# P sentence example

p

- He'd better watch his P's and Q's.
- ft., are round or square, and for these sizes, and shapes, and of course for a flat surface, the relation P = .003 is fairly correct.
- The Spaniards skilfully avoided a battle, and in Alva November the invaders were compelled to withdraw triumph- p ant.
- Groen van Prinsterer, Archives ou correspondance ine'dite de la maison d'0range, P serie (9 vols., 1841-1861); Poullet et Piot, Correspondance du cardinal Granvelle (12 vols., 1879-1899); J.
- Open-air conventicles were held in all parts of the provinces, and the fierce Calvinist preachers raised the religious excitement of their hearers to such aitch that it found vent in a furious outburst The lcono- P oasts.Advertisement
- then to the paying-out drum P, from it to the dynamometer D, and finally to the stern pulley, over which it passes into the sea.
- The whole system provides the means of giving sufficient back-pull to the cable to make it grip the drum P, round which it passes several times to prevent slipping.
- On the same shaft with P is fixed a brake-wheel furnished with a powerful brake B, by the proper manipulation of which the speed of paying out is regulated, the pull on the cable being at the same time observed by means of D.
- The shaft of P can be readily put in gear with a powerful engine for the purpose of hauling back the cable should it be found necessary to do so.
- One very great advantage in this method is that the instrument used between P and Q may be of any ordinary form, i.e.Advertisement
- The length paid out and the rate of paying out are obtained approximately from the number of turns made by the drum P and its rate of turning.
- The earliest successful form was " Bright's bell " sounder, which consisted of two bells of distinct tone or pitch, one of which was sounded when the current was sent in one [[International Code O]] --- 4 - 5 p-- - 6 R - 7 '...'
- joined between P and Q.
- The P Line Receiving Instrument R FIG.
- Each J~ 1 1 / Stelein bundle has its own ~ investment of tissue P corresponding with external conjunctive, and now called peridesm.Advertisement
- Apical cell, p. Wall marking limit between the plerome k, initial segment of root-cap. P and the pleriblem Pb.
- This baptism may not be conferred until the candidate has reached an age of discrimination and capacity to remember obligations, p y cere seven years being fixed as the earliest age, but it is generally deferred until manhood.
- P. P.)
- By a modification of the bridge method, applied with excellent results by Dr Muirhead to submarine work, condensers are substituted for a and b, one being also placed in the circuit between P and Q.
- 28, and the levers are adjusted so that the left-hand one moves a, b, c and punches a row of holes across the paper (group i in the figure), the middle one moves b only and punches a centre hole (2 in the figure), while the right-hand one moves a, b, d, e and punches O p p Oa Oa' Ob Od 0?Advertisement
- A and A' by means of two metal pins P, P'.
- The average total inductive value of these bridges to received signals is about 40 henrys, and the coil is so arranged that the arms contain three sections or blocks of winding each, two of which are joined up to strap connexions, and the a p :?; .?
- Elec. Eng., 2 7, p. 869.) In 1899 experiments were made atMenai Straits to put the lighthouse at the Skerries into communication with the coastguard station at Cemlyn.
- Elec. Eng., 27, p. 938.) It may be explained as follows: - Suppose a battery on shore to have one pole earthed and the other connected to an insulated submarine cable, the distant end of which was also earthed; if now a galvanometer is inserted anywhere in the cable, a current will be found flowing through the cable and returning by various paths through the sea.
- Elec. Eng., 27, p.Advertisement
- (Id., 27, p. 852.) In addition to the systems of wireless or space telegraphy depending upon conduction through earth or water, and the in ductive system based upon the power of a magnetic Eelson.
- P: M FIG.
- "3 Schafer, Science Abstracts, 1901, 4, p.
- Ann., 1890, 40, p. 56) employed an arrangement as follows: Four fine platinum or iron wires were joined in lozenge shape, and two sets of these R and S were connected up with two resistances P and Q to form a bridge with a galvanometer G and battery B.
- - A, antenna; P S, jigger or oscillation transformer; C, condenser; 0, Fleming oscillation valve; B, working battery; T, telephone; R, rheostat; E, earth-plate.Advertisement
- 1 p, G r, 2 s, X t and d, V u and o, 8 f, d s (i.e.
- 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.
- Inasmuch as the debenture stocks and preference shares would have to be redeemed in 1911 at premiums ranging from 3 to 5 per cent., the state would have to pay the company £253,000 in excess of the total of the outstanding securities in order to enable the ordinary shares to receive par, and in the council's view this payment would diminish the p robability of the Post Office being able to afford a substantial reduction in the telephone charges.
- p, Pistillate, s, staminate flowers; h, sterile flowers forming a circlet of stiff hairs closing the mouth of the chamber formed by the lower part of the spathe.
- - Stauridium productum, portion of the colony magnified; p, polyp; rh, hydrorhiza.Advertisement
- B, C. multicornis, natural size; p, polyp; gon, gonophores; rh, hydrorhiza.
- to enclose the club in a protective covering form- ?0 ing a cup or vesicle, at first open distally; finally the opening closes and J' P g, ,.
- in this sub-order have received Such are the " snake-like zoids " and as such are generally inter 4"0 ' 'Y p P After Allman, Gymnoblastic Hydroids, by permission of the council of the Ray Society.
- - p elagic floating Hydrozoa with great differentiation of parts, each performing a special function; generally regarded as colonies showing differentiation of individuals in correspondence with a physiological division of labour.
- p, Pneumatophore.Advertisement
- (1750), p.
- BM- Within quite recent years, however, a special school q Y P has arisen with the main object of treating the processes of evolution quantitatively.
- The diocesan synod P Y Y system.
- The relations of their bishops, priests or other ministers and lay office-bearers inter se and to their lay folk depend upon contract; and these Y P P contracts will be enforced by the ordinary courts of law.
- equivalent reQaapa?coo-n) (now superseded by the term p roTEta " the fast"), are derived from the Sunday which was the fortieth day before Easter, as Quinquagesima and Sexagesima are the fiftieth and sixtieth, Quadragesima being until the 7th century the capul jejunii or first day of the fast.Advertisement
- P, Part of spiral hydroid (tracheid) of Phanerogam (Flowering Plant).
- (p) Assimilating (palisade) cells.
- P
- cluding bush-forest in Africa and campos serrados in Brazil P
- The natural su p position that the earth Greek .Advertisement
- The Arctic voyages of Barents were quickly followed by the establishment of p u a Dutch East India Company; and the Dutch, ousting the Portuguese, not only established factories on the mainland of India and in Japan, but acquired a preponderating influence throughout the Malay Archipelago.
- The pseudo-coprolites of the Suffolk Crag have been estimated by Herapath to be as rich in phosphates as the true ichthyo-coprolites and saurio-coprolites of other formations, the proportion of P 2 O 5 contained varying between 12.5 and 37.25%, the average proportion, however, being 32 or 33%.
- The acid renders it available as a manure by converting the calcium phosphate, Ca 3 P 2 O 8, that it contains into the soluble monocalcium salt, CaH 4 P 2 O 8, or "superphosphate."
- p, Parietal.
- P tO u:..,.. ?
- It has several marked deficiencies compared with Australia, among which are the babblers (Timeliidae), weaver birds (Ploceidae), the Platycercinae among parrots, diurnal birds of p rey and the emeus.
- In the exile, but probably after 50o B.C., an important section of the Hexateuch, usually called the Priest's Code (P), was drawn up. At various times in the same century are to be placed the book of Job, the post-exilic parts of Isaiah, the books of Joel, Jonah, Malachi and the Song of Songs.
- P ?
- In the Geonic period there came into prominence the sect of the Karaites (Bene migra, " followers of the Scripture", the Protestants of Judaism, who rejected rabbinical authority, basing their doctrine and practice exclusively on The g P Y ICaraltes.
- He was born at Cordova in 1135, fled with his parents from persecution in 1148, settled at Fez in i 160, passing P g there for a Moslem, fled again to Jerusalem in 1165, and finally went to Cairo where he died in 1204.
- From Garmat Ali, where the Tigris and Euphrates at present unite,' under the title of Shattel-Arab, the river sweeps on to Basra, Ex p o yds.
- Disulphuryl chloride, S 2 O 5 C1 2, corresponding to pyrosulphuric acid, is obtained by the action of sulphur trioxide on sulphur dichloride, phosphorus oxychloride, sulphuryl chloride or dry sodium chloride: 650 3- + 2POC1 3 = P 2 O 5 + 3S 2 O 5 C1 2; S2C12+ 5503 = S 2 0 5 C1 2 + 550 2; SO 3 + SO 2 C1 2 = S 2 0 5 C1 2; 2NaC1 + 3SO 3 = S 2 0 5 C1 2 -1 Na 2 SO 4.
- p apal s.
