How to use S in a sentence
If the reading for coincidence of the movable with the fixed webs is known, we then obtain from the single reading of S the difference from coincidence of the divisions of the two scales.
In Asia Minor, Syria and Mesopotamia there is little to record of progress in material development beyond the promises held out by the Euphrates Valley railway concession to a A s i a German company.
The latent heat L at any temperature is given by L=Lo - f 0 64 0 (s - s')dT, where Lo is value at To and s--s' is the difference in the specific heats of water and ice.
In addition to these modifications, which are common to nearly all orchids, there are others generally but not so universally met with; among them is the displacement of the flower arising from the twisting of the inferior ovary, in consequence of which the flower is so completely turned round that the "lip," which originates in that part of the flower, conventionally called the posterior or superior part, or that S c ?
The prostomium overhangs the mouth, and is often of considerable size and, as a rule, quite distinct from the segment following, being A„ f s / 6/ ' A B I.Advertisement
The brain con sists not only of a group of six capsules corre sponding to the archi cerebrum of the Oligo chaeta, but of a further mass of cells surrounding S S and existing below the alimentary canal, which can be analysed into five or six more separate ganglia.
The success of the Hussite raids in Germany gave fresh confidence to the Sla y s of Poland.
In systematic chemistry, sodium hyposulphite is a salt of hyposulphurous acid, to which Schutzenberger gave the formula H 2 S0 2, but which Bernthsen showed to be H 2 S 2 0 4.
Unfortunately, from the tenable theory that the intensity of a sensation increases by definite additions of stimulus, Fechner was led on to postulate a unit of sensation, so that any sensation s might be regarded as composed of n units.
His general formula for getting at the number of units in any sensation is S = C log R, where s stands for the sensation, R for the stimulus numerically estimated, and c for a constant that must be separately determined by experiment in each particular order of sensibility.Advertisement
But in Aplysia the mantle is reflected over the edge of the shell, and grows over its upper surface so as to completely enclose it, excepting at the small central area s where the naked shell is exposed.
On the under side of the free edge of the mantle are situated the numerous small cutaneous glands which, in the large A plysia camelus (not in other species), form the purple secretion which was known to s the ancients.
The blastopore now closes along the middle part of its course, which coincides z s FIG.
Porphyry says of Origen, Kara Tds rrepi lrpay f caTWV Kai Belot) bo s as `EXX vt cav (Euseb.
This is followed s s, by a sub-costal which some times shows two main branches.Advertisement
Aristotle was the first serious author on ornithology with whose writings we are acquainted, but even he had, as he tells us, predecessors; and, looking to that portion of his works on animals which has come down to us, one Early s.
Lewin s Natural History of the Birds of New South Wales (4to, 1822), which reached a third edition in 1838.
C. Smith's Spring Tour in Portugal s to be named, and these only partially cover the ground.
The whole site of Venice is dominated by the existence of one great main canal, the Grand Canal, which, winding through the town in the shape of the letter S, divides it into two equal parts.
For the siege see Imp. Gazetteer of India (Oxford, 1908), s.Advertisement
Males of the Argyopidae hang on the outskirt s of the webs of the females and signal their presence to her by jerking the radial threads in a peculiar manner.
The important sections of these acts were incorporated in the Agricultural Holdings Act 1908, s.
Some arrivals have been diverted to Manchester since the opening of the Manchester ship s canal; shipments through the canal from the 1st of entry, September to the 30th of August in each year for the decade 1894-1895 to 1904-1905 are appended - six to eight times as much is still unloaded at Liverpool.
Rivetted iron casing, made of s -in.
F, Fixed coil; D, Movable coil; S, Spiral spring; T, Torsion head; MM, Mercury cups; I, Index needle.Advertisement
Its consonants are k, g, ng, ch, j, n, t, d, n, p, b, m, y, r, l, w, s, h.
Of the total population 71.36% were Sla y s, who were scarcely distinguishable from their Bohemian neighbours.
The name of Czech, however, is usually reserved for the Bohemians, while the Sla y s of Moravia and West Hungary are called Moravians and Slovacs.
At this period there seemed a strong probability of the junction of the north-western and southeastern Sla y s, and the formation of a great Slavonic power to east of the German empire.
Roman C s ern 3.
Subsequent attempt,s of the princess to reinstate her son in his dominions were unsuccessful, and it was not till the peace of Westphalia in 1648 that he regained a portion of them,.
Of the tri-substitution derivatives, 1.2.3.-compounds are known as " adjacent " or " vicinal " (v), the 1.2.4 as " asymmetrical " (as), the 1.3.5 as " symmetrical " (s), of the tetrasubstitution derivatives, 126.96.36.199-compounds are known as " adjacent," 188.8.131.52 as " asymmetrical," and 184.108.40.206 as " symmetrical."
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.
Of other syntheses of true benzene derivatives, mention may be made of the formation of orcinol or [3 s]-dioxytoluene from dehydracetic acid; and the formation of esters of oxytoluic acid (5-methyl3-oxy-benzoic acid), C6 H3 CH3.
Thus benzene, (CH) gives thiophene, (CH) S, from which it is difficultly distinguished; pyridine, (CH) N, gives thiazole, (CH) N S, which is a very similar substance; naphthalene gives thionaphthen, C 11 S, with which it shows great analogies, especially in the derivatives.
Thus if s be known, an approximate value of W is determinate.
The relation they suspected to be of the form -yS = KT, where K is a constant analogous to R, and S the surface containing one gramme-molecule, y and T being the surface tension and temperature respectively.
Hence S may be replaced by (Mv) 3.
One has hitherto supposed that he was related to the Mediterraneans, the race to which the Bronze Age Greeks and Italians belonged; but this supposed connexion may well break down in the matter of skull form, as the Hittite skull, like that of the modern Anatolian, probably inclined to be brachycephalic. whereas that of the Mediterranean inclined in the other direction, And now the Bohemian Assyriologist Prof. Hrozny has brought forward evidence s that the cuneiform script adopted by the Hittites from the Mesopotamians expressed an Indo-European tongue, nearly akin to Latin!
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.
The development from the angular to the curved shape of S may be seen in its occurrences on the early cippus found in the Roman Forum in 1899.
Herodotus says nothing of a difference in shape, but most authorities regard the form M, which with the value of s is practically confined to Doric areas, as being san.
Hence in transcription from foreign languages and in works on phonetics it is represented by s or š.
The difference in formation between s and s is that the former is dental or alveolar, the latter is produced farther back and has .at least two varieties.
The voiced sound to this is generally written z as in azure, but sometimes s as in pleasure.
The sound of sh is also sometimes represented by s, as in sure, sugar.
In Egypt we find them classified as avyyeve;s, 46rtpot rag cvyyevEat y, apXcvwµarocuAalEs, 7rpwTot 0LAot, q5LAot (in the narrower sense),Sca60xoc. For the Seleucid kingdom vwyyEvEis,7rpWToc 0LAoc and 4'LAot are mentioned.
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.
The Peloponnesian War introduced a change; s and after that time the proprietors resided at Athens, and the cultivation was in the hands of slaves.
He could not in general be examined ` s a witness, except by torture.
The United State s h a d in 1 forbidden any a 794 Y m par ticipation by American subjects in the slave trade to foreign countries; they now prohibited the importation of slaves from Africa into their own dominions.
