On the other hand, how could Alex be a positive influence if his Uncle truly felt that way?
Alex said it might not have made any difference, and reminded her that she needed to think positive.
Think positive, and pray.
Think of something else - something positive.
On the positive side, at that rate their conversation should be over by five minutes after nine.
I'm sorry I'm so positive about this.
I was so positive it was impossible.
Are we positive we've got this right?
Even Quinn showed more positive emotion than previously expressed.
We crammed in five sessions with three positive achievements, a new record.
We constantly longed to follow up on our endeavors and make sure what Howie discovered was brought to a positive conclusion.
Only a few flying saucer advocates spoke from the fringes with a positive slant.
I was pleased our conversation at least ended on a positive note.
She was positive she'd be lost for life.
While I knew we were helpless to do anything positive in Howie's absence, I never-the-less opened the site where Betsy located cases for our attention.
While she was concerned about the rift in our associates' relationship, she felt Quinn and Howie getting together might produce some positive results, in spite of how acrimonious they might be to each other.
"The command center," I said, possessing an over whelming need to do something tangible or at least be where positive attempts were undertaken.
I resolved to remain calm for her sake and talked of nothing but positive certainty of our escape.
The massive vamp hadn't attacked or turned his back at the first sight of him, a sign Jule took as positive.
But I thought you were positive it was Fitzgerald who switched the bones.
While he was thrilled that Dean might now be running unopposed, he was positive Lydia had killed her boss.
His logic and acceptance of the deformity was amazingly positive and mature for a 9-year-old.
She had to adopt a positive attitude.
I'm positive she didn't notice us the first time.
I was positive all she did was substitute a different one for each letter in the alphabet.
She lacks any kind of positive self-image.
First and foremost was an overwhelming urge to punch his lights out but past similar responses hadn't produced positive results.
I didn't say anything to Weller 'cause he's so positive everything is all wrapped up and tied with a bow, but I knew you and me would want to make double-dipped sure.
I don't see how noticing a different color ink on Shipton's check made you so positive you set off after him the way you did.
Positive. She smelled amazingly human, only more so.
No. Just the opposite, but it's too early to be positive.
At first everyone was positive he'd taken a hike, but personally, I haven't seen a thing yet to tell me he didn't just do something stupid and pay the price for it.
Dean wanted to be positive the son of a bitch was dead so he could have his wife; admit it, it was as simple as that.
Dean reiterated the obvious—Burgess was less than positive and the picture he sort-of identified was years old.
We still have to wait a little while and there are lots of details to iron out, but Ms. Rosewater says it looks positive.
Now, the way I see it, there's three ways to prove Byrne's alive—fingerprints, positive ID, or handwriting.
I never could understand how Winston was so positive the person you were following was Jeff when you knew all along it was that other horrid man.
I was just thinking that you've had a decidedly positive influence on me.
It wouldn't hurt to adopt a more positive outlook.
Her answer came swift and positive.
But Vico maintained that the one was continually progressing towards the other, positive law showing an increasing tendency to draw nearer to natural and rational law.
This is the moment to examine whether there is a more complete polarization in a direction somewhat oblique; and it is found that with 0 positive there is, in fact, a direction of more complete polarization, while with 0 negative the polarization is more imperfect than in the perpendicular direction itself.
"Tetrahedral co-ordinates" are a system of quadriplanar co-ordinates, the fundamental planes being the faces of a tetrahedron, and the co-ordinates the perpendicular distances of the point from the faces, a positive sign being given if the point be between the face and the opposite vertex, and a negative sign if not.
Hard on this came the recognition of the fact that freely charged positive and negative ions are always present in the atmosphere, and that a radioactive emanation can be collected.
In dry weather the electric potential in the atmosphere is normally positive relative to the earth, and increases with the height.
The largest positive and negative values recorded are met with during disturbed weather.
a negative charge is lost much faster than a positive charge.
The air, as is now known, has always present in it ions, some carrying a positive and others a negative charge, and those having the opposite sign to the charged body are attracted and tend to discharge it.
A cylinder condenser has its inner surface insulated and charged to a high positive or negative potential.
The volume of air from which the ions have been extracted being known, a measure is obtained of the total charge on the ions, whether positive or negative.
I + is used to denote the charge on positive ions, I_ that on negative ions.
A diminution in the number of positive ions would thus naturally be accompanied by a rise in potential gradient.
the velocities in unit field-he takes to be 1 3 X300 for the positive, and I.
The positive and ation.
That great separation of positive and negative electricity sometimes takes place during rainfall is undoubted, and the charge brought to the ground seems preponderatingly negative.
