G sentence example
When the band moves to the C chord, you slide your fingers along the same strings until you're at the eighth fret of the E (which is C) and the ninth fret of the G (which is E) and you've created the same sort of harmony for the G chord.
Induction is the strictest phase, and recommends eating fewer than 20 g of carbohydrates per day from low carb foods, including animal proteins, leafy green vegetables, and full-fat dairy products such as butter, heavy cream, and cheese.
The thermal G G detectors are especially useful for the purpose of quantitative measurements, because they indicate the true effective or square root of mean square value of the current or train of oscillations passing through the hot wire.
The histology described above for the polyp may be taken as the primitive type, from which that From Allman's G y mnoblastic Hydroids, by permission of the Council of the Ray Society.
Ch is always to be sounded as in church, g is always hard; y always represents a consonant; whilst kh and gh stand for gutturals.Advertisement
This map was repeatedly revised, Antgria- g P P Y ?
In the Amynodontidae, represented by the North American Middle Eocene Amynodon and Metamynodon, the premolars may be either 4 or g, making the total number of teeth either 44 or 40.
Fully realizing, the difficult P Y g?
Within rising of g g 1875.
In the same year another series of bonds (hazin g tahvili), bearing 6% interest, and repayable in 1861, was issued; in 1861 the term of reimbursement was prolonged until 1875.Advertisement
The Kurds, the constant oppressors of that people, had received official recognition and almost complete immunity from the control o f the civil law by being formed into a Y g eo Y manry frontier-guard known as the Hamidian cavalry.
A regenerated Ottoman Empire might in time be strong enough to demand the evacuation of Bosnia and Herzegovina, g and to maintain or extend the nominal suzerainty over Bulgaria which the sultan had exercised since 1878.
Dresden was the last great victory of the First Empire, By noon on the 27th August the Austrians and Russians were completely beaten and in full retreat, the French pressing hard behind them, but meanwhile Napoleon himself again succumbed G Beereri B eip \ ii g?
In the Domesday Survey it appears as a me g ne borough under Juhel of Totnes, founder of the castle and priory; it had 95 burgesses within and 15 without the borough, and rendered military service according to the custom of Exeter.
All symmetric functions are expressible in terms of the quantities ap g in a rational integral form; from this property they are termed elementary functions; further they are said to be single-unitary since each part of the partition denoting ap q involves but a single unit.Advertisement
The motion of the node of this plane is found with great exactness from observaMass, of the g tions of the transits of Venus.
For the mean motion of the earth in one second in circular measure, we have n 8149' l o g.
K is a commutator for reversing the direction of the magnetizing current, and G a galvanometer for measuring it.
He made use of the expression F =Wg=27r12+HI, where W is the weight in grammes per square centimetre of sectional area, and g is the intensity of gravity which was taken as.
How otherwise are we to explain such Hebraisms (or Syriacisms) as Evui pEEC rb g Xacov E ct ro (§ 9), ov elir€v.Advertisement
But the Brazilian colonists, now that the mother country had thrown off the Spanish yoke, determined even without assist ance from the homeland to rise in revolt against foreign Revolt g g against domination.
The pp g y Dutch were unable, however, to extend their power beyond the limits of the town, until the arrival of Count John Maurice of Nassau-Siegen in 1636.
Its position, at the point where the Volscian Hills reach the coast, leaving no space for passage between them and the sea, commanding the Pomptine Marshes (urbs pron g in paludes, as Livy calls it) and possessing a small harbour, was one of great strategic importance; and it thus appears very early in Roman history.
Da Gama made no landing here and, like Discovery the rest of South Africa, Natal was neglected by the and early g Y his tory.
He had designated as his successor his natural son, g the highly gifted Janos (John) Corvinus, a youth of seventeen.Advertisement
P g g the emperor Maximilian and Sigismund of Poland, might be dispensed with.
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.
Study), and B I c (G.
At first sight it appears difficult to understand how g PP the complicated series of actions which are definitely exhibited as so-called " instincts " by a variety of animals can have been due to the selection of congenital variations, or can be otherwise explained than by the transmission of habits acquired by the parent as the result of experience, and continuously elaborated and added to in successive generations.
By differentiation with respect to g i it may be proved that from g, = - oo to g i = - 2h1, from g, = - 2h, to g1=0, from g, = 0 to g, =2h,, from g,=2h, to g,=oo.
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.
For example, when u = o, M = o, N =o, and consequently G =H = 2.
From the series for G and H just obtained it is easy to verify that dH = - 7rvG, dv av - dG _ 7rvH -1.
We have ultimately G =o, H = (7rV)- 1, so that 1 2 = I / 12V 2, or the illumination is inversely as the square of the distance from the shadow of the edge.
So far, however, energy and Successes v i g i lance made them successful.
It was in the fullest sense a Uaaish g Invasions.
Y g g The air passes through a reducing valve from the main to an auxiliary tank, in which the pressure is, say, 125 lb, and thence to the driving cylinders.
It is more economical Lowerin g to save the men's strength, however, by raising men.
In this case the piston is solid, and the outlet pipe, G which is placed at the bottom of the cylinder, has a valve F opening outwards, the inlet pipe and valve are the same as before.
On again F J J raising the piston the valve E opens ?g G admitting more liquid whilst F re- mains closed.
In this table n is the refractive index of the glass for sodium light (the D line of the solar spectrum), while the letters C, F and G' refer to lines in the hydrogen spectrum by which dispersion is now generally specified.
Guru Gu g Go Har Govind promptly ordered that the articles should be relegated to his treasury, the museum of the period.
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.
To give an idea of what can be done in this way, it may be stated that gold can be beaten out to leaf of the thickness of - j g - mm.; and that platinum, by judicious work, can be drawn into wire 2?o o mm.
Ballasted with G at B, the righting couple when the ship is heeled through 0 is given by W.BM.
Clebsch has shown, from purely analytical considerations (Crelle, lvi.); and then = Z d(?G, m), ?
When the cylinder r =a is moved with velocity U and r =b with velocity U 1 along Ox, = U b e - a,1 r +0 cos 0 - U ib2 - 2 a, (r +Q 2 ') cos 0, = - U be a2 a2 (b 2 - r) sin 0 - Uib2 b1)a, (r - ¢2 sin 0; b and similarly, with velocity components V and V 1 along Oy a 2 b2 ?= Vb,_a,(r+r) sin g -Vi b, b2 a, (r+ 2) sin 0, (17) = V b, a2 a, (b2 r) cos 0+Vi b, b, a, (r- ¢ 2) cos h; (18) and then for the resultant motion z 2zz w= (U 2 + V2)b2a a2U+Vi +b a b a2 U z Vi -(U12+V12) b2 z a2b2 Ui +VIi b 2 - a 2 U1 +Vii b 2 - a 2 z The resultant impulse of the liquid on the cylinder is given by the component, over r=a (§ 36), X =f p4 cos 0.ad0 =7rpa 2 (U b z 2 + a 2 Uib.2bz a2); (20) and over r =b Xi= fp?