Wesley s spirit at this time is seen from his sermon on "The Circumcision of the Heart," preached before the university on the 1st of January 1733.
The formula is Fe n, Sn+, where n may vary from 5 to 16; usually it is Fe, S8 or Fe l s S12, the latter being also the composition of the artificially prepared compound.
The addition and multiplication of two relation-numbers is defined by taking two relations R and S, such that (I) their fields have no Cf.
Its central bureau, with departments of the interior, religion and education, finance and justice, was established at Serajevo; and its members were largely recruited among the Austrian Sla y s, who were better able than the Germans to comprehend the local customs and language.
The Ciudad gallantry of the troops made it successful, though with Rodrigo, the loss of Generals Craufurd and McKinnon, and 1300 ulfrary s men, and Marmont's battering train of 150 guns here fell into the allied hands.
Hamburg probably had its origin in a fortress erected in 808 by Charlemagne, on an elevation between the Elbe and Alster, as a defence against the Sla y s, and called Hammaburg because of the surrounding forest (Hamme).
The town, rebuilt after this disaster, was again more than once devastated by invading Danes and Sla y s.
The resemblance is further sustained by a broad belt of elevated plains, 'ranging from 1200 to 1700 ft., which s The upper Bukhtarma valley in the Sailughem range of the Altai system appears to belong to the same type.
The coast-line of Siberia is very extensive both on the Arctic Ocean and on the Pacific. The former ocean is ice-bound for at least ten months out of twelve; and, though Nordenskjold and Captain Wiggins demonstrated (1874-1900) the possibility of navigation along its shores, it is exceedingly is s.
For since A 11 A 22 -Ar 2 =,,a 33, with similar relations, we have a number of relations similar to A 11 A 22 =AM 2, and either Ars = +11 (A rr A ss) or - (A r .A ss) for all different values of r and s.
Writing these results Dif = D(1)f, D = D(2)f+D(l2)f, D3f = D(3)f+ (21)f+ D(13)f, s =1 (J1)11(J3)12(J3)13...
It is thus possible to study simultaneously all the theories which depend upon operations of the group. Symbolic Representation of Symmetric Functions.-Denote the s 8 s elementar symmetric function a s by al a 2 a3 ...at pleasure; then, Y y si,, si,...
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.
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.
We write;L 22 = a 1 a 2 .b 1 n-2 b2s 3 n - 3 3 n-3 3 n-3 3 a 3 = a 1 a 2 .b 1 b 2 .c 1 c2, and so on whenever we require to represent a product of real coefficients symbolically; we then have a one-to-one correspondence between the products of real coefficients and their symbolic forms. If we have a function of degree s in the coefficients, we may select any s sets of umbrae for use, and having made a selection we may when only one quantic is under consideration at any time permute the sets of umbrae in any manner without altering the real significance of the symbolism.
If (f,4) 1 be not a perfect square, and rx, s x be its linear factors, it is possible to express f and 4, in the canonical forms Xi(rx)2+X2(sx)2, 111(rx)2+1.2 (sx) 2 respectively.
In fact, if f and 4, have these forms, it is easy to verify that (f, 4,)i= (A j z) (rs)r x s x .
On this principle the covariant j is expressible in the form R 2 j =5 3 + BS 2 a+4ACSa 2 + C(3AB -4C)a3 when S, a are the above defined linear forms.
Hence, solving the cubic, R 2 j = (S -m i a) (S - m 2 a) (S - m3a) wherein m 1 m2, m 3 are invariants.
In General It Is A Seminvariant Of Degrees 0, 0', And Weight 0 0' S; To This There Is An Exception, Viz., When 0=O, Or When 0'=O, The Corresponding Partial Degrees Are 1 And 1.
To assist us in handling the symbolic products we have not only the identity (ab) cx + (bc) a x + (ca) bx =0, but also (ab) x x+ (b x) a + (ax) b x = 0, (ab)a+(bc)a s +(ca)a b = 0, and many others which may be derived from these in the manner which will be familiar to students of the works of Aronhold, Clebsch and Gordan.
The linear invariant a s is such that, when equated to zero, it determines the lines ax as harmonically conjugate to the lines xx; or, in other words, it is the condition that may denote lines at right angles.
They consist of a square citadel (Bairam Ali Khan kalah), s z m.
Denoting the two pairs of magnetic poles by N, S and N', S', there is attraction between N and S', and between S and N'; repulsion between N and N', and between S and S'.
Similarly, the forces acting in the opposite direction on the negative poles of the filaments have a resultant at another point S, which is called the south or negative pole.
If the distance of the mirror from the scale is equal to n scale divisions, and if a deflection 0 of the needle causes, the reflected spot of light to move over s scale divisions, we shall have s/n = tan 20 exactly, s/2n = tan 0 approximately.
If the conductor consists of a coil of wire the ends of which are connected with a suitable galvanometer, the integral electromotive force due to a sudden increase or decrease of the induction through the coil displaces in the circuit a quantity of electricity Q=SBns R, where SB is the increment or decrement of induction per square centimetre, s is the area of the coil, n the number of turns of wire, and R the resistance of the circuit.
Let s be the area of a single turn of the standard coil, n the number of its turns, and r the resistance of the circuit of which the coil forms part; and let S, N and R be the corresponding constants for a coil which is to be used in an experiment.
When the switch S is closed, K acts simply as a commutator or current-reverser, but if K is thrown over from right to left while S is opened, not only is the current reversed, but its strength is at the same time diminished by the interposition of the adjustable resistance R2.
The reversing key K having been put over to the left side, the short-circuit key S is suddenly opened; this inserts the resistance R, which has been suitably adjusted before hand, and thus reduces the current and therefore the magnetizing force to a known value.
To continue the process, the key K is turned over to the right-hand side, and then, while S is open, is turned back, thereby not only reversing the direction of the current, but diminishing its strength by an amount depending upon the previous adjustment of R2.
The play of the beam is limited by a stop S and a screw R, the latter being so adjusted that when the end Y of the beam is held down the two air-gaps are of equal width.
The weight W is moved along the scale until the yoke just tilts over upon the stop S; the distance of W from its zero position is then, as can easily be shown, proportional to F, and therefore to B 2, and approximately to I 2.
B r (S) = strongly magnetized.
As H regards the effec t s FIG.
It can be shown that if a current i circulates in a small plane circuit of area S, the magnetic action of the circuit for distant points is equivalent to that of a short magnet whose axis is perpendicular to the plane of the circuit and whose moment is iS, the direction of the magnetization being related to that of the circulating current as the thrust of a right-handed screw to its rotation.
If S is the area of the orbit described in time T by an electron of charge e, the moment of the equivalent magnet is M = eST; and the change in the value of M due to an external field H is shown to be OM = - He'S/47rm, m being the mass of the electron.
The collective name for the corps was celeres (" the swift," or possibly from Kan s, "a riding horse"); Livy, however, restricts the term to a special body-guard of ' Romulus.
The segmentation of the prosoma and the form of the appendages bear a homoplastic similarity to the head, pro-, meso-, and meta-thorax of a Hexapod with mandibles, maxillary palps and three pairs of walking legs; while the opistho io i e d c b o a S' S" 2 I VT V S IV III II I Opisthosoma Prosoma FIG.
