frac{1}{2}\frac{v^{2}}{V^{2}}=\frac{1}{2}(10^{-4})^{2}=5\times10^{-9}$,|undefined

or about 1600 times greater than the smallest effect which could be observed.

The effect of a change in the frequency of the order $$\tfrac{v^{2}}{2V^{2}}$$ on the index of the moving molecular vibrations relatively to the aether impulses in the direction of motion, is far too small to be observed. Thus the index of water for frequency $$5.1\times10^{14}$$ is 1.334 and for $$6.9\times10^{14}$$ is 1.341. This gives for a fractional increase in frequency of 4/3 a fractional increase in index of $$0.007\times\tfrac{4}{3}$$. Hence the fractional increase in index due to a change of frequency of order $$0.5\times10^{-8}$$ is

$\frac{0.5\times10^{-8}}{\frac{4}{3}\times10^{14}}\times9\times10^{-3}=3.5\times10^{-23}$,|undefined

while the smallest observable change was $$7.8\times10^{-13}$$.

Two different arrangements were tried with glass. In the first a large slab of "optical" glass (crown) was cut lengthwise and the edges of the two halves ground square. These were then cemented together side by side so as to give approximately square end-surfaces for grinding and polishing. Those end-surfaces were "built up" in the usual way so as to ensure a "flat" surface. These two prisms were then cemented end to end, giving a prism 42 cms. long with polished ends 10 cms. by 3.8 cms. These end-surfaces were silvered and a strip at the bottom and top of each removed. The system was then mounted on a support within the trough so that light from the polarizer could pass in and lie reflected backwards and forwards until it passed out through the unsilvered space at the other end, where it was again reflected back into the prism by a concave mirror 3 in. radius of curvature, approximately. After the same number of reflexions it passed out to one side of the entering ray and was received by the half-shade analysing system already

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326 described. It was found impossible to obtain a satisfactory match with the half-shade system alone without some other compensation. On examining with the analyser, vertical bands (they appeared horizontal of course) were seen which were quite regular and symmetrical on each side of a central black band. The distance apart of these bands and their distinctness were less as the number of internal reflexions were increased. The total number of passages through the prism varied from ten to eighteen, or a total distance in the glass of from 420 cms. to 756 cms. An attempt was made to compensate by means of the horizontal strip of glass with the clamp for producing flexure. This system was mounted on a universal system so as to bring the black band in the glass strip vertically in front of the analyser. In one position, under flexure, the resulting bands became narrower. On reversing it, so as to interchange the compressed and dilated portions of the strip, the bands became wider and finally disappeared as the flexure was increased up to a certain point. They then reappeared and became narrower with increasing flexure. This compensation increased the sensibility so that a moderate pinch of the prism by the fingers gave a marked shift of the central band which could be observed by means of the two cross-wires already referred to. However, the compensation was not sufficiently satisfactory to obtain good matches with the half-shade. Furthermore, the slightest flexure of the trough or deviation of the beam of sunlight caused the "match" to change in the one case or the band to shift in the other, owing to the narrowness of the beam. Observations with this arrangement would thus be likely to prove unreliable, and the system was finally given up for another which could be rendered more stable, optically, and in which artificial light could be used.

Two cylinders of flint-glass, each 22.3 cms. long and 2.4 cms. in diameter, and of mean index nD=1.77, were mounted on adjustable supports between the polarizing and analysing systems. The former consisted of the nicol and half-shade system used previously as the analysing system. This was observed through the analysing nicol by a low-power telescope. The source of light was an acetylene flame into which was injected, broadsides, a flat stream of oxygen through a fish-tail burner. This increased the brightness of the field of view several times, and extended the sensibility of the settings by a corresponding amount. The entire system was mounted on a common base, so that once a match was obtained it could be moved without disturbing it. These cylinders were especially well annealed Jena glass used a