The difficulty is in accounting for the continuance in extensive fine weather districts of large positive charges in the atmosphere in face of the processes of recombination always in progress.
Wilson supposes that by the fall to the ground of a preponderance of negatively charged rain the air above the shower has a higher positive potential than elsewhere at the same level, thus leading to large conduction currents laterally in the highly conducting upper layers.
The colour and appearance differ in the two cases, red predominating in a positive, blue in a negative discharge.
Positive law, at least in progressive societies, is constantly tending to fall behind public opinion, and the expedients adopted for bringing it into harmony therewith are three, viz, legal fictions, equity and statutory legislation.
The explorations conducted in 1905 added positive evidence.
In pure algebra Descartes expounded and illustrated the general methods of solving equations up to those of the fourth degree (and believed that his method could go beyond), stated the law which connects the positive and negative roots of an equation with the changes of sign in the consecutive terms, and introduced the method of indeterminate coefficients for the solution of equations.'
Thereupon the power of church and state enforced by positive enactments the passive resistance of old institutions to the novel theories.
Borelli (1608-1679) as its most notable name, entered in a way on the mechanical study of anatomy suggested by Descartes, but was probably much more dependent upon the positive researches of Galileo.
The "immediate object of theological knowledge is the faith of the community," and from this positive religious datum theology constructs a "total view of the world and human life."
A few instances will illustrate Ritschl's positive systematic theology.
But a positive identity of pitch cannot be claimed for any period of time, and certainly not for the early organs; the foot-rule of the organ-builder, which had to do with the lengths of the pipes, and which varied in every country and province, could easily cause a difference of a semitone.
Napier uses abundantes and defectivae for positive and negative, defining them as meaning greater or less than nothing ("Abundantes sunt quantitates majores nihilo: defectivae sunt quantitates minores nihilo").
Strictly speaking, therefore, the Sabbath was neither a day of relief to toiling humanity nor a day appointed for public worship; the positive duties of its observance were to wear one's best clothes, eat, drink and be glad (justified from Isa.'viii.
He does not use this general anticipation of future judgment, as he might have done, as a positive argument for immortality.
Cromwell was essentially a conservative reformer; in his attempts to purge the court of chancery of its most flagrant abuses, and to settle the ecclesiastical affairs of the nation, he showed himself anxious to retain as much of the existing system as could be left untouched without doing positive evil.
For working " double current," two sets of accumulators are provided, one set to send the positive and the other set the negative currents; that is to say, when, for example, a double current Morse key is pressed down it sends, say, a positive current from one set, but when it is allowed to rise to its normal position then a negative current is transmitted from the second set of accumulators.
the working of several instruments from one set of batteries or accumulators, is adopted, the positive and negative currents have to be sent from independent batteries, as shown by fig.
Suppose the arm c of the switch S to be in contact with 2; thin when the key is manipulated it sends alternately positive and negative currents into the line.
If the positive is called the signalling current, the line will be charged positively each time a signal is sent; but as soon as the signal is completed a negative charge is communicated FIG.
Thus for a dot, first a negative and then a positive current is sent to the line, the effect of the current continuing during the time required for the paper to travel the space between two holes.
Thus for a dash the interval between the positive and the negative current is equal to the time the paper takes to travel over twice the space between two successive holes.
In the raised position a negative battery is connected to the distributor and in the depressed position a positive battery.
In the Rowland multiple method of telegraphic working, the transmitter consists of a mechanical keyboard provided with a series of levers, which effect certain combinations of positive and negative currents for each letter.
Each transmitter is therefore able to transmit a separate series of positive and negative currents in different combinations; these are distributed, by suitably arranged distributors and relays at the receiving end of the line, into their respective receivers.
The function of the " combiner " in each receiving instrument is so to group the received combination of positive and negative currents that they operate polarized relays in such a manner that the position of the tongues corresponds with the operation of the levers on the transmitter.
Since each letter is represented by a specific combination of positive and negative currents, it is possible, by means of the combinations, to close a local circuit at any given interval, and so cause the paper to be pressed against the periphery of the type-wheel at the time when the letter required is opposite.
At the sending station one battery was to have its positive pole connected to the earth and its negative pole to an insulated condenser.
The electric arc is formed between cooled copper (positive) and carbon (negative) electrodes in an atmosphere of hydrogen or coal-gas.
The four telephones on a circuit are so wired that the relays 9-- P ..,, connect two of the bells between each wire and fl-- 0 7-..9 *"y earth, and further that one of each pair of bells responds to positive and the other to negative o-- pulsations.
This system of course requires that the exchange equipment shall include machines _ capable of delivering a positive pulsating current and a negative pulsating current, besides the usual alternations required for the ringing of ordinary subscribers.