His style is, however, often barbarous; and the obvious S cholia.
It is also produced by the action of sodium on a mixture of epichlorhydrin and methyl iodide, C 3 H S OC1+CH 3 I+2Na= C 3 H 4 0+NaI+NaC1+CH 4.
The mark of Meissen was originally a district centring round the castle of Meissen or Misnia on the Middle Elbe, which was built about 920 by the German king Henry I., the Fowler, as a defence against the Sla y s.
As Meissen was relieved from the attacks of the Sla y s by the movement of the German boundary to the east, its prosperity increased.
Throughout the middle ages it was the scene of vigorous struggles between Sla y s, Byzantines, Franks, Turks and Venetians, the chief memorials of which are the ruined strongholds of Mistra near Sparta, Gerald (anc. Geronthrae) and Monemvasia, "the Gibraltar of Greece," on the east coast, and Passava near Gythium.
The year of her death (1380) was that of the birth of St Bernardino Albizzeschi (S Bernardino of Siena), a popular preacher whose sermons in the vulgar tongue are models of style and diction.
In the 13th century we find Guido (da Siena), painter of the wellknown Madonna in the church of S Domenico in Siena.
A single sentence in Porphyry's Isagoge or " introduc tion " to the Categories of Aristotle furnished the i o, s text of the discussion.
The two systems were nothing more as yet than two different ways of interpreting a phrase of Porphyry, and they remained unnoticed in the for nearly two centuries not so much for its dialectics S' and philosophy as for its humanistic culture.
The son was sent in 1812 to the Protestant gymnasium at Pressburg, where he came in contact with the philologist S afafik and became a zealous student of the Slav languages.
This forcible intrusion of a nonAryan race altered the whole history of Europe; but its peculiar significance lay in the fact that it permanently divided the northern from the southern and the eastern from the western Sla y s.
Jellachich, who as a soldier was devoted to the interests of the imperial house, realized that the best way to break the revolutionary power of the Magyars and Germans would be to encourage the Slav national ideas, which were equally hostile to both; to set up against the Dualism in favour at Pest and Vienna the federal system advocated by the Sla y s, and so to restore the traditional Habsburg principle of Divide et impera.
All hope of crushing revolutionary Vienna with Magyar aid was thus at an end, and Jellachich, who on the 10th issued a proclamation to the Croat regiments in Italy to remain with their colours and fight for the common fatherland, was free to carry out his policy of identifying the cause of the southern Sla y s with that of the imperial army.
In the Hungarian diet, which met on the 2nd of July, the influence of the conservative cabinet was wholly overshadowed by that of Kossuth, whose inflammatory orations - directed against the disruptive designs of the Sla y s and the treachery of the Austrian government - precipitated the crisis.
Meanwhile the negotiations continued, Ministry, s o secretly that when, on the 9th of April, the appoint- 1906.
The grammatical forms are expressed, as in Turkish, by means of affixes modulated according to the high or low vowel power of the root or chief syllables of the word to which they are appended-the former being represented by e, o, S, ii, i l l, the latter by a, d, o, 6, u, it; the sounds e, i, i are regarded as neutral.
S is pronounced as sh in English, the sound of simple s being represented by sz.
A close observer of the multifarious low life of Hungary, Mikszath has, in his short stories, given a delightful yet instructive picture of all the minor varied phases of the peasant life of the Sla y s, the Palocok, the Saxons, the town artisan.
X= i s.
We cannot solve the equation 7X =4s.; but we are accustomed to subdivision of units, and we can therefore give a meaning to X by inventing a unit w s.
We thus get P=kQ+m.Q/r+S=(k+m/r)Q+S, where S is less than Q/r.
We thus express P=Q in the form of a continued fraction, k+ + I, which is usually written,for conciseness, k+ s + t + &c., s t+&c.
Hence the successive remainders are successively smaller multiples of L, but still integral multiples, so that the series of quotients k, s, t,.
Similarly the statements P+Q - R - S = T and P+ Q - R= T+ S are the same.
This is the foundation of the use of recurring decimals; thus we can replace = s s = 1 o o /(' - 1 + 0 -)1 by .363636(=36/102 +36/ 104 +3 6 / 106), with an error (in defect) of only 36/(10 6.99).
We know that log l oN(I+9) = log l oN+log 10 (I+0), and inspection of a table of logarithms shows that, when 0 is small, log 10 (I+B);s approximately equal to X0, where X is a certain constant, whose value is.
The sum and product of two quaternions are defined by the formulae mi ase + F+lases = (a s + 133) es 2arer X ZO,es = Fiarfseres, where the products e,e, are further reduced according to the following multiplication table, in which, for example, the eo e1 e2 e3 second line is to be read eieo = e1, e 1 2 = - eo, e i e 2 = es, eie3 = - e2.
These may be compared and contrasted with such quaternion formulae as S(VabVcd) =SadSbc-SacSbd dSabc = aSbcd - bScda+cSadb where a, b, c, d denote arbitrary vectors.
The unknown he terms arithmos, the number, and in solutions he marks it by the final s; he explains the generation of powers, the rules for multiplication and division of simple quantities, but he does not treat of the addition, subtraction, multiplication and division of compound quantities.
Canton was laid out as a town in 1805, became the county-seat in 1808, was incorporated as a village in 1822 and in 1854 V S chartered as a city.
During the 'seventies Austro-Hungarian policy was increasingly successful in checking intercourse between the Yugosla y s of the monarchy and those outside its bounds.
The period between 1883 and 1903 is the most humiliating in the modern history of the southern Sla y s.
Disunion had reduced the Yugosla y s to an almost negligible quantity in Balkan politics.
The Serbian court, instead of being a centre of perpetual scandal and misrule, resumed its true position as a focus of national aspirations, and this change was not lost upon the Yugosla y s of " the other side."
The Serbian and Bulgarian anthems were sung on the streets, collections were made in every village for the Balkan Red Cross funds, and when Austria-Hungary mobilized, protests were heard on every side against the bare possibility of war with Serbia, which to the Yugosla y s would be a veritable civil war.
Among the Yugosla y s the students had always dabbled unduly in politics, and this tend-.
The entry of Italy into the war was a serious set-back to the Yugoslav cause, for under the Treaty of London (April 27 1915) she was to obtain, in the event of an Entente victory, wide districts in Gorizia, Carniola, Istria and Dalmatia, peopled by not less than 700,000 Yugosla y s.
By this time it was sufficiently obvious that the Yugosla y s were tacitly if not explicitly agreed upon a triple parallel policy, framed for all contingencies.
The growing self-confidence of the Austrian Sla y s was shown by the bluntness of their refusal to cooperate with the new Premier, Doctor von Seidler, whose offer of portfolios to their leaders drew from Count Tisza a strong protest in the Hungarian Parliament.
The Czechs and Yugosla y s, finding the door thus shut in the face of their national aspirations, even in the modified Habsburg form, naturally stiffened in their opposition.
The Yugosla y s were represented by Trumbic and his Committee and by 12 deputies of the Serbian Skupstina, the Czechoslovaks by Benes and Stefanik, the Poles by Zamorski, Skirmunt and Seyda, the Rumanians by Draghicescu, Lupu and Mironescu.