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Rh number of years ago in experiments on the double refraction of light propagated at right angles to the lines of force in a magnetic field. Each showed the black cross in certain azimuths between crossed nicols. In order to use this portion of the glass only, diaphragms 3 mms. to 4 mms. in aperture were placed at each of the ends of the cylinders along the optic axis of the system. One cylinder was then inserted and adjusted so as to give the most satisfactory match of the half-shade. The aperture was sufficient for obtaining a close setting, and the field could be made of nearly uniform intensity so that a vanishing-line was approximately realized. The slightest contact of the fingers, however, usually disturbed the match, in consequence of temperature changes. This match could be seen slowly to recover itself on removal of the fingers. Also the slightest flexure in the process of adjustment made itself at once manifest. This entire system was placed upon the large trough, and observations, with the polarizer at 45° to the vertical, made when the same was rotated. At first irregular changes in the match were observed, but these were found to be due to a shift of the eye and head of the observer. To eliminate this a seat was mounted so that the observer could move undisturbed with the trough, the head being steadied by means of a clamp. In this way no change in the field could be observed except in a very few instances. These were attributed to an accidental shift of the eye or to slight temperature changes. Observations were made at noon and at 6 P. M. in the early part of December. At this latter time occasional change could be detected similar to those which had been noted several times in the noon observations. The difficulty in maintaining the conditions for so high a sensibility as was attained, rendered the fictitious effects quite possible. When the greatest care was exercised no change could be detected. Under the most favourable conditions a rotation of the compensator of 0°.2 approximately could be detected. This corresponds, as shown above, to a change in the relative retardation of $$6.5\times10^{-5}\lambda$$ for the mean portion of the spectrum, λ=.000055 cm. The total path in the glass was 44.5 cms., and hence the total number of waves is

$\frac{44.5\times1.77}{.000055}=1.43\times10^{6}$.

Thus the fraction of the total becomes

$6.5\times10^{-5}\div(1.43\times10^{6})=4.5\times10^{-11}$,

which is the greatest difference in velocity or in index

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328 between the two components which could exist in this kind of glass.

If we estimate the contraction from the change in density by means of the excess of the index above unity, as was done in the case of water and as assumed by Rayleigh, the above fraction would become

$\frac{1.77}{.77}\times4.5\times10^{-11}$ or 10-10,

approximately. This is 50 times smaller than $$0.5\times\left(10^{-4}\right)^{2}$$, the change to be expected on the "contraction" hypothesis, and is 30 times less than the sensibility obtained with water.

If, on the other hand, we take Wertheim's results for glass, we have approximately for Faraday's flint, 5 x 1011n as Young's Modulus and $$2.4\times10^{7}$$ dynes on a millimetre cube to give a relative retardation of one λ. From above we have

$\frac{6.5\times10^{-5}\lambda}{445}=1.46\times10^{-7}\lambda$

as the relative retardation for 1 mm.

Thus, the force to produce the least observable effect is

$2.4\times10^{7}\times1.46\times10^{7}=3.4$ dynes per 1 mm.

Young's Modulus for 1 mm. square becomes $$5\times10^{9}$$ and the contraction becomes

$\frac{3.4}{5\times10^{9}}=6.8\times10^{-10}$,|undefined

which is seven times smaller than that expected on the "contraction" hypothesis. If we correct by ¼ for Poisson's ratio, as we should if the interference problem were done on a glass support, the calculated contraction becomes

$0.5\times\left(10^{-4}\right)^{2}\times\frac{4}{5}=4\times10^{-9}$

or six times larger than our margin for glass.

Hence, if the test is a valid one, the "contraction" hypothesis cannot explain the negative results of the interference experiments; and, with the same reasoning, we also conclude either that the aether moves with the embedded matter, or that the effect of the relative motion on the intermolecular forces and the possible consequent relative change in dimensions are very small.

 * Physical Laboratory,
 * University of Nebraska, Lincoln.

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Rh [Note. These experiments were repeated during the early part of February, 1904, when the earth's orbital velocity conspires approximately with that of the solar system in space. The conditions for observation were quite as favourable as before; but no effect could be detected. With glass, the optical system was rotated through several quadrants consecutively so as to observe any possible trace of an effect. Observations were made at noon and at 6 P.M.

Hicks, in a more rigorous discussion than that of Lorentz, of the effect to be expected in the Michelson-Morley experiment, shows that instead of a contraction of $$\tfrac{v^{2}}{2V^{2}}$$ in the direction of drift, there should be an elongation of $$\tfrac{v^{2}}{2V^{2}}$$, to account for the negative results of the observations. The experiment itself should thus disprove the FitzGerald-Lorentz hypothesis. Either, on any of the suppositions possible from Lorentz's point of view, viz. contraction along the drift and zero change at right angles, no contraction but extension at right angles to the drift or elongation along and at right angles to the drift, such that the difference is $$-\tfrac{v^{2}}{2V^{2}}$$, or, on the conclusion of Hicks, the effect to be observed by means of double refraction in the preceding experiments would be the same.— D. B. B.]