- On the whole it seems most likely that, while the kernel of the Roman plebs was rural or belonged to the small towns admitted to the Roman franchise, the Attic demos, largely at least, though doubtless not wholly, arose out of the mixed settlers who had come together in the city, answering to the p rotKot of later times.
- Thus at Athens 1 its history is in its main outlines very much the same as its history at Rome up to a Y Y P certain point, while there is nothing at Athens which at all answers to the later course of things at Rome.
- P.
- In addition to this there are certain writings by his son Isidorus H€pc irpoaOuous, liuxiis; EO iy17ruca on the prophet Parchor (HapXci p); 'HBcrca.
- (P. A.)
- Y g Y P process, so manipulated as to secure an overwhelming preponderance for the wealthy, and especially the landed classes, and also for the representatives of the Russian as opposed to the subject peoples.
- Each province of the empire, except the now disfranchised steppes of Central Asia, 7 returns a certainro ortion of members (fixed in each case by P P (Y law in such a way as to give a preponderance to the Russian element), in addition to those returned by certain of 2 M.
- As a legislative body the powers of the Council are co-ordinate with those of the Duma; in practice, however, it has seldom if ever initiated legislation.6 The Duma of the Empire or Imperial Duma (Gosudarstvennaya Duma), which forms the Lower House of the Russian parliament, consists (since the ukaz of the znd of June 1907) on the 27th of April 1906, while the name and princi p le of autocracy was jealously preserved, the word " unlimited " vanished.
- Every industrial concern employing fifty hands or over elects one or more delegates to the electoral P ?
- ': opal e ° °o T A R ple ' ag a ',ap iJ,wl Karkinit A C K r B L Scale, English Miles D S E A 32 Stavropol P O L A PI A N L A s E Derbent ° I?
- By the law of the 18th of October (November i) 1905, to assist the emperor in the supreme administration a Council of Ministers (Sovyet Ministrov) was created, under a ministerresident the first a earance of a rime P, PP P minister in Russia.
- p principles: the separation of the judicial and administrative functions, the independence of the judges and courts, the publicity of trials and oral procedure, the equality of all classes before the law.
- Those of them who lived on the outskirts of the pacified territory adopted a mode of life similar to that of their hereditary opponents, and constituted a peculiar class known as Cossacks, living more by flocks and The h e rds and by marauding expeditions than by a ri y g p ?'
- p p These had been detected and pointed out by learned ecclesiastics of Kiev, where some of the ancient learning of Byzantium had been preserved, and Nikon determined to make the necessary corrections.
- obtained for the Roman Catholics certainrivile es with regard to the Holy Places in The Holy P g ?'
- 2 The law establishing individual peasant-proprietorship was p assed on December 21st.
- More recently legislation has beenassed to safeguard the lives and interests of Hours of P g Lab ur.
- P Y of risk, it has during recent years come to notice that the number of casualties among railway servants is still unduly great, and in 1899 a Royal Commission was appointed to investigate the causes of the numerous accidents, fatal and nonfatal, to railway men.
- The points over which a train travels when directed from the main to a branch line are called " facing points " (F P), while those which it passes when running from a branch to a main line are " trailing points " (TP).
- Where, as at a double-line junction, one pair of rails crosses another pair, " diamond " crossings (p) are formed.
- Between A and B, A and C, and A and D, there may be a string of stations, p, q, r, s, &c., all receiving goods from a, b, c and d, and it would manifestly be inconvenient and wasteful of time and trouble if the trains serving those intermediate stations were made up with, say, six wagons from a to p next the engine, five from b to p at the middle, and four from c to p near the end.
- The weight W 1 carried by the part of the frame supported by the wheel (whose diameter is D) is transmitted first to the pins P 1, P2, which are fixed to the frame, and then to the spring links L 1, L2, which are jointed at their respective ends to the spring S, the centre of which rests on the axle-box.
- Let p be the mean pressure in pounds per square inch, calculated from an indicator diagram taken from a particular cylinder when the speed of the crank-shaft is n revolutions per second.
- The plotting of the torque curve is laborious, but the average torque acting, which is all that is required for the purposes of this article, can be found quite simply, thus: - Let p be the mean effective pressure acting in one cylinder, a, the area of the cylinder, and 1, the stroke.
- Assuming that the mean pressure in the other cylinder is also p, the total work done per revolution is 4pla.
- Hence, if p is the maximum value of the mean effective pressure corresponding to about 85% of the boiler pressure,, uW = pd 2 le /D (26) is an expression giving a relation between the total weight on the coupled wheels, their diameters and the size of the cylinder.
- If p is the mean pressure at any speed the total tractive force which the engine is exerting is given by equation (25) above.
- per second, the total resistance R, which the engine can overcome at this s p eed, is by equation (10) R=(1190X550)/88=7.400 lb.
- For a stated value of the boiler pressure and the cut-off the mean pressure p is a function of the piston speed v.
- 164.) Substituting this value of p in (27) I.H.P. _ (c av (29) 550 the form of which indicates that there is a certain piston speed for which the I.H.P. is a maximum.
- This type has the advantage of economy in first construction, there being the minimum amount of material to be excavated, and no interference during construction with street traffic or subsurface structures; it has, however, the disadvantage of the cost of o p eration of lifts at the stations.
- The cable is slow; and unless development along new lines of com p ressed air or some sort of chemical engine takes place, electricity will monopolize the field.
- (Leben des Ministers Freiherrn vom Stein (6 vols., 1849-1855); also, in an abridged form, Aus Steins Leben (2 vols., 1856) ° Scale, 1:12,000,000 English Miles p 50 Boundaries of Departments & Provinces Capitals Departments & Prouinces Railways Tumbez Trujillo
- The documents underlying the Pentateuch and book of Joshua, represented by the ciphers J, E, D and P, are assumed to have been drawn up in the chronological order in which those ciphers are here set down, and the period of their composition extends from the 9th century B.C., in which the earlier portions of J were written, to the 5th century B.C., in which P finally took shape.
- The view of Professor Dillmann, who placed P before D in the regal period (though he admitted exilic and postexilic additions in Exod., Levit.
- On the other hand, according to P (Ex.
- It should be noted that in P (Code of Holiness) Lev.
- p: 564 (ed.
- To a certain extent it would seem that even as Chronicles (q.v.) has passed through the hands of one who was keenly interested in the Temple service, so the other historical books have been shaped not only by the late priestly writers (symbolized in literary criticism by P), but also by rather earlier writers, also of priestly sympathies, but of " southern " or half-Edomite affinity.
- To this age we may ascribe the literature of the Priestly writers (symbolized by P), which differs markedly from the other sources.
- Wolf, Menasseh ben Israel's Mission to Cromwell, p. lxxv.).
- It is clear that the rulers, as so P p commonly in ancient states, fulfilled priestly as well as royal functions.
- About forty years later (197) the question was discussed in a very different spirit between Victor, bisho p of Rome, and Polycrates, metropolitan of proconsular Asia.
- And as in Hebrew, the six letters b g d k p t are aspirated when immediately preceded by any vowel sound.
- Such a mitre appears on a seal of Archbisho p Thomas Becket (Father Thurston, The ?P allium, London, 1892, p. 17), The custom was, however, .already growing up of setting the horns over the front and back of the head instead of the sides (the mitre said to have belonged to St Thomas Becket, now at Westminster Cathedral, is of this type), 1 and with this the essential character of the mitre, as it persisted through the middle ages, was established.
- They have continued to be worn, however, by the bishops of the Scandinavian Lutheran Y P Churches.
- P - P.)
- (P. VI.)
- p1, pl, The two lateral divisions p, p,1, The three inner, of the inner perianth.
- p-- st--- FIG.
- p, Petals.
- The Hebrew titles ascribe to him seventy-three psalms; the Septuagint adds some fifteen more; and later opinion, both Jewish p and Christian, claimed for him the authorship of the whole Psalter (so the Talmud, Augustine and others).
- Brunelli in L'Arte, 1907, p. 47.) The crypt contains three ancient sarcophagi.
- Among the Terebelloidea there is a remarkable differentiation of the ne p hridia into two series.
- b.z, Budding zone; p, anterior region of the parent worm; 1-5, buds.
- Let AB be the major axis of the orbit, B the pericentre, F the focus or centre of motion, P the position of the body.
- Drop the perpendicular RPQ through P, the position of the planet, upon the major axis.
- - (Residence at the Court of London, p. 286.) Bentham's love of flowers and music, of green foliage and shaded walks, comes clearly out in this pleasant picture of his home life and social surroundings.
- One of the most p im ortant ways of keeping insect pests in check is by " spraying " or " washing."
- But in his character as phenomena must be examined or what may be neglected p y g in economic inquiry.
- burr.- p T 9 pl.y ped.g: reversal of the cleavage planes in sinistral as compared with dextral forms. The facts, however, strongly suggest that the original cause of the torsion was the weight of the exogastric shell and visceral hump, which in an animal creeping on its ventral surface necessarily fell over to one side.