The effect of the congress and of this propaganda was to hasten the disintegration in the Austro-Hungarian army, and the High Command (in a communiqué of July 27) admitted that wholesale defections of the Czechoslovaks and the Yugosla y s had.
That this recognition had not already been accorded before the collapse of the Central Powers began was due to disunion among the Yugosla y s themselves.
Trumbic on his part could not enter a purely Serbian Cabinet without prejudicing that freedom of choice of his compatriots in the Dual Monarchy, upon which the moral case of the Yugosla y s depended.
Pa s ic was appointed principal delegate at the Peace Conference, with Trumb16, Vesnic (minister in Paris) and Zolger (a Slovene professor who had held office under Seidler in Austria).
Meanwhile the whole Nationalist press of Italy, actively, encouraged by Sonnino and his entourage, opened a fierce campaign against the Yugosla y s and their western supporters, which rapidly developed into agitation against the Allies.
On March 3, however, Italy, who had steadily refused to recognize the accomplished fact of Yugoslav unity and insisted on the Conference only admitting the Yugosla y s as a " Serbian " delegation, declined American arbitration and threatened to withdraw altogether from Paris unless their territorial demands were conceded.
This in turn strengthened the hands of the extreme section among the Yugosla y s, who now advanced the full ethnographic claim, involving Trieste and Gorizia as well as Dalmatia and Istria, and at the same time increased their demands against Bulgaria, Austria and Albania.
Tardieu suggested a compromise by which the port and district of Fiume with most of eastern Istria and a total population of over 200,000 (mainly Yugosla y s) would form a small buffer state between Italy and Yugoslavia, under the guarantee of the League of Nations.
The sole justification for such a claim lay in the terms of the Treaty of London, which the Yugosla y s could not adopt as a basis without stultifying their whole position against Italy.
It abolished the conception of life s an entity above and beyond the common properties of matter, and led to the conviction that the marvellous and exceptional qualities of that which we call " living " matter are nothing more nor less than an exceptionally complicated development of those chemical and physical properties which we recognize in a gradually ascending scale of evolution in the carbon compounds, containing nitrogen as well as oxygen, sulphur and hydrogen as constituent atoms of their enormous molecules.
Lamarck believed in a single progressive series of forms, whilst Cuvier introduced s the conception of branches.
We readily find (with substitution for k of 27r/X) a2b S n J s in fl „2a2E2 „2b2n2 f2X2 f2X2 as representing the distribution of light in the image of a mathematical point when the aperture is rectangular, as is often the case in spectroscopes.
If the image of the line be =o, the intensity at any point E, n of the diffraction pattern may be represented by ?2a2t2 S A2f2 the same law as obtains for a luminous point when horizontal directions are alone considered.
Writing for brevity k =p, k =q, (1), we have for the general expression (§ 11) of the intensity X2 f 212 = S 2 +C 2..
When, as in the application to rectangular or circular apertures, the form is symmetrical with respect to the axes both of x and y, S = o, and C reduces to C = ff cos px cos gy dx dy,.
Trans., 1834) in his original investigation of the diffraction of a circular object-glass, and readily obtained from (6), is z z 3 25 27 J1(z) = 2 2 2.4 + 2 2.4 2.6 2 2.4 2.6 2.8 + When z is great, we may employ the semi-convergent series Ji(s) = A/ (7, .- z)sin (z-17r) 1+3 8 1 ' 6 (z) 2 220.127.116.11.1.3.5 5 () 3 1 18.104.22.168 1 3 cos(z - ?r) 8 ' z (z) 22.214.171.124.126.96.36.199.7 1 5 + 188.8.131.52.40 (z
According to the standard adopted, the condition of resolution is therefore that AP, or s, should exceed 1X/sin a.
Calculation shows that, if the aperture be s in., an achromatic lens has no sensible advantage if the focal length be greater than about II in.
B) - f S,u ds (along The new wave-surface is formed in such a position that the optical distance is constant; and therefore the dispersion, or the angle through which the wave-surface is turned by the change of refrangibility, is found simply by dividing (5) by the distance AB.
If, as in common flint-glass spectroscopes, there is only one dispersing substance, f Sy ds = Sµ.s, where s is simply the thickness traversed by the ray.
All the errors, except that depending on a, and especially those depending on -y and S, can be diminished, without loss of resolving power, by contracting the vertical aperture.
Now a = (a+b)s 2 /2ab..
By separation of real and imaginary parts, C =M cos 27rv 2 +N sin 27rv2 1 S =M sin 27rv 2 - N cos 27rv2 where 35+357.9 N _ 7rv 3 7r 3 v 7 + 1.3 184.108.40.206 220.127.116.11.9.11 These series are convergent for all values of v, but are practically useful only when v is small .
Comparing the expressions for C, S in terms of M, N, and in terms of G, H, we find that G = z (cos u+sin u)-M, H = z (cos u-sin u) +N.
It is easy to see that the length of the chord (which passes in all cases through 0) increases to a maximum near the place where the phase-retardation is s of a period, then diminishes to a minimum when the retardation is about a of a period, and so on.
In the limiting case in which the medium is regarded as absolutely incompressible S vanishes; but, in order that equations (2) may preserve their generality, we must suppose a at the same time to become infinite, and replace a 2 3 by a new function of the co-ordinates.
Claudius Ptolemy (130) rectified this error, and in the so-called syntonous or intense diatonic scale reduced the proportions of his tetrachord to s, iii, f, -i.
Ptolemy, following the invariable Greek method, placed them thus---1, s, .ib.
Uranyl sulphide, UO 2 S, is a black precipitate obtained by adding ammonium sulphide to a uranyl solution.
He is also found confirming his old rival Arnulf in the see of Reims; summoning Adalbero or Azelmus of Laon to Rome to answer for his crimes; judging between the archbishop of Mainz and the bishop of Hildesheim; besieging the revolted town of Cesena; flinging the count of Angouleme into prison for an offence against a bishop; confirming the privileges of Fulda abbey; granting charters to bishoprics far away on the Spanish mark; and, on the eastern borders of the empire, erecting Prague as the seat of an archbishopric for the Sla y s.
A number of British subjects resident in Comman- the Transvaal, in spite of their having no political status, were commandeered to suppress a native r i s i ng.
Stannous salt solutions yield a brown precipitate of SnS with sulphuretted hydrogen, which is insoluble in cold dilute acids and in real sulphide of ammonium, (NH 4) 2 S; but the yellow, or the colourless reagent on addition of sulphur, dissolves the precipitate as SnS 2 salt.
The Peshitta New Testament - according to the convincing theory which at present holds the field s - is not the oldest form of the Syriac version, at least as regards the Gospels.
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.
The attacks of the Sla y s and Avars upon Thessalonica were heroically repulsed by the inhabitants.
S ?thepperton i 1 0, ..
Io,680 Local Government Board-Common Poor Fund 756 £24,703,087 The total expenditure was equal to a rate in the pound of s.
A stope is that portion of the working assigned to a party of miners, and the block of ground is usually A s /u//, ?l'?//?
The beaches which had been selected were, enumerating from right to left, " S " in Morto Bay, " V " and " W " on either side of Cape Helles at the south-western end, and " X " and " Y " on the outer shore; " V " and " W " were regarded as of primary importance, as those two beaches offered suitable landing places from the point of view of subsequent operations.
