Resolving Sentence Examples

While Martha was as upset as Betsy and I, she wanted no part in resolving the matter.

The best general method of calculating logarithms consists, in its simplest form, in resolving the number whose logarithm is required into factors of the form I - i r n, where n is one of the nine digits, and making use of subsidiary tables of logarithms of factors of this form.

Soon after the introduction of the literary journal in England, one of a more familiar tone was started by the eccentric John Dunton in the Athenian Gazette, or Casuistical Mercury, resolving all the most Nice and Curious Questions (1689-1690 to 1695-1696), afterwards called The Athenian Mercury, a kind of forerunner of Notes and Queries, being a penny weekly sheet, with a quarterly critical supplement.

A prism or a train of prisms. These are employed in instruments of small power, especially when luminosity is a consideration; but their advantage in this respect is to a great extent lost, when, in order to secure increased resolving power, the size of the prisms, or their number, is unduly increased.

The optical effect as regards resolving power is the same as with a grating of N lines in the nth order, but, nearly all the light not absorbed by the glass may be concentrated in one or two orders.'

The power of a spectroscope to perform its main function, which is to separate vibrations of different but closely adjacent frequencies, is called its " resolving power."

We may say therefore that if the difference between the frequencies n 1 and n, of the two waves is such that in the combined image of the slit the intensity at the minimum between -the two maxima falls to 0.81, the lines are just resolved and n l /(n l n 2) may then be called the resolving power.

Lord Rayleigh's expression for the resolving power of different instruments is based on the assumption that the geometrical image of the slit is narrow compared with the width of the diffraction image.

Unfortunately considerations of luminosity compel the observer often to widen the slit much beyond the range within which the theoretical value of resolving power holds in practice.

With an indefinitely narrow slit the purity is equal to the resolving power.

As purity and resolving power are essentially positive quantities, n i in the above expression must be the greater of the two frequencies.

If we write P=p R where P denotes the purity and R the resolving power, we may call p the " purityfactor.

With a slit equal in width to eight times the normal one the purity is reduced to o 45R, so that we lose rather more than half the resolving power and increase the light 3.7 times.

It follows that for observations in which light is a consideration spectroscopes should be used which give about twice the resolving power of that actually required; we may then use a slit having a width of nearly eight times that of the normal one.

Theoretical resolving power can only be obtained when the whole collimator is filled with light and further (as pointed out by Lord Rayleigh in the course of discussion during a meeting of the " Optical Convention " in London, 1905) each portion of the collimator must be illuminated by each portion of the luminous source.

Every observer should not only record the resolving power of the instrument he uses, but also the purity-factor as defined above.

The resolving power in the case of gratings is simply mn, where m is the order of spectrum used, and n the total number of lines ruled on the grating.

In the case of prisms the resolving power ist (dµ/dX), where t is the effective thickness of the medium traversed by the ray.

In interpreting the phenomena observed in a spectroscope, it is necessary to remember that the instrument, as pointed out by Lord Rayleigh, is itself a producer of homogeneity within the limits defined by its resolving power.

He carried metaphysical idealism to its height, by not only resolving the bodily into the mental, but also elevating the action of mind into absolute mental construction; not inferring things in themselves beyond, but originating things from within, mind itself.

Hegel only extended a priori forms to things by resolving things into thoughts.

They raised him on a shield and acclaimed him as a king; leader and followers both resolving (says Jordanes the Gothic historian) "rather to seek new kingdoms by their own labour, than to slumber in peaceful subjection to the rule of others."

Aristotle had fallen into the paradox of resolving a mental act into verbal elements.

Resolving AA,

Resolving horizontally we find T (COS 02 - COS 01)+2gp (y22-3/12) =0, whence cos 02 = COS gpy12 - gpy22, 2T 2 T or if we suppose P 1 fixed and P2 variable, we may write cos constant - Zgpy2/T.

Resolving vertically we find that the weight of the liquid raised above the level must be equal to T(sin 0 2 - sin 01), and this is therefore equal to the area P 1 P 2 A 2 A 1 multiplied by gp. The form of the capillary surface is identical with that of the " elastic curve," or the curve formed by a uniform spring originally straight, when its ends are acted on by equal and T 2 opposite forces applied either to the ends themselves or to solid pieces attached to them.