The polar equation of the cross-section being rI cos 19 =al, or r + x = 2a, (3) the conditions are satisfied by = Ur sin g -2Uairi sin IB = 2Uri sin 10(14 cos 18a'), (4) 1J/ =2Uairi sin IO = -U1/ [2a(r-x)], (5) w =-2Uaiz1, (6) and the resistance of the liquid is 2lrpaV2/2g.
A relative stream line, along which 1/,' = Uc, is the quartic curve y-c=?![2a(r-x)], x = 4a2y2-(y g)4, r- 4a2y2 +(y c) 4, 7) 4 a (y-c) 4a(y and in the absolute space curve given by 1', dy= (y- c)2, x= 2ac_ 2a log (y -c) (8) 2ay y - c 34.
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.
The cuneiform system of writing Semitic. w as still in process of growth when it was borrowed influence p g and adapted by the new comers, and the Semitic Babylonian language was profoundly influenced by the older language of the country, borrowing its words and even its grammatical usages.
After his death, the Assyrians, who were still nominally the vassals of Babylonia, threw off neser L - g n a ll disguise, and Shalmaneser I.
Calah was burned thou h the stron walls g YP, g g of Nineveh protected the relics of the Assyrian army which had taken refuge behind them; and when the raiders had passed on to other fields of booty, a new palace was erected among the ruins of the neighbouring city.
This g Y P Y PP Y infamous law, however, aroused so much opposition that some of the very men who had proposed it assembled in secret to discuss its abolition, and a quarrel between the Albizzi and the Ricci having weakened the parte, a balia of 56 was agreed upon.
The signory appointed Piero Capponi, a man of great ability and patriotism, and experienced in diplomacy, the gonfaloniere Francesco Valori, the Dominican Giorgio Vespucci, and the jurisconsult and diplomatist Domenico Bonsi, rule, 's every five years, appointed all the magistrates and Y Y PP g syndics to conduct the negotiations with the French king.
On the 1st of September 1512 Retur e Medici G i ul i ano and Giovanni de' Medici, and their nephew (1512).
Notices in Greek authors are collected by P. Paulitschke, Die geographische Erforschung des afrikanischen Continents (Vienna, 1880); the inscriptions were edited and interpreted by G, Maspero, Revue archeol.
Outline of the ventral surface to show the external apertures and nervous system; a, rosette-organ; b, uterine pore; c, terminal sucker; e, vaginal pore; g, male gonopore; n, o, p, nervous system.
G, six-hooked embryo, highly magnified.
G shows formation of proglottides.
Certain g' he were the owner.
On his death in 1897 his nephew Abdul-Aziz, son of the murdered amir Matab, succeeded; during his reign a new element has been introduced into Nejd politics by the rising importance of Kuwet (Koweit) and the attempts R t g P () P history.
Extracts from this book are given by M`G.
Damiri) is not zoological but legendary, and the works on minerals are practical and not scientific. See ARABIAN PHIaOSOPHY and historical sections of such scientific articles as ASTRONOMY, &c. (G.
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.
The ovary (a) leads into (bb) the oviduct, which is joined at (g) by the duct of the yolk-glands (h).
A, Dorsal view showing the nervous system and digestive system; a, mouth; b, pharynx; c, d, e, gut; E, post-genital union of two limbs of gut; f, excretory pore; g, vaginal pore; h, j, k, brain and nerves; 1, dorsal nerves; m, ventral nerves; n, adoral sucker; o, posterior sucker; p, hooks on posterior sucker; r, vitello-intestinal duct.
The country was still labouring under the curse of an inconvertible currency originatingwith the Legal Tender Act res - paperY g dncy.
He was received with distinguished honours in England and on the continent of Europe, g whence he made his way to India, China and Japan.
Occasional g ruptions are mentioned, e.g.
While through a great crisis due to the conflict of two 0 os g g PP Classifica= from a single trunk, - is to give to science the ensemble tion of sciences.
In all these cases the sound represented was a hard G (as in gig).
A further peculiarity of the use of C in Latin is in the abbreviation for the district Subura in Roma and its adjective Suburanus, which appears as SVC. Here C no doubt represents G, but there is no interchange between g and b in Latin.
As the district was full of traders, Subura may very well be an imported word, but the form with C must either go back to a period before the disappearance of g before v or must come from some other Italic dialect.
The symbol G was a new coinage in the 3rd century B.C. The pronunciation of C throughout the period of classical Latin was that of an unvoiced guttural stop (k).
There was some talk of inducing d J Y Th f i $ g Glad stone to join the Tory government, and on the 29th of November Lord Malmesbury dubiously remarked, " I cannot make out Gladstone, who seems to me a dark horse."
Having been returned again for the university of Oxford, he entered on the active duties of a great office for which he was pre-eminently g P Y House of government in power, but on the 18th of October the commons.
On the 23rd of January 1874 Gladstone announced the dissolution in an address to his constituents, declaring that the authority of the government had o f187atioa g y g of 1874.
He was now sixty-four, and his life had been a continuous experience of exhausting Temporary p g retirement.
In the United Kingdom the excise duty is eleven shillings per proof gallon of alcohol, while the customs duty is eleven shillings and 5' g fivepence; the magnitude of these imposts may be more readily understood when one remembers that the proof gallon costs only about sevenpence to manufacture.
The metal slips are so placed that, as the disk revolves, the middle brush, connected to one terminal of the condenser C, is alternately put in conductive connexion with first one and then the other outside brush, which are joined respectively to the battery B and galvanometer G terminals.
The amount of heat absorbed in any small change of state, as from E to G in fig.
The condition of stable equilibrium is that G should be a minimum, for which reason it has been called the " thermodynamic potential at constant pressure."
The function G is represented by the negative area D"DM under the isothermal, bounded by the isopiestic DM and the axis of pressure.
The increment of 00 is always greater than that of the total heat F=E+pv, except in the special case of an equilibrium change at constant temperature and pressure, in which case both are equal to the heat absorbed in the change, and the function G remains constant.
If G' and G" are the values of the function G for the two states in equilibrium at the same pressure and temperature, we must have G' =G".
Assuming the function G to be expressed in terms of p and 0, this condition represents the relation between p and 0 corresponding to equilibrium between the two states, which is the solution of the relation (v" - v')dp/dO=L/D, (5).