The banner of the church waves above the camp of those who aim at positive prosperity and republican equality.
(2) In the 19th century theism is generally used of positive belief in God, either with or without belief in the claim of Christianity to be a revelation, but unassociated with any peculiarities of 18thcentury deists.
If the word " deism " emphasizes a negative element - rejection of church Christianity - " theism " generally emphasizes the positive element - belief in God.
Zwingli and Calvin on the other hand prefer the positive view of law as instituted by God far back in history in the days of the Old Covenant; but,, when exegesis or controversy puts pressure upon them, they fall into line and reiterate the appeal to a Natural Law.
The good man is the perfectly rational or perfect self-consistent man; and that is a full account of virtue, though Kant professes to re-interpret it still further in a much more positive sense as implying the service of humanity.
Hegel offers a supposed proof that Time and Space, Matter, Nature, are ascertainable and definable 2 This is Kant's positive refutation of Hume's scepticism.
And there was the positive ethical element in Kant's theism.
The evolution of mind (the positive pole) proceeds by 1 Kant calls the doctrine of the transmutation of species " a hazardous fancy of the reason."
We may here quote Newton (Encyclopaedia Britannica, 9th ed., " Birds," p. 738) on the remarkable differences between this region and the rest of the Old World: - " The prevalent zoological features of any Region are of two kinds - negative and positive.
But the positive characteristics of the region as a whole are not its peculiar forms alone; there are at least four families which, being feebly represented elsewhere, here attain the maximum of development.
Of the same school were Menahem ben Simeon of Posquieres, a commentator, who died about the end of the 12th century, and Moses ben Jacob of Coucy (13th century), author of the Semag (book of precepts, positive and negative) a very popular and valuable halakhic work.
But we see no sign of the growth of a body made up of patricians and leading plebeians who contrived to keep office to themselves by a social tradition only less strong than positive law.
Schleiermacher rejects natural religion in favour of the positive religions, while the school of A.
The economic and moral condition of the peasantry was little improved by freedom, and in many districts there were signs of positive impoverishment and demoralization.
By this positive enactment all the high places outside the one sanctuary in Jerusalem became illegitimate.
Indeed, as one of the acutest and most sympathetic of his critics has remarked, the deep and settled grudge he has betrayed towards every form of Christian belief, in all the writings of his maturity, may be taken as evidence that he had at one time experienced in his own person at least some of the painful workings of a positive faith.
In 1869 he gave a course of lectures at Harvard on the Positive Philosophy; next year he was history tutor; in 1871 he delivered thirty-five lectures on the Doctrine of Evolution, afterwards revised and expanded as Outlines of Cosmic Philosophy (1874); and between 1872 and 1879 he was assistant-librarian.
The chemical symbols stand for quantities measured in grammes, and heat-evolution is reckoned as positive, heat-absorption as negative.
This heat of formation, like that of most hydrocarbons, is comparatively small: the heat of formation of saturated hydrocarbons is always positive, but the heat of formation of unsaturated hydrocarbons is frequently negative.
When substances readily combine with water to form hydrates, the heat of solution in water is usually positive; when, on the other hand, they do not readily form hydrates, or when they are already hydrated, the heat of solution is usually negative.
Hence, in the absence of more complete external evidence one is obliged to recognize the limitations of Old Testament historical criticism, even though this recognition means that positive reconstructions are more precarious than negative conclusions.
A priori considerations suggest that they may have been akin to the Siceli, but of this at present no positive evidence can be given.
But there is positive evidence that much of the north and east of Asia has been land since the Palaeozoic era, and it has been conclusively proved that the peninsula of India has never been beneath the sea since the Carboniferous period at least.
Any general statement as to the debt owed by early European civilizations to western Asia would at present be premature, for though important discoveries have been made in Crete and Babylonia the best authorities are chary of positive conclusions as to the relations of Cretan civilization to Egypt and Babylonia.
Such was Mirabeau's programme, from which he never diverged, but which was far too statesmanlike to be understood by the poor king, and far too positive regarding the altered condition of the monarchy to be palatable to the queen.
Not that this date rests on positive evidence.
It is in the adaptation of biological conceptions and methods, in the positive contributions of jurisprudence, law and history, in the rigorous application, where possible, of quantitative tests, that the explanation of the present position of economics is to be found.
He then draws a positive demonstration of the truth of his religion from the effects of the new faith, and especially from the excellence of its moral teaching, and concludes with a comparison of Christian and Pagan doctrines, in which the latter are set down with naïve confidence as the work of demons.
that it is the first positive pedal of a rectangular hyperbola with regard to the centre.