Since the two circular streams have different speeds, Fresnel argued that it would be possible to separate them by oblique refraction, and though the divergence is small, since the difference of their refractive indices in the case of quartz is only about o 00007, he succeeded by a suitable arrangement of alternately rightand left-handed prisms of quartz in resolving a plane-polarized stream into two distinct circularly polarized streams. A similar arrangement was used by Ernst v.

The lower limit of the resolving power of the eye is reached when the distance is approximately 3438 times the size of the object.

This expresses I as the resolving power in the case of direct lighting.

It is possible to almost double the resolving power, as in the case FIG.

To determine the utility of an' objective for resolving fine details, one experiments with definite objects, which are usually employed simultaneously for examining its other properties.

The Fraunhofer formula permits the determination of the most useful magnification of such an objective in order to utilize its full resolving power.

The table shows at the same time the great superiority of the immersion-system over the dry-system with reference to the resolving power.

The smallest resolving detail with oblique lighting is 6 =A/ 2A, where A = 275 µµ.

As the microscopist usually estimates the resolving power according to the aperture with ordinary day-light, Kohler introduced the " relative resolving power " for ultra-violet light.

Then the denominator of the fraction, the numerical aperture, must be correspondingly increased, in order to ascertain the real resolving power.

If the magnification be greater than the resolving power demands, the observation is not only needlessly made more difficult, but the entrance pupil is diminished, and with it a very considerable decrease of clearness, for with an objective of a certain aperture the size of the exit pupil depends upon the magnification.

From the section Regulation of the Rays (above) it is seen that the resolving power is opposed to the depth of definition, which is measured by the reciprocal of the numerical aperture, I/A.

By dark-field illumination it is even possible to make such small details of objects perceptible as are below the limits of the resolving power.

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 resolving power of an objective depends on its numerical aperture.

If the numerical aperture be known the resolving power is easily found.

The resolving power can also be determined by using different fine test objects.

Even if a mixture of several oils and fats be present, the iodine value assists greatly in the identification of the components of the mixture, and furnishes the most important key for the attacking and resolving of this not very simple problem.

Resolving the VAT anomaly remains the most obvious means of promoting more sustainable approaches to the housing stock.

This effect means that abreaction starts forcing his problems into his everyday awareness and drives him to seek ways of resolving them.

We must work at resolving these conflicts or finding a way through.

Further, we introduce a flexible approach to resolving non- determinism which gives this translation a practical advantage.

All costs of resolving the disagreement must be paid by the party whose argument is rejected.

Completion of the changeover would have many benefits in addition to resolving the current muddle.

We have always been told retaliation is not the key to resolving problems.

See the -R name resolve order parameter for details on changing this resolving mechanism.

Chris McGreal outlines the crisis facing Hamas as it attempts to find a way of resolving the standoff in Gaza.

The selection stage should give the user as much help as possible in resolving this uncertainty.

They are utterly useless for resolving any connection problems.

Resolving to devote himself and his means wholly to the advancement of Christianity, his first proposal for that end, made in 1796, was to organize a vast mission to Bengal, of which he was, to provide the entire expense; with this view the greater part of his estate was sold, but the East India Company refused to sanction the scheme, which therefore had to be abandoned.

The peculiar art therein is that while the discords owe their intelligibility and softness to the smooth melodic lines by which in " resolving " they prove themselves but transient rainbow-hues on or below the surface, they owe their strangeness to the intense vividness with which at the moment of impact they suggest a mysteriously remote foreign key.

This latter class he discussed so assiduously that they are often known as Diophantine problems, and the methods of resolving them as the Diophantine analysis (see Equation, Indeterminate).

Our investigations and estimates of resolving power have thus far proceeded upon the supposition that there are no optical imperfections, whether of the nature of,, a regular aberration or dependent upon irregularities of material and workmanship. In practice there will always be a certain aberration or error of phase, which we may also regard as the deviation of the actual wavesurface from its intended position.