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text: Dictionary of National Biography, 1885-1900/Steward


text: Author:Thomas Herbert Dickinson

title: Author:Thomas Herbert Dickinson


text:
The Encyclopedia Americana (1920)/Schiff, Jacob Henry

SCHIFF, shĭf, Jacob Henry, American banker and philanthropist: b. Frankfort-on-the-Main, Germany, 1847. He came to New York in 1868, where he entered a banking house and became in a few years head of the firm of Kuhn, Loeb and Company. His leadership in finance was quickly acknowledged and his firm has been identified with many prominent enterprises. He has devoted a large portion of his wealth to charitable and educational purposes and among his most noted benefactions are the Semitic Museum at Harvard University, and in New York the Nurses' Settlement, the Young Men's Hebrew Association building and the Jewish Theological Seminary. He is president of the Montefiore Home for Chronic Invalids of New York; vice-president and trustee of the Baron de Hirsch Fund; member of the American Museum of Natural History; the Metropolitan Museum of Art; the American Society of Fine Arts, and is an ex-vice-president of the New York Chamber of Commerce. He has long been associated with movements for civic reform.


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[Dewitt Bristol Brace, Professor of Physics, University of Nebraska. b. Wilson, New York, 1859; died, October 2, 1905. A.B. Boston, 1881; A.M. Boston, 1882; Ph.D. Berlin, 1885; post-graduate, Massachusetts Institute of Technology, 1879-81; Johns Hopkins University, 1881-83; University of Berlin, 1883-85. Acting Assistant Professor of Physics, University of Michigan, 1886. Vice-President of American Association for the Advancement of Science; Vice-President of American Physical Society. Author of Radiation and Absorption.]

question whether the luminiferous ether passes freely through matter or participates in the translation of the same, considered as a moving system, stands to-day without positive answer, notwithstanding the numerous experimental attempts and the varied hypotheses which have been made since the discovery of aberration by Bradley in 1726. The simple explanation of this phenomenon on the corpuscular theory may have caused the century of delay in the closer examination of the question until it became necessary to consider it from the standpoint of undulations in an ether. As compared with the many efforts to examine the question in the second or ether period we have perhaps but two belonging to the first or corpuscular period. Boscovich, in 1742, reasoning from this theory on the ground of a difference of velocity in air and water, proposed to examine the aberration of a star with a telescope whose tube was filled with water. This experiment was not carried out till long after by Airy in 1872, who found that the variation in the aberration was absolutely insensible. Arago, in the second instance, reasoning on the same theory, concluded that the deviation produced by a prism would vary with the direction of the earth's motion; but he was unable to detect any such change, a result verified later by more delicate means in the hands of Maxwell, Mascart, and others. This experiment, which demonstrated the absence of any effect of the earth's movement on refraction is of great historical interest. This negative result, which to Arago was inconsistent with the corpuscular theory, suggested to Fresnel the important hypothesis of a quiescent ether penetrating the earth freely but undergoing a change

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106 of density within the medium proportional to the square of its index and being convected in proportion to this excess of density, which would give an apparent velocity to the ether of $$\left(1-\mu^{-2}\right)\nu$$, instead of the velocity of the earth. Stokes suggested, as a simpler idea, that we suppose the ether is not convected but passes freely through the earth, being condensed as it passes into a body in the ratio of 1 to μ², so that its velocity within the refracting medium becomes $$\left(1-\mu^{-2}\right)\nu$$, from the law of continuity.

Babinet in the second-century period attempted to test Fresnel's theory by examining the interference of two rays traversing a piece of glass, the one in the direction of the earth's motion and the other in the opposite direction. Stokes showed that a negative result was not contrary to the theory of aberration, since the retardation would be the same as if the earth were at rest.