- k, 1, p, J affords a means of test ing the conclusion that we have in Lankester's 4 capito-pedal bodies the rudimentary ctenidia.
- p, Pedal nerve.
- p, Snout.
- p, Penis.
- P, Pedal ganglion with otocyst attached.
- P sp, Supra - intestinal visceral ganglion on the course of the right visceral cord.
- P, A, FIG.
- p, Liver.
- - P l e u r o c e r i d a e.
- k, Opening of the albuphrodite duct, which very soon becomes miniparous gland into P Y the hermaphrodite entwined in the spire of a gland - the duct.
- greatest differences as to the amount p of food-material by which the egg-shell is encumbered.
- Cephalic disk enlarged anteriorly, forming an open tube posteriorly; shell external, thick, with p:ominent spire; no operculum.
- o and p, The liver.
- In the district, and es p ecially at Salobrena, 3 m.
- - Thorax of Saw-Fly (P I, Dorsal view.
- p, Coxa of hind leg.
- p, Pericardial septum.
- p YP, gg FIG.
- The same deficiency became still more apparent when, between 1869 and 1871, he published his Hand-List of Genera and Species of Birds in three 1813-1814, p. xxviii.); but, through the derangements of that stormy period, the order was never carried out (Mem.
- p. xcvii.).
- Among contem p orary writers in a more popular style are John Burroughs; Herbert K.
- Y Y P > > much skill, elaborated from them the excellent work known as Nitzsch's Pterylographie, which was published at Halle in 1840, and translated into English, for the Ray Society in 1867.
- This thereat German comparative anato- Johannes great p mist did in two communications to the Academy of Sciences of Berlin, one on the 26th June 1845 and the other on the 14th May 1846, which, having been first briefly published in the Academy's Monatsbericht, were afterwards printed in full, and illustrated by numerous figures, in its Abhandlungen, though in this latter and complete form they did not appear in public until 1847.
- No doubt they all agreed in saying that they were prosecuting Y g Y g Y P g a search for what they called the true system of nature; but that was nearly the end of their agreement, for in what that true system consisted the opinions of scarcely any two would coincide, unless to own that it was some shadowy idea beyond the present power of mortals to reach or even comprehend.
- The dates of the various parts of the existing ducal palace are indicated on the plan; the rebuilding was carried on in the following order, P, Q, R, S, T, U, V.
- The pedal equation is r 3 =a 2 p, which shows FIG.
- According to the system of phonetic changes generally known as "Grimm's law," an original b appears in English as p, an original bh as b.
- An original medial p preceding the chief accent of the word also appears as b in English and the other members of the same group. It is not certain that any English word is descended from an original word beginning with b, though it has been suggested that peg is of the same origin as the Latin baculum and the Greek (6 KTpov.
- (P. G1.)
- y P P to assume heavy risks.
- The work of the committee is by no means simple, as frequently very few transactions take place p ?
- p in the kinds of cotton of which quotations are given.
- This question can readily be answered as regards the past forty years or so, for which material g p y y ?
- P, Proboscis.
- ' °° p Q; i r ' Afayette A(l.
- P f'
- y, P J ° c.
- > Ft.Drum O,p t ?S 1 1 ?
- p ff"Nocatee ti Braden n atee ?i ?
- A change of the Hebrew text seems necessary; possibly we should read S1p $t"', "low is the voice," instead of 51p$ o'p', "he rises up at the voice."
- Its consonants are k, g, ng, ch, j, n, t, d, n, p, b, m, y, r, l, w, s, h.
- This paper is principally based on the following general theorem, which is a remarkable extension of Pascal's hexagram: "If a polygon move so that each of its sides passes through a fixed point, and if all its summits except one describe curves of the degrees m, n, p, &c., respectively, then the free summit moves on a curve of the degree 2mnp. ..
- P. A.)
- We put e for the eccentricity of the ellipse, represented P, by the ratio M CF: CA.
- Let P, P' be two consecutive positions of the radius vector.
- Since the area of the triangle FPP' is one half the product of FP into the perpendicular p from P on FP', it follows that if these perpendiculars were equal all round the orbit, the areas described during the infinitesimal time would be smallest at the pericentre and continually increase during the passage of the body to B.
- It follows that p must be greatest at pericentre, where its distance from F is least.
- By geometrical consideration it can be shown that the angle subtended by p, as seen from F, must be inversely as the square of its distance r.
- Representing by P this position, it follows that the area of that portion of the ellipse contained between the radii vectores FB and FP will bear the same ratio to the whole area of the ellipse that t does to T, the time of revolution.
- The p y ?
- g p Atticus in memory of his wife Regilla, is comparatively well preserved; it was excavated in 1848 and in 1857-1858.
- When Athens became the capital in 1833 the ancient name of The P 33 Peiraeus.
- Bibliography.-C. Imbault-Huart, L' p le Formose, histoire et description (Paris, 1893), 40; J.
- in which to keep his 6, 6, North and south vaulted transepts p (the dotted lines show the curve clothes and books; these of the vault).
- g p p from the earliest times.
- Group V.: N, trivalent and pentavalent, but divalent in nitric oxide; P, As, Sb, Bi, trivalent and pentavalent, the last being possibly divalent in BiO and BiC1 2.
- 1.2 or 1.6, named ortho- (o), 1.3 or 1.5, named meta- (m), and 1.4, named para- compounds (p).
- Di-derivatives x x x p v as $ v as s Here we have assumed the substituent groups to be alike; when they are unlike, a greater number of isomers is possible.
- 1 7, p. 1 347), who has also suggested the use of manganese carbonate instead of magnesite, since the change of colour enables one to follow the decomposi 411=ThEIZ P; FIG.
- Eliminating a and b between these relations, we derive P k V k /Tk= 8R, a relation which should hold between the critical constants of any substance.
- If, however, an amount of energy a is taken up in separating atoms, the ratio is expressible as C p /C„= (5+a)/(3-Fa), which is obviously smaller than 5/3, and decreases with increasing values of a.
- These relations may be readily tested, for the ratio C p /C„ is capable of easy experimental determination.
- Let double bonds be present, in number p, and let the energy due to such a bond be Y.
- ' C 6 Hcooh C?H 4`C'p C s H COOH Polymorphism.
- Mitscherlich, in the case of the acid phosphate and acid arsenate of potassium, KH 2 P(As)04, who adopted the term isomorphism, and regarded phosphorus and arsenic as isomorphously related elements.
- By taking appropriate differences the following facts will be observed: (1) the replacement of potassium by rubidium occasions an increase in the equivalent volumes by about eight units, and of rubidium by caesium by about eleven units; (2) replacement in the same order is attended by a general increase in the three topic parameters, a greater increase being met with in the replacement of rubidium by caesium; (3) the parameters x and, p are about equally increased, while the increase in w is always the greatest.
- S, Se; Te (in tellurides); Cr, Mn, Te (in the acids H 2 RO 4); As, Sb (in the glances MR2) As, Sb, Bi; Te (as an element); P, Vd (in salts); N, P (in organic bases).
- In Greek, where I is the twentieth letter of the alphabet, or, if the merely numerical and p are excluded, the eighteenth, another form 1 or S according to the direction of the writing is also widespread.
- (P. Gx.)
- Lumby (Cambridge, 1883), supplemented a little„by Edward Hall (Chronicle, p p. 3 6 3-3 6 4).
- A distinguished philosopher or man of letters would find them bidding f o r his presence, and most of the great names are p ?
- Ducarla, published his La France consideree da p s les dijferentes hauteurs de ses plaines (1791), upon which equidistant contours at intervals of 16 toises found a place.
- O IXC a P orrelln, nafurr d Yae?a?
- _? ?w?lan F?,o i o a p oba - ?
- Of SchOner we know that he produced four globes, three printed from segments (1515, 1523, 1 533), and p SCF12MER.S FIG.
- This map was repeatedly revised, Antgria- g P P Y ?
- Although many " General " and other meetings were held in different Period of parts of the country for the purpose of setting P Y P P g forth Quakerism, the notion that the whole Christian church would be absorbed in it, and that the Quakers were, in fact, the church, gave place to the conception that they were " a peculiar people " to whom, more than to others, had been given an understanding of the will of God.
- woman to offer vocal prayer, to read the Scriptures, p or to utter such exhortation or teaching as may seem to be called for.
- ` Hv6 X aQOV µ7 7 EA p s.
- This identification can only be p urchased at the cost of a complete renunciation of the Avestan genealogy.
- 40p i i), pasture, (b p(3ecv, to feed, Sans.
- 10), protected ° - - from irreverence by lattice work (tra p - ` j '.?- ' `- sennae) of marble.
- 4 p .`3 D ° a d a D ?aD?paD paoDL,?
- p ©?ii 'o ?e0 ?? ?
