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Once grant the above definition of disease, and even the most trivial aberrations from the normal must be regarded as diseased conditions, quite irrespective of whether, when structural, they interfere with the function of the part or not.

If there are four chairs, he argued, devoted to the history of philosophy, that is to say, the minute study of all sorts of dreams and aberrations through the ages, surely there ought to be at least one to explain the formation and progress of our real knowledge?

The parallelism, which is required to avoid aberrations, otherwise introduced by the prism or grating, may often be omitted in instruments of small power.

Excessive reading of Revelation seems to have been the chief cause of the aberrations of the Minster fanatics.

The practical difficulty of constructing Gregorian telescopes of good defining quality is very considerable, because if spherical mirrors are employed their aberrations tend to increase each other, and it is extremely difficult to give a true elliptic figure to the necessarily deep concavity of the small speculum.

It is, moreover, more exactly adequate to the actual situation, for the Principe has a divine spark of patriotism yet lingering in the cinders of its frigid science, an idealistic enthusiasm surviving in its moral aberrations; whereas a great Italian critic of this decade has justly described the Ricordi as "Italian corruption codified and elevated to a rule of life."

On the north bank of the great river, lands of this sort run down the whole length of the valley, except where they are interrupted by the beds of the hill streams. The breadth of these plains is in some places very trifling, whilst in others they comprise a tract of many miles, according to the number and the height of the rocks or hills that protect them from the aberrations of the river.

Consequently the monochromatic class includes the aberrations at reflecting surfaces of any coloured light, and at refracting surfaces of monochromatic or light of single wave length.

All that at present can be attempted is, to reproduce a single plane in another plane; but even this has not been altogether satisfactorily accomplished, aberrations always occur, and it is improbable that these will ever be entirely corrected.

With a considerable aperture, the neighbouring point N will be reproduced, but attended by aberrations comparable in magnitude to ON.

In the mathematical sense, however, this selection is arbitrary; the reproduction of a finite object with a finite aperture entails, in all probability, an infinite number of aberrations.

This connexion is only supplied by theories which treat aberrations generally and analytically by means of indefinite series.

On account of the aberrations of all rays which pass through 0, a patch of light, depending in size on the lowest powers of E, x, y which the aberrations contain, will be formed in the plane I'.

The aberrations can also be expressed by means of the "characteristic function " of the system and its differential coefficients, instead of by the radii, &c., of the lenses; these formulae are not immediately applicable, but give, however, the relation between the number of aberrations and the order.

Sir William Rowan Hamilton (British Assoc. Report, 18 33, p. 360) thus derived the aberrations of the third order; and in later times the method was pursued by Clerk Maxwell (Proc. London Math.

1), who thus discovered the aberrations of the 5th order (of which there are nine), and possibly the shortest proof of the practical (Seidel) formulae.

Phys., 1905, 18, p. 941) founded his theory of aberrations on the differential geometry of surfaces.

The aberrations of the third order are: (1) aberration of the axis point; (2) aberration of points whose distance from the Aberra- axis is very small, less than of the third order - the tions of deviation from the sine condition and coma here fall together in one class; (3) astigmatism; (4) curvature of the field; (5) distortion.

The total aberration of two or more very thin lenses in contact, being the sum of the individual aberrations, can be zero.

The problem of finding a system which reproduces a given object upon a given plane with given magnification (in so far as aberrations must be taken into account) could be dealt with by means of the approximation theory; in most cases, however, the analytical difficulties are too great.

there are " chromatic differences " of the distances of intersection, of magnifications, and of monochromatic aberrations.

If, in the first place, monochromatic aberrations be neglected - in other words, the Gaussian theory be accepted - then every reproduction is determined by the positions of the focal planes, and the magnitude of the focal lengths, or if the focal lengths, as ordinarily happens, be equal, by three constants of reproduction.

The Gaussian theory is only an approximation; monochromatic or spherical aberrations still occur, which will be different for different colours; and should they be compensated for one colour, the image of another colour would prove disturbing.

von Rohr specially dealing with aberrations.

So a black whirl and torment of rapine, violence and fraud was encircling the Western world, as a life went out which, notwithstanding some eccentricities and some aberrations, had made great tides in human destiny very luminous.

If the ordinary convex lens be employed as magnifying glass, great aberrations occur even in medium magnifications.

When the pupil regulates the aperture of the rays producing the image the aberrations of the ordinary lenses increase considerably with the magnification, or, what amounts to the same thing, with the increase in the curvature of the surfaces.

To reduce the aberrations Sir David Brewster proposed to employ in the place of glass transparent minerals of high refractive index and low dispersion.

The individual components required weaker curvatures and permitted of being more correctly manufactured, and, more particularly, the advantage of reduced aberrations was the predominant factor.