The attacks at " S " and " Y " were intended to be subsidiary; but great importance was attached to that at " X " owing to the vicinity of this point to " W."
As it turned out, the actual disembarkations at " S," " X " and " Y " were carried out without any very great difficulty; but the troops detailed for " W " beach only gained a footing after incurring very heavy losses and by a display of indomitable resolution, while at " V " the operation went very near to failing altogether.
But the forces which had landed at " W " and " X " beaches had joined hands, the one battalion detailed for " S " beach had secured a good position, and during the night the troops still left aboard the " River Clyde " contrived to disembark.
Additional infantry was got ashore at " W " and " X " beaches, the first elements of the French division began disembarking at " V " beach in the afternoon, and before evening touch had been gained with the battalion that had made good at " S " beach.
See Tacitu s, [[Annals]], iv.
The cartesian equation referred to the axis and directrix is y=c cosh (x/c) or y = Zc(e x / c +e x / c); other forms are s = c sinh (x/c) and y 2 =c 2 -1-s 2, being the arc measured from the vertex; the intrinsic equation is s = c tan The radius of curvature and normal are each equal to c sec t '.
Har Rai was charged with friendship for Dara Shikoh, the son of Shah Jahan, and also with preaching a religion di s tinct from Islam.
Plauen was probably founded by the Sla y s.
Of the heavy metals, copper is the one which exhibits by far the greatest avidity for sulphur, its subsulphide Cu 2 S being the stablest of all heavy metallic sulphides in opposition to dry reactions.
Generally if S denotes any closed surface, fixed in the fluid, M the mass of the fluid inside it at any time t, and 0 the angle which the outward-drawn normal makes with the velocity q at that point, dM/dt = rate of increase of fluid inside the surface, (I) =flux across the surface into the interior _ - f f pq cos OdS, the integral equation of continuity.
The time rate of increase of momentum of the fluid inside S is )dxdydz; (5) and (5) is the sum of (I), (2), (3), (4), so that /if (dpu+dpu2+dpuv +dpuw_ +d p j d xdyd z = o, (b)` dt dx dy dz dx / leading to the differential equation of motion dpu dpu 2 dpuv dpuv _ X_ (7) dt + dx + dy + dz with two similar equations.
Negative values of n must be interpreted by a streaming motion on a parallel plane at a level slightly different, as on a double Riemann sheet, the stream passing from one sheet to the other across a cut SS' joining the foci S, S'.
The velocity of a liquid particle is thus (a 2 - b 2)/(a 2 +b 2) of what it would be if the liquid was frozen and rotating bodily with the ellipse; and so the effective angular inertia of the liquid is (a 2 -b 2) 2 /(a 2 +b 2) 2 of the solid; and the effective radius of gyration, solid and liquid, is given by k 2 = 4 (a 2 2), and 4 (a 2 For the liquid in the interspace between a and n, m ch 2(0-a) sin 2E 4) 1 4Rc 2 sh 2n sin 2E (a2_ b2)I(a2+ b2) = I/th 2 (na)th 2n; (8) and the effective k 2 of the liquid is reduced to 4c 2 /th 2 (n-a)sh 2n, (9) which becomes 4c 2 /sh 2n = s (a 2 - b 2)/ab, when a =00, and the liquid surrounds the ellipse n to infinity.
Denoting the cross-section a of a filament by dS and its mass by dm, the quantity wdS/dm is called the vorticity; this is the same at all points of a filament, and it does not change during the motion; and the vorticity is given by w cos edS/dm, if dS is the oblique section of which the normal makes an angle e with the filament, while the aggregate vorticity of a mass M inside a surface S is M - l fw cos edS.
The image of a source of strength p at S outside a sphere of radius a is a source of strength pa/f at H, where 'OS' =f, OH =a2/f, and a line sink reaching from the image H to the centre 0 of line strength - A la; this combination will be found to produce no flow across the surface of the sphere.
Taking Ox along OS, the Stokes' function at P for the source S is p cos PSx, and of the source H and line sink OH is p(a/f) cos PHx and - (p/a) (PO - PH); so that = p (cos PSx+f cos PHx PO a PH), (q) and Ili = -p, a constant, over the surface of the sphere, so that there is no flow across.
When the source S is inside the sphere and H outside, the line sink must extend from H to infinity in the image system; to realize physically the condition of zero flow across the sphere, an equal sink must be introduced at some other internal point S'.
If p denotes the density of the air or medium W' = sird 3 xp, (23) W' I p __ W I -1 3 k12 I k22 x2 ±i a 2= 101-1 3 '111 2= 2 tan g S = Q (l - a) x 2+ I (26) in which a/p may be replaced by 800 times the S.G.
Table of Rifling for Stability of an Elongated Projectile, x Calibres long, giving S the Angle of Rifling, and n the Pitch of Rifling in Calibres.
In the meantime we have proper names to argue from; and these give us at least the significant indication that the Hittite nominative ended in s and the accusative in m.
For outdoor culture the long-rod s y stem is generally preferred.
Alcoy s is built on high ground at the entrance to a gorge in the Moncabrer range (4547 ft.).
The uterus (X in figure C) begins in all cases at the shell gland (c, d) and may exhibit a swelling (R S) for the retention of the spermatozoa..
S i milarly soils can be improved by applying to them marl, a substance consisting of a mixture of clay with variable proportions of lime.
The manufacturer having prepared his mixture of leaves, proceeds to damp them, pure water alone being used in the United Kingdom, whereas on the Continent and in America certain S mo ki ng sauces are employed, which consist of mixtures of mixtures.
Deep valleys winding through the barren foothills lead gradually up to the higher mountains, and as the track ascends the scenery and vegetation change their character; the trees which line the banks of the wadi are overgrown with creepers, and the running stream is dammed at frequent intervals, and led off in artificial channels to irrigate the fields on either side; the steeper parts of the road are paved with large stones, substantially built villages, with their masonry towers or da y s, crowning every height, replace the collection of *mud walls and brushwood huts of the low country; while tier above tier, terraced fields cover the hill slopes and attest the industry of the inhabitants and the fertility of their mountains.
The agricultural Sla y s of the Dnieper and the Oka were reduced to tribute, and before the end of the 7th century the Khazars had annexed the Crimea, had won complete command of the Sea of Azov, and, seizing upon the narrow neck which separates the Volga from the Don, had organized the portage which has continued since an important link in the traffic between Asia and Europe.
The arrival of the Varangians amidst the scattered Sla y s (862) had united them into a nation.
They offered a singular attraction to the Romans, and their presence in remote parts of the Mi nera country no doubt was often the principal cause of Roman S pr i ngs.
He was active in raising troop s xx1.5 FIG.
The epidermis has lost its connected epithelial character and its cilia, and the isolated cells have become sunk inwards retaining their S t- FIG.
A, Fasciola hepatica, from the ventral surface (X 2); the alimentary and nervous systems only shown on the left side of the figure, the excretory only on the right; a, right main branch of the intestine; c, a diverticulum; g, lateral ganglion; n, lateral nerve; o, mouth; p, pharynx; s, ventral sucker; cs, cirrus sac; d, left anterior dorsal excretory vessel; m, main vessel; v, left anterior ventral trunk; x, excretory pore.
Although the Finns are not Sla y s, on topographical grounds mention may here be made of Wainamoinen, the great magician and hero of the Finnish epic Kalevala (" land of heroes ").