To find the border curve of equilibrium between the two states, giving the saturation pressure as a function of the temperature, we have merely to equate the values of G and G".
This simple result is generally true, and the corresponding expressions for G" and J" are valid, provided that c - b in formula (17) is a function of the temperature only.
Although the value of G in any case cannot be found without that of 0, and although the consideration of the properties of the thermodynamic potential cannot in any case lead to results which are not directly deducible from the two fundamental laws, it affords a convenient method of formal expression in abstract thermodynamics for the condition of equilibrium between different phases, or the criterion of the possibility of a transformation.
The loose aggregation of agricultural households gives place t o the organized community with new needs and new g y ideals, and at the same time in religious thought the old vague notion of the numen is almost universally superseded by the more definite conception of the dens - not even now quite anthropomorphic, but with a much more clearly realized personality.
The screw, turned by the wheels at g', acts in a toothed arc, whence, as shown in the figure, equal and opposite motion is communicated to the slides by the jointed rods v, v.
Tancred now sought to win over the towns by extensive grants of privileges, and at Gravina (June 1192) was reco g nized by the pope, whose ineffectual support he gained by surrendering the royal legateship over Sicily.
The sinking of colliery shafts, however, differs considerably from that of other mines, owing to their generally large size, and the difficulties nkingof g g y g ?
The shaft is lined with a cylinder of wrought iron, within which a tubular chamber, provided with doors above and below, known as an P g air-lock, is fitted by a telescopic joint, which is tightly sinkin packed so as to close the top of the shaft air-tight.
The surface arrangements of a modern deep colliery are of considerable extent and complexity, the central feature being the head gear or pit frame carrying the guide pulleys Surface which lead the winding roes from the axis of the it arrange= g P P to the drum.
One of the scarps or steps is the result of a great fault or displacement of the earth's crust, and is known as the Balcones fault scarp; others are due to erosion and weatherin g of alternate layers of hard and soft rocks lying almost horizontal.
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 =.
Clearly the integral is the sum of the values of mu g for all the molecules of the first kind in unit volume, thus p=v mu l +v'm'u 2 +...
Twinning is not uncommon, the twinplanes M (i io) and g (roi) being the same as in marcasite.
The most important is the Deutsch-Ostafrikanische G esellschaft, founded in 1885, which has trading stations in each seaport, and flourishing plantations in various parts of the country.
In the Eastern province the rocks are mainly quartz, gneiss and granite, with sandstone in Busoga, basalt round Mt Elgon, slate (Busoga) and iron- g stone (Busoga and Bukedi).
The revenues from ecclesiastical foundations, as well as those from the industrialilds were to be placed in a g ?
As might have been anticipated, this caused no break in the policy of the English king and his parliament, and a series of famous acts passed in the year 1534 completed and confirmed the independence of the Church of England, which, except during five years under Queen Mary, p g Y Q Y?
Whether with Payne it is assumed that in some remote time a The speechless anthropoid passed over a land bride now American P P P g ?
There is no dividing line between first-contact ethnology and -s y g gY gy Th J o pre-contact archaeology.
It passes over equal spaces in equal times, but falls with an accelerating velocity according to the formula h = zgt 2, where h is the height fallen through, g the force of gravity, and t the time of flight.
Now the height to which the tangent sight has been raised in order to direct the axis on G' is evidently proportional to the tangent of the angle OMS =AXS.
An automatic sight is a sight connected in such a manner with the elevating gear of the gun, that when the sight is directed on the water-line of a target at any range the gun will ---- have the proper quadrant g B elevation for that range.
The rocking-bar is moved by a rack g into which a pinion on a cross-spindle j gears; the cross-spindle is moved by means of a worm-wheel into which a worm on the longitudinal FIG.
Then MA'B'N is a right trapezium, whose area is equal to that of Cabd; and it is related to the latter in such a way that, if any two lines parallel to AC and BD meet AB, CD, MN, A'B', in E, G, P, E', and F, H, Q, F', respectively, the area of the piece PE'F'Q of the right trapezium 'B.
On any line OX take a length ON equal to xG, and from N draw NP at right angles to OX and equal to uH; G and H being convenient units of length.
Then we may, ignoring the units G and H, speak of ON and NP as being equal to x and u respectively.
The corresponding solid figure, in its most general form, is such as would be constructed to represent the relation of a magnitude E to two magnitudes F and G of which it is a function; it would stand on a plane base, and be comprised within a cylindrical boundary whose cross-section might be of any shape.
The - - 4X + g tangential area may be expressed in terms of chordal areas.
The disks fall down the tube G to a receptacle on the floor.
The collar A' is then raised by the lever G so as to encircle the blank, and the upper die which is held at A is brought down.
This guard wire prevents any current which leaks over the surface of the insulator from passing through the galvanometer G, and the galvanometer indication is therefore only determined by the amount of current which passes through the insulator, or by its insulation-resistance.
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.
Now suppose we take G as the key-note and form its diatonic scale.
Taking the successive key-notes D, A, E, B, it is found that besides small and negligible differences, each introduces a new sharp, and so we get the five sharps, C, D, F, G, A, represented nearly by the black keys.
In works on sound it is usual to adopt Helmholtz's notation, in which the octave from bass to middle C is written c d e f g a b c'.
The octave above is c' d'e' f' g' a' b' c".
Saps were then pushed on against Erh-Lung, and to help in their progress a Russian advanced work called " G " was captured on the 16th, by a skilfully combined attack of infantry and artillery.
At " G " they took a portion of the Chinese Wall and lost it again, other trenches with a cross fire being behind.
Hence the moment of the load on Am at C is wy0m, and the moment of a uniform load over any portion of the girder is w X the area of the influence curve Ip' G' E ' under that portion.
Let P be the cost of one pier; G the cost of the main girders for one span, erected; n the number of spans; 1 the length of one span, and L the length of the bridge between abutments.
That is, G = a1 2, where a is a constant.
Let G be the cost of superstructure ?
Any error of this kind will merely affect the form of the frame; if, however, another member be introduced between A and D, then if BC be shortened AD will be strained so as to extend it, and the four other members will be compressed; if G CB is lengthened AD will thereby be compressed, and the four other members extended; if the workman does not make CB and AD of exactly the right length they and all the members will be permanently strained.
Lord Melbourne saw her Public g g affairs.
Many candidates qualifica- approach the calling with a very imperfect a reciaPP g Y P PP tion of its exacting character.
As the English technical terms reli g doctrinegious.
The polarization itself is determined from the electric force (P,Q,R) by the usual statical formula of linear type which becomes tor an isotropic medium (.f',g',h') = c2(P,Q,R), because any change of the dielectric constant K arising from the convection of the material through the aether must be independent of the sign of v and therefore be of the second order.