The same name is also given to the first positive pedal of any central conic. When the conic is a rectangular hyperbola, the curve is the lemniscate of Bernoulli previously described.
Von Hartmann thus combines "pantheism" with "panlogism" in a manner adumbrated by Schelling in his "positive philosophy."
The positive aspect is presented in the third clause.
" The question can be stated fairly as depending on a balance of evidence, a certain amount of positive evidence in favour of miracles, and a negative presumption from the general course of human experience against them " (Essays on Religion, p. 221).
The existence of " a certain amount of positive evidence in favour of miracles " forbids the sweeping statement that miracles are " contrary to experience."
Some positive idea of his speculations may be derived from two of his observations: the one in which he notices that the parts of animals and plants are in general rounded in form, and the other dealing with the sense of hearing, which, in virtue of its limited receptivity, he compares ' If this be the proper translation of Aulus Gellius, Noctes Atticae, x.
3: though a man have the great good fortune to live long and to have many children, yet, if he have not proper burial the blank darkness of an untimely birth is better than he: this latter is merely the negation of existence; the former, it appears to be held, is positive misfortune, the loss of a desirable place in Sheol, though elsewhere (ix.
7); its positive assertion is not in accord with the doubt expressed in iii.
at Paris and Leiden, are quite dissimilar from the Latin works attributed to Geber, and show few if any traces of the positive chemical knowledge, as of nitric acid (aqua dissolutiva or fortis) or of the mixture of nitric and hydrochloric acids known as aqua regis or regia, that appears in the latter.
From the behaviour of substances on electrolysis he assumed that all substances had two components, one bearing a negative charge, the other a positive charge.
For example, positive iron combined with negative oxygen to form positive ferrous oxide; positive sulphur combined with negative oxygen to form negative sulphuric acid; positive ferrous oxide combined with negative sulphuric acid to form neutral ferrous sulphate.
Those elements which are disengaged at the negative pole are termed electro-positive, or positive, or basylous elements, whilst those disengaged at the positive pole are termed electro-negative, or negative, or chlorous elements.
The following, however, are negative towards the remaining elements which are more or less positive:-Fluorine, chlorine, bromine, iodine, oxygen, sulphur, selenium, tellurium.
The tendency of positive elements to unite with positive elements, or of negative elements to unite with negative elements, is much less than that of positive elements to unite with negative elements, and the greater the difference in properties between two elements the more powerful is their affinity for each other.
Thus, the affinity of hydrogen and oxygen for each other is extremely powerful, much heat being developed by the combination of these two elements; when binary compounds of oxygen are decomposed by the electric current, the oxygen invariably appears at the positive pole, being negative to all other elements, but the hydrogen of hydrogen compounds is always disengaged at the negative pole.
The affixes -ous and sub- refer to the compounds containing more of the positive element, -ic and per- to those containing less.
Klaproth in 1799, is obtained when pure carbon (graphite or charcoal) is oxidized by alkaline permanganate, or when carbon forms the positive pole in an electrolytic cell (Ber., 1883, 16, p. 1209).
In the effort to reduce the practice of economy to a fine art he arrived at the conviction that the less labour a man did, over and above the positive demands of necessity, the better for him and for the community at large; he would have had the order of the week reversed - six days of rest for one of labour.
Thus it happened that the viceroy of Italy felt himself compelled to depart from the positive injunctions of the emperor to hold on at all costs to his advanced position at Posen, where about 14,000 men had gradually rallied around him, and to withdraw step by step to Magdeburg, where he met reinforcements and commanded the whole course of the lower Elbe.
In the absence of positive information the 4th-century writers (on whom Plutarch and Nepos mainly rely) seized upon his surname of "Just," and wove round it a number of anecdotes more picturesque than historical.
the plate attached to the so-called positive terminal of the battery or other source of current, dissolves away, the copper going into solution as copper sulphate.
That a body carrying a positive electric charge should move against the direction of the electric intensity is contrary to all our notions of electric forces, and we are compelled to seek some other explanation.
The heats of formation thus obtained may be either positive or negative, and by using them to supplement the heat of formation of water, Arrhenius calculated the total heats of neutralization of soda by different acids, some of them only slightly dissociated, and found values agreeing well with observation (Zeus.
When the zinc and copper plates are connected through a wire, a current flows, the conventionally positive electricity passing from copper to zinc in the wire and from zinc to copper in the cell.
The electric forces then soon stop further action unless an equivalent quantity of positive ions are removed from the solution.
In order that positively electrified ions may enter a solution, an equivalent amount of other positive ions must be removed or negative ions be added, and, for the process to occur spontaneously, the possible action at the two electrodes must involve a decrease in the total available energy of the system.