S' 3' S' p called voluntary loans was abolished, and replaced by a tax of ro% (la decima) on all real property.
Thus Norman-French spelt its palatalized c-sound (= tsh) with ch as in cher and the English palatalized cild, &c. became child, &c. In Provençal from the 10th century, and in the northern dialects of France from the 13th century, this palatalized c (in different districts is and tsh) became a simple s.
English also adopted the value of s for c in the 13th century before e, i and y.
Otto marched against them, and in a battle fought on the Lechfeld on the 10th of August 955 the king's troops gained a brilliant victory which completely freed Germany from these invaders; while in the same year Otto also defeated the Sla y s who had been ravaging the Saxon frontier.
In 822 and 823 two great diets were held in the palace, and at the former there were present deputies from the eastern Sla y s, the Avars and the Normans.
This phenomenon was first noticed in the case of the plain on which s, stands the capital, TOkyO.
Of these, one of the most interesting s called kiribame (insertion).
See Hughes, General Johnston, in "Great Commanders S?ries" (1893).
Two-thirds of the inhabitants are Germans; the remainder, chiefly found in the valleys of the Drave and Save, are Sla y s (Slovenes).
Towards the end of the 6th century the last-named began to give way to the Sla y s, who ultimately made themselves masters of the entire district.
The critical weeklies of the past include the New York Literary Gazette (1834-1835, 1839), De Bow's Review (1846), the Literary World (1847-1853), the Criterion (1855-1856), the Round Table (1863-1864), the Citizen (1864-1873), and Appleton' s Journal (1869).
The small eyes are some- T y p h l o p s bra- times covered by transparent shields.
This sub-family contains about woo species; few of them reach a length of more than two yards, some of the largest belonging to the Indian Zaocys s.
Coelopeltis, with concave, or grooved scales; C. lacertina s.
Probably these were the original genii of the necropolis, and in fact the same lean animal figured passant is s;b " jackal" or "fox."
Moreover, the three solids S,D and W will differ in minute structure and therefore, probably, in mechanical properties.
S netona President of the State, and composed the statute for the election of the Constituent Assembly by universal, equal, direct and secret franchise according to a proportional system based on d'Hondt's distributive principle which contains elaborate safeguards against the tyranny of the majority.
Thus if Q is the surface density, S the thickness of the shell at any point, and p the assumed volume density of the matter of the shell, we have v =Abp. Then the quantity of electricity on any element of surface dS is A times the mass of the corresponding element of the shell; and if Q is the whole quantity of electricity on the ellipsoid, Q =A times the whole mass of the shell.
This mass is equal to 47rabcp,u; therefore Q = A47rabcp s and b =pp, where p is the length of the perpendicular let fall from the centre of the ellipsoid on the tangent plane.
If S is the surface of each plate, and d their distance, then the electric force E in the space between them is E = es.
Then the electric force due to the point s' charge q at distance x is q/x, and the resolved part normal to the element of surface dS is q cos0/x 2.
He also showed that the difference of the specific heats at constant pressure and volume, S - s, must be the same for equal volumes of all gases at the same temperature and pressure, being represented by the expression R/TF'(t).
The heat evolved in this process may be represented by s"(o' - o"), where s" is the specific heat of the substance in the second state at saturation pressure.
Dividing by (0' - e"), and writing dp/do and dL/do for the limiting values of !the ratios (p' - p")/(o' - o") and (L' - L")/(o' - o"), we obtain the important relations s' - s"+dL/do= (v" - v')dp/do=L/o,..
The same equations apply to the case of fusion of a solid, if L is the latest heat of fusion, and v', s', v", s" the specific volumes and specific heats of the solid and liquid respectively.
The whole quantity of heat required to raise the temperature from 0" to 0' at constant pressure along the path EC is H+h, which is equal to S(0' - o"), where S is the specific heat at constant pressure.
Since h = s (o' - 0"), the difference S - s between the specific heats at constant pressure and volume is evidently H/(o' - o").
Substituting for H its value from (3), and employing the notation of the calculus, we obtain the relation S - s =0 (dp /do) (dv/do),.
The value of the specific heat s at constant volume can also be measured in a few cases, but it is generally necessary to deduce it from that at constant pressure, by means of relation (6).
A similar expression for the variation of the specific heat S at constant pressure is obtained from the second expression in (8), by taking p and 0 as independent variables; but it follows more directly from a consideration of the variation of the function (E+pv).
Observing that F is a function of the co-ordinates expressing the state of the substance, we obtain for the variation of S with pressure at constant temperature, dS/dp (0 const) '=' 2 F/dedp =-0d 2 v/d0 2 (p const) (12) If the heat supplied to a substance which is expanding reversibly and doing external work, pdv, is equal to the external work done, the intrinsic energy, E, remains constant.
If we also assume that they are constant with respect to temperature (which does not necessarily follow from the characteristic equation, but is generally assumed, and appears from Regnault's experiments to be approximately the case for simple gases), the expressions for the change of energy or total heat from 00 to 0 may be written E - Eo = s(0 - 0 0), F - Fo = S(0-00).
If we assume that s is a linear function of 0, s= so(I +aO), the adiabatic equation takes the form, s 0 log e OW +aso(0 - Oo) +R loge(v/vo) =o
Putting d0/dp=A/0 2 in equation (15), and integrating on the assumption that the small variations of S could be neglected over the range of the experiment, they found a solution of the type, v/0 =f(p) - SA /30 3, in which f(p) is an arbitrary function of p. Assuming that the gas should approximate indefinitely to the ideal state pv = R0 at high temperatures, they put f(p)=Rip, which gives a characteristic equation of the form v= Re/p - SA /30 2 .
In working to a first approximation, the small term nc/V may be omitted in the expression for s.
In the case of a solid or a liquid, the latent heat of isothermal expansion may often be neglected, and if the specific heat, s, be also taken as constant, we have simply 0-00 =s log e0/00.
The values of the corresponding functions for the liquid or solid cannot be accurately expressed, as the theoretical variation of the specific heat is unknown, but if we take the specific heat at constant pressure s to be approximately constant, and observe the small residual variation dh of the total heat, we may write F'=s'D+dh+B'.
The value of B is determined by observing the latent heat, Lo = F"o - F'0, which gives B =B" - B' =L0+(s' - So)00+(n+r)copo - bpo+dho (45) This constant may be called the absolute latent heat, as it expresses the thermal value of the change of state in a manner independent of temperature.
So, Limiting value of S when p=o.
Recent discoveries have made it practically certain that there existed, prior to the extant romances, a collection of short episodic poems, devoted to the glorification of Arthur's famous nephew and his immediate kin (his brother Ghaeris, or Gareth, and his son Guinglain), the authorship of which was attributed to a Welshman, Bleheris; fragments of this collection have been preserved to us alike in the first continuation of Chretien de Troyes Perceval, due to Wauchier de Denain, and in our vernacular Gawain poems. Among these "Bleheris" poems was one dealing with Gawain's adventures at the Grail castle,where the Grail is represented as non-Christian, and present s features strongly reminiscent of the ancient Nature mysteries.
