Think positive, and pray.
I'm positive she didn't notice us the first time.
She had to adopt a positive attitude.
I was positive all she did was substitute a different one for each letter in the alphabet.
Positive. She smelled amazingly human, only more so.
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.
Let's consider examples of how the effect is positive for some, negative for some, but the net is a gain in the overall wealth of the system.
We constantly longed to follow up on our endeavors and make sure what Howie discovered was brought to a positive conclusion.
Next came a lesson on words expressive of positive quality.
She was positive she'd be lost for life.
His logic and acceptance of the deformity was amazingly positive and mature for a 9-year-old.
"The command center," I said, possessing an over whelming need to do something tangible or at least be where positive attempts were undertaken.
On the positive side, at that rate their conversation should be over by five minutes after nine.
It wouldn't hurt to adopt a more positive outlook.
Only a few flying saucer advocates spoke from the fringes with a positive slant.
Economic changes that have long-term positive benefits for society often have short-term negative ones.
On the other hand, how could Alex be a positive influence if his Uncle truly felt that way?
If jump ropes or board games or ice cream turn out to have positive externalities—that is, if they help society—a subsidy could lower the prices of these items.
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.
Even Quinn showed more positive emotion than previously expressed.
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.
The largest positive and negative values recorded are met with during disturbed weather.
My dear Carrie--You are to look upon it as a most positive proof of my love that I write to you to-day.
I was pleased our conversation at least ended on a positive note.
the velocities in unit field-he takes to be 1 3 X300 for the positive, and I.
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.
I'm sorry I'm so positive about this.
Dean reiterated the obvious—Burgess was less than positive and the picture he sort-of identified was years old.
She lacks any kind of positive self-image.
But in spite of the relative economic displacement they all cause, free trade, outsourcing, and technological displacement all have a positive net effect on the economics of the planet.
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.
I + is used to denote the charge on positive ions, I_ that on negative ions.
I was so positive it was impossible.
A great way to solve a dilemma is to make a decision table, listing all the positive and negative aspects for each option.
First and foremost was an overwhelming urge to punch his lights out but past similar responses hadn't produced positive results.
"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.
While he was thrilled that Dean might now be running unopposed, he was positive Lydia had killed her boss.
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.
Are we positive we've got this right?
The positive and ation.
Now, the way I see it, there's three ways to prove Byrne's alive—fingerprints, positive ID, or handwriting.
In dry weather the electric potential in the atmosphere is normally positive relative to the earth, and increases with the height.
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.
We crammed in five sessions with three positive achievements, a new record.
To some extent, we have this in the form of high taxes on cigarettes, which are seen to have negative externalities, and a home interest deduction on income taxes, as home ownership is viewed as having positive social good.
A diminution in the number of positive ions would thus naturally be accompanied by a rise in potential gradient.
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.
The net effect is positive, but the laid-off workers will probably have a hard time appreciating it.
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.
I resolved to remain calm for her sake and talked of nothing but positive certainty of our escape.
I was just thinking that you've had a decidedly positive influence on me.
But I thought you were positive it was Fitzgerald who switched the bones.
A cylinder condenser has its inner surface insulated and charged to a high positive or negative potential.
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.
Most of the luxuries, and many of the so-called comforts of life, are not only not indispensable, but positive hindrances to the elevation of mankind.
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.
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.
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.
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.
Alex said it might not have made any difference, and reminded her that she needed to think positive.
No. Just the opposite, but it's too early to be positive.
Think of something else - something positive.
We still have to wait a little while and there are lots of details to iron out, but Ms. Rosewater says it looks positive.
Her answer came swift and positive.
a negative charge is lost much faster than a positive charge.
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.
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.
AUGUSTE [ISIDORE AUGUSTE MARIE FRANpOIS] COMTE (1798-1857), French Positive philosopher, was born on the 19th of January 1798 at Montpellier, where his father was a receiver-general of taxes for the district.
He announced a course of lectures (1826), which it was hoped would bring money as well as fame, and which were to be the first dogmatic exposition of the Positive Philosophy.
As has been justly said, if Newton once suffered a cerebral attack without forfeiting our veneration for the Principia, Comte may have suffered in the same way, and still not have forfeited our respect for Positive Philosophy and Positive Polity.