The ions carry their charges with them, and, as a matter of fact, it is found that water in contact with a solution takes with respect to it a positive or negative potential, according as the positive or negative ion travels the faster.
As we have seen above, when a solution is placed in contact with water the water will take a positive or negative potential with regard to the solution, according as the cation or anion has the greater specific velocity, and therefore the greater initial rate of diffusion.
The liquid thus acquires a positive charge, and the metal a negative charge.
- zn +9 1 -z2.1 -z3....1-z8; and since this expression is unaltered by the interchange of n and B we prove Hermite's Law of Reciprocity, which states that the asyzygetic forms of degree 0 for the /t ie are equinumerous with those of degree n for the The degree of the covariant in the variables is e=nO-2w; consequently we are only concerned with positive terms in the developments and (w, 0, n) - (w - r; 0, n) will be negative unless nO It is convenient to enumerate the seminvariants of degree 0 and order e=n0-2w by a generating function; so, in the first written generating function for seminvariants, write z2 for z and az n for a;.
As we have to do only with that part of the expansion which involves positive powers of z, we must try to isolate that portion, say A n (z).
(1-20) The actual form of a perpetuant of degree 0 has been shown by MacMahon to be +1 K0_1+1 K 3+20-4 K2, 01, 0-2, 0-3, ...3, 2), K 0, Ke -1, ...K 2 being given any zero or positive integer values.
1Bzl' The Positive Part Of Which Is 1 1 Az.
This is a plausible and even attractive theory; its weakness seems to lie in the absence of any positive evidence in the prophecy itself, as is illustrated by the fact that even G.
The inequality in question has its greatest negative value near the time of the moon's first quarter, and the greatest positive value near the third quarter.
According to the recognized convention, the unit pole is that which acts upon an equal pole at unit distance with unit force: a north pole is reckoned as positive (+) and a south pole as negative (-).
A pole which points north is reckoned positive, one which points south negative.
If m, and m 2 are the strengths of two poles, d the distance between them expressed in centimetres, and f the force in dynes, f=ml m2/d2 (I) The force is one of attraction or repulsion, according as the sign of the product m l m 2 is negative or positive.
A more precise definition is the following: When the magnet is placed in a uniform field, the parallel forces acting on the positive poles of the constituent filaments, whether the filaments ' For the relations between magnetism and light see Magnetooptics.
The point N, which is the centre of the parallel forces, is called the north or positive pole of the magnet.
The strength or intensity of a magnetic field at any point is measured by the force in dynes which a unit pole will experience when placed at that point, the direction of the field being the direction in which a positive pole is urged.
From the equation K=(µ - I)/47r, it follows that the magnetic susceptibility of a vacuum (where µ = I) is o, that of a diamagnetic substance (where, u I) is positive.
Forces acting on a Small Body in the Magnetic Field.-If a small magnet of length ds and pole-strength m is brought into a magnetic field such that the values of the magnetic potential at the negative and positive poles respectively are V 1 and the work done upon the magnet, and therefore its potential energy, will be W =m(V2-Vi) =mdV, which may be written W =m d s- = M d v= - MHo = - vIHo, ds ds where M is the moment of the magnet, v the volume, I the magnetization, and Ho the magnetic force along ds.
The coefficient K/(i +171-K) is positive for ferromagnetic and paramagnetic substances, which will therefore tend to move from weaker to stronger parts of the field; for all known diamagnetic substances it is negative, and these will tend to move from stronger to weaker parts.
For small bodies other than spheres the coefficient will be different, but its sign will always be negative for diamagnetic substances and positive for others; hence the forces acting on any small body will be in the same directions as in the case of a sphere' Directing Couple acting on an Elongated Body.
Since i +47-K' can never be negative, the apparent susceptibility will be positive or negative according as is greater or less than Thus, for example, a tube containing a weak solution of an iron salt will appear to be diamagnetic if it is immersed in a stronger solution of iron, though in air it is paramagnetic.4 Circular Magnetization.
In order to establish the cyclic condition, it is sufficient to apply alternately the greatest positive and negative forces employed in the test (greatest H=about ?5 C.G.S.
The twist effect exhibited by iron under moderate longitudinal magnetization has been called by Knott a positive Wiedemann effect; if the twist were reversed, the other conditions remaining the same, the sign of the Wiedemann effect would be negative.
The Wiedemann effect being positive for iron is negative for nickel.
Let each of the effects A, B, C, D and E be called positive when it is such as is exhibited by moderately magnetized iron, and negative when its sense is opposite.