Of the minerals containing gold the most important are sylvanite or graphic tellurium (Ag, Au) Tee, with 24 to 26%; calaverite, AuTe2, with 42%; nagyagite or foliate tellurium (Pb, Au)16 Sba(S, Te)24, with 5 to 9% of gold; petzite, (Ag, Au) 2 Te, and white tellurium.
Aurous sulphide, Au 2 S, is a brownishblack powder formed by passing sulphuretted hydrogen into a solution of potassium aurocyanide and then acidifying.
Sodium aurothiosulphate, 3Na 2 S 2 O 3 Au2S203.4H20, forms colourless needles; it is obtained in the direct action of sodium thiosulphateongoldinthe presence of an oxidizing agent, or by the addition of a dilute solution of auric chloride to a sodium thiosulphate solution.
Between s o and 176 the authority of the episcopate had been immensely strengthened, and along with it a settled order had been introduced into the Churches.
Every endeavour is made to gloss over, or modify, expressions which seemed derogatory to the ancestors of ' According to Zunz, Gottesdienstliche Vortrdge, 2nd ed., p. 80, its contents bear the following proportions to Genesis, z o o to Exodus, about 1 1 4 to Leviticus, s to Numbers, and 4 to Deuteronomy.
I,151,210 II 1 Czechs, Magyars, Sla y s Bohemia 77,247 01 Hungary 256,347 2.5 Poland 141,908 Rumania 10,377 0.1 Russia 500,797 0 I Total Europe 9,197,014 88.9 3.6 Grand Total 10,339,539 Total Swiss-Switzerland Greeks-Greece Turks-Turkey Europe, not specified 135,736 7,325 3,411 294 North America All other countries 77 6, 071 7.5 366,454 100 0 1'4 4.8 9.5 A very important transformation has taken place in the proportionate number coming from different countries during the last half of the 19th century.
Numerous sulphonic acids derived from 0-naphthylamine are known, the more important of which are the 2.8 or Badische, the 2.5 or Dahl, the 2.7 or S, and the 2.6 or Bronner acid.
The average cost per pupil in these schools was 35 s.
He took a share in the unsuccessful attempts to raise the siege of Athens in 1827, and made an effort to prevent the disastrous massacre of the Turkish garrison of fort S Spiridion.
None of them, in point of fact, has held its ground, and even his proposal to denote unknown quantities by the vowels A, E, I, 0, u, Y - the consonants B, c, &c., being reserved for general known quantities - has not been taken up. In this denotation he followed, perhaps, some older contemporaries, as Ramus, who designated the points in geometrical figures by vowels, making use of consonants, R, S, T, &c., only when these were exhausted.
Subsequently the Sla y s were cut off from relations with Taurida by the Mongols, and only made occasional raids, such as that of the Lithuanian prince Olgierd.
On his father's death in 912 he became duke of Saxony, which he ruled with considerable success, defending it from the attacks of the Sla y s and resisting the claims of the German king Conrad I.
Charlemagne's wars in Italy, Spain and Saxony formed part of the common epic material, and there are references to his wars against the Sla y s; but especially he remained in the popular mind as the great champion of Christianity against the creed of Mahomet, and even his Norman and Saxon enemies became Saracens in current legend.
The only connexion between the type-wheel and the screwhead S is by the pin p (which is screwed into S), the cylindrical end of which acts in a slot cut in the typewheel.
Simi larly the prism may be used for the study and elim- " ination of personal errors depending on the angle made s by a double star with the vertical.
There is a collar, clamped by the screw at S, which is so adjusted that the eye-piece is in focus when pushed home, in its adapter, to this collar.
This hypothesis, however, does not accord with the theory of the development of the earth from the state of a sphere of molt s en rock surrounded by an atmosphere of gaseous metals by which the first-formed clouds of aqueous vapour must have been absorbed.
According to Knudsen the salinity is given in weight per thousand parts by the expression S = o 030+ I.
The classification of the different kinds of coal may be considered from various points of view, such as their chemical composition, their behaviour when subjected to heat aa s sifica= or when burnt, and their geological position and iron.
Under ordinary conditions, from s to 4 of the whole amount of sulphur in a coal is volatilized during combustion, the remaining 4 to being found in the ash.
Cs 2 S 4H 2 0, Cs 2 S 2 H 2 O, Cs 2 S 3 H 2 0, Cs 2 S 4 and, Cs 2 S 5 H 2 0, are also known.
Its area is 999 s q.
If P represent the average value of the component of a force in the direction of the displacement, s, of its point of application, the product Ps measures the work done during the displacement.
The factors s or 0 are observed independently.
The angular displacement, 0, of the disk is made proportional to the displacement, s, of the point of application of the force by suitable driving gear.
Their centres s l, s2, are held respectively by the pieces A, B, which together form a sliding pair.
The second line in E2 will represent the energy (or part of the energy) of s' similar molecules of the second kind, and so on.
If each of the fractions (3) is put equal to i/4h, it is readily found, from the first property of the normal state, that, of the s molecules of the first kind, a number sal (h3m3 /13)e hm (u2+v2+w2)dudvdw (4) Velocities.
If 2mu 2 denote the mean value of 2mu 2 averaged over the s molecules of the first kind, equations (3) may be written in the form Z mu g = 2 mv 2 = 2 mw 2 = 2x,0 2 1 =.
Let us fix our attention on a small area dS of the boundary of the s (3) qi „ and so on.
In 1882 Islam gained an ascendancy, and s the French withdrew for a time.
Pop. (1880) 11,183, (1890) 50,395, (1900) 102,479, of whom 19,964 were foreign-born; s the growth in population since 1900 has been very rapid and in 1 9 10 it was 31 9, 1 9 8.
From the centre, processes (s) go to circumference(t), ending in curved placentaries bearing the ovules.
D is the dispart sight, S the tangent sight, A'DS the clearance angle.
The Council will rely chiefly upon Scripture s in reformandis dogmatibus et instaurandis in ecclesia moribus; the Roman reply to the two sets of articuli of Augsburg, and the Roman counterpart to the (later) Protestant assertion that the Bible 7 is the " only rule of faith and practice."
Thirlwall replied by pointing out that no provision for theological instruction wa,s in fact made by the colleges except compulsory attendance at chapel, and that this was mischievous.
Blucher, based on Napoleon s places.
Volume = 3(a+b+c)S.
If R and S are the ends of a prismoid, A and B their areas, h the perpendicular distance between them, and C the area of a section by a plane parallel to R and S and midway between them, the volume of the prismoid is *h(A+4C+B).
The volume comprised between the cross-section whose area is S and a consecutive cross-section at distance 0 from it is ultimately SO, when B is indefinitely small; and the area between the corresponding ordinates of the trapezette is (S/1).
In the case of the sphere, for instance, whose radius is R, the area of the section at distance x from the centre is lr(R 2 -x 2), which is a quadratic function of x; the values of So, Si, and S2 are respectively o, 7rR 2, and o, and the volume is therefore s.
In cases other than those described in § 82, the pth moment with regard to the axis of u is given by Pp = XPrA where A is the total area of the original trapezette, and S 2 _ 1 is the area of a trapezette whose ordinates at successive distances h, beginning and ending with the bounding ordinates, are o, x1P -1A, x2 P-1 (AI+AI),.
The value of S 13 _ 1 has to be found by a quadrature-formula.