In 1828 the lectures were renewed, and in 1830 was published the first volume of the Course of Positive Philosophy.
improvement in the conceptions of logical method was derived from the Positive Philosophy.
singularly conscientious fashion of elaborating his ideas made the mental strain more intense than even so exhausting a work as the abstract exposition of the principles of positive science need have been.
For example, he began and completed in about six weeks a chapter in the Positive Philosophy (vol.
After he had acquired what he considered to be a sufficient stock of material, and this happened before he had completed the Positive Philosophy, he abstained from reading newspapers, reviews, scientific transactions and everything else, except two or three poets (notably Dante) and the Imitatio Christi.
Comte lost no time, after the completion of his Course of Positive Philosophy, in proceeding with the System of Positive Polity, for which the earlier work was designed to be a foundation.
In 1848, when the political air was charged with stimulating elements, he founded the Positive Society, with the expectation that it might grow into a reunion as powerful over the new revolution as the Jacobin Club had been in the revolution of 1789.
In proceeding to give an outline of Comte's system, we shall consider the Positive Polity as the more or less legitimate of the Positive Philosophy, notwithstanding co the deep gulf which so eminent a critic as J.
In the Positive Philosophy, again (vol.
Even the readaptation of the Catholic system to a scientific doctrine was plainly in his mind thirty years before the final execution of the Positive Polity, though it is difficult to believe that he foresaw the religious mysticism in which the task was to land him.
The Positive Philosophy opens with the statement of a certain law of which Comte was the discoverer, and which has always been treated both by disciples and dissidents as the key to his system.
These three stages are the Theological, the Metaphysical and the Positive.
In the Positive state, inherent volition or external volition and inherent force or abstraction personified have both disappeared from men's minds, and the explanation of a phenomenon means a reference of it, by way of succession or resemblance, to some other phenomenon, - means the establishment of a relation between the given fact and some more general fact.
In the Theological and Metaphysical state men seek a cause or an essence; in the Positive they are content with a law.
- (Dr Bridges.) The first and greatest aim of the Positive Philosophy is to advance the study of society into the third of the three stages, - to remove social phenomena from the sphere of theological and metaphysical conceptions, and to introduce among them the same scientific observation of their laws which has given us physics, chemistry, physiology.
Comte's special object is a study of social physics, a science that before his advent was still to be formed; his second object is a review of the methods and leading generalities of all the positive sciences already formed, so that we may know both what system of inquiry to follow in our new science, and also where the new science will stand in relation to other knowledge.
The first step in this direction is to arrange scientific method and positive knowledge in order, and this brings us to another cardinal element in the Comtist system, the classification of the sciences.
It is the method and knowledge of the abstract sciences that the Positive Philosophy has to reorganize in a great whole.
It follows that the crowning science of the hierarchy, dealing with the phenomena of human society, will remain longest under the influence of theological dogmas and abstract figments, and will be the last to pass into the positive stage.
They are thus the double key of The double Comte's systematization of the philosophy of all the key of sciences from mathematics to physiology, and his positive analysis of social evolution, which is the base of philo= sociology.
The co-ordination of all these partial philosophies produces the general Positive Philosophy.
The Positive Philosophy is novel as a.
He always claimed to be the founder of the Positive Philosophy.
That he had every right to such a title is demonstrable to all who distinguish between the positive sciences and the philosophy which co-ordinated the truths and methods of these sciences into a doctrine."
This work is accomplished in the last three volumes of the Positive Philosophy, and the second and third volumes of the Positive Polity.
When the positive method has been finally extended to society, as it has been to chemistry and physiology, these social facts will be resolved, as their ultimate analysis, into relations with one another, and instead of seeking causes in the old sense of the word, men will only examine the conditions of social existence.
The Positive Philosophy has another object besides the demonstration of the necessity and propriety of a science of society.
Thus we acquire a bodyof empirical generalizations as to social phenomena, and then we connect the generalizations with the positive theory of human nature.
On the other hand, if laws of social phenomena, empirically generalized from history, can, when once suggested, be affiliated to the known laws of human nature; if the direction actually taken by the developments and changes of human society, can be seen to be such as the properties of man and of his dwelling-place made antecedently probable, the empirical generalizations are raised into positive laws, and sociology becomes a science."