By introducing a dispersive lens of flint the magnifying glass could be corrected for both chromatic and spherical aberrations.

The aberrations, both spherical and chromatic, increase very rapidly with the aperture.

Owing to these aberrations, the fine structure, which in consequence of the large aperture could be resolved, could not be perceived.

In other words, a sufficiently good and distinct image as the resolving power permits cannot be arrived at, until the elimination, or a sufficient diminution, of the spherical and chromatic aberrations has been brought about.

the spherical aberrations.

The spherical aberrations, however, can be overcome, or at least so diminished that they are quite harmless, by forming appropriate combinations of lenses.

Thus it is possible to correct a system by combining a convex and a concave lens, if both have aberrations of the same amount but of opposite signs.

A well-corrected microscope objective with a wide aperture therefore can only represent, free from aberrations, one object-element situated on a definite spot on the axis.

By experiment Abbe proved that old, good microscope objectives, which by mere testing had become so corrected that they produced usable images, were not only free from spherical aberrations, but also fulfilled the sine-condition, and were therefore really aplanatic systems.

This refers to systems with small apertures, but still more so to systems with large ones; chromatic aberrations are exceptionally increased by large apertures.

Although such systems have been made recently for special purposes, this construction was abandoned, and a more complex one adopted, which also made the production of better objectives possible; this is the principle of the compensation of the aberrations produced in the different parts of the objective.

This method makes it specially possible to overcome the chromatic and spherical aberrations of higher orders and to fulfil – the sine-condition, and the chief merit of this improvement belongs to Amici.

In the apochromats the chromatic difference of the spherical aberrations is eliminated, for the spherical aberration is completely avoided for three colours.

The definition is better according as the chromatic and spherical aberrations are removed; there always remains in even the best constructions some slight aberration.

In consequence of these residual aberrations, every object-point is not reproduced in an ideal image-point, but as a small circle of aberration.

aberrations of the spherical lenses were much reduced relative to the original design (figure 5 ).

They are good value for money but are not optically brilliant, a small aperture essential to eliminate the aberrations of the lens.

If you wish to maximize the polarization or minimize the aberrations of the TGM output this is done with this mask.

The outstanding feature, being its superb ability to correct chromatic aberrations.

aberrations associated with it being an escape from captivity.

However, no excess chromosomal aberrations in circulating human lymphocytes have been observed in patients treated for 8 months.

A typical breast cancer, for example, will have 10 to 20 chromosome aberrations.

The theoretical resolution is never obtained due to lens aberrations which are difficult to fully compensate for in electron optical systems.

The three models are summarized in Table 3.1 Table 3.1: A brief summary of the three models used for the NOT mirror aberrations.

The outstanding feature, being its superb ability to correct chromatic aberrations.

chromosome aberrations associated with the pathogenesis of this malignancy.

However, the identification of all chromosomal aberrations in a complex karyotype was often not possible from such patterns.

PFOA did not induce chromosomal aberrations in cultured human whole blood lymphocytes nor in mouse bone marrow erythrocytes.

micronucleuschromosome aberrations and micronuclei in human blood lymphocytes.

sockme psychologists explain such aberrations as being akin to the crowd behavior mechanism at work in the " bobby sox craze.

Yet no one can doubt the sincerity of her narrative, or even the permanence of her religious feelings under all her many phases of faith and aberrations of conduct.

listless and ugly, with large heads and particularly prominent ears, flat noses, tumid bellies, slender limbs and sallow complexions; the children are impregnated with malaria from their birth, and their growth is attended with aberrations from the normal which practically amount to the disease of rickets.

Once grant the above definition of disease, and even the most trivial aberrations from the normal must be regarded as diseased conditions, quite irrespective of whether, when structural, they interfere with the function of the part or not.

If there are four chairs, he argued, devoted to the history of philosophy, that is to say, the minute study of all sorts of dreams and aberrations through the ages, surely there ought to be at least one to explain the formation and progress of our real knowledge?

The parallelism, which is required to avoid aberrations, otherwise introduced by the prism or grating, may often be omitted in instruments of small power.

Excessive reading of Revelation seems to have been the chief cause of the aberrations of the Minster fanatics.

The practical difficulty of constructing Gregorian telescopes of good defining quality is very considerable, because if spherical mirrors are employed their aberrations tend to increase each other, and it is extremely difficult to give a true elliptic figure to the necessarily deep concavity of the small speculum.

This form has two distinct advantages: (I) if spherical mirrors are employed their aberrations have a tendency to correct each other; grain' (2) the instrument is shorter than the Gregorian, caeteris paribus, by twice the focal length of the small mirror.