If we write -fxo f yox s yiu dx dy, we first calculate the raw values coo., ai,o, 0.1,1,
If the coin is light the rod S fits into the uppermost step and the shoot stops over the right-hand slot.
If the coin is heavy, S fits into the lowest step and the shoot stops over the left-hand slot.
His mathematical writings, which account for some forty entries in the Royal Society's catalogue of scientific papers, cover a wide range of subjects, such" s the theory of probabilities, quadratic forms, theory of integrals, gearings, the construction of geographical maps, &c. He also published a Traite de la theorie des nombres.
On the whole the air S within ABCD neither gains nor g D loses momentum, so that on the whole it receives as much through AB as it gives up to CD.
At the instant that the original wave reaches F the wave from E has travelled to a circle of radius very nearly equal to EF-not quite, as S is not quite in the plane of the rails.
As these " secondary waves " return to S their distance apart is nearly equal to twice the distance between the rails, and the observer then hears a note of wave-length nearly 2EF.
But if an observer is stationed at S' the waves will be about half as far apart and will reach him with nearly twice the frequency, so that he hears a note about an octave higher.
Let S' be its position one second later, its velocity being u.
Let the velocity of the air from S to R be w, and let U be the velocity of sound in still air.
If d is measured for two gases in succession for the same frequency N, we have 72 p 2P1 d22 71 p i p s d12' where the suffixes denote the gases to which the quantities relate.
Under Britishrule Colombo has shared in the prosperity brought to the island by the successive industri e s of coffee and teaplanting.
Zarubayev, who had used only about half his forces in the battle, nevertheless S' retired in the night, fearing to be cut off by a descent of the approaching 4th Army on Haicheng, and well content to have broken the spell of defeat.
Leaving Libau on the 13th-15th of October 1904, the fleet steamed down the North Sea, expecting every night s to be attacked by torpedo-boats.
The people of Saxony are chiefly of pure Teutonic stock; a proportion are Germanized Sla y s, and to the south of Bautzen there is a large settlement of above 50,000 Wends, who retain their peculiar customs and language.
By the treaty of Verdun in 843 Saxony fell to Louis the German, but he paid little attention to the northern part of his kingdom which was harassed by the Normans and the Sla y s.
Liudolf, who is sometimes called " duke of the East Saxons," carried on a vigorous warfare against the Sla y s and extended his influence over other parts of Saxony.
The Sla y s were driven back, the domestic policy of Henry the Fowler was continued, the Saxon court became a centre of learning visited by Italian scholars, and in 968 an archbishopric was founded at Magdeburg for the lands east of the Elbe.
These proceedings aroused suspicion and discontent, which were increased when the emperor assembled an army, ostensibly to attack the Sla y s.
Lothair quickly made himself independent, defeated Henry at Welfesholz in 1115, and prosecuted the war against the Sla y s with vigour.
These items are Historical S' value.
And Yahweh-Elohim planted a garden s in Eden, east ward; and there he put the man whom he had formed."
The Common Law Procedure Act (Ireland) 1856, which is incorporated by s.
It is not easy to fix the average stress s per sq.
Let t be the statical breaking strength of a bar, loaded once gradually up to fracture (t = breaking load divided by original area of section); u the breaking strength of a bar loaded and unloaded an indefinitely great number of times, the stress varying from u to o alternately (this is termed the primitive strength); and, lastly, let s be the breaking strength of a bar subjected to an indefinitely great number of repetitions of stresses equal and opposite in sign (tension and thrust), so that the stress ranges alternately from s to -s.
Wohler's and Bauschinger's experiments give values of t, u, and s, for some materials.
The total shear at a b is S = R-E(W1+W2 ...) where the summation extends to all the loads to the left of the section.
Let s be the perpendicular from 0, the join of C and T on the direction of S; t the perpendicular from A, the join of C and S on the direction of T; and c the perpendicular from B, the join of S and T on the direction of C. Taking moments about 0, Rx - W 1 (x+a) - W 2 (x+2a) =Ss; taking moments about A, R3a-W 1 2a-W 2 a =Tt; and taking moments about B, Rea-W I a = Cc.
Or generally, if M 1 M2 M3 are the moments of the external forces to the left of 0, A, and B respectively, and s, t and c the perpendiculars from 0, A and B on the directions of the forces cut by the section, then Ss=M11 Tt=M2andCc=M3.
Draw a vertical at D, intersecting fh, kg, in s and q.
Let the length of half the parabolic chain be called s, then 4.
Then the deflection at the centre is the value of y for x = a, and is _ 5 wa4 S - 14 EI' The radius of curvature of the beam at D is given by the relation R=EI/M.
In 1840 he ', as thus enabled to give a quantitative statement of the law acc s rding to which heat is produced in a conductor by the pas ageof an electric current, and in succeeding years he publish d a series of valuable researches on the agency of electricity in ansformations of energy.
It was the liberal-minded Germans who were instrumental in the first place in getting them passed; while the Sla y s from the beginning took up - to their own disadvantage - a hostile or at least passive attitude towards the establishment of these laws."
Vienna had for long been the hope of the Southern Sla y s, and many of them had dreamed of a union under the Crown of Austria (" trialism ").
The claim set up by the Italians to a university of their own within the territory inhabited by them led to various controversies with the Germans and Southern Sla y s.
In June 1913 the Government considered itself justified by necessity of the State in adopting a measure which in many respects was held to be a breach of the constitution; it appointed a commission for Bohemia, the members of which were nominated by the State, to deal with the autonomous affai s of this country.
The Italians demanded Trieste; but the Government was afraid to let this Adriatic port become the centre of an irredenta; moreover the Southern Sla y s of the city wished it kept free from an Italian educational establishment.
Kdrber' s successor, Clam-Martinitz,' who belonged to the violently Czech feudal nobility, tried to form a national coalition Cabinet, including two German politicians.
The Sla y s, on the other hand, demanded the " unconditional " summoning of Parliament.
Since the Northern and Southern Sla y s had absented themselves and the Poles were in opposition, the Reichsrat was adjourned (May 3), and the Germans now again demanded the grant of a revised constitution, with German as the language of State, a special status for Galicia and Dalmatia, access for the Germans to the Adriatic, and the partition of Bohemia.
This programme met with a cool reception; the Poles by now were expecting a new organization from the Peace Congress; the Southern Sla y s desired union with those of their race in Hungary also; the Czechs opposed the division of the administrative commission into two parts; they did not want autonomy for their nation, but incorporation of the German Bohemians in their State, and refused all negotiations.
About 804 Charlemagne, in order to defend the line of the Saale against the Sla y s, founded the Thuringian mark, which soon became practically coextensive with the former duchy.
The fall of Missolonghi, followed as this was by the submission of many of the more notable chiefs, left Reshid free to turn his attention to East Hellas, where Gouras had been ruling Karaa s a practically independent chief and in the s irit P Y P P?
For the weighing of gold, gems, opium, &c., the fuang, equal to s tical, and the salung, equal to 4 tical, are used.
Begun by the Countess Matilda of Tuscany in 1099, after the designs of Lanfranc, and consecrated in 1184, the Romanesque cathedral (S Geminiano) is a low but handsome building, with a lofty crypt, under the choir (characteristic of the Tuscan Romanesque architecture), three eastern apses, and a façade still preserving some curious sculptures of the 12th century.