He showed further, what Fresnel had not proven to be true in general, that on Fresnel's theory the laws of reflection and refraction for single refracting media are uninfluenced by the motion of the earth. In fact, Rayleigh has shown that, in using terrestrial sources, no optical effect can be produced by any system of reflecting or refracting optical surfaces moving as a rigidly connected system relatively to the ether, if we take into account the Doppler "effect," and neglect quantities of the second order of the aberration. Since, as Stokes says, the theory of a quiescent ether may be dispensed with, and as there is no good evidence that the ether moves quite freely through the solid mass of the earth, he proposes to explain the phenomenon of aberration on the undulation theory of light, upon the supposition that the earth and the planets carry a portion of the ether along with them, so that the ether close to their surfaces is at rest relatively to those surfaces and diminishes in velocity till at no great distance in space there is no motion. Cauchy had previously discussed the theory of a mobile ether, and had proposed to explain aberration by a shearing of the wave-fronts due to the translatory motion of the medium, but he did not develop his method sufficiently to explain how much the aberration would be.

On the other hand Stokes has specifically indicated his assumptions and formulated his conclusions. He examines the displacements of a wave-front in its passage from the ether at rest, across the region of transition to the ether in the neighborhood of the observer, which is at rest relatively to him. Adopting the same method which is used in the case of an ether at rest in determining the wave-front at any future time from that of a given one at any instant, he shows,

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 Rh on the one condition, viz. that the motion of the ether is differentially irrotational, that if we neglect the square of the aberration and of the time, the change in direction of the ray as it travels along is nil, and therefore the course of a ray is a straight line, notwithstanding the motion of the ether. Following out the analysis on this supposition, a body, a star for example, will appear displaced toward the direction in which the earth is moving through an angle equal to the ratio of the velocity of the earth to that of light, when moving normal to the star's direction. This rectilinearity of propagation of a ray, which would likely seem to be interfered with in the motion of the ether, is the tacit assumption made in explaining aberration. If the physical causes, in consequence of which the motion of the ether becomes irrotational, could be adduced, the theory of Stokes would satisfy completely aberration and the negative results of the many and various experimental investigations which have thus far been made and whose validity is unquestioned, whether in refraction, interference, diffraction, rotary polarization, double refraction, induction, electric convection, etc. In an ordinary fluid, tangential forces proportional to the relative velocities destroy the irrotational condition in a steady state of motion. If we suppose these forces to be diminished indefinitely we obtain now a motion totally different from that for the steady state when these forces are assumed to be absent initially; and hence such a motion would be unstable. When, however, tangential forces depending on relative displacements in the ether are considered, it becomes possible to explain the irrotational condition. Any deviation from this state, for example at a surface of slip, would be dissipated away into space with the velocity of light by means of transverse vibrations. He illustrates such apparent incompatibilities in physical states by successive dilutions of gelatine. Such a medium shows elastic tangential forces for small constraints, and yet apparent fluidity for motions through it, mending itself as soon as dislocated. He regards these qualities as consistent and self-sufficient to explain the phenomena in question. Against the view of Stokes, Lorentz raises objection to his assumptions concerning the ether motions in the neighborhood of the earth, which he considers inconsistent, a difficulty which he is unable to set aside. Larmor demurs against an appeal to a highly complex medium, such as pitch, for studying the behavior of a simple one like the ether. A time-rate much shorter than the time of relaxation will of course provide approximate rigidity, while a timerate much longer will provide approximate fluidity, but this requires inevitable dissipation. This objection would be valid for a viscous solid, but such Stokes apparently did not have in mind, since he specifically proves such a case unstable. A solid like pitch is a very different type of solid from that of a vesicular solid like jelly. An ether

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108 after the model of a viscous solid would always contain the viscous terms, so that even for the high time-rates of light-waves there would be dissipation however small. Such a condition, it can be proven, would give coloration to the remote members of the stellar system; a fact inconsistent with observation. On the other hand, a soft vesicular solid like gelatine may not necessarily contain the time-factor, and yet be so soft that dislocation may occur even with constraints of the order of aberration, but not of the square of that order. Such an ether without a time of relaxation factor would fulfill completely the conditions of a luminiferous ether, if, as Stokes tried to show, it could be reconciled with the phenomena of aberration and the motions of the heavenly bodies. The method of double refraction shows that a solution of gelatine of one part in a thousand is rigid, while at the same time it appears as mobile as water, and its rate of flow through small tubes does not vary largely from the same. This experiment illustrates very markedly Stokes's example. When such a solution is continuously dislocated between two surfaces in relative motion, the same double refraction is present, indicating that the stress is still active during dislocation. Also a metal, like copper, shows a similar stress while being strained beyond its elastic limit. If this takes place by slip or dislocation throughout the mass which, though irregular, may give a mean uniformity for sensible dimensions, such a medium might serve as our model. Any deviation from perfect regularity in molecular distribution and activity we might anticipate would give such minute irregular dislocations at the limit of elasticity. Such a medium would thus transmit completely any disturbance within this strain limit.