- In the Titanotheroidea the dentition may be expressed by the formula i: oru, ci, p T 4,, my.
- The dentition is i, c 1, p 4, m L total 42.
- Fully realizing, the difficult P Y g?
- If a brief definition of instinct, from the purely biological point of view be required, that given in the Dictionary of Philosophy and Psychology may be accepted: "An inherited reaction of the sensori-motor type, relatively complex 3'p 3' p and markedly adaptive in character, and common to a group of individuals."
- Originally - P Y g Y residents at Santiago de Cuba, the captains-general resided after 1589 at Havana.
- Piron, L' p le de Cuba (Paris, 1876).
- P For sulphonic acids containing nitrogen see Ammonia.
- Berthelot, Comptes rendus (1907), 1 44, P z69
- (P. Vi.)
- p I .,' a I ??
- p n, 5 1 ?
- 'P V y ndina st .
- P Mctso^o Gr/ 4 ?
- bn a p.
- When he had ruthlessly quelled the resistance offered to his accession by his brothers, who both fell in the struggle for the throne, Selim undertook his campaign in Persia, having first extirpated the Shia heresy, prevalent 5 e 12 m, g P Y, P 1512152.0.
- P Europe, after the suppression of a revolt of the governor of Damascus, who had thought to take advantage of the new sultan's accession to restore the independent rule of the Circassian chiefs.
- He imroved the laws and institutions established by p i his predecessors and adapted them to the require ments of the age; to him are due important modifications in the feudal system, aimed.
- Y P P importance.
- p expenditure, facilitated by the enthusiasm created in Europe by Turkey's admission to the ranks of the powers which loosened for her the purse-strings of the foreign investor.
- p. 197.) From 1890 Crete was frequently the scene of disturbance., the Christian communities in other parts of Turkey began to.
- Their central organization was in Paris and their objects were known throughout Europe, but except at Yildiz Kiosk their power was P P p almost everywhere underrated.
- P. Pick; but in the present state of our knowledge, however, p g > the older classification of E.
- In 734 their king Sanip(b)u was a vassal of Tiglathpileser IV., and his successor, P(b)udu-ilu, held the same position under Sennacherib and Esarhaddon.
- Chemie, 1889, p. 96; and 1892, 9, p.
- The result of the investigation shows that the electrical work Ee is given by the_equation Ee =1 where v is the volume of the solution used and p its osmotic pressure.
- On the analogy between this case and that of the interface between two solutions, Nernst has arrived at similar logarithmic expressions for the difference of potential, which becomes proportional to log (P 1 /P 2) where P2 is taken to mean the osmotic pressure of the cations in the solution, and P i the osmotic pressure of the cations in the substance of the metal itself.
- Yet later the co p e seems to have been authoritatively proscribed with the rest.
- Tubes are generally made up around mandrels, and allowed throughout the curing to remain imbedded i n p u lverized French chalk, which affords a useful support for many articles that tend to lose their shape during the process.
- To the east of the Yablonoi border-range p l ateau: lies the lower terrace of the high plateau, reaching 2000 to 2500 ft.
- P, Peduncle.
- On the opposite side of Betanzos Bay (the p yas Acµl i v or Portus Magnus of the ancients) is the great port of Corunna or Coruna.
- b., we obtain by comparison with the middle series the symbolical representation of all symmetric functions in brackets () appertaining to the quantities p i, P2, P3,ï¿½ï¿½ï¿½ To obtain particular theorems the quantities a l, a 2, a 3, ...a, n are auxiliaries which are at our entire disposal.
- p, g 5
- Since the determinant having two identical rows, and an3 an3 ï¿½ï¿½ï¿½ ann vanishes identically; we have by development according to the elements of the first row a21Au+a22Al2 +a23A13+ï¿½ï¿½ï¿½ +a2nAin =0; and, in general, since a11A11+a12A12 +ai 3A13+ï¿½ï¿½ ï¿½ +ainAin = A, if we suppose the P h and k th rows identical a A +ak2 A 12 +ak3A13+ï¿½ï¿½ï¿½ +aknAin =0 (k > i) .and proceeding by columns instead of rows, a li A lk +a21A2k + a 31A3k+ï¿½ï¿½ï¿½+aniAnk = 0 (k .>
- so that A breaks u p into a sum of determinants, and we also obtain a theorem for the addition of determinants which have rows in common.
- We can solve these, assuming them independent, for the - i ratios yl, y2,...yn-iï¿½ Now a21A11 +a22Al2 ï¿½ ï¿½ ï¿½ = 0 a31A11+a32Al2 +ï¿½ ï¿½ï¿½ +a3nAln = 0 an1Al1+an2Al2 +ï¿½ï¿½ï¿½+annAln =0, and therefore, by comparison with the given equations, x i = pA11, where p is an arbitrary factor which remains constant as i varies.
- Resultant Expressible as a Determinant.-From the theory of linear equations it can be gathered that the condition that p linear equations in p variables (homogeneous and independent) may be simultaneously satisfied is expressible as a determinant, viz.
- For if u, v, w be the polynomials of orders m, n, p respectively, the Jacobian is (u 1 v 2 w3), and by Euler's theorem of homogeneous functions xu i +yu 2 +zu 3 = mu xv1 +yv2 +zv3 = /IV xw 1+y w 2+ zw 3 = pw; denoting now the reciprocal determinant by (U 1 V2 W3) we obtain Jx =muUi+nvVi+pwWi; Jy=ï¿½.., Jz=..., and it appears that the vanishing of u, v, and w implies the vanishing of J.
- Further, if m '=' p, we obtain by differentiation 7+x =m (u;1-2xl.
- p 1 p 2 ...p n), it is necessary to bring under view other functions associated with the same series of numbers: such, for example, as P P3 P2 P4 Pn -2 /, /, /, F i a i 1 a 2 Fi a 1 a 2 ...
- A partition, (pipipip2p2p3) = can be separated in the manner (p 1 p 2) (PIP2) (p1P3) = (1)12,2) 2 (plp3), and we may take the general form of a partition to be (pi i p2 2 p3 3 ...) and that of a separa tion (J 1) 1 1(J 2) 5 2(J 3) 1 3...
- (P i +Y2+t' +...-1)!
- ï¿½ ï¿½ P1 v2 v3...) ï¿½ For, writing as before, Xm 'Xm 2 Xm '= zzo(SQls:2s73...) xi'x12x13..., 1 2 3" 1231 2 3 = EPxi l x A2 x A3, P is a linear function of separations of(/ 1 / 2 A2 / 4 3 3 ...) of specification (m"`1mï¿½2m"`3...), and if X; 1 X 3 2X8 3 ' ..
- The law of reciprocity shows that p(s) = zti (m 1te2tmtL3t) t=1 st It 2t 3t viz.: a linear function of symmetric functions symbolized by the k specifications; and that () St =ti ts.
- A table may be formed expressing the k expressions Pa l), P(2),...P(1) as linear functions of the k expressions (m"`'smï¿½2smï¿½3s...), s =1, 2, ...k, and the numbers BSc occurring therein is 2s 3s possess row and column symmetry.
- P(s) _ /ll8!/12s!/23s!...
- appertaining to the function (li'l32l3...), each separation having a specification m" ` ' 8 m ï¿½2s m ï¿½38 multiply b P (is 2s 3s .ï¿½ï¿½), P Y by ls!
- so that f (al, a 3, a3,.ï¿½.an) =f, a rational integral function of the elementary functions, is converted into f(a1 +12, a2+ p a1,...
- Write also s l d1= D, so that f(a i a2+ p al, ...an+Ilan-1) =f +FLDif +F4 2 D2f + t i 3 D 3 f -}-....
- The introduction of the quantity p converts the symmetric function 1 2 3 into (XiX2X3+...) -Hu Al (X 2 A 3 .-) +/l02(X1X3.ï¿½.) +/103(A1X2.ï¿½.) +....
- p operators D upon a monomial symmetric function is clear.
- +AsDs ...) p Di p2 D2+...
- +an we may write in general D s f = ZD(p l p 2 p 3 ï¿½ï¿½) the summation being for every partition (piP2p3...) of s, and D(p iP2 p 3 ...)f being =2 (Dpifi)(DP2f2) (DL'h3f3)f4...f,n.
- We have the theorem (I I, v; m, n) (/l l, v l; ml, n i) - (Il l, P 1; m l, n ') (/l, v; m, n) = (11, vl; ml, ni); where 1 /l1= (ml +m-1) ml (/l +nlv) - u-2 Cu '+nvl) 1 1 m-1 1 m1-1 vl =(n -n)vv-E ml / lY- m /lv, m i =7111+m-I, n1=nl+n, and we conclude that qua " alternation" the operators of the system form a " group."
- p, taking n equal to 00, we may write 1 +aix +a2x2 +...
- _ (1 + p ix) (1 + P2x) ...