The book was written in Greek, though not improbably the middle portion, the Testament of Hezekiah, was originally composed in Semitic. The Greek in its original form, which we may denote by G, is lost.
It has, however, been in part preserved to us in two of its recensions, G 1 and G2.
G 2 denotes the Greek text from which the Slavonic and the second Latin Version (consisting of vi.-xi.) were translated.
This version is on the whole a fai t hful reproduction of G 1.
Its universal acceptance is perhaps du g to the fact that it exists in two forms (the variata and the invariata) which vary slightly in the way in which they state the doctrine of the sacrament of the Supper.
He instinctively recognized not only the vital necessity of the maintenance of the union between the two states, but also the fact that the chief source of danger to the union lay Gas;m11 IV., g y in Lithuania, in those days a maelstrom of conflicting political currents.
That glorious epithet belonged of right to Hungary,which g p g g had already borne the brunt of the struggle with the Ottoman power for more than a century.
During the earlier part of the 1 th P g P 5 century the Lithuanian princes had successfully contested Muscovite influence even in Pskov and Great Novgorod.
The equations of motion are now, the co-ordinates x and y being measured in feet, 2 (26) - -rr- - C, dt2 dty - g' * These numbers are taken from a part omitted here of the abridged ballistic table.
The general effect of the recommenda g tions already made would be to begin the study of foreign languages with French, and to postpone the study of Latin to the age of twelve and that of Greek to the age of thirteen.
On the eve of the Revolution, France was enjoying the study of the institutions of Greece in the attractive pages of the P g Voyage du jeune Anacharsis (1789), but the study of Greek was menaced even more than that of Latin.
Greek fell still further into the background; and Homer and Demosthenes The age of g Y g Y iFrenchnfluence.
Absalon died on the 21st of March 1201, at the family monastery of Sor g, which he himself had richly embellished and endowed.
Gulf of Gabes I o g Lemg.W.of Greenwicir 0 Longitude East of Greenwich B 4 D very complete sequence of formations from the Lias to those of recent date.
One terminal of the galvanometer can then be shifted to the junction 6 7 g between any pair of consecutive coils and the slider shifted to any point on the potentiometer wire.
It is necessary in the first er P g Y Y Criticism.
The picture of Apostolical Christianity found in the New Testament offered indeed a glaring g g contrast to the papal system of the later middle ages.
Since loge(I +x) =x-2x 2 -3x 3 - 4x4+&c., we have, by changing the sign of x, log e (I - x) _ - x - zx 2 - 3x 3 - x 4 - &c.; whence g 1 +x to=2(x+ix'+1x5+&c.), e l - x and, therefore, replacing x by p +q, log e q =2 p +q +3 () 3T ?
I o g.
Even when seen in minute features only he recognized them as constant progressive characters or " chronologic varieties " in 3b --i C D E F G H I -14-21 -I-31 1 - I - 41 contrast with contemporaneous or " geographic varieties," which he considered inconstant and of slight systematic value.
His family was of patrician rank and traced a legendary descent from lulus, the founder of Alba g Y, Longa, son of Aeneas and grandson of Venus and Anchises.
G, enlarged view of the antenna f.
Asplanchnopus myrmeleo, showing horseshoe-shaped germarium (left), blind saccate stomach (right), apical bladder, foot, &c.; g, Asplanchna ebbesbornii - the coiled tube at left is a kidney; h, i, incudate jaws of Asplanchna brightwellii and girodii chiefly formed of rami, with the rudimentary mallei parallel and external to them; j, Ascomorpha hyalina.
It was also natural that these attempts g p should be made where the need was most pressing, derings.
P g 4 535 is evident that Coverdale must have been engaged on the preparation of the work for the press at almost as early a date as Tyndale.
Y g themselves of its advantages.
The equations finally arrived at are DX2(A2_ 2) (x2_ A2m)2+g2A2 ' DgA3 (A A l m) 2 +g 2 A2 ' where is the wave-length in free ether of light whose refractive index is n, and A m the wave-length of light of the same period as the electron, is a coefficient of absorption, and D and g are constants.
A strikin,g contrast between New England and the rest of the Appalachians is found in the descent of the New England uplands Th At!
The outer court, which is much the larger, contains the granaries and storehouses (K), and the kitchen (H) and other offices connected with the refectory (G).
Opening from the western side of the cloister, but actually standing in the outer court, is the refectory (G), a large cruciform building, about loo feet each way, decorated within with frescoes of saints.
Facing the west are the stables (e), ox-sheds (f), goatstables (g), piggeries (h), sheep-folds (i), together with the servants' and labourers' quarters (h).
The nave (G) had double vaulted aisles on either side.
The best Cluniac. Cluniac houses in England are Castle Acre, preserved g, Norfolk, and Wenlock, Shropshire.
Immediately on the right of entrance was the abbot's house (G), in close proximity to the guest-house (F).
This inner gate conducted into the base court (T), round which were placed the barns, stables, cow-sheds, &c. On the eastern side stood the dormitory of the lay brothers, fratres conversi (G), detached from the cloister, with cellars and storehouses below.
The co-ordinates of its centre are - g/c, f/c; and its radius is (g 2 +f 2 - c) I.
Obviously these equations show that the curves intersect in four points, two of which lie on the intersection of the line, 2 (g - g')x +2 (f - f')y+c - c'=o, the radical axis, with the circles, and the other two where the lines x2+y2= (x+iy) (x - iy) =o (where i = - - I) intersect the circles.
If we compare (I) with the general equation of the second degree ua2 + v/ 32 +wy2 this equation to represent a circle we must have - kabc =vc 2 +wb 2 -2u'bc=wa g +uc 2 - 2v'ca = ub 2 +va - 2w'ab.
France's plan for a great empire in America was now taking shape and there, as in Europe, a deadly Struggles g P P with struggle with England was inevitable.
Since the advance of civilization and indis c riminate slaughter have deprived them of the bison, g p so long their natural means of subsistence, the northwest tribes have been maintained chiefly at the expense of the country.
The chief executive authority is vested in the sovereign, as is the supreme command g p of the military and naval forces.
The gall-bladder (g), when it is present, is always situated on the caudal surface or in the substance of the right central lobe.
Thus the Roman letters E and F are liable to be confused in capital script, but not in cursive (e, f), C, G, in capitals, c, e in the cursive writing called Caroline minuscule, c, t, in the angular cursive of the 13th century and later.
