How to use Sphere in a sentence
His sphere of action, however, was not in parliament.
The continental area is on one side of the sphere and the oceanic on the other.
Let a conductor, say a metallic sphere, be supported by a metal rod of negligible electric capacity whose other end is earthed.
By a treaty made between Great Britain and Siam in 1902 the northern Malay states of the peninsula were admitted to lie within the Siamese sphere of influence, but by a treaty of 1909 Siam ceded her suzerain rights over the states of Kelantan, Trengganu, Kedah and Perlis to Britain.
The Stoic philosophers, especially Crates of Mallus, arguing from the love of nature for life, placed an oekumene in each quarter of the sphere, the three unknown worldislands being those of the Antoeci, Perioeci and Antipodes.Advertisement
She stepped out of the sphere.
It ended the old Aristotelian distinction between the sphere beneath the moon and the starry spaces beyond.
A small light sphere hanging from the end of 30 or 40 ft.
Probably a sphere would prove most useful for a pressure anemometer, since owing to its symmetrical shape it would not require a weathercock.
But the notes of the flute came home to his ears out of a different sphere from that he worked in, and suggested work for certain faculties which slumbered in him.Advertisement
His love for Natasha, Antichrist, Napoleon, the invasion, the comet, 666, L'Empereur Napoleon, and L'russe Besuhof--all this had to mature and culminate, to lift him out of that spellbound, petty sphere of Moscow habits in which he felt himself held captive and lead him to a great achievement and great happiness.
The latter position, ascribed by the schoolmen to the Averroists, becomes dominant among the later Nominalists, William of Occam and his disciples, who withdraw all doctrines of faith from the sphere of reason.
The co-operative spirit of the Great Russians shows itself in another sphere in the artel, which has been a prominent feature of Russian life since the dawn of history.
A great part of the eastern section of the railway was constructed on Chinese territory, and elaborate preparations were made for bringing Manchuria within the sphere of Russian influence.
It is probable that Moses held the larger rather than the narrower conception of Yahweh's sphere of influence.Advertisement
Prophetic personality now moved in a larger sphere than that of divination, important though that function be in the social life of the ancient state as instrumental in declaring the will of the deity when any enterprise was on foot.
This problem of religion was solved by Amos and by the prophets who succeeded him through a more exalted conception of Yahweh and His sphere of working, which tended to detach Him from His limited realm as a national deity.
After the Armistice the unsatisfactory consequences of the peace negotiations, the heavy burden of suffering and loss caused by the war, and, above all, the intolerable internal policy of the Nitti Cabinet, brought about the return of Giolitti to the sphere of practical politics once more.
The prophets taught that the national existence of the people was bound up with religious and social conditions; they were in a sense the politicians of the age, and to regard them simply as foretellers of the future is to