Among other central thoughts in Comte's explanation of history are these: - The displacement of theological by positive conceptions has been accompanied by a gradual rise of an industrial regime out of the military regime; - the great permanent contribution of Catholicism was the separation which it set up between the temporal and the spiritual powers,; - the progress of the race consists in the increasing preponderance of the distinctively human elements over the animal elements; - the absolute tendency of ordinary social theories will be replaced by an unfailing adherence to the relative point of view, and from this it follows that the social state, regarded as a whole, has been as perfect in each period as the co-existing condition of humanity and its environment would allow.
The elaboration of these ideas in relation to the history of the civilization of the most advanced portion of the human race occupies two of the volumes of the Positive Philosophy, and has been accepted by very different schools as a masterpiece of rich, luminous, and far-reaching suggestion.
The third volume of the Positive Polity treats of social dynamics, and takes us again over the ground of historic evolution.
As it was composed in rather less than six months, and as the author honestly warns us that he has given all his attention to a more profound co-ordination, instead of working out the special explanations more fully, as he had promised, we need not be surprised if the result is disappointing to those who had mastered the corresponding portion of the Positive Philosophy.
The main principles of the Comtian system are derived from the Positive Polity and from two other works, - the Positivist Catechism: a Summary Exposition of the Universal Religion in Twelve Dialo ues between a Woman and a The g, g Elvis f Priest of Humanity; and, second, The Subjective Synthesis (1856), which is the first and only volume of a work upon mathematics announced at the end of the Positive Philosophy.
The system for which the Positive Philosophy is alleged to have been the scientific preparation contains a Polity and a Religion; a complete arrangement of life in all its aspects, giving a wider sphere to Intellect, Energy and Feeling than could be found in any of the previous organic types, - Greek, Roman or Catholic-feudal.
This basis is to be found in the Positive stage, in Humanity, past, present and to come, conceived as the Great Being.
When religion has be come positive, and society industrial, then the influence of the church upon the state becomes really freeandindependent,which was not the case in the middle ages.
- WOrkS, Editions and Translations: Cours de philosophie positive (6 vols., Paris, 1830-1842; 2nd ed.
Bridges, London, 1852); Systeme de politique positive, ou Traite de sociologie (4 vols., Paris, 1852-1854; ed.
Gordon Jones, Fundamental Principles of Positive Philos.
And so he became a positive religious teacher by virtue of the very ideas that made the words of the Hebrew prophets so potent and sublime.
4 The echoes of the dying controversy are thus distinct and not very distant in this book, though it also offers in its larger outlook, in the author's evident uneasiness under the burden of inherited beliefs, and his inability to reconcile them with his new standpoint and accepted principles, a curious forecast of his later development, while in its positive premisses it presents a still more instructive contrast to the conclusions of his later dialectic. Nor did the sound of the ancient controversy ever cease to be audible to him.
Yo = the positive principle.
This is illustrated by the difficulties inherent in the conception of Cause, Space, Time, Matter, Motion, the Infinite, and the Absolute, and by the" relativity of knowledge,"which precludes knowledge of the Unknowable, since" all thinking is relationing."Yet the Unknowable may exist, and we may even have an" indefinite knowledge "of it, positive, though vague and extralogical.
and vi.; Negative and Positive Beneficence, 1893).
&c., where p+pq is the quantity whoseTi power or root is required, p the first term of that quantity, and q the quotient of the rest divided by p, m the power, which may be a positive or negative integer or a fraction, and a, b, c, &c., the several terms in order, In a second letter, dated the 24th of October 1676, to Oldenburg, Newton gave the train of reasoning by which he devised the theorem.
Newton gave no proof, and it was in the Ars Conjectandi (1713) that James Bernoulli's proof for positive integral values of the exponent was first published, although Bernoulli must have discovered it many years previously.
The morality of these is almost amusing in its downright positive character.
In algebra, if a be a real positive quantity and w a root of unity, then a is the amplitude of the product aw.
In Berzelius' system + potassium sulphate is to be regarded as K 2 0.S0 3; electrolysis should simply effect the disruption of the positive and negative components, potash passing with the current, and sulphuric acid against the current.
It is apparent that metallic salts of organic acids would, in aqueous solution, be ionized, the positive ion being the metal, and the negative ion the acid residue.
The greatest size to which some species attain, according to positive observation, is about 12 ft., and therefore far short of the statements as to the length of the so-called sea-serpents (q.v.).
The expedition which followed produced negative successes, but the absence of any positive success and the pressure of financial difficulty, coupled with the defection of Jason (probably before 37 1), and the high-handed action of Thebes in destroying Plataea (373), induced Athens to renew the peace with Sparta which Timotheus had broken.
