This is the reason of the number of the planets;" and also of the magnitudes of their orbits.
It is obvious that the magnitude, PRT, is entirely dependent on the magnitudes of PR, and T.
The base of the whole of mathematics or rather the starting point of mathematics was “psychological truths,” axioms concerning normal numbers, and magnitudes that were tangible for the senses.
Accordingly an earth-man and a sun-man have only neglected effects whose quantitative magnitudes all contain the factor 1/10⁸.
A regular variable, [chi] Cygni, has extreme magnitudes of 5 to 13.
It is moreover clear, that the relative variations of different magnitudes connected with each other by any laws whatever are calculated, all but the characteristic, almost exactly in the same manner as the differentials.
What has been stated respecting curves may, moreover, evidently be applied to any magnitudes whatever, regarded, by the aid of suitable images, as produced by motion.
Before this first research is completed, every attempt to determine numerically the value of one of these two magnitudes from the other would evidently be premature, for it would have no basis.
Every equation of finite differences is truly, at bottom, an equation directly relating to the very magnitudes whose successive states are compared.
This consists essentially in that admirable property of the signs + and-, of representing analytically the oppositions of directions of which certain magnitudes are susceptible.
First; the magnitudes of inclosed spaces, whether superficial or solid, are completely determined by the magnitudes of the lines and angles which bound them.
Some writers have asserted that this law of nature is a mere verbal definition; that the expression "equal magnitudes" means nothing but magnitudes which can be so applied to one another as to coincide.
The equality of two geometrical magnitudescannot differ fundamentally in its nature from the equality of two weights, two degrees of heat, or two portions of duration, to none of which would this pretended definition of equality be suitable.
Of all forms of matter the gas has the simplest molecular structure, and, as might be anticipated, our knowledge of molecular magnitudes is as yet chiefly confined to materials of this class.
Here, indeed, the word "similarity" is applied to magnitudesin a sense other than to quality.
The existing differences between magnitudes do not deprive them of their property of being magnitudes, just as the difference between essences does not affect their essentiality.
If similar magnitudes be identical, we must then consider the other properties of quantity and quality which might be present in them (so as clearly to contrast their differences).
Why should we be surprised at magnitudesbeing similar to sounds, which grow weaker as their form decreases in distinctness?
If then they be differences of magnitude, the different magnitudes which are derived from differences of magnitude should be classified according to the species constituted by them (when considered in the light of being magnitudes).
Stars are, we know, of differentmagnitudes and different degrees of glory.
It is proper to remark, however, that all representations of the solar system by maps and planetariums must give an exceedingly erroneous view either of the magnitudes or distances of its various members.
The number of these asteroids increases as their magnitudes diminish; and this doubtless continues to be the case far below the limit of telescopic discovery.
This is true, not only in regard to the magnitudes and densities of the bodies composing it, but also in respect to the forms of their orbits.
This method centers the attention of the student on the relation of magnitudes represented and develops visualization.
Magnitudes must be located behind or below the drawing surface.
The use of the third angle presents new difficulties, such as that of locating the positions of magnitudes in space in relation to their projections.
These two inequalities of very different magnitudes connected with the cause which produces them by analytical combinations of totally different kinds have, however, both conducted to the same value of the ellipticity.
He also made numerous observations on the intensities and comparative magnitudes of its satellites.
On the other hand, the elaboration of artificial problems with fictitious units of measure just to have relative magnitudes as in the exercises on page 5 is a wasteful sacrifice.
All the real merit in the drills on relative magnitude advocated by Speer, McLellan and Dewey, and others can be secured without spending time in relating magnitudes for the sake of relative magnitude alone.
Here, no one of the measuring magnitudes can vanish without the tone vanishing too, and all three are so bound up together, in the single resulting sensation, that none can exist without a finite quantity of the others.
Measurement consists in a superposition of the magnitudes to be compared.
All we require is, that it shall be impossible, while the rest of space is unaffected, to alter the magnitude of any figure, as compared with other figures, while leaving the relative internal magnitudes of its parts unchanged.
And therefore that measurement, as above defined, involves, as an à priori condition, that magnitudes are unchanged by motion?
The absolute magnitudes of Metageometry, therefore, are absolute only as against any other particular magnitude, not as against other magnitudes in general.
Setting this aside, however, the problem, owing to the fact that measurement consists in superposition, becomes identical with the determination of the most general manifold in which magnitudes are independent of place.
But if "measurement consists in a superposition of themagnitudes compared" (p.
But this gives a sufficient criterion only when themagnitudes to be compared already occupy the same position.
In order, therefore, that there may be any question of rigidity or non-rigidity, the measurement of spatial magnitudes must be already possible.
In either case, what are the magnitudes to be compared?
The whole science of Dynamics, in short, is fundamentally dependent on Geometry, and but for the independent possibility of measuring spatial magnitudes, none of the magnitudes of Dynamics could be measured.
The usual photographic plates, which have their principal sensibility in the violet parts of the spectrum, give us the photographic magnitudes of the stars.
The magnitudes which have been mentioned in the preceding paragraphs all refer to observations taken with the eye, and are called visual magnitudes.
In order to make the magnitudes of the stars comparable with each other it is convenient to reduce them to their value at a certain unit of distance.
If the magnitudes are given in another scale than the Harvard-scale (H.
The magnitudes being themselves logarithms of a kind, it is evidently more convenient to use a simple value of the logarithm of the ratio of intensity than to use this ratio itself.