It is, moreover, more exactly adequate to the actual situation, for the Principe has a divine spark of patriotism yet lingering in the cinders of its frigid science, an idealistic enthusiasm surviving in its moral aberrations; whereas a great Italian critic of this decade has justly described the Ricordi as "Italian corruption codified and elevated to a rule of life."

On the north bank of the great river, lands of this sort run down the whole length of the valley, except where they are interrupted by the beds of the hill streams. The breadth of these plains is in some places very trifling, whilst in others they comprise a tract of many miles, according to the number and the height of the rocks or hills that protect them from the aberrations of the river.

Reference should be made to the articles Reflexion, Refraction, and Caustic for the general characters of reflected and refracted rays (the article Lens considers in detail the properties of this instrument, and should also be consulted); in this article will be discussed the nature, varieties and modes of aberrations mainly from the practical point of view, i.e.

Aberrations may be divided in two classes: chromatic (Gr.

Xpco,ua, colour) aberrations, caused by the composite nature of ?

Ã¯¿½ovos, one) aberrations produced without dispersion.

Consequently the monochromatic class includes the aberrations at reflecting surfaces of any coloured light, and at refracting surfaces of monochromatic or light of single wave length.

All that at present can be attempted is, to reproduce a single plane in another plane; but even this has not been altogether satisfactorily accomplished, aberrations always occur, and it is improbable that these will ever be entirely corrected.

With a considerable aperture, the neighbouring point N will be reproduced, but attended by aberrations comparable in magnitude to ON.

These aberrations are avoided if, according to Abbe, the " sine condition," sin u'1/sin u, = sin u' 2 /sin u 2, holds for all rays reproducing the point O.

==Analytic Treatment of Aberrations== The preceding review of the several errors of reproduction belongs to the " Abbe theory of aberrations," in which definite aberrations are discussed separately; it is well suited to practical needs, for in the construction of an optical instrument certain errors are sought to be eliminated, the selection of which is justified by experience.

In the mathematical sense, however, this selection is arbitrary; the reproduction of a finite object with a finite aperture entails, in all probability, an infinite number of aberrations.

with each degree of approximation to reality (to finite objects and apertures), a certain number of aberrations is associated.

This connexion is only supplied by theories which treat aberrations generally and analytically by means of indefinite series.

Writing A ' = ' - 'o and 077' =7 1' - 770, then g' and 077' are the aberrations belonging to, and x, y, and are functions of these magnitudes which, when expanded in series, contain only odd powers, for the same reasons as given above.

On account of the aberrations of all rays which pass through 0, a patch of light, depending in size on the lowest powers of E, x, y which the aberrations contain, will be formed in the plane I'.

The aberrations can also be expressed by means of the "characteristic function " of the system and its differential coefficients, instead of by the radii, &c., of the lenses; these formulae are not immediately applicable, but give, however, the relation between the number of aberrations and the order.

Sir William Rowan Hamilton (British Assoc. Report, 18 33, p. 360) thus derived the aberrations of the third order; and in later times the method was pursued by Clerk Maxwell (Proc. London Math.

1), who thus discovered the aberrations of the 5th order (of which there are nine), and possibly the shortest proof of the practical (Seidel) formulae.

Phys., 1905, 18, p. 941) founded his theory of aberrations on the differential geometry of surfaces.

The aberrations of the third order are: (1) aberration of the axis point; (2) aberration of points whose distance from the Aberra- axis is very small, less than of the third order - the tions of deviation from the sine condition and coma here fall together in one class; (3) astigmatism; (4) curvature of the field; (5) distortion.

The total aberration of two or more very thin lenses in contact, being the sum of the individual aberrations, can be zero.

The problem of finding a system which reproduces a given object upon a given plane with given magnification (in so far as aberrations must be taken into account) could be dealt with by means of the approximation theory; in most cases, however, the analytical difficulties are too great.

Since the index of refraction varies with the colour or wave length of the light (see Dispersion), it follows that a system of lenses (uncorrected) projects images of different colours in somewhat different places and sizes and with different aberrations; i.e.

there are " chromatic differences " of the distances of intersection, of magnifications, and of monochromatic aberrations.

If, in the first place, monochromatic aberrations be neglected - in other words, the Gaussian theory be accepted - then every reproduction is determined by the positions of the focal planes, and the magnitude of the focal lengths, or if the focal lengths, as ordinarily happens, be equal, by three constants of reproduction.

The Gaussian theory is only an approximation; monochromatic or spherical aberrations still occur, which will be different for different colours; and should they be compensated for one colour, the image of another colour would prove disturbing.

von Rohr specially dealing with aberrations.

So a black whirl and torment of rapine, violence and fraud was encircling the Western world, as a life went out which, notwithstanding some eccentricities and some aberrations, had made great tides in human destiny very luminous.