The words introducing this form (6Tav bE TO '&TL Tptrov irpoo-KaTnyopijTac, chap. so, s 9 b s 9), which are the origin of the phrase tertii adjacentis, disengage the verb of being (g un) partially but not entirely, because they still treat it as an extra part of the predicate, and not as a distinct copula.
It is well known in England for its graceful habit, the slender, grey - or white - barked stem, the delicate, drooping branches and the quivering leaves, a bright, clear green in s p r i n g, becoming duller in the summer, but often keeping their greenness rather late into the 5 autumn.
For The Sake Of Greater Generality, The Days Of The Week Are Denoted By The First Seven Letters Of The Alphabet, A, B, C, D, E, F, G, Which Are Placed In The Calendar Beside The Days Of The Year, So That A Stands Opposite The First Day Of January, B Opposite The Second, And So On To G, Which Stands Opposite The Seventh; After Which A Returns To The Eighth, And So On Through The 365 Days Of The Year.
Now If One Of The Days Of The Week, Sunday For Example, Is Represented By E, Monday Will Be Represented By F, Tuesday By G, Wednesday By A, And So On; And Every Sunday Through The Year Will Have The Same Character E, Every Monday F, And So With Regard To The Rest.
Thus, For 1840, We Have 1840-9966 2 1 G; Therefore (1849) R= 1, And The Year 1840 Is The First Of The Solar Cycle.
The branched intestine (G) is drawn on one side of the animal only; it opens to the exterior by means of a pharynx (not shown).
The spherical granules (G) are probably gland-secretions; the dark bodies (Z) are probably xanthellae, i.e.
The rota of judges for g the trial of election petitions is also supplied by the king's bench division.
But, at least in the south, market centres had sprung up, town life was beginning, houses of a better type were perhaps coming into use, and the southern tribes employed a gold coinage and also a currency of iron bars or ingots, attested by Caesar and by surviving examples, which weigh roughly, some two-thirds of a pound, some 21 lb, but mostly I g lb.
Secondly, there is the so-called " Vallum," in reality no vallum at all, but a broad flat-bottomed ditch out of which the earth has been cast up on either side into g Bremen (Rochester) ijffabilasrciu.n
G, Outer wall of the colonnade built of brick, now missing.
The superintendent, who is a naval officer, has to investigate the magnetic character of the ships, to point out the most suitable positions for the compasses when a ship is designed, and subsequently to keep himself informed of their behaviour from the tin g e of the ship's first trial.
In the concordat of 1801 the papacy recognized the validity of the sales of Church of 180E g Y property, and still further reduced the number of dioceses; it provided that the government should appoint and support the archbishops and bishops, but that the pope should confirm them; and France recognized the temporal power, though shorn of Ferrara, Bologna and the Romagna.
Y g P relations with most of the powers, but also of having entered into a convention with the great powers of the North, which accorded him, in conjunction with the three emperors, a leading position as champion of the conservative interests of humanity.
The result obtained was that any body allowed to fall from rest would, in a vacuum move re to the earth with constant o G av.
Scale of Metres o co 20 30 40 5 Scale of Yards 0 i p zo g o 40 ?o climbing plants with slender herbaceous or shrubby shoots, to which belong the yam and the British black bryony, Tamus communis.
It was at this stage that the language spread in Lahul and Spiti, where the superscribed letters were silent, the d and g finals were hardly heard, and as, os, us were ai, oi, ui.
P g on the 31st of March 1904, the first hostile encounter took place at Guru, when the Tibetans (the aggressors) were defeated.
The lodgings of the prior (G) occupy the centre of the outer court, immediately in front of the west door of the church, and face the gateway of the convent (0).
By moving the lens G up and down the image can be formed in the correct position for the eyepiece at all extensions of the mast.
And such bodies placed under the command of a sovereign or grand master, regulated by statutes, and enriched by ecclesiastical endowments would have been precisely what in after times such orders as the Garter in England, the Golden Fleece in Burgundy, the Annunziata in Savoy and the St Michael and Holy Ghost in France actually were.4 During the 14th and 15th centuries, as well as somewhat earlier and later, the general arrangements of a European army were always and everywhere pretty much the same.5 Under the sovereign the constable and the marshal g or marshals held the chief commands, their authority being partly joint and partly several.
But in what particular g P year this event occurred is and has been the subject of much difference of opinion.
Peltigera canin g, which formed the basis of the celebrated " pulvis antilyssus " of Dr Mead, long regarded as a sovereign cure for hydrophobia; Platysma juniperinum, lauded as a specific in jaundice, no doubt on the similia similibus principle from a resemblance between its yellow colour and that of the jaundiced skin; Peltidea aphthosa, which on the same principle was regarded by the Swedes, when boiled in milk, as an effectual remedy for the aphthae or rash on their children.
Although the Bab g (4) g Y lonian religion presents a very gloomy view of the world of the dead, it is not without a few faint glimpses of a hope that a few mortals at least may gain deliverance from the dread doom.
The last point of departure was at a point called G in lat.
His published works include Le four g lectrique (1897), and Le fluor et ses composes (1900), besides numerous papers in the Comptes rendus and other scientific periodicals.
Thence to the Reschen Scheideck Pass the main chain is ill-defined, though on it rises the Corno di Campo (10,844 ft.), beyond which it runs slightly north-east past the sources of the Adda and the Fra g ile Pass, sinks to form the depression of the Ofen Pass, soon bends north and rises once more in the Piz Sesvenna (10,568 ft.).
The rays, rendered parallel by the collimator objective, meet a plane mirror (f) of silvered glass, which reflects them to the prisms (g, g').
The axis N 0 passes through the brass piece M, which stands on an insulating pillar of glass, and supports the plates A and C. At one extremity of this axis is the ball D, and the other is connected with a rod of glass, N P, upon which is fixed the handle L, and also the piece G H, which is separately insulated.
The piece K is parallel to G H, and both of them are furnished at their ends with small pieces of flexible wire that they may touch the pins E, F in certain points of their revolution.
Q' Penan?h g Prov.Welleley 3 s 0 -.._ .,.0 1=Higher 2 = Longitude East too ore Arch.
But the attention of the Spanish king was at this time con P g centrated upon the success of the Invincible Armada.
But it was in the Portuguese g g colonies that the conquests of the Dutch East and with West India Companies had been made, and the France question of the Indies as between Netherlander and Spaniard assumed henceforth quite a different complexion.
It met at 3' g the Hague on the 18th of January 1651.
With this view he entered into secret negotiations for a French alliance g which, as far as can be gathered from extant records, had for its objects the conquest and partition by the United allies of the Belgic provinces, and joint action in was widened.
In 1659 a treaty of peace was with concluded between France, England and the United education of theer under was e ounce prince of Orange d Y e P g taken by the States of Holland under the super intendence of de Witt.