It is difficult, however, to conceive of the transmissions of a disturbance across a surface of dislocation. For many ordinary media, we should expect at such a surface total reflection. If we suppose such a transmission of disturbance, its mode is not apparent, even if we suppose a thin lamina in rotational motion which would diffuse at least a portion, if not all, of the incident disturbance. Similar difficulties would arise if we assume the ether a solid which becomes fluid under stress and thus allows bodies to pass through it (as, for example, through a block of ice, as Fitzgerald suggested). While such solutions may seem highly artificial and do violence to our convictions, the consequences of a quiescent ether may, when fully developed and tested, demonstrate its impossibility and command a more extended examination into the structural qualities of an allsufficient medium than the single case of an essentially vesicular medium like jelly brought forward by Stokes and in a different form as a contractile ether by Kelvin. The theory of Fresnel of a quiescent ether in space presupposes a change of its density proportional to μ² within a ponderable medium, and a convection coefficient

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Rh $$\left(1-\mu^{2}\right)\nu$$. This hypothesis satisfies the phenomena of aberration and the uniformity of the laws of reflection and refraction of a body, whether in motion or at rest, and, as already mentioned, does not affect interference, as Stokes showed, so far as the earth's motion is concerned. That the ether apparently is carried along within moving matter not with its full velocity, but diminished to the extent indicated by Fresnel's coefficient of convection, Fizeau demonstrated in his famous interference experiment with streaming water, repeated later with greater refinement by Michelson and Morley. The significance of this experiment in its bearings on the question of the drift of the ether has perhaps been overestimated. In fact, neglecting the square of the aberration, it is exactly what we should expect from the dynamical reaction of a moving material system on a periodic disturbance, propagated through it without reference to the motion of translation of the interpenetrating medium, but simply to the frequency of the vibration impressed upon the system by this ether. Thus if we transform the ordinary differential equations of motion of the material system from fixed to moving axes, the form of the solution contains Fresnel's convection coefficient as a factor exactly, neglecting quantities of the second order of the aberration. This experiment cannot then be adduced as a positive result in favor of a quiescent ether. On account of its physical consequences, however, it should be extended to the case of gases and to absorbing substances, using light corresponding to the natural frequences of the latter if possible. Although negative results have heretofore been obtained with a gas, yet, with high pressures and greater dimensions and velocities, the test is within present experimental limitations. Results with solid bodies are still lacking, but a preliminary examination of the problem encourages us to expect successful results, at least with double-refracting substances. Reasoning in a similar manner as on the dynamical reaction of a moving system, we should look for the acceleration of a circularly polarized ray propagated coaxially within a rapidly rotating medium. This may possibly be brought within experimental limits. Again we have the important experiment of Lodge on the effect of moving masses upon the motion of the ether near them. This experiment, like that of the preceding one of Fizeau, is a first order test, i. e. the effect to be observed would arise from a change in the first power of the aberration factor. Two interfering beams were sent around several times in opposite directions between two rotating steel disks, and the effect on the bands noted from rest to motion or reversal. With a linear velocity not far from one twohundredth that of the earth's orbital motion, and a distance of some ten meters or more, no influence on the interfering rays could be detected, thus making the effect, calculated from the aberration factor if the ether were carried around between the disks, something