For each of the metals tabulated in the first column all the effects hitherto observed have the same sign; there is no single instance in which some are positive and others negative.
Hall, the positive sign indicating that the electromotive force is in the same direction as the mechanical force acting upon the conductor.
Ber., 1886, 94, 560) have found that the rotational coefficient of tellurium is more than fifty times greater than that of bismuth, its sign being positive.
Thomson (Lord Kelvin), who in 1856 announced that magnetization rendered iron and steel positive to the unmagnetized metals.'
Nickel when magnetized is always positive to the unmagnetized metal.
[[[Feebly Susceptible Substances]] different specimens were tested, all of which became, like iron, thermo-electrically positive to the unmagnetized metals.
2 The results are too numerous to discuss in detail; some of those to which special attention is directed are the following: In Swedish iron and tungsten-steel the change of elastic constants (Young's modulus and rigidity) is generally positive, but its amount is less than 0.5%; changes of Young's modulus and of rigidity are almost identical.
As to whether the magnetized plate becomes positive or negative to the other, different experimenters are not in agreement.
An electrically neutral atom is believed to be constituted in part, or perhaps entirely, of a definite number of electrons in rapid motion within a " sphere of uniform positive electrification " not yet explained.
The only positive piece of evidence produced is the passage from Thomas Nash's "Epistle to the Gentlemen of the Two Universities," prefixed to Greene's Arcadia, 1859, in which he upbraids somebody (not known to be Shakespeare) with having left the "trade of Noverint" and busied himself with "whole Hamlets" and "handfuls of tragical speeches."
The Hungarian scholar Samuel Brassai published, in 1896, Az igazi pozitiv filozofia (" The True Positive Philosophy ").
Juristic literature has been stimulated by the activity in positive legislation.
(All the numbers are, of course, pb +qd supposed to be positive.) 27.
(ii.) The law of indices (positive integral indices only) follows at once from the definition of a 2, a 3, a 4,..
Elementary Algebra of Positive Numbers.
The principles of arithmetical transformation follow from those stated in ï¿½ï¿½ 15-18 by replacing X, A, B, m, M, x, n, a and p by any expressions involving or not involving the unknown quantity or number and representing positive numbers or (in the case of X, A, B and M) positive quantities.
This is the binomial theorem for a positive integral index.
Hence it is true for all positive integral powers of n.
This process consists in proving that a property involving p is true when p is any positive integer by proving (I) that it is true when p= 1, and (2) that if it is true when p=n, where n is any positive integer, then it is true when p = n+ I.
Then the assumption is that, whatever positive integral value n may have, n [P] is divisible by p!.
(3) Therefore n1P+11 is divisible by (p+ I) !, whatever positive integral value n may have.
The binomial theorem for positive integral index may then be written (x + y) n = -iyi +.
that can be formed with positive integral indices out of n letters x, y, z,..
do not involve x, and the indices of the powers of x are all positive integers, is called a rational integral function of x of degree n.
+nr, where r is a positive integer.
These constructed symbols may be called positive and negative coefficients; or a symbol such as (- p) may be called a negative number, in the same way that we call 3 a fractional number.
The result of the extension is that the number or quantity represented by any symbol, such as P, may be either positive or negative.
The argument involves the theorem that, if 0 is a positive quantity less than I, 0 t can be made as small as we please by taking t large enough; this follows from the fact that tlog 0 can be made as large (numerically) as we please.
Comparison with the table of binomial coefficients in ï¿½ 43 suggests that, if m is any positive integer, (I +x)-m =Sr+Rr (25), where Sr=I -mx+mx2...+(-)rm[r]xr (26), Rr_(_)r+1xr+11m[r] (1Fx) - 1+(m - I[r](I+x) m) (27).
(iii.) From (21) of ï¿½ 43 (iv.) we see that I R r l is less than m[r+l]xr+1 if x is positive, or than 1 m [r+1] x m+1 (I+x)- m I if x is negative; and it can hence be shown that, if 1 x I < 1, 1 R r I can be made as small as we please by taking r large enough, so that we can make S r approximate as closely as we please to (r +x)-1n.
(v.) The further extension to fractional values (positive or negative) of n depends in the first instance on the establishment of a method of algebraical evolution which bears the same relation to arithmetical evolution (calculation of a surd) that algebraical division bears to arithmetical division.
The application of the method to the calculation of (I +x) n, when n= p/q, q being a positive integer and p a positive or negative integer, involves, as in the case where n is a negative integer, the separate consideration of the form of the coefficients b 1, b 2, ...
(vi.) The definition of no.), which has already been extended in (iv.) above, has to be further extended so as to cover fractional values of n, positive or negative.