The defeat of Leipzig in 1813 was the signal for a general revolt in the Netherlands; the prince of Orange (son of William V.) was recalled, and amidst general Creation provinces to form the kingdom of the Netherlands, of the p g Kingdom which was also to include the bishopric of Liege and of the the duchy of Bouillon, and the prince of Orange was Nether- placed upon the throne on the 15th of March 1815 as lands.
This proposal caused a cleavage right through P P g g g all parties.
It has been shown especially in the Uredineae and Erysiphaceae that many forms which can hardly be distinguished morphologically, or which cannot be differentiated at all by structural characters, are not reall y homogeneous but consist of a number of forms which are se se s g sharply distinguishable by their infecting power.
A pair of electric arcs play between these electrodes and the molten steel, passing through the layer of slag, G, and generating much heat.
The town was governed until the 19th century by two bailiffs, chosen annually at a court le g it of the royal manor o Wimborne borough, part of the manor of Kingston Lacy.
It was not till sixteen years later, on the collapse of the united kingdom of urnes re' A ?eltre' G'`h e n.
He is also charged with the executive power which he delegates to a cabinet composed of ministers g P chosen from the party representing the majority in the chamber.
The cardinal arch- Peace of g duke Ferdinand, governor-general from 1634-1641, was a capable ruler, and by his military skill prevented in a succession III.
He selected as his victim a powerful popular leader at Brussels, Francis Anneesens, syndic of the gild of St Nicholas, who was Y g ?
Among these was the closing of the Scheldt to all ships, a clause which was ruinous to the commerce of the Belgic provinces, by cutting them off from their only to the impoverished land by the introduction of new but visited Belgium in person and governor-general,g p showed a great and active interest in its affairs.
Ministers were to be appointed by him, but be responsible to the cham bers The legislature was composed of two chambers - g P the senate and the chamber of deputies.
Leopold s i n ified his readiness to accept the crown after having of the g P g Belgians.
Addresses were unanimously voted urging the king to resist separation, great excitement was g P ?
Three hundred and twenty delegates met and drew up an Act of Federation and a programme of The conditions were far less favourable to Belgium of g than had been hoped, and it was not without much heart-burning and considerable opposition, that the senate and chamber of deputies gave their assent to them.
Hitherto since 1842 in all primary schools instruction by the clergy in the Catholic faith was obligatory,children belonging School g g law of to other persuasions being dispensed from attendance.
Some way below Bellegarde, between Le Parc and Pyrimont, the Rhone becomes officially "navigable," though as far as Lyons the navigation now consists all but wholly of the floating of flat-bottomed boats, named g igues, laden chiefly with stone quarried from the banks of the river.
Lorenz, assuming that the ratio k/k'=aG, had previously given 0 2 maz Bo g = E2/4a, (12) which is practically identical with the preceding for small differences of temperature.
All these controversial writings on mathematics and physics represent but one half of his activity after the age of p y g Years.
The size of this depends water is usually preferable for grass land, thick for y P g upon the quantity of water required, but whatever its size its bottom at its origin should be as low as the bed of the river, in order that it may carry down as much as possible of the river mud.
Their procedure is less rigorous than g hat of the Roman Church, and as yet has been but imperfectly studied.
Its true source is in some small lakes near the head of the Fra g ile glen, but its volume is increased by the union with several smaller streams, near the town of Bormio, at the Raetian Alps.
The Total in Reichskanzler is the sole responsible official, In the Pacific and conducts all the affairs of the empire, with German New G the exception of such as arc of a purely military Bismarck Archrj character, anti is the intermediary between the Caroline, Pelewa emperor, the Bundesrat and the Reichstag.
Aimoin, who died about ioio, must be distinguished from Aimoin, a monk of St Germain-des-Pres, who wrote De miraculis sancti Germani, and a fragment De Normanorum gestis circa Parisiacam urbem et de divin g in eos ultione tempore Caroli calvi.
Wilhelmshaven is visited for its sea-bathin g.
Austria and Spain were thus divided, and, in spite of the efforts of the archduke Charles in the Spanish Succession War, were never again united, for at the battle of Mohacs, on the 28th of August 1526, Suleiman the Mohacs Magnificent defeated and killed Louis, king of Bohemia and its g g results.
The first war, due to Ottoman aggression in Transylvania, ended with Montecuculi's victory over the grand vizier at Wars with Y g Turkey.
The efforts of Turkey to regain her ascendancy in eastern Europe at the expense of the Habsburgs had ended p p g in failure, and henceforward Turkish efforts were confined to resisting the steady development of Austria in the direction of Constantinople.
Treaty g 7 After a campaign of varying fortunes the Turks beat 1739.
Vienna again became the centre g of a despotic government the objects of which were to Germanize the Magyars and Sla y s, to check all agitation for a constitution, and to suppress all attempts to secure a free press.
From both the Hungarian and the Austrian parliament there was to be elected a Delegation, consisting of sixty members; to these Delegations the common ministers were to be re g of the court of Vienna were entrusted to Beust, whom the emperor appointed chancellor of the empire and also minister-president of Austria.
Y Y g 73 For some years there had been active speculations on 1873.
What ruined the government was the want of g unity in the party, and their neglect to support a ministry which had been taken from their own ranks.
There seems no doubt that the condition of the workmen in the factories of Moravia and the oil-mines of Galicia was peculiarly unfortunate; the hours of work were very long, the Count convictions, and on the first day of the session Rieger S' g unless he could speak and write German.
The Austrian Socialistencouraged by this manifestation and Franchise party, g Y reform.
The intimate connexion be tween old Hellas and Sicily begins with the foundation Y g?
It fell with the coming back of the xile Dion in The tyranny had lasted so long 3 5 7 Y Y g that it was less easy than at the overthrow of the elder tyrants to fall back on an earlier state of things.
Greek Ci t ies now arose in all its provinces, superseding in g many cases native market places and villages, and holding the vantage-points of commerce.
The spirit of the Sassanian monarchy was more jealously national than that of the Arsacid, and alienrafts could hardly have flourished g y under it.
The part referring to North Africa was edited by M`G.
It was based mainly on the MS. called G above, and is the chief source of our knowledge of that MS. which perished, all but three leaves, in the Cottonian fire of 1723.
The young king, a man Christian of character andenius had wide views and original IL, 1513= g 1523.
Th is contest began in 18 2 when a com- g g g %, bination of all the Radical parties, known as the United Left," passed a vote of want of confidence against the government and rejected the budget.
P g PY en P however, the cotyledon is not really terminal.