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110 like twice the limit of observation. Lodge estimates from this experiment that the disks must have communicated less than the eighthundredth part of their velocity to the ether. It is to be noted that the masses of these disks were not great, being only some two or three centimeters thick and about one meter in diameter. If we suppose the ether to be set in motion by means of reactions of a viscous nature, the experiment would be conclusive. To this extent, that the ether is not viscous, the test seems to be valid, but as there are other modes conceivable by which such movement might be brought about, it is not conclusive. If now we have to give up the notion of a quiescent ether, it will be necessary to suppose such motions are engendered in some way depending on the mass of the moving system, which we might imagine to be the fact in the case of the earth and the surrounding ether (possibly as, Des Coudres suggests, through gravitational action). It would be desirable to repeat this experiment, using great masses, and also testing to a much higher degree of sensibility (the third order would be possible) by means of double refraction. Michelson has recently attempted to determine directly whether the velocity of the ether diminished as we recede from the earth, but with negative results. He sent two interfering rays in opposite directions around the four sides of a rectangle of iron piping from which the air had been exhausted, the same being in a vertical east and west plane, the horizontal length of which was 200 feet and the height 50 feet. Assuming an exponential law for the variation in the velocity of the ether as we recede from the earth, he finds that if the earth carries the ether with it, this influence must extend to a distance comparable with the earth's diameter. The negative result in many of the experiments on refraction and interference which different investigators have obtained and which apparently follow on the assumption of a mobile ether have been usually experiments capable of giving only second order effects instead of the first order effects looked for, which, as mentioned above, are quite as consistent with a quiescent ether, as Stokes and Rayleigh have shown. Among these may be mentioned the experiments of Hoek, Ketteler, Mascart, and others on interference in ponderable media, over opposite paths relatively to the earth's motion; as also those of the two latter with doublerefracting media. All of the experiments were first order tests, and hence should give negative results on either theory, since, with a terrestrial source of light, the phenomena are independent of the orientation of the apparatus neglecting second order effects.

The positive results of Fizeau and of Ångström have not been confirmed and should not be seriously considered. In the experiments of the latter, the variation of the position of the Frauenhofer lines, as obtained by a grating when observed in directions with and opposite to the earth's orbital motion, has never been noted since, beyond

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Rh the anticipated displacement calculated from the purely kinetical principle of Döppler. The experiments of the former, as a first order test, on the rotation of the plane of polarization of a ray after passing through a pile of plates has perhaps offered the greatest difficulty to the exponents of both theories in reconciling the observations with the results which should follow from each theory. In this experiment, performed in 1859, the optical systems was mounted so as to be rotated about a vertical axis alternately from east to west, or vice versa. This system consisted of the usual polarizing nicol or sensitive tint-system and analyzing nicol between which were placed several piles of plates and compensating systems for producing the rotations and the magnifying of the same, and also for compensating for the rotary dispersion and elliptic polarization of the transmitted light which was polarized in an azimuth of 45°. In a series of observations extending over some time the mean of the rotations of the plane of polarization showed a maximum excess in the direction toward the west at noon and at the time of the solstice. It is to be noted that light from a heliostat was reflected into the system alternately by two fixed mirrors when the system was rotated. This required an interruption and readjustment of the heliostat during a single observation, i. e. from east to west and west to east, the difference in the setting of the analyzer in the two positions to give the same field of view being, of course, the effect sought for. Fizeau refers to the irregularities arising from successive settings of the heliostat. The calculated effect was much below that which could have been observed directly with the usual polarizing system. To magnify any such effect, a second system of plates was used which gave an amplification as high as eighty times. Thus any residual rotation from whatever cause would receive the corresponding amplifications. Now, in experiments with polarizing systems using sunlight as a source of illumination, it has frequently been noted that any shift in the direction of the light through the apparatus, either due to a change in the direction of the beam (arriving, say, from the heliostat) or to a shift in the optical system itself, produced a change in the field of view, whether with a half-shade system or otherwise. In the former the match was destroyed, the change being of an order much greater than that which Fizeau anticipated from calculation. Further, with such limited beams of light, a mere shift of the eye may produce an effect of similar magnitude. Hence, in all polariscopic experiments where sunlight is used, it is absolutely essential that, during any single observation, the ray of light pass through the system and into the eye over exactly the same path. This Fizeau failed to carry out, and this is entirely sufficient to explain the very great discrepancies in his various series of observations, and probably the apparent constant difference in the results of his settings in the two directions.