Certain relations still hold, the most important being (22) of ï¿½ 44 (ii.), which holds whatever the values of m and of n may be; r, of course, being a positive integer.
This accounts for the fact that the same table of binomial coefficients serves for the expansions of positive powers of i+x and of negative powers of i - x.
ï¿½; the successive terms of this series, after the first, are alternately positive and negative, and consist of fractions with numerators I and denominators continually increasing.
The development of the theory of equations leads to the amplification of real numbers, rational and irrational, positive and negative, by imaginary and complex numbers.
A point A in space may be associated with a (real, positive, or negative) numerical quantity a, called its weight, and denoted by the symbol aA.
In this work, which is one of the most valuable contributions to the literature of algebra, Cardan shows that he was familiar with both real positive and negative roots of equations whether rational or irrational, but of imaginary roots he was quite ignorant, and he admits his inability to resolve the so-called lation of Arabic manuscripts.
Stifel introduced the sign (+) for addition or a positive quantity, which was previously denoted by plus, pia, or the letter p. Subtraction, previously written as minus, mene or the letter m, was symbolized by the sign (-) which is still in use.
In the first hybrid generation formed by the union of the reproductive germs of the positive variety (that possessing the structural character selected for observation) with those of the negative variety, it is not surprising that all or nearly all the individuals were found to exhibit, as a result of the mixture, the positive character.
In subsequent generations produced by self-fertilization of the hybrids it was found that the positive character was not present in all the individuals, but that a result was obtained showing that in the formation of the reproductive cells (ova and sperms) of the hybrid, half were endowed with the positive character and half with the negative.
The failure of the material carrying a positive character to divide so as to distribute itself among all the reproductive cells of a hybrid individual, and the limitation of its distribution to half only of those cells, must prevent the swamping " of a newly appearing character in the course of the inter-breeding of those individuals possessed of the character with those which do not possess it.
the race with the positive character simply and the race with the total absence of it.
To calculate the roots of (5) we may assume u=(m+1)7r-y= U-y, (3), where y is a positive quantity which is small when u is large.
This expresses the retardation of the extreme relatively to the central ray, and is to be reckoned positive, whatever may be the signs of w, and 0 .
If we write p = 27rR/A (6), we must regard p as a function of f, and we may take with sufficient approximation under any ordinary circumstances where p' denotes the value of p at 0, and is a constant, which is positive when the retarding plate is held at the side on which the blue of the spectrum is seen.
The possibility of dark bands depends upon a being positive.
The formation of bands thus requires that the retarding plate be held upon the side already specified, so that zs be positive; and that the thickness of the plate (to which z is proportional) do not exceed a certain limit, which we may call 2T 0.
Then the displacement at 0 will take place in a direction perpendicular to 0 1 0, and lying in the plane Z0 1 0; and, if 1' be the displacement at 0, reckoned positive in the direction nearest to that in which the incident vibrations are reckoned positive, = 4?y (1 +cos 0) sin 4 f' (bt - r).
The force operative upon the positive half is parallel to OZ, and of amount per unit of area equal to - b 2 D = b 2 kD cos nt; and to this force acting over the whole of the plane the actual motion on the positive side may be conceived to be due.
Now it is evident that the force in question, supposed to act upon the positive half only of the medium, produces just double of the effect that would be caused by the same force if the medium were undivided, and on the latter supposition (being also localized at a point) it comes under the head already considered.
Finally, on the 26th of October 1740, a so-called "positive declaration" signed by 194 dignitaries, in the name of the Russian nation, conferred the regency on Biren.
4 See Batifol, Etudes d'histoire et de theologie positive, 2 me serie.
In 1882 also began that alteration of the franchise law which subsequently developed into positive exclusion of practically all save the original Boer burghers of the country from the franchise.
These then pass into the blood stream in very large numbers, and appear to be specially attracted to the point of injury by a positive chemiotactic action.
Leber experimented with several chemical compounds to find what reaction they had on these cells; by using fine glass tubes sealed at the outer end and containing a chemical substance, and by introducing the open end into the blood vessels he found that the leucocytes were attracted - positive chemiotaxis - by the various compounds of mercury, copper, turpentin, and other substances.
It was also found that a weak solution may have a marked positive attraction whilst a strong solution of the same substance will have the opposite effect.
Then we have the property of adaptation, in which the negative reaction may be changed into a positive; a given toxin may at first repel the cell, but by a gradual process the cell becomes accustomed to such a toxin and will move towards it.
The influence of the chemical substance is either that of attraction or repulsion, the one being known as positive, the other as negative chemiotaxis.