This proves the existence of two kinds of electricity, called positive and negative.
The sign of the electrification imparted to the electroscope when so charged - that is, whether positive or negative - can be determined by rubbing the sealing-wax rod with flannel and the glass rod with silk, and approaching them gently to the electroscope one at a time.
The sealing-wax so treated is electrified negatively or resinously, and the glass with positive or vitreous electricity.
Hence if the electrified sealing-wax rod makes the leaves collapse, the electroscopic charge is positive, but if the glass rod does the same, the electroscopic charge is negative.
The electrified ebonite is said to act by " electrostatic induction " on the tray, and creates on it two induced charges, one of positive and the other of negative electricity.
The leaves of the electroscope will diverge with positive electricity.
In the same manner, if an electrified body carries a positive charge Q electrostatic units and is placed in an electric field at a place where the electric force or electromotive intensity has a value E units, it is urged in the direction of the electric force with a mechanical force equal to QE dynes.
If we consider a very small conductor charged with a unit of positive electricity to be placed in an electric field, it will move or tend to move under the action of the electric force in a certain direction.
(iii.) Association of Positive and Negative Electricities.
- The third leading fact in electrostatics is that positive and negative electricity are always created in equal quantities, and that for every charge, say, of positive electricity on one conductor there must exist on some other bodies an equal total charge of negative electricity.
Let the ball and lid be removed by the silk, and let a charge, say, of positive electricity (-}- Q) be given to the ball.
The explanation is as follows: the charge (-}- Q) of positive electricity on the ball creates by induction an equal charge (- Q) on the inside of the canister when placed in it, and repels to the exterior surface of the canister an equal charge (+ Q).
The potential of a conductor has already been defined as the mechanical work which must be done to bring up a very small body charged with a unit of positive electricity from the earth's surface or other boundary taken as the place of zero potential to the surface of this conductor in question.
Thus, consider a sphere uniformly charged with Q units of positive electricity.
Every tube of electric force must therefore begin and end on electrified surfaces of opposite sign, and the quantities of positive and negative electricity on its two ends are equal, since the force E just outside an electrified surface is normal to it and equal to a/41r, where a is the surface density; and since we have just proved that for the ends of a tube of force EdS = E 1 dS', it follows that adS = a'dS', or Q = Q', where Q and Q' are the quantities of electricity on the ends of the tube of force.
Since the potential of a conductor is defined to be the work required to move a unit of positive electricity from the surface of the earth or from an infinite distance from all electricity to the surface of the conductor, it follows that the work done in putting a small charge dq into a conductor at a potential v is v dq.
5) a point-charge of positive electricity +q _q/ +q and an infinite conducting plate PO, shown in section, connected to earth and therefore at zero potential.
The same reasoning can be applied to determine the electrical image of a point-charge of positive electricity in a spherical surface, and therefore the distribution of induced electricity over a metal sphere connected to earth produced by a point-charge near it.
Let +q be any positive point-charge placed at a point A outside a sphere (fig.
In the special case of a substance isolated from external heat supply, dH=o, the change of entropy is zero in a reversible process, but must be positive if the process is not reversible.
Gold is also attacked when strong sulphuric acid is submitted to electrolysis with a gold positive pole.
Effects of Immigration.-The effects of emigration are negative in character; those of immigration are positive.
362 Cyril would find " a natural occasion for the revision of the public creed by the skilful insertion of some of the conciliar language, including the term which proclaimed the restoration of full communion with the champions of Nicaea, and other phrases and clauses adapted for impressing on the people positive truth."
A follower of the positive philosophy, but in conflict with Richard Congreve as to details, he led the Positivists who split off and founded Newton Hall in 1881, and he was president of the English Positivist Committee from 1880 to 1905; he was also editor and part author of the Positivist New Calendar of Great Men (1892), and wrote much on Comte and Positivism.
Corps for assistance, which its commander, under positive orders from Steinmetz, refused to give.
The point is of no very great significance, however, since no one has pretended that the Western civilization compared with the Eastern in point of antiquity; and in any event, no amount of negative evidence weighs a grain in the balance against the positive evidence of the Cretan inscriptions.