The resolving power and the width of the emergent beam fix the optical character of the instrument.

The gods are represented as resolving to banish from the heavens the constellations, which served to remind them of their evil deeds.

Starting with the exact equations of motion in a resisting medium, (43) d2t cos i = ds, d 2 y d 44 dt2 = -r sin i-g= -rds-g, and eliminating r, (45) dt - - cos z, or the equation obtained, as in (18), by resolving normally in the trajectory, but di now denoting the increment of i in the increment of time dt.

The sensitive vane or strip may then be placed behind the slit; its width will not affect the resolving power though there may be a diminution of sensitiveness.

Pierre unfolded his cold table napkin and, resolving to break the silence, looked at Natasha and at Princess Mary.

We only accept political and diplomatic ways of resolving existing disagreements.

In the past, wireless adapters used a single antenna for input and a single antenna for output, resolving only one stream of each at a time, and improvements involved more powerful antennae for more efficient processing.

Resolving identity theft may take months or years.

The good news is that identity theft victims are becoming more savvy and are generally catching the problem quicker, which decreases the amount of time they spend resolving the problem.

Study and education is a good approach to resolving the question, what is joint custody?

Disagreements come up in all relationships, but co-parenting can present even more difficulties in resolving the conflicts.

Apologizing is always a great first step in resolving a conflict, especially if the discussion degenerated into personal attacks.

In this way, a person can use their anger as a tool for protecting their interests and resolving problems, rather than simply making a situation worse.

In addition, counseling can help you find better ways of resolving problems by communicating more directly and constructively and by being assertive rather than aggressive.

This website offers a wealth free dog training tips about basic manners, preventing and resolving behavioral issues, and other information useful to dog owners.

A solid foundation of good nutrition is the first step in preventing and resolving many health issues such as food allergies.

It is normally a time-limited condition with manifestations arriving almost immediately after the appearance of the pressure-causing event and resolving within six months of the elimination of the stressor.

Treatment of rashes focuses on resolving the underlying disorder and providing relief of the itching that often accompanies them.

These exercises are designed to increase bladder capacity but are only successful in resolving bed-wetting in a small number of patients.

These skills are crucial in initiating and maintaining relationships and in resolving conflicts.

As they grow, the ureter lengthens, changing its angle of entry into the bladder and resolving the reflux.

Recurring nightmares may indicate an ongoing problem that the child is having difficulty resolving.

If there is an underlying cause, such as unhappiness at home, then resolving the underlying problem usually resolves the stealing behavior, although the stealing itself should never be ignored.

An individual who dealt with a similar problem one time rather than having a history of success resolving the issue.

Depending upon the size and structure of your company, the human resources manager may also be able to provide assistance in resolving the issue.

By resolving potential difficulties prior to approaching a lender, any mortgage can be made easier.

The struggle between good and evil is also very clear in kids' movies, with the movie's villains typically being thwarted and the protagonist resolving all or most of the story's problems.

Getting help is the first step to resolving karmic entanglement and elevating your soul toward true enlightenment, not only in this life but also in your future lives to come.

Thank you again for your help in resolving this issue so quickly.

This includes resolving consumer complaints, offering qualifying businesses BBB accreditation, and educating consumers about new or existing scam risks.

No load life insurance provides the comfort many families need for less, resolving a long-standing problem for people who need the maximum amount of coverage at a reasonable rate.

In addition, Progressive has claims offices available in each state which make it easy for you to get immediate assistance in resolving claims issues.

It is necessary to notice, however, that although the general course of the stream of life is certain, there is not the same certainty as to the actual individual pedigrees of the existing forms. In the attempts to place existing creatures in approximately phylogenetic order, a striking change, due to a more logical consideration of the process of evolution, has become established and is already resolving many of the earlier difficulties and banishing from the more recent tables the numerous hypothetical intermediate forms so familiar in the older phylogenetic trees.

She, resolving to apply the remedy for his grief, questions him for that purpose.