That both these attributes here really cooperate may be seen from the absolute magnitudes (M).
The observations of visual magnitudes are performed almost exclusively with the photometer of ZÖLLNER in a more or less improved form.
The photographic magnitudes are then unequivocally determined.
A consequence of the definition of m is that we also have to do with negative magnitudes (as well as with negative logarithms).
The apparent and the absolute magnitudes are for these stars nearly equal, the means for both been approximately 7m.
The photographic magnitudes are however not reduced for the zero-point (compare §6).
A very important, and in one respect even still more comprehensive, catalogue of visual magnitudes is the “Potsdam General Catalogue” (P.
The kinetic theory takes temperature, as well as heat itself, to be a quantity of energy, and thus seems to connect this notion with the magnitudes of mechanics.
But even when we suppose that some magnitudes can never be connected with mass, length, and time, it still holds a preponderating place, and its progress finds an echo throughout the whole domain of the natural sciences.
They study the various magnitudesdirectly accessible to their observation without busying themselves as to their essence.
There were thus discovered, by translating the principle of equivalence, numerical relations between the magnitudes of electricity, for instance, and the magnitudes of mechanics.
They content themselves with representing phenomena by equations, and think that they ought to submit to calculation magnitudes experimentally determined, without asking themselves whether these calculations retain a physical meaning.
Magnitudes to which we attribute like dimensions may be qualitatively irreducible one to the other.
It is not easy to see how, on the theory of the quantity law, such a report could affect very rapidly the magnitudes on which the value of the note is supposed to depend, viz.
I do not accept his conclusions with reference to the magnitudes of V, the velocity of money, partly because I do not accept his doctrine that "banks are the home of money" (p.
The effort has also been made to determine the magnitudes of banking transactions, and the relation of banking transactions to the volume of trade.
The utility theory, as will appear in the chapter on "Marginal Utility," has failed to give psychological magnitudes corresponding to any point on the demand-curve.
The value-scales, and the absolute magnitudes of value at different points on the scale, are assumed, are data.
The price-level is always effect, and never cause (with slight modifications of the doctrine for transition periods) in its relations to the other magnitudes in the equation of exchange.
In no other way can the price-level of the United States be prevented from rising above that of other nations in which we have assumed this level and the other magnitudes in the equation of exchange to be quiescent.
But, while the pecuniary magnitudes of organized speculation in New York are very great, the range of items dealt in is restricted.
The absolute magnitudes of the elements in the equation of exchange he was not trying to measure.
He finds other condensations of stars; the nearest is one of which our sun is a member, chiefly composed of stars of the higher magnitudes which "thin out rapidly as the Milky Way is approached.
There are other condensations: one in stars of magnitudes 6.
The Harvard photometric measures make it nearly one magnitude brighter than the zero magnitude, about twomagnitudes brighter than Aldebaran, and about half the brightness of Sirius.
But he seems to have accepted Al-Sufi's star magnitudes without any attempt at revision.
This seems supported by Sir John Herschel's observations in the southern hemisphere, where he found in some places "a tissue as it were of large stars spread over another of very small ones, the immediate magnitudes being wanting.
The star [Greek: k] Toucani is a binary star with components of magnitudes 5 and 7.
In the preface to his translation of Al-Sufi's work, Schjellerup mentions some remarkable discrepancies between the magnitudes assigned to certain stars by Ptolemy and Argelander.
Al-Sufi's star magnitudes (tenth century) with modern estimates and measures, tend strongly to confirm the above views.
This is unfortunate, for an independent estimate of star magnitudes made in the fifteenth century would now be very valuable for comparison with Al-Sufi's work and with modern measures.
The scale of the magnitudes is quite arbitrary, but by means of photometers, the classification has been made to tenths of a magnitude.
Vectors are said to be equal when their directions are the same their magnitudes equal.
Defn: A method of analysis developed by Newton, and based on the conception of all magnitudes as generated by motion, and involving in their changes the notion of velocity or rate of change.
This was expressed by D'Alembert in the eighteenth century as "Magnitudes which are the limits of equal magnitudes are equal," or this in substance.
It defines what is meant by saying that magnitudes are in the same ratio; in other words, it defines a proportion.
Let magnitudes which have the same ratio be called proportional.
An acute angle is defined as "an angle less than a right angle," and is considered as positive under the general understanding that all geometric magnitudes are positive unless the contrary is stated.
The second definition is intended to exclude zero and infinite magnitudes, and to show that incommensurable magnitudes are included.
Magnitudes are said to have a ratio to one another which are capable, when multiplied, of exceeding one another.
He, for example, proves that "If fourmagnitudes be proportional, they will also be proportional alternately.
These entered into such propositions as, "If four magnitudes are proportional, they will also be proportional alternately.
It should be said, however, that it is scientifically correct, that it covers the case of incommensurablemagnitudes as well as that of commensurable ones, and that it is the Greek forerunner of the modern theories of irrational numbers.
The following four definitions from Euclid are the basal ones of the ancient theory: A ratio is a sort of relation in respect of size between two magnitudes of the same kind.
In the latter method the investigation usually concerns the magnitudes of A, which are independent of dispersion.
Thus, for instance, in the case of naphthalene the calculated and observed magnitudes of the heat of solution differ but slightly from each other.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "magnitudes" in a variety of sentences. We hope that you will now be able to make sentences using this word.