Here is proof positive that Crawford does not copy Letter but gives Darnley's words as reported to him by Darnley - words that Darnley was proud of, - while Mary, returning on the second day of writing to the topic, does not quote Darnley's brave words, but merely contrasts his speaking "very bravely at the beginning" with his pitiful and craven later submission; "he has ever the tear in his eye," with what follows.
He knew the connexion existing between the positive roots of an equation (which, by the way, were alone thought of as roots) and the coefficients of the different powers of the unknown quantity.
A keen and positive political intelligence emerged in the Italian race.
His originality consists in having extended the positive intelligence of his century from the sphere of contemporary politics and special interests to man at large regarded as a political being.
17) are the eye lens and field lens respectively of a Merz positive eye-piece.
It is essentially the same in principle as Amici's micrometer, except that the divided lens is an achromatic positive instead of a negative lens.
The former is the basis of the negative part of his argument; the latter supplies him with all the positive account he has to give, and that is meagre enough.
The moment of W 1 may be positive or negative.
In line with this, too, is his demand that psychology shall be cleared of metaphysics; and to his lead is no doubt due in great measure the position that psychology has now acquired as a distinct positive science.
of the Thirty-nine Articles, he emphasized a positive and constructive statement of the Anglican position.
This work caused some commotion, as much by the novelty of its method as by the heterodoxy of its matter, and more by its omissions than by its positive teaching, though everywhere the author seeks to put theological doctrines in a decidedly modern form.
By this lexicon Teller had put himself amongst the most advanced rationalists, and his opponents charged him with the design of overthrowing positive Christianity altogether.
His character, with its mixture of greatness and gentleness, was thus read by Carlyle: "A right solid, honest-hearted man, full of knowledge and sense, and, in spite of his positive temper, almost timid."
Like all the Reformers, he was strictly Augustinian in theology, but he dwelt chiefly on the positive side of predestination - the election to salvation - and he insisted upon the salvation of infants and of the pious heathen.
The positive side of his teaching resembles in all essentials that of Arcesilaus (q.v.).
3, if AN and NB are regarded as positive, then SF, TG, ET and SA are negative, but the products ET.
TG are positive.
This will be seen by taking the mid-ordinate as the ordinate for which x = o, and noticing that the odd powers of x introduce positive and negative terms which balance one another when the whole area is taken into account.
The desire to learn what the future has in store is nearly as old as the sense of responsibility in mankind, and has been the parent of many empirical systems of fortune-telling, which profess to afford positive knowledge whereby the affairs of life may be regulated, and the dangers of failure foretold.
Its positive side, with its sense of the wider fellowship of " the Brotherhood " (I Pet.
Congregationalism, however, " denotes a positive theory of the organization and powers of Christian churches," having as corollary independency of external control, whether civil or ecclesiastical.
The remarkable junction or fusion of the Independents or " Separatists " who emigrated from Leiden to Plymouth, Massachusetts, with the Puritan Nonconformists of Massachusetts Bay, modified Independency by the introduction of positive fraternal relations among the churches.
He is keen, positive, logical, combining with curious dashes of scepticism many genuine moral convictions and a good knowledge of the various national religions and mythologies whose relative value he is able to appreciate.
He is a man of the world, of philosophic culture, who accepts much of the influential Platonism of the time but has absorbed little of its positive religious sentiment.
Its two halves have each a negative and a positive scene.
A positive testimony for the critical conclusion is derived from the existence of a group of Asia Minor Christians who about 165 rejected the Gospel as not by John but by Cerinthus.
We see at once that, where u=o, the velocity has its " normal " value, while where u is positive the velocity is in excess, and where u is negative the velocity is in defect of the normal value.
This was a decidedly complicated one, and neglect of it has led some readers to adopt a more positive idea of Montaigne's scepticism than is fully justified by all the facts.
As to anemometer pressures, it should be observed that the recorded pressure is made up of a positive front and negative (vacuum) back pressure, but in structures the latter must be absent or only partially developed.
= the range of stress, where A is always positive.
When the load is at F', the reaction at B' is m/l and the moment at C' is m(l-x)ll, which will be reckoned positive, when it resists a tendency of the right-hand part of the girder to turn counter-clockwise.
When the worn-out old Emperor was succeeded by an immature boy, the serious, positive and somewhat " schoolmasterish " Kdrber did not strike the right note with him.
So far as positive records go, Aries was always the first sign.