- Denote by brackets () and [] symmetric functions of the quantities p and a respectively.
- Then 1111 + a i[ 1 ]+ a i [12 1+a2[ 2 ]+ a 7 [13] +ala2[ 21 ]+a3[3]+-ï¿½ + a p1 a p2 a P 3 ï¿½ï¿½ .ap rn[Y1 p 2t' 3 ...
- +amaa.)sm, (ll, v; m P -"O a an + (l l + v) (ll +2 v) (m (11 +3v) +...], m - 2 2 !2 a 0 a 1 aan +2 !
- ï¿½, and (alai +(72a2+a3a3+ï¿½ï¿½ ï¿½) P = (Pith +P2t2 +P3f 3 3+ ï¿½ ï¿½ ï¿½) P ï¿½ Instead of the above symbols we may use equivalent differential operators.
- P y q +...
- /,) (-)P+4-laP4 (p i+ g l - 1) !
- Further writing 1 +hlox+holy+...+ hpgx P y {-...
- Writing D = gi d od p!
- 1 exp(Adlo + vdol) = (1+/oD10+ v Doi +..ï¿½+ VQ +.ï¿½.)f; now, since the introduction of the new quantities 1.1., v results in the addition to the function (plglp2g2p3g3...) of the new terms A PI Pg1 (p 2q2 p 3g3ï¿½ï¿½ï¿½) +/ AP2Pg2 (p 1 g 1P343 ...)+/ Z3vg3 (p l g i p 2 g 2 ...)+ ï¿½, we find DP141(plqip2q2p3q3ï¿½ï¿½ï¿½) = (p 2 q 2 p 3 q 3ï¿½ï¿½ï¿½), and thence D P141 D P242 D P343 ï¿½ï¿½.
- (p g p, g p, g3 ï¿½ï¿½ï¿½) = I; while D rs f =o unless the part rs is involved in f.
- P141 P242 ï¿½ï¿½ï¿½ -1 hp, - hpg = is converted into where dlo = d a P,q-1 - dapg vanish.
- In the present particular case putting m 10 = 1 2, mot= v and m P4 =o otherwise M10t+M01n+...+Mpot P n 4 +...
- =log (1 +ï¿½t+vn) M P4 = (_)p+4 -1(p+g 1)!ï¿½p p 4; p!g!
- +1,q p l !gll p2!g2!
- Recalling the formulae above which connect s P4 and a m, we see that dP4 and Dp q are in co-relation with these quantities respectively, and may be said to be operations which correspond to the partitions (pq), (10 P 01 4) respectively.
- p. 493) that the operation 1 1 d P?
- We may remark the particular result (-) p + p q!
- Since dp4+(-)P+T1(p +q qi 1)!dd4, the solutions of the partial differential equation d P4 =o are the single bipart forms, omitting s P4, and we have seen that the solutions of p4 = o are those monomial functions in which the part pq is absent.
- =d P 4 lodp+1,4 -holdp,4+1+...+(-)r+shrsdp+r,4+s+..
- )- (p+4-1 (p - - q -1)!dpq+ ?l -) 1)!D'1 DT2 p!g!
- the i t " power of that appertaining to a x and b x multiplied by the j t " power of that appertaining to a x and c x multiplied by &c. If any two of the linear forms, say p x, qx, be supposed identical, any symbolic expression involving the factor (pq) is zero.
- possess the invariant property, and we may write (AB) i (AC)'(BC) k ...A P E B C...
- The existence of such forms seems to have been brought to Sylvester's notice by observation of the fact that the resultant of of and b must be a factor of the resultant of Xax+ 12 by and X'a +tA2 for a common factor of the first pair must be also a common factor so we obtain P: = of the second pair; so that the condition for the existence of such common factor must be the same in the two cases.
- The Hessian 0 =A 2 is such that (f, 2 and if f is expressible in the form X(p x) 3 +,i(g x) 3, that is as the sum of two perfect cubes,.
- we find that Di must be equal to p x g x for then t x (p x) 3 +, u (g x) 3, Hence, if px, qx be the linear factors of the Hessian 64, the cubic can be put into the form A(p x) 3 +ï¿½(g x) 3 and immediately solved.
- For it is easy to establish] the formula (yx) 2 0 4 = 2f.4-2(f y 1) 2 connecting the Hessian with the quartic and its first and second polars; now a, a root of f, is also a root of Ox, and con se uentl the first polar 1 of of q y p f?
- Remark.-The invariant C is a numerical multiple of the resultant of the covariants i and j, and if C = o, p is the common factor of i and j.
- v., established the important result that in the case of a form in n variables, the concomitants of the form, or of a system of such forms, involve in the aggregate n-1 classes of aa =5135 4 +4B8 3 p) =0, =5(135 4 - 4A 2 p 4) =0, P yield by elimination of S and p the discriminant D =64B-A2.
- When a z and the invariants B and C all vanish, either A or j must vanish; in the former case j is a perfect cube, its Hessian vanishing, and further f contains j as a factor; in the latter case, if p x, ax be the linear factors of i, f can be expressed as (pa) 5 f =cip2+c2ay; if both A and j vanish i also vanishes identically, and so also does f.
- Solving the equation by the Ordinary Theory Of Linear Partial Differential Equations, We Obtain P Q 1 Independent Solutions, Of Which P Appertain To S2Au = 0, Q To 12 B U =0; The Remaining One Is Ab =Aobl A 1 Bo, The Leading Coefficient Of The Jacobian Of The Two Forms. This Constitutes An Algebraically Complete System, And, In Terms Of Its Members, All Seminvariants Can Be Rationally Expressed.
- The General Term Of A Seminvariant Of Degree 0, 0 And Weight W Will Be A A A Appb°Ob°1B°2...B°4 _ 0 1 2 P 0 1 2 Q P Q P Q Where Ep S =0, Eas=0 And Esp, A Es,=W.
- 1111 The Number Of Such Terms Is The Number Of Partitions Of W Into 0 0 Parts, The Part Magnitudes, In The Two Portions, Being Limited Not To Exceed P And Q Respectively.
- Denote This Number By (W; 0, P; 0'.
- The Number Of Linearly Independent Seminvariants Of The Given Type Will Then Be Denoted By (W; 0, P; 0', Q) (W; 0, P; 0', Q); And Will Be Given By The Coefficient Of A E B E 'Z W In L Z 1 A.
- 1 Ze'; Which Preserves Its Expression When 0 And P And 0 And Q Are Separately Or Simultaneously Interchanged.
- Taking The First Generating Function, And Writing Az P, Bz4, 2 For A, B And Z Respectively, We Obtain The Coefficient Of Aobe'Zpo 0' 2W That Is Of A E B E 'Z ï¿½, In 1 Z 2 1 Azp. 1 Azp 2....1 A2 P 2.1 Az P .
- Thus, For Two Linear Forms, P =Q = I, We Find 1 Z 2 1 Az.
- If Hebrew, it might be derived from the root p rr (to embrace) as an intensive term of affection.
- p, a thickened line on the walls forming the placenta; c, calyx; d, ovary; s, hooded stigma terminating the short style.
- p, placenta; o, ovules; s, suture, or median line of carpel.
- b, pair of bracteoles below the flower; s, sepals; p, petals; st, stamens; o, ovary.
- No purely astronomical enterprise was ever carried out on so Transits of P large a scale or at so great an expenditure of money and labour as was devoted to the observations of these transits, and for several years before their occurrence the astronomers of every leading nation were busy in discussing methods of observation and working out the multifarious details necessary to their successful application.
- For the resultant force at P, F=-VF r 2.
- Since p can never be infinite, complete shielding is not possible.
- If P is the weight of the magnet, l the length of each of the two threads, 2a the distance between their upper points of attachment, and 2b that between the lower points, then, approximately, MH = P(ab/l) sin 0.
- If 2l is the distance between the poles m and - in, d the distance from either pole to a point P on the line AB (fig.
- 5), we have for the resultant force at P R = - 2cosO X m/d' = - elm/d 3 = - M/d3.
- When P is the neutral point, H is equal and opposite to R; therefore M = Hd 3, or the moment is numerically equal to the cube of the distance from the neutral point to a pole, multiplied by the M.
- The magnetized body which is to be tested should be placed in such a position that the force H P due to its poles may, at the spot occupied by the suspended needle, act in a direction at right angles to that due to the earth - that is, east and west.
- The angle B is indicated by the position of the spot of light upon the scale, and the horizontal intensity of the earth's field H E is known; thus we can at once determine the value of H P, from which the magnetization I of the body under test may be calculated.
- d3H P = d3H And I = v tan B.
- Denoting the distance AM by d 1, BM by d2, and AB by 1, we have for the force at M due to the magnetism of the rod H P =d 12 - horizontal component (dla - d 2 3).