The middle element alone contributes without deduction; the effect of every other must be found by introduction of a resolving factor, equal to cos 0, if 0 represent the difference of phase between this element and the resultant.

The contraction of the diffraction pattern with increase of aperture is of fundamental importance in connexion with the resolving power of optical instruments.

The actual finiteness of A imposes a limit upon the separating or resolving power of an optical instrument.

The reason of the augmentation of resolving power with aperture will now be evident.

The definition of a fine vertical line, and consequently the resolving power for contiguous vertical lines, is thus independent of the vertical aperture of the instrument, a law of great importance in the theory of the spectroscope.

The resolving power of a telescope with circular or rectangular aperture is easily investigated experimentally.

Merely to show the dependence of resolving power on aperture it is not necessary to use a telescope at all.

In estimating theoretically the resolving power on a double star we have to consider the illumination of the field due to the superposition of the two independent images.

The statement of the law of resolving power has been made in a form appropriate to the microscope, but it admits also of immediate application to the telescope.

If 2R be the diameter of the objectglass and D the distance of the object, the angle subtended by AP is E/D, and the angular resolving power is given by X/2 D sin a = X/2 R (3) This method of derivation (substantially due to Helmholtz) makes it obvious that there is no essential difference of principle between the two cases, although the results are conveniently stated in different forms. In the case of the telescope we have to deal with a linear measure of aperture and an angular limit of resolution, whereas in the case of the microscope the limit of resolution is linear, and it is expressed in terms of angular aperture.

The visibility of a star is a question of brightness simply, and has nothing to do with resolving power.

Throughout the operation of increasing the focal length, the resolving power of the instrument, which depends only upon the aperture, remains unchanged; and we thus arrive at the rather startling conclusion that a telescope of any degree of resolving power might be constructed without an object-glass, if only there were no limit to the admissible focal length.

As the minimum focal length increases with the square of the aperture, a quite impracticable distance would be required to rival the resolving power of a modern telescope.

A rotation of this amount should therefore be easily visible, but the limits of resolving power are being approached; and the conclusion is independent of the focal length of the mirror, and of the employment of a telescope, provided of course that the reflected image is seen in focus, and that the full width of the mirror is utilized.

We will now consider the important subject of the resolving power of gratings, as dependent upon the number of lines (n) and the order of the spectrum observed (m).

According to our former standard, this gives the smallest difference of wave-lengths in a double line which can be just resolved; and we conclude that the resolving power of a grating depends only upon the total number of lines, and upon the order of the spectrum, without regard to any other considerations.

It is especially to be noticed that the resolving power does not depend directly upon the closeness of the ruling.

There will be destruction by interference of the first, third and odd spectra generally; while the advantage gained in the spectra of even order is not in dispersion, nor in resolving power, but simply in brilliancy, which is increased four times.

If we now suppose half the grating cut away, so as to leave 1000 lines in half an inch, the dispersion will not be altered, while the brightness and resolving power are halved.

There is clearly no theoretical limit to the resolving power of gratings, even in spectra of given order.

But it is possible that, as suggested by Rowland,' the structure of natural spectra may be too coarse to give opportunity for resolving powers much higher than those now in use.

In the above discussion it has been supposed that the ruling is accurate, and we have seen that by increase of m a high resolving power is attainable with a moderate number of lines.

All the errors, except that depending on a, and especially those depending on -y and S, can be diminished, without loss of resolving power, by contracting the vertical aperture.

This is proved by taking the two points A and B in the same vertical line, and considering the equilibrium of the prism by resolving vertically.

Certain classes of names being explained in this way, legitimate and fairly reliable conclusions can be drawn for many others belonging to the same class or group. The proper names of the numerous business documents of the Khammurabi period, when phonetic writing was the fashion, have been of special value in resolving doubts as to the correct reading of names written ideographically.

This blow probably decided his career; but he endured two years of misery and mental conflict before resolving to abandon his medical studies and become a monk.

Resolving normally in the trajectory, and supposing the resistance of the air to act tangentially, (18) v(di/dt) =g cos i, where di denotes the infinitesimal decrement of i in the infinitesimal increment of time dt.