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112 In fact, Fizeau himself has stated since that his observations were not absolutely decisive. While the test is now probably within experimental limits with the more highly refined half-shade systems, other modes of experimenting on different optical principles with greater sensibilities have given negative results, thus disproving the existence of a phenomenon which Fizeau's experiment apparently established, and making a repetition of this experiment, which is of doubtful execution, unnecessary.

The effect of the motion of a natural rotative substance through the ether on the rotation of the plane of polarization is of considerable importance in its bearings on certain controverted points in some of the recent theories of a quiescent ether. Mascart, who first studied the problem in the case of quartz, was unable to detect any difference in the rotation when a ray was propagated in and against the direction of motion of the earth. This variation in the total rotation, which he could detect, was one part in 20,000, or one part in 40,000 on reversal. This experiment as thus carried out corresponds to a first order effect. Rayleigh quite recently has repeated this experiment with a sensibility five times as great, and obtained negative results, likewise. The impossibility of obtaining quartz in sufficient quantity and purity, or natural rotary liquids of sufficient power, to attain the extreme limit of polariscopic possibilities seems to make even an approximation to a second order effect entirely improbable, although the higher frequencies might be used, where the power may be ten times as great. On the other hand, the effect of the mechanical rotation of such a medium on the circular components is, however, probably not beyond experimental possibilities in polariscopic work.

On the electrical side several first order experiments have been made which likewise have given negative results. Des Coudres has attempted to determine the difference in the induction on each of two coils placed symmetrically, with respect to a third coaxial coil between them. On compensating for the effects of each on the galvanometer when the axis of the system was in the direction of drift, and then reversing the direction of the system, no influence on the galvanometer could be observed. The effect which should be observed corresponds to the second order of the aberration. However, without compensating factors, the theory of induction phenomena shows that second order effects should be looked for in systems moving through the ether. The same may be said of other electrical experiments.

The difficulties in formulating a theory which will explain the results of all experiments involving tests to the first order of sensibility only on the assumption of either a quiescent or a convected ether, are much easier met than when second and higher orders have to be taken into consideration. Here we find what, at first sight,

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Rh appear as rather startling assumptions; but it is only in this manner that present observational facts can be reconciled with a quiescent ether. With each advance in experimental refinement, theory has had to adapt itself by the adoption of new hypotheses. This has now been done up to second order phenomena for a quiescent ether. Thus far, however, no hypothesis has been brought forward to adapt specifically the theory of a quiescent ether to observations which have already been carried up to the third order of the aberration constant.

The first second order experiment was carried out by Michelson and Morley, and was an optical test in which the method of interference of two rays passing over paths mutually at right angles to one another was used. The apparent intent of the originators of this experiment was initially to look for a first order change in the aberration factor by means of a second order interference effect. The difficulty in reconciling the negative results of this test has, however, given rise to hypotheses involving second order dimensional factors, so that from this point of view it becomes a second order experiment. It could not, however, show a first order change in the velocity of the moving system, which latter, referred to the velocity of light, is taken as a magnitude of the first order, and hence the former change would count as a second order magnitude. In this experiment the entire system was mounted on a float so that the optical system could be rotated consecutively through all quadrants of the circle while the interference bands were being continuously observed. If now the difference in time of passage of one of the rays, say along the line of drift, and the other at right angles to it, is calculated on the basis of a moving ether, we find it to be equivalent to the time of passage over a length corresponding to a diminution of this length, in the direction of drift, proportional to the square of the aberration. Their results show that had there been an effect, it must have been probably sixteen times, certainly eight times, less than that calculated. It is understood that Morley and Miller will soon report as the result of a repetition, during the present year, of this experiment on a much larger scale, that, if there is any effect, it must be one hundred times less than the calculated value. This result is entirely consistent with a moving ether, but seemingly contradictory to a quiescent ether, as proposed by Fresnel. Apparently, then, either some condition in the fundamental hypothesis of such a medium has been overlooked, or a supplementary hypothesis must be imagined. Similar hypotheses were conceived of by both Lorentz and Fitzgerald independently, shortly after the publication of the experiments of Michelson and Morley in 1887. They assume that a contraction in the direction of motion takes place in a system moving through the ether, so that this dimension is reduced by a fraction of itself equal to one half the square of the constant of aberration. This of course, as an assumption,

title: Page:BraceStLouis1904.djvu/9