- The force acting on the magnetism of one of the faces, and urging this face towards the other, will be less than B by 27r1, the part of the total force due to the first face itself; hence the force per unit of area with which the faces would press against each other if in contact is P = (B-27rI)I =27rT 2 +HI = (B 2 -H 2) =/81r.
- The width of the gap may be diminished until it is no greater than the distance between two neighbouring molecules, when it will cease to be distinguishable, but, assuming the molecular theory of magnetism to be true, the above statement will still hold good for the intermolecular gap. The same pressure P will be exerted across any imaginary section of a magnetized rod, the stress being sustained by the intermolecular springs, whatever their physical nature may be, to which the elasticity of the metal is due.
- The whole of the rod will therefore be subject to a compressive longitudinal stress P, the associated contraction R, expressed as a fraction of the original length, being R = P/M = (B 2 -H2)/87-M, where M is Young's modulus.
- P. Harrison.?
- The equites remained' at home, or only went out as members of the general's staff, their places being taken by the equites equo p y ivato, the cavalry of the allies and the most skilled horsemen of the subject populations.
- (After Lankester, toe cit.) Magnified MOO p GC. D R.
- p 6 (90e00 b ", o o.
- o o 'e ' e c m_o 'o - _ - o i: (t __ '®moo?p ®04 ??a:a??
- p. 152.) in regard to the ovary, and by Benham (14) in regard to the testis.
- p O ??o?, ?_ 0 c?
- p, Pecten.
- p, Telsonic carapace.
- p, The tergal stigmata of the tergo-sternal muscles.
- The sperm is removed by the male from the genital aperture into a special receptacle on the terminal segment P FIG.
- Under side of the uplifted genital or first opisthosomatic somite of the female; g, genital aperture; p, pitted plate, probably a gland for the secretion of adhesive material for the eggs; 1, the edges of the lamellae of the lung-books of the first pair.
- p. 19.)
- It is usually prepared by the so-called "Reimer" reaction (Ber., 1876, 9,p. 1268), in which chloroform acts on phenol in the presence of a caustic alkali, C 6 H 5 OH+CHC1 3 +4KHO = 3KCI+3H20+KOï¿½C6H4ï¿½CHO, some para-oxybenaldehyde being formed at the same time.
- r //,p, r ' an ho ?
- P .Antbpio S.Christovao sranaia imbo inhas antos ?
- 9 eneZd He .aop elo P-or o Alegre VP P'S Continuatio Southward ul (Same Scale) G 46° na, Sao own Para Blumenau 4d
- Among other manufactures are butter and cheese, canned fruits and vegetables, glass and earthenware, printing and wrapping paper, furniture, matches, hats, clothing, pharmaceutical products, soaps and - p erfumery, ice, artificial drinks, cigars and cigarettes, fireworks anc candles.
- The proud minister had been resisted p in his plans of reform at home by the Jesuits, and, determining to attack the power of the order, first deprived them of all temporal power in the state of Maranhao and Para.
- According to these men, even though rationality did not exist in any individual, its existence in nature would still remain intact " (Cousin, Introduction, &c., p. cxx.).
- His authority, was absolute p 3'> too, > being tempered only by the shadowy right of the Magyar nation to meet in general assembly; and this authority he was careful not to compromise by any slavish imitation of that feudal polity by which in the West the royal power was becoming obscured.
- During the long reign of Sigismund (1387-1437) Hungary was brought face to face with the Turkish peril in its most threatening shape, and all the efforts of the king were directed Turkish Turks crossed the Hellespont from Asia Minor and p began that career of conquest which made them the terror of Europe for the next three centuries.
- P g g the emperor Maximilian and Sigismund of Poland, might be dispensed with.
- Ferdinand was elected (Dec. 16) by a scratch assembly consisting of deputies from Croatia and the towns Ferdinand of Pressburg and Sopron; but he speedily improved °fAustr;a g P Y P elected.
- whole of Hungary except Syrmia and the territory g Y p Y Y the peace of Passarowitz (July 21, 1718), by which the Temeskaz was also freed from the Turks, and Servia, Northern Bosnia and Little Walachia, all of them ancient conquests of Hungary, were Once more incorporated with the territories of the crown of St Stephen.
- In 1823, when the reactionary powers were meditating joint action to suppress the - revolution in Spain, the government without consultin P ?
- 26-2 Y P (26-27), was forced to retreat.
- On the 17th of February 1867 a responsible inde pendent ministry was formed under Count Gyula 'p y y ' of 1867.
- " F r ee Principle " party, left p) p y?
- P g P P ment a royal autograph letter stating the reasons which had actuated the king in taking this course, and giving as the task of the new ministry the continuance of negotiations with the Coalition on the basis of the exclusion of the language question.
- Y, 9 P ?, PP ment of a Coalition cabinet 2 under Dr Sandor Wekerle was announced, the world was taken completely by surprise.
- playersg p heroes.
- Thus, while of German periodicals ap p earing in Hungary there were in 1871 only 85, they increased in 1880 to 114, in 1885 to 141; and they were, at the beginning of 1895, still 128, in spite of the constant spread of that process of Magyarization which has, since 1880, considerably changed the linguistic habits of the people of Hungary.
- (b) If A=x times M, then x (iii.) (a) If n= P then x = ?i n.
- (iii.) (a) If p = log i n, then n = (b) If a = n, then n =a'.
- For multiplication, for instance, we have the statement that, if P and Q are two quantities, containing respectively p and q of a particular unit, then p X Q = q X P; or the more abstract statement that p X q= q X p.
- (a) If a = d, then each = p b qd.
- The theory may be extended to the cases of p= i and p = o; so that a 3 means a.a.a.1, a 2 means a.a.i, a 1 means a.i, and a° means I (there being then none of the multipliers a).
- In n = a P, a is the root or base, p is the index or logarithm, and n is the power or antilogarithm.
- But a P is sometimes incorrectly described as " a to the power p "; the power being thus confused with the index or logarithm.
- It should be observed that, by analogy with the definition of a fraction, a P l q mean (al/q)P, not (aP)llq.
- (i.) To divide P by Q, we cut off from P successive portions each equal to Q, till we have a piece R left which is less than Q.
- Thus P = kQ+R, where k is an integer.
- Having obtained R, which is less than Q, we now repeat with Q and R the process that we adopted with P and Q; i.e.
- (iv.) If P and Q can be expressed in the forms pL and qL, where p and q are integers, R will be equal to (p-kq)L, which is both less than pL and less than qL.
- Hence u is the greatest common measure of p and q.
- In order that a monomial containing a m as a factor may be divisible by a monomial containing a p as a factor, it is necessary that p should be not greater than m.
- is then an expression of the form a p b e c r d s, where p, q, r, s have the greatest possible values consistent with the condition that each of the given expressions shall be divisible by a p b e c r d s .
- is of the form a p b e c r d s, where p, q, r, s have the least possible values consistent with the condition that a P PC'd s shall be divisible by each of the given expressions.
- 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.
- Thus from the equation P+Q - R+S=T and the identity P+Q - R+S= P - R +S+Q we have the equation P - R +S+Q=T, which is the same statement as P - R +S=T - Q.
- Thus from P+Q - R+S=T we deduce P+(Q - R+S)=P+(T - P).
- Thus, if we have an equation P=Q, where P and Q are numbers involving fractions, we can clear of fractions, not by multiplying P and Q by a number m, but by applying the equal multiples P and Q to a number m as unit.
- The standard form is usually taken to be ax2+bx+c =0, from which we find, by transformation, (2 ax+b) 2 =b 2 - 4ac, 4 (}b 2 -4ac} -b and thence x = 2a (ii.) In an equation of the form Q=V, the expressions P, Q, U, V are usually numerical.
- It should be observed that, for r=o, (4) is replaced by n (o) _ (n - I)(o) (9), and similarly, for the final terms, we should note that P0)= 0 if 4> p (io).
- 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.
- (b) Let us assume that the product of every set of p consecutive integers is divisible by p!, and let us try to prove that the product of every set of p+ I consecutive integers is divisible by (p+i)!.
- Then the assumption is that, whatever positive integral value n may have, n [P] is divisible by p!.
- But, by hypothesis, n 1P1 is divisible by p!.
- Therefore n 1P+11 -(n-I) (P+11 is divisible by p!.
- Therefore, if (n-i) 1P+11 is divisible by (p+I)!, 'n 1P+11 is divisible b y (p +i) !.
- (c) Thus, if the theorem of ï¿½ 41 (v.) is true for r= p, it is true for r= p+1.
- r!) = (n + r)(r) = (n+r)(n) (17)ï¿½ (iv.) By means of (17) the relations between the binomial coefficients in the form p (4) may be replaced by others with the The most important relations are n[r] = n[r-i]+(n - I)(r) (r8); O[r] = 0 (19); n[r]-(n-s)[r] =n[r-i]+(n- I) [r-1]+...+ (n-s+I)[r-1] (20); n[r] =n[r-1]+(n-I)[r-1]+...+I[r-1] (21).