The female organs of certain cryptogams, for instance, exert a positive chemiotactic action upon the spermatozoids, and probably, as Pfeffer suggests, the chemical agent which exerts the influence is malic acid.
It was fortunate, however, that the accumulation of positive knowledge in medicine did not cease.
This, the old "Vienna School," was not distinguished for any notable discoveries, but for success in clinical teaching, and for its sound method of studying the actual facts of disease during life and after death, which largely contributed to the establishment of the "positive medicine" of the 19th century.
Here the chief home of positive medicine was still for a long time Vienna, where the "new Vienna school" continued and surpassed the glory of the old.
- In recent times the positive bent of modern knowledge and methods in other spheres of science and thought, and especially in biology, has influenced medicine profoundly.
Schbnlein thus did something to introduce new and positive conceptions and exacter methods into Germany; but unfortunately his own mind retained the abstract habit of his country, and his abilities were dissipated in the mere speculations of Schelling.
At the risk no doubt of some defects of culture, the newer education cleared the way for a more positive temper, awoke a new sense of accuracy and of verification, and created a sceptical attitude towards all conventions, whether of argument or of practice.
The abdomen is still "full of surprises"; and he who has most experience of this deceptive region will have least confidence in expressing positive opinions in particular cases of disease without operative investigation.
In our conceptions of the later stages of assimilation and of excretion, with the generation of poisons (auto-intoxication) in the intestinal tract, there is still much obscurity and much guess-work; yet in some directions positive knowledge has been gained, partly by the physiologist, partly by the physician himself.
It was not his ideas or his commanding personality, nor any positive programme, that brought the Liberals back to power, but the country's weariness of their predecessors and the successful employment at the elections of a number of miscellaneous issues.
That his characteristic is for the most part an almost superhuman cleverness rather than positive genius is also true.
Positive blowers and exhausting apparatus of a great variety of forms have been used in mines for producing artificial ventilation.
Further, it is certain that Hero used physical and mathematical writings by Posidonius, the Stoic, of Apamea, Cicero's teacher, who lived until about the middle of the 1st century B.C. The positive arguments for the more modern view of Hero's date are (1) the use by him of Latinisms from which Diels concluded that the 1st century A.D.
However this may be, the earliest positive evidence of the existence at Venice of a worker in glass would seem to be the mention of Petrus Flavianus, phiolarius, in the ducale of Vitale Falier in the year 1090.
From the gas-equation in general, in the atmosphere n d dp _ I dp 1 de _ d0 de i de (8) z p dz-edz-p-edz-k-edz' which is positive, and the density p diminishes with the ascent, provided the temperature-gradient de/dz does not exceed elk.
therwise, if A is positive rt= J y-s1 (A+2By+Cy') dy sh1 A'/ (A+2By+Cy 2) I ch1 A+By (26) -V A ch1 31, (B2--AC) - A sh - 1 (B2-AC)' nd the axis falls away ultimately from its original direction.
well as of the body from the vector OF to O'F' requires an impulse couple, tending to increase the angle F00', of magnitude, in sec. foot-pounds F.00'.sin FOO'=FVt sin (0-0), (4) equivalent to an incessant couple N=FV sin (0-0) = (F sin 0 cos 0-F cos 0 sin ¢)V = (c 2 -c i) (V /g) sin 0 cos 4) =W'(13-a)uv/g (5) This N is the couple in foot-pounds changing the momentum of the medium, the momentum of the body alone remaining the same; the medium reacts on the body with the same couple N in the opposite direction, tending when c 2 -c 1 is positive to set the body broadside to the advance.
An elongated body like a ship has c 2 -c 1 positive, and the couple N tends to disturb the axial movement and makes it unstable, so that a steamer requires to be steered by constant attention at the helm.
When is absent, dx/dt is always positive, and the centre of the body cannot describe loops; but with E, the influence may be great enough to make /dt change sign, and so loops occur, as shown in A.
Jerablus was confidently identified with Carchemish (but without positive proof to this day), and the occurrence of Hamathite monuments there was held to confirm the Hittite theory.
This rod was connected with the positive pole of the dynamo or electric generator.
When the furnace with this well-known regulating device was to be used, say, for the melting of metals or other conductors of electricity, the fragments of metal were placed in the crucible and the positive electrode was brought near them.
This action completed the furnace-circuit, and current passed freely from the positive carbon through the fragments of metal to the negative carbon, thereby reducing the current through the shunt.
The positive carbon was in some cases replaced by a water-cooled metal tube, or ferrule, closed, of course, at the end inserted in the crucible.
The positive Christian ideal which " the saints " should attain, " the Lord enabling," it is the business of the Shepherd to set forth.
The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.