Surrounding the church (which stands in a highlying portion of the g own known as Chipping Hill) there are earthworks, possibly the remains of a fortification recorded as made by order of Edward the Elder in 913, but perhaps of British origin.
Until 1855 no colonial bishop was consecrated outside the British Isles, the first instance being Dr MacDougall of Labuan, con- autoitual g g ?
To consider the Cyanophyceae excludingacteriaceae from algae altogether, notwith g g g ?
The possibility of theoun states entering into a combination which Y g g would enable them to offer a united resistance to foreign interference while simultaneously effecting a compromise in regard to their national aims, has at various times occupied the attention of Balkan politicians.
The historical causes which kept the nations separate were mainly racial, though, from a very early period, the majority of the people of Scotland were, if not purely English by blood, anglicized in language and to a great extent, Earl gand, g ?
In the reign of his successor, Alexander II., the risings of Celtic claimants died out; he converted Argyll into a sheriffdom, and (1237) resigned the claims to Northumberland, in exchange for lands in the northern English counties g g with a rental of £200 yearly.
Six custodians of the realm were then appointed, including the bishop g p of Glasgow (Wishart) and the bishop of St Andrews (Frazer).
The parliamentary committee capitulated g P y P with the extremists, who sent friendly messages to Cromwell, and Argyll met him on the Tweed.
Cromwell, who now crossed the border, impressed this truth, as far as he might, on the preachers, who made in g ?
The grounds of strife were the spread in the Y y g P of " liberal " religious ideas; on one side heretical and anti-Calvinistic doctrines, and on the other a tendency to stretch Calvinistic principles till they were scarcely to be distinguished from Antinomianism.
This page gives an overview of all articles in the 1911 Brittanica which are alphabetized under G to Gan.
The line FL perpendicular to the axis, G D and passing through the focus, is the semilatus rectum, the latus rectum being the focal chord parallel to the directrix.
The usual method is to saw a log into planks or boards by n g P y of Timber.
There are conflicting ideas of death and the dead, and among them the belief in the very human feelings and needs of the dead and in their influence for good or ev11.2 Moreover, the proximity of burial-place and sanctuary and the belief in the kindly care of the famous dead for their descendants reflect " primitive " and persisting ideas which find their Holy parallel in the holy tombs of religious or seckular p y g?
Oriental law is primitive or advanced according to the social conditions, with the result that antiquity of ideas is no criterion of date, and modern desert custom is more archaic than the great code of the Babylonian king Khammurabi Babylonian g y g Law.
The salt is conveyed to the furnace by a chain of buckets running on the pulley (g), and passing into the hopper (h), and through the pipe (i) is mixed with the proper amount of acid supplied by the pipe (f).
A large fire-grate (ab), having a cave (c) to facilitate stoking and stepped back at (d), is bounded on one side by a fire-bridge (e); on the other side of this, separated by an air-channel (g), there is first the proper fluxing bed (h), and behind this the "back-bed "(i) for pre-heating the charge.
Plumptre was a man of great versatility and attained high reputation as a translator of the plays of Sophocles (1865) and Aeschylus (1868), and of the Divin g commedia of Dante (1886).
The numerous invasions p g have naturally introduced a certain amount of foreign blood among the tribes fringing the Mediterranean, but those farther inland have preserved their racial purity to a surprising degree.
One, called turanjbin, appears to exude, in small round tears, from the camelthorn, and also from the dwarf tamarisk; the other, sir-kasht, in large grains and irregular masses or cakes with bits of twig imbedded, is obtained from a tree which the natives call si g h chob (black wood), thought by Bellew to be a Fraxinus or Ornus.
In 1633 eight Englishmen from Masulipatam, under Ralph Cartwright, sailed northward to Harishpur near Cuttack on the mouth of the Mahanadi, and entered into negotiations to trade with the governor of Orissa; and' in June Bengal 1633 Cartwright founded a factory at Balasore, which settle- 33 g Y ?
He was succeeded by Sir Henry (afterwards Lord) Hardinge, =slit Y Y () g ?
On the side of the telescope opposite to the horizontal axis is attached a graduated circle g, and, turning concentrically with this circle, is a framework h, to which the readers and verniers of the circle are fixed.
This frame carries two very sensitive levels, k and 1, and the whole frame can be clamped to the circle g by means of the clamping screw m.
Assuming, for example, that the northern star has the smaller right ascension, the instrument is first, with the aid of the stop, placed in the meridian towards the north; the verniers of the graduated circle g are set to read to the reading 40-2(Sn+Ss) where 0 is the approximate latitude of the place and Sn, Ss the declinations of the northern and southern star respectively; then the level frame h is turned till the levels k and I are in the middle of their run, and there clamped by the screw m, aided in the final adjustment by the adjoining slow motion screw shown in the figure.
While the vessels were being prepared for the voyage to Toulon all the hostages in the castles were liberated save four; but on the 24th of June Nelson arrived with his fleet, and on hearing of the capitulation he refused to g p recognize it save in so far as it concerned the French.
On the 8th of July, King Ferdinand arrived from Palermo, and the state trials, conducted in the most arbitrary fashion, resulted in wholesale butchery; hundreds of persons were executed, including some of the best men in the veng g country, such as the philosopher Mario Pagano, the scientist Cirillo, Manthone, the minister of war under the republic, Massa, the defender of Castel dell' Uovo, and Ettore Caraffa, the defender of Pescara, who had been captured by treachery, while thousands of others were immured in horrible dungeons or exiled.
Joseph's reforms, swept away many old abuses and reorganized the army; and although he introduced g y ?
The Power Was Transmitted To The Paddles By Bevel Wheels F, G, Rotating A Spindle Passing Through A Stuffing Box In The Bottom Of The Calorimeter.
The history of logic shows that the linguistic distinction between terms and propositions was the sole analysis of reasoning in the logical treatises of Aristotle; that the mental distinction between conceptions (g vvocac) and judgments (a uiwara in a wide sense) was imported into logic by the Stoics; and that this mental distinction became the logical analysis of reasoning under the authority of St Thomas Aquinas.
Dialectic then, though it may prove to be the ultimate method of establishing principles in philosophy, 5 starts from probable and conceded premises, 6 and deals with them only in The the light of common principles such as ma be reason g p p y ably appealed to or easily established against challenge.
If alleged Psycho- P g Logy.ic a priori constituents of knowledge - such rubrics as substance, property, relation - come to be explained psychologically, the formal logic that has perforce to ignore all that belongs to psychology is confined within too narrow a range to be able to maintain its place as an independent discipline, and tends to be merged in psychology.
We must not confuse ouvia with Eivat, nor g m with yiyvEoOat.