- The number (n P r) of permutations of r individuals out of a stock of n, all being distinguishable, is n`r).
- If, out of every N cases, where N may be a very large number, a is A in pN cases and not-A in (I - p) N cases, where p is a fraction such that pN is an integer, then p is the probability or frequency of occurrence of A.
- we can replace pr or -pr by (+p)r or (- p)r, subject to the conditions that (+p) (+q) = (-p) (- q) = (+pq), (+p) (-q) = (- p) (+ q) = (-pq), and that + (-s) means that s is to be subtracted.
- 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 numerical value is then represented by (P (; thus " (x (< i " means that xis between -1 and +1.1 50.
- If P and M are rational integral functions of x, arranged in descending powers of x, the division of P by M is complete when we obtain a remainder R whose degree (ï¿½ 45) is less than that of M.
- If R= o, then M is said to be a factor of P.
- (ii.) If x = a satisfies the equation P = o, then poan+plan-1+.
- + p n = o; and therefore the remainder when P is divided by x-a is o, i.e.
- x-a is a factor of P.
- (iii.) Conversely, if x-a is a factor of P, then poand plan - 1 +...
- + p n = o; i.e.
- x= a satisfies the equation P = o.
- (iv.) Thus the problems of determining the roots of an equation P = o and of finding the factors of P, when P is a rational integral function of x, are the same.
- (v.) In particular, the equation P = o, where P has the value in (i.), cannot have more than n different roots.
- We therefore define algebraical division by means of algebraical multiplication, and say that, if P and M are multinomials, the statement " P/M = Q " means that Q is a multinomial such that MQ (or QM) and P are identical.
- 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, ...
- (a+r+ p - i ï¿½b), we divide the product of the p+1 factors which occur either in the nth or in the (n+i)th term by p+ 1, and by the common difference of the factors, and add to a constant, whose value is found by putting n= o.
- obtained by taking the qth root of I + p (1) x+ p (2) x 2 + ..., is an infinite series, i.e.
- The generating functions of the two series, mentioned above, for example, are (I +x)-' n and (I+x) P / Q.
- It can be proved by geometry that (aA-H3B) +yC = aA+(aB+- y C) = (a + 1 3+ 7) P, where P is in fact the centroid of masses a, 13, y placed at A, B, C respectively.
- If ABCD is a tetrahedron of reference, any point P in space is determined by an equation of the form (a+13+ - y+5) P = aA+sB +yC +SD: a, a, y, b are, in fact, equivalent to a set of homogeneous coordinates of P. For constructions in a fixed plane three points of reference are sufficient.
- P Class II.
- Classes: Arachnida, Insecta (including Sub-Classes M y riapoda, Hexapoda), Crustacea (including Sub-Classes Entomostraca, Malacostraca), Epizoa (Epizootic Crustacea), Annellata (Chaeto p ods and Leeches), Cirripedia.
- We imagine a wave-front divided o x Q into elementary rings or zones - often named after Huygens, but better after Fresnelby spheres described round P (the point at which the aggregate effect is to be estimated), the first sphere, touching the plane at 0, with a radius equal to PO, and the succeeding spheres with radii increasing at each step by IX.
- There are thus marked out a series of circles, whose radii x are given by x 2 +r = (r-{- 2nX) 2, or x = nar nearly; so that P ?
- The component vibrations at P due to the successive zones are thus nearly equal in amplitude and opposite in phase (the phase of each corresponding to that of the infinitesimal circle midway between the boundaries), and the series which we have to sum is one in which the terms are alternately opposite in sign and, while at first nearly constant in numerical magnitude, gradually diminish to zero.
- Journ., 18 43, 3, p. 46), determine the law of the secondary wave, by comparing the result of the integration with that obtained by supposing the primary wave to pass on to P without resolution.
- Now as to the phase of the secondary wave, it might appear natural to suppose that it starts from any point Q with the phase of the primary wave, so that on arrival at P, it is retarded by the amount corresponding to QP. But a little consideration will prove that in that case the series of secondary waves could not reconstitute the primary wave.
- Further, it is evident that account must be taken of the variation of phase in estimating the magnitude of the effect at P of the first zone.
- If the primary wave at 0 be cos kat, the effect of the secondary wave proceeding from the element dS at Q is dS 1 dS - p cos k(at - p+ 4 A) = - -- sin k(at - p).
- If dS =27rxdx, we have for the whole effect 27r œ sin k(at - p)x dx, f P ' or, since xdx = pdp, k = 27r/A, - k fr' sin k(at - p)dp= [- cos k(at - p)]°° r.
- If a formal proof be desired, it may be obtained by introducing into the integral a factor such as P, in which h is ultimately made to diminish without limit.
- Taking co-ordinates in the plane of the screen with the centre of the wave as origin, let us represent M by, n, and P (where dS is situated) by x, y, z.
- Then p2 (x +(y - n)2+z2, f +y 2 +z 2; so that p 2 = f 2 -2x - 2yn +S2+n2.
- In the applications with which we are concerned, t, n are very small quantities; and we may take P = x yn - At the same time dS may be identified with dxdy, and in the de nominator p may be treated as constant and equal to f.
- In the case of the circular aperture the distribution of light is of course symmetrical with respect to the focal point p=o, q=o; and C is a function of p and q only through 11 (p 2 -}-q 2).
- Thus, if x = p cos 4), y= p sin 0, C =11 cos px dx dy =f o rt 2 ' T cos (pp cos 0) pdp do.
- p 2 ?
- 2 2 2.4 + 2 2.4 2.6 ' =7-R 2.2J p R) as before.
- In these expressions we are to replace p by ks/f, or rather, since the diffraction pattern is symmetrical, by kr/f, where r is the distance of any point in the focal plane from the centre of the system.
- The greatest brightness is at the centre, where dC = 27rp d p, C = 7rR2.
- Now by (17), (18) z 1 J1(z) =Jo(z)- (z); where P increases.
- When the interval is very small the discrepancy, though mathematically existent, produces no practical effect, and the illumination at B due to P is as important as that due to A, the intensities of the two luminous sources being supposed equal.
- Under these conditions it is clear that A and P are not separated in the image.
- This is necessarily a question of degree; but it does not require detailed calculations in order to show that the discrepancy first becomes conspicuous when the phases corresponding to the various secondary waves which travel from P to B range over a complete period.
- The illumination at B due to P then becomes comparatively small, indeed for some forms of aperture evanescent.
- The extreme discrepancy is that between the waves which travel through the outermost parts of the object-glass at L and L'; so that if we adopt the above standard of resolution, the question is where must P be situated in order that the relative retardation of the rays PL and PL' may on their arrival at B amount to a wave-length (X).
- The distance f i, which the actual focal length must exceed, is given by d (f1 2 R2) x; so that f1 = 2 R2/X (1) Thus, if X = p j, R= i ?, we find f1= 800 inches.
- If x and y be co-ordinates in the plane of the wave-surface, the axis of y being parallel to the lines of the grating, and the origin corresponding to the centre of the beam, we may take as an approximate equation to the wave-surface -- -} z =+Bxy 2, +ax 3 13x2 2pp p y+-yxy2-?-Sy3+..
- In spite of any inequality between p and p', the definition will be good to this order of approximation, provided a and y vanish.
- A similar expression can be found for Q'P - Q"A; and thus, if Q' A =v, Q' AO = where v =a cos (0", we get - - -AQ' = a sin w (sin 4 -sink") - - 8a sin 4 w(sin cktan 4 + sin 'tan cl)').
- If "=4), the term of the first order vanishes, and the reduction of the difference of path via P and via A to a term of the fourth order proves not only that Q and Q' are conjugate foci, but also that the foci are exempt from the most important term in the aberration.
- In the present application 4' is not necessarily equal to; but if P correspond to a line upon the grating, the difference of retardations for consecutive positions of P, so far as expressed by the term of the first order, will be equal to mX (m integral), and therefore without influence, provided v (sin 0-sin0') = nzX (11), where a denotes the constant interval between the planes containing the lines.
- k p h s i n h .
- 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.
- Only in this case can cos {p' +(m- -27th/Af) f } retain the constant value - I throughout the integration, and then only when and a = 27Th/A f (8) cos p'=- 1 ..
- In the second term if we observe that cos {p'+ 27rh/Af)E} =cos{p' - g,E} = cos p cos g, +sin p sin giE, we see that the second part vanishes when integrated, and that the remaining integral is of the form w = f +.0 sin z h, cos where h,=7rh/Af, g,=a-27Th/Af.
- (11), when g i numerically exceeds 2h 1; and, when g i lies between 2h,, I = 7r{2h,+ (2h, g, 2) cos p'}.
- The linear width of the band (e) is the increment of which alters p by 27r, so that e =27r /tr.