If the ordinary convex lens be employed as magnifying glass, great aberrations occur even in medium magnifications.

When the pupil regulates the aperture of the rays producing the image the aberrations of the ordinary lenses increase considerably with the magnification, or, what amounts to the same thing, with the increase in the curvature of the surfaces.

To reduce the aberrations Sir David Brewster proposed to employ in the place of glass transparent minerals of high refractive index and low dispersion.

The individual components required weaker curvatures and permitted of being more correctly manufactured, and, more particularly, the advantage of reduced aberrations was the predominant factor.

By introducing a dispersive lens of flint the magnifying glass could be corrected for both chromatic and spherical aberrations.

The aberrations, both spherical and chromatic, increase very rapidly with the aperture.

to eliminate the spherical and chromatic aberrations, the large angular aperture of the objective, which is necessary for its resolving power, would be valueless.

Owing to these aberrations, the fine structure, which in consequence of the large aperture could be resolved, could not be perceived.

In other words, a sufficiently good and distinct image as the resolving power permits cannot be arrived at, until the elimination, or a sufficient diminution, of the spherical and chromatic aberrations has been brought about.

such different functions that as a rule it is not possible to correct the aberrations of one system by those of the other.

Consider the aberrations which may arise from the representation by a system of wide aperture with monochromatic light, i.e.

the spherical aberrations.

The spherical aberrations, however, can be overcome, or at least so diminished that they are quite harmless, by forming appropriate combinations of lenses.

Thus it is possible to correct a system by combining a convex and a concave lens, if both have aberrations of the same amount but of opposite signs.

A well-corrected microscope objective with a wide aperture therefore can only represent, free from aberrations, one object-element situated on a definite spot on the axis.

Hence the importance of observing the length of the tube in strong systems. If the sine-condition is not fulfilled but the spherical aberrations in the axis have been removed, then the image shown in fig.

If however the object-point does not lie in the medium with the index n, but before it, and the medium is, for example, like a front lens, still limited by a plane surface, just in front of which is the object-point, then in traversing the plane surface spherical aberrations of the under-corrected type again arise, and must be removed.

By experiment Abbe proved that old, good microscope objectives, which by mere testing had become so corrected that they produced usable images, were not only free from spherical aberrations, but also fulfilled the sine-condition, and were therefore really aplanatic systems.

The transverse sections of these cones of rays diverge more or less from the transverse section of the chosen blue and red cones, and produce a secondary spectrum in the image, and the images still appear to have a slightly coloured edge, mostly greenish-yellow or purple; in other words, a chromatic difference of the spherical aberrations arises (see fig.

This refers to systems with small apertures, but still more so to systems with large ones; chromatic aberrations are exceptionally increased by large apertures.

Although such systems have been made recently for special purposes, this construction was abandoned, and a more complex one adopted, which also made the production of better objectives possible; this is the principle of the compensation of the aberrations produced in the different parts of the objective.

This method makes it specially possible to overcome the chromatic and spherical aberrations of higher orders and to fulfil - the sine-condition, and the chief merit of this improvement belongs to Amici.

He used chiefly a highly curved piano-convex front lens, which has since always been employed in strong systems. Even if the object-point on the axis cannot be reproduced quite free from aberration through such a lens, because aberrations of the type of an under-correction have been produced by the first plane outer limiting surface, yet the defects with the strong refraction are relatively small and can be well compensated by other systems. Amici chiefly employed cemented pairs of lenses consisting of a plano-convex flint lens and a biconvex crown lens(fig.

Amici was likewise the first to produce practical and good immersion-systems. The slight difference of the refractive indexes of the glass cover and the immersion-liquid involves a diminution of the aberrations, by which the objective will become less sensitive to the differences in thickness of the glass covers and admits of a more perfect adjustment.

In the apochromats the chromatic difference of the spherical aberrations is eliminated, for the spherical aberration is completely avoided for three colours.

As both eyepieces are used with very small apertures (about f : 20) no attempt has been made to overcome the spherical aberrations, which are usually very slight; neither, as a rule, are the eyepieces chromatically corrected, care has only to be taken by a suitable choice of the distance of one lens from the other, that the coloured images derived from a colourless object should have the same apparent size.

The definition is better according as the chromatic and spherical aberrations are removed; there always remains in even the best constructions some slight aberration.

In consequence of these residual aberrations, every object-point is not reproduced in an ideal image-point, but as a small circle of aberration.

As soon as indiscriminant breeders started to flood the market, aberrations such as dwarfism in Toy Poodles appeared, along with a host of genetic problems that dedicated and diligent breeders are still trying to irradicate to this day.

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