The displacer (E),which takes its motion through a rod (I) from a rocking lever (F) connected by a short link to the crank-pin, is itself the regenerator, its construction being such that the air passes up and down through it as in one of the original Stirling forms. The cooler is a water vessel (G) through which water circulates from a tank (H).
Some phonetic characteristics of the dialect may be regarded as quite certain; (I) the change of the original short o to a (as in the last syllable of the genitive kalatoras); (2) of final -m to -n (as in g ran); (3) of -ni- -ti- -si- respectively to -nn- -to- and -ss- as in dazohonnes " Dasonius," dazohonnihi " Dasonii"; dazetOes, gen.
It was greatly stimulated American g 9 Y g Y during the Spanish-American revolutions (the Lima and Panama trade dating from about 1813), for, as the Californian authorities practically ignored the law, smuggling was unnecessary; this was, indeed, much greater after 1822 under the high duties (in 1836-1840 generally about loo %) of the Mexican tariffs.
Siegfried bathed in the blood of heals in g g healing the dragon he slew and thus became invulnerable; the blind emperor Theodosius recovered his sight when a grateful serpent laid a precious stone upon his eyes; Cadmus and his wife were turned into serpents to cure human ills.
The rounded form ofy is found with the value of G in R EC E I, which is probably the dative of rex.
K in time passed out of use except as an abbreviation, its place being taken by C, which, as we have seen, is in the earliest inscription still g.
There is some evidence which seems to point to a pronunciation of the voiced mutes which, like the South German pronunciation of g, d, b, but slightly differentiated them from the unvoiced mutes, so that confusion might easily arise.
Owing to this confusion, the new symbol G, differentiated from C, took the place of the useless I.
In abbreviations, however, C remained as before in the value of G, as in the names Gaius and Gnaeus.
This mysterious language, despite the existence of more than 6000 inscriptions, and the publication in 1892 of a book written in the language and handed down to us by the accident of its use to pack an Egyptian mummy, remains as obscure as ever, but apparently it underwent very great phonetic changes at an early period, so that the voiced mutes B, D, G disappeared.
Latin D; while the symbol for the voiced spirant o is doubled, it is difficult to believe that the symbol for the spirant g, viz.
Glagolitic has a symbol for the palatalized g (5), but it is used only in the transcription of Greek words, y having become y early between vowels in the popular dialects.
The force R is the geometric sum of the given forces, and the moment (G) of the couple is equal to the sum of the moments of the given forces about 0.
The value of G will in general vary with the position of 0, and will vanish when 0 lies on the line of action of the single resultant.
Hence any three-dimensional system can be reduced to a single force R acting in a certain line, together with a couple G in a plane perpendicular to the line.
Hence a couple of moment G, whose axis has the direction (1, m, n) relative to a right-handed system of rectangular axes, FIG.
The work is therefore R(r cos 0sh sin 0)+ G cos 8
The displacement of G is at right angles to JG; this shows that for equilibrium JG must be vertical.
Again, the locus of G is an arc of an ellipse whose centre is in the intersection of the planes; since this arc is convex upwards the equilibrium is unstable.
For equilibrium, the altitude of the centre of gravity G must be stationary; hence G must lie in the same vertical line with the point of contact J of the two curves.
If the body be supposed to roll - (say to the right) until the curves touch at J, and if JJ=bs, the angle through which the u,pper figure rotates is Is/p +Is/p, and the horizontal displace- V ment, of G is equal to the product of this expression into h.
Is cos 4,, the vertical through the new position of G will fall to the left of J and gravity will tend to restore the body to its former position.
The point G determined by (I) is called the mass-centre or centre of inertia of the given system.
The formula (16) expresses that the squared radius of gyration about any axis (Ox) exceeds the squared radius of gyration about a parallel axis through G by the square of the distance between the two axes.
A, B, C are the moments of inertia about the co-ordinate axes, and F, G, H are the products of inertia with respect to the pairs of co-ordinate planes.
It possesses thi property that the radius of gyration about any diameter is half thi distance between the two tangents which are parallel to that diameter, In the case of a uniform triangular plate it may be shown that thi momental ellipse at G is concentric, similar and similarly situatec to the ellipse which touches the sides of the triangle at their middle points.
This acceleration is denoted by g; its value at Greenwich is about 981 centimetre-second units, or 322 feet per second.
We learn also that on account of the variation of g with the locality a gravitational system of force-measurement is inapplicable when more than a moderate degree of accuracy is desired.
This indicates an experimental method of determining g with considerable accuracy, using the formula g 41r2l/T2.
The deviation of the earths figure from sphericity, and the variation of g with latitude, are here ignored.
For it can only depend on the mass m of the bob, the length 1 of the string, and the value of g at the place in question; and the above expression is the only combination of these symbols whose dimensions are those of a time, simply.
The range on a horizontal plane through 0 is got by putting y=o, viz, it is 2uovo!g.
Now the moment of this localized vector with respect to any axis through G is zero, to the first order of &, since the perpendicular distance of G from the tangent line at G is of the order (ot)2.
It follows, by the preceding kinematic theory, that the mass-centre G of thc system will move exactly as if the whole, mass were concentrated there and were acted on by the extraneous forces applied paralle to their original directions.
If there are no extraneous forces, or if the extraneous forces have zero moment about any axis through G, the vector which represents the resultant angular momentum relative to G is constant in every respect.
A plane through G perpendicular to this vector has a fixed direction in space, and is called the invariable plane; it may sometimes be conveniently used as a plane of reference.
If K be the radius of gyration about a parallel axis through G, we have kf=K2+h2 by If (16), and therefore i=h+K1/h, whence GO.GP=K2.
A pendulum is constructed with two parallel knife-edges as nearly as possible in the same plane with G, the position of one of them being adjustable.
As a final example we may note the arrangement, often employed in physical measurements, where a body performs small oscillations about a vertical axis through its mass-centre G, under the influence of a couple whose moment varies as the angle of rotation from the equilibrium position.
The motion being assumed to be small, the tensions of the two strings may be taken to have their statical values Mgb/(a+b), Mga/(a+b), where a, b are the distances of G from the two threads.
When the body is twisted through an angle 0 the threads make angles aC/i, be/I with the vertical, and the moment of the tensions about the vertical through G is accordingly Kg, where K = M gab/i.
Proceeding to the general motion of a rigid body in two dimensions we may take as the three co-ordinates of the body the rectangular Cartesian co-ordinates x, y of the mass-centre G and the angle C through which the body has turned from some standard position.
If the extraneous forces be re p duced to a force (X, Y) at G and a couple N, we have Mx=X,My=Y,IO=N.
If the extraneous forces have zero moment about G the angular velocity 0 is constant.