Positive proof of the high antiquity of the Hindu lunar zodiac is nevertheless afforded by the undoubted fact that the primitive series opened with Krittika (the Pleiades) as the sign of the vernal equinox.
heat; but the essential idea of moving electric ions of both kinds, positive and negative, in the molecules had still to be introduced.
A dielectric substance is electrically polarized by a field of electric force, the atomic poles being made up of the displaced positive and negative intrinsic charges in the atom: the polarization per unit volume (f',g',h') may be defined on the analogy of magnetism, and d/dt(f',g',h') thus constitutes true electric current of polarization, i.e.
The usual definition of the component current in any direction, as the net amount of electrons which crosses, towards the positive side, an element of surface fixed in space at right angles to that direction, per unit area per unit time, here gives no definite result.
The establishment and convection of a single polar atom constitutes in fact a quasi-magnetization, in addition to the polarization current as above defined, the negative poles completing the current circuits of the positive ones.
13 1920, with Rumania April 23 1921), positive in so far as it aimed at the establishment and maintenance of peace, security and normal economic conditions in central Europe, and defensive in so far as it was directed against all attempts at reaction menacing the existence of the new states.
The symbol (alp) which is known as Legendre's symbol, and denotes the positive or negative unit which is the remainder when au s (-1) is divided by a prime number p, does not appear in this memoir, but was first used in the Essai sur la theorie des nombres.
He extended the "law of continuity" as stated by Johannes Kepler; regarded the denominators of fractions as powers with negative exponents; and deduced from the quadrature of the parabola y=xm, where m is a positive integer, the area of the curves when m is negative or fractional.
On placing a piece of potash on a platinum plate, connected to the negative of a powerful electric battery, and bringing a platinum wire, connected to the positive of the battery, to the surface of the potassium a vivid action was observed: gas was evolved at the upper surface of the fused globule of potash, whilst at the lower surface, adjacent to the platinum plate, minute metallic globules were formed, some of which immediately inflamed, whilst others merely tarnished.
The posterior end of the organ is positive, the anterior negative, and the current, passes from the tail to the head.
There was not only no obvious reason why it should write, but there was a positive reason why it should not write.
No such theories can be counted as more than coincidences which have been adopted, unless we find a very exact connexion, or some positive statement of origination.
The claim of positive religion to be something more than the intellectual apprehension of the reason in the universe is thus acknowledged.
numbers in which the integral part is o) the mantissa is still kept positive, so that, for example, log 25613 =7-4084604, 4084604, log 0025613 = 3.4084604, &c.
This equation defines log x for positive values of x; if o the formula ceases to have any meaning.
that x-"' log x tends to zero as x tends to 00 for every positive value of m however small.
It is positive for all values of y and increases steadily from o toward as y increases from -co towards + oo.
+ ...)x, where the right-hand side denotes the positive xth power of the number I +I +1/2 !
Thus even when the argument is real log x has an infinite number of values; for putting 71 =o and taking positive, in which case a = o, we obtain for log the infinite system of values log +2n7ri.
Napier said that he had already thought of the change, and pointed out a further improvement, viz., that the characteristics of numbers greater than unity should be positive and not negative, as suggested by Briggs.
As for the builders of Quemada, in Zacatecas, nothing positive is known.
Public attention was powerfully attracted by these vague hints of a new system which promised something more positive, as regards religion in particular, than the apparent results of Hegel's teaching.
No authentic information as to the nature of the new positive philosophy was obtained till after his death (at Bad Rogaz, on the 20th of August 1854), when his sons began the issue of his collected writings with the four volumes of Berlin lectures: vol.
the thought of the identical, indifferent, absolute substratum of both nature and spirit, the advance to Identitdtsphilosophie; (3) the opposition of negative and positive philosophy, an opposition which is the theme of the Berlin lectures, though its germs ma y be traced back to 1804.
merely rational philosophy, and positive, of which the content is the real evolution of the divine as it has taken place in fact and in history, and as it is recorded in the varied mythologies and religions of mankind.
C. Frantz, Schelling's Positive Philosophie (3 vols., 1879-1880); Watson, Schelling's Transcendental Idealism (1882); Groos, Die reine Vernunftwissenschaft.
It is the inverse of a central conic for the focus, and the first positive pedal of a circle for any point.
Other alleged discoveries, such as' the construction of early Roman history out of still earlier ballads, have not been equally fortunate; but if every positive conclusion of Niebuhr's had been refuted, his claim to be considered the first who dealt with the ancient history of Rome in a scientific spirit would remain unimpaired, and the new principles introduced by him into historical research would lose nothing of their importance.