- Taking as the standard phase that of the secondary wave from A, we may represent the effect of PQ by cos 27r (_) .ds, where, l = BP - AP is the retardation at B of the wave from P relatively to that from A.
- as the point P is more and more deeply immersed in the shadow, the illumination continuously decreases, and that without limit.
- " Let E = o,7 7 = o, =f (bt - x) be the displacements corresponding to the incident light; let O l be any point in the plane P (of the wave-front), dS an element of that plane adjacent to 01; and consider the disturbance due to that portion only of the incident disturbance which passes continually across dS.
- But against this explanation of the heading ry;p' 2 there is an almost insuperable objection; for, since both the first and second books contain psalms with this heading, it is clear that the " Chief Musician's - or Director's - Psalter " must have been in existence before either of these books; in which case, apart from the difficulty of the antiquity which we should be compelled to assign to this earliest Psalter, it is impossible to understand on what principle the first book of Psalms was formed.
- Now we have seen that the 5 prefixed to n-'p 'p cannot refer to authorship; we seem therefore shut up to one of two alternatives, either the psalms inscribed 's?
- the day after the surrender of Jameson congratulating Kruger that " without a appealing to the help of friendlypowers" he had PP g P Y P repelled the raiders.
- 7, 1910, p. 15.) x xvu.
- The main p Boer effort was made in Natal, where their forces were commanded by P. J.
- p g g On the r 5th of December Buller made his effort and failed.
- It may be safely said of all those living things which are large enough to enable us to trust the evidence of microscopes, that they are heterogeneous optically, and that their different parts, and especially the surface layer, as Life and contrasted with the interior, differh sicall and organiza- P Y ?
- But many of the simpler P Y ler P forms of life may undergo desiccation to such an extent as to arrest their vital manifestations and convert them into the semblance of not-living matter, and yet remain potentially alive.
- Rugheimer, Ber., 1882, 15, p. 1390.)
- He has no claim to be regarded as a genius; but, as SainteBeuve has said, he well deserves a place "da p s la classe des esprits infiniment distingues" - distinguished, however, it ought to be added by intelligence rather than by intellect, and less by the power of saying much than by the power of saying a little well.
- (P. LA.) Climate.
- chemie, 1868,'p. 343).
- v, remains of volva or velum p, the pileus.
- It is no exa eration to say that this epoch-making work gg }' p g brought to birth a world of conceptions as new as the work of Copernicus.
- of which in a sense it is but an aspect, and on another by making ground of its own in the post mortem room Medical Y g g P Training.
- The present London residence of the sovereign is Buckingham Palace, on the west side of St p James's Park, with beautiful gardens behind it.
- p N°ahalto.
- 1y 0 r d Warfield mkfleld'p?
- L' o ?'? ?a` G,QQtpington, p?, ? ?,?
- P of the city was its special property, and it extended as far as the limits of the territorium of the nearest Roman city or as near thereto as the natural boundaries."
- Except in a few instances these were long ago superseded by ron-wire ropes, which in turn have p been replaced by steel because of its greater strength.
- While the mine workings are small the overlying rocks support themselves of and the full pressure does not come upon the mine Caving p i llars.
- _ 'P pnt` °" %s.
- of Middle Andaman Ca p l +rr North 'r h ?
- ' o P B Sentinel Q A Rutland /, 5 a ssage Paialankw e ?
- The fighting spirit of the people of for iveness and endurance, upheld Guru Nanak's g p was roused and satisfied by the spiritual and military leader.
- His elder brother Ram Rai was passed over p was put to death for refusal to embrace Islam b.
- p by Aurangzeb in A.D.
- 2 enclosing a point B, the pressure p at B is the limit of OP/DA; and p =lt(AP/DA) =dP/ dA, (I) in the notation of the differential calculus.
- Let P, Q denote the normal thrust across the sides bc, ca, and R the normal thrust across the base ab.
- Then, since these three forces maintain equilibrium, and R makes equal angles with P and Q, therefore P and Q must be equal.
- But the faces bc, ca, over which P and Q act, are also equal, so that the pressure on each face is equal.
- If a thrust P lb is applied to one piston of area A ft.
- 2, it will be balanced by a thrust W lb applied to the other piston of area B ft.', where p = P/A=W/B, (I) the pressure p of the liquid being supposed uniform; and, by making the ratio B/A sufficiently large, the mechanical advantage can be increased to any desired amount, and in the simplest manner possible, without the intervention of levers and machinery.
- 2, the pressure at A and By by Po and p lb/ft.
- AB, p = Thus in water,.
- For if the liquid of density a rises to the height h and of density p to the height k, and po denotes the atmospheric pressure, the pressure in the liquid at the level of the surface of separation will be ah+Po and pk +po, and these being equal we have Uh = pk.
- (I) The principle is illustrated in the article Barometer, where a column of mercury of density a and height h, rising in the tube to the To:ricellian vacuum, is balanced by a column of air of density p, which may be supposed to rise as a homogeneous fluid to a height k, called the height of the homogeneous atmosphere.
- Ignoring temperature effect, and taking the density as a function of the pressure, surfaces of equal pressure are also of equal density, and the fluid is stratified by surfaces orthogonal to the lines of force; n ap, dy, P d z, or X, Y, Z (4) are the partial differential coefficients of some function P, =fdplp, of x, y, z; so that X, Y, Z must be the partial differential coefficients of a potential -V, such that the force in any direction is the downward gradient of V; and then dP dV (5) ax + Tr=0, or P+V =constant, in which P may be called the hydrostatic head and V the head of potential.
- As an example of the general equations, take the simplest case of a uniform field of gravity, with Oz directed vertically downward; employing the gravitation unit of force, 1 dp i dp t dp dp/dz = p = pzn (4) z n+I pz 1 /n p-p n-H ?t), (5) supposing p and p to vanish together.
- These equations can be made to represent the state of convective equilibrium of the atmosphere, depending on the gas-equation p = pk =RA (6) where 0 denotes the absolute temperature; and then d9 d p R dz - dz (p) n+ 1' so that the temperature-gradient deldz is constant, as in convective equilibrium in (I I).
- 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.
- With uniform temperature, taking h constant in the gas-equation, dp / dz= =p / k, p=poet/ k, (9) so that in ascending in the atmosphere of thermal equilibrium the pressure and density diminish at compound discount, and for pressures p 1 and 1, 2 at heights z 1 and z2 (z1-z2)11?
- = loge(P2891) =2.3 logio(p2/p1) (io) In the convective equilibrium of the atmosphere, the air is supposed to change in density and pressure without exchange of heat by conduction; and then PIN = (e/e0) n+1, d5 -(n-{--I) P -(n+I)R ' y - where is the ratio of the specific heat at constant pressure and constant volume.
- In the more general case of the convective equilibrium of a spherical atmosphere surrounding the earth, of radius a, (1-1?-=(n+ I) Po --a 2 dr, (12) gravity varying inversely as the square of the distance r from the centre; so that, k = po/po, denoting the height of the homogeneous atmosphere at the surface, 0 is given by (n+I)k(I -9/6 0) =a(I -a/r), (13) or if c denotes the distance where 0=o, 0 _a (14) 0 r c -a' When the compressibility of water is taken into account in a deep ocean, an experimental law must be employed, such as p - po=k(P - Po), or P/po=I+(p-p0)/A, A=kpo, (15) so that A is the pressure due to a head k of the liquid at density under atmospheric pressure po; and it is the gauge pressure required on this law to double the density.
- Then dp/dz=kdp/dz = P, = Poe ik, p - po= kpo(ez Ik -1); (16) and if the liquid was incompressible, the depth at pressure p would be (p - po) 1po, so that the lowering of the surface due to compression is ke h I k -k -z= 1z 2 /k, when k is large.
- (2) (3) Suppose the density p varies as some nth power of the depth below 0, then (7) and the lowering of the surface is 2 ° - z=klog po - z= - k log(1 - k) - zt12 k (20) Po as before in 17).
- of a plane lamina bounded by the area, in which the surface density is p. If p is uniform, the C.P. and C.G.
- For a homogeneous liquid at rest under gravity, p is proportional to the depth below the surface, i.e.
- of the area A, f f xdxdy = o, ffydxdy = 0, (6) R = p hA, (7) xhA = - cos a f f x 2 dA - sin affxydA, fxydA, (8) yhA = - cos a ff xydA - sin ail y 2 dA.
- Suppose P tons is moved c ft.
- of the fluid, equal to the weight vertically upward through the movement of a weight P through a distance c will cause the ship to heel through an angle 0 about an axis FF' through F, which is conjugate to the direction of the movement of P with respect to an ellipse, not the momental ellipse of the water-line area A, but a confocal to it, of squared semi-axes a 2 -hV/A, b 2 - hV/A, (I) h denoting the vertical height BG between C.G.