This pessimistic attitude is far removed from the positive hedonism of Aristippus.
His tendency towards mystical speculation formed a not less fundamental quality of his mind than its strong grasp of positive scientific truth.
Beck maintains that the real meaning of Kant's theory is idealism; that of objects outside the domain of consciousness, knowledge is impossible, and hence that nothing positive remains when we have removed the subjective element.
The salt and gypsum constitute a positive argument for aridity.
Finally he died without completing some of his works, such as the Politics, and notably that work of his whole philosophic career and foundation of his whole philosophy - the Metaphysics - which, projected in his early criticism of Plato's philosophy of universal forms, gradually developed into his positive philosophy of individual substances, but remained unfinished after all.
(2) Positive assertion of the doctrine that things are individual substances in the Categories, but with the admission that attributes sometimes inhere in substance without being predicates of it, and that universal species and genera are " secondary substances."
When, Therefore, E Is Greater Than 23, We Must Add 30 In Order That P And 1 May Have Positive Values In The Formula P =24 E And 1=27 E.
It Will Be Remarked, That As L 1 Cannot Either Be O Or Negative, We Must Add 7 To Las Often As May Be Necessary, In Order That L 1 May Be A Positive Whole Number.
Thus he devoted one summer vacation to the careful analysis of Comte's Politique positive.
Dogmatik (1810), and his Judas Ischarioth (2 vols., 1816, 2nd ed., 1818), were all written in the spirit of Schelling, the last of them reflecting a change in Schelling himself from theosophy to positive philosophy.
But the negative part of Ruskin's teaching on economics, social and political problems, has been much more effective than the positive part of his teaching.
Even Grotius, who reduced the tendencies existing in his time to a sort of orderly expression, addressed himself to the law of war as the positive part of international jurisprudence and dealt only with peace as its negative alternative.
In other words peace among nations has now become, or is fast becoming, a positive subject of international regulation, while war is 1 This has been incorrectly rendered in the English official translation as " the sincere desire to work for the maintenance of general peace."
As purity and resolving power are essentially positive quantities, n i in the above expression must be the greater of the two frequencies.
If N be the frequency of a homogeneous vibration sent out by a molecule at rest, the apparent frequency will be N (1 v/ V), where V is the velocity of light and v is the velocity of the line of sight, taken as positive if the distance from the observer increases.
Now it follows from Rydberg's second law put on a more accurate basis by Ritz that in one case at any rate a negative period has reality and must be interpreted just as if it were positive.
The band fades towards the red or violet according as A is positive or negative, and the appearance is sometimes complicated by the fact that several sets of lines start from identical or closely adjoining heads.
This gives a real value for s only when a is positive.
If we only assign positive values to n and a, the band fades away from the head, the lines at first increasing in distance.
Close to and on either side of the absorptive band µ 2 has large positive and negative values, and if the above expression remains correct the change of frequency would, close to the centre of absorption, be 2 k-2"+3, which for n =3 and k= Io is 1/2000, or 500 times greater than the observed shifts, but this represents now the maximum displacement and not the displacement of the most intense portion of the radiation.
The conclusion seemed natural that the spectra which showed the Doppler effect were due to vibratory systems which had an excess of positive charge.
Whatever ideas we may form on this point, the observations of Stark and Siegl 4 have shown that there is a Doppler effect, and therefore a positive charge, for one of the lines of the trunk series of potassium, and E.
He now distinguished two philosophies: negative philosophy starting from notions, and positive philosophy starting from being; the former a philosophy of conditions, the latter of causes, i.e.
the panlogistic confusion of the essences of things with the notions of reason, to construct a positive philosophy without falling into fresh mysticism, which failed to exorcise the effect of his earlier philosophy of identity in the growing materialism of the age.
In his tract entitled Schelling's positive Philosophie als Einheit von Hegel and Schopenhauer (1869) he further showed that, in his later philosophy, Schelling had already combined reason and will in the Absolute.
Sometimes it is used for any positive fact, as distinguished from its cause.
When, on the other hand, the objects of science are properly described as phenomena, what is meant is not this pittance of sensible appearances, but positive facts of all kinds, whether perceptible or imperceptible, whether capable of being experienced or of being inferred from, but beyond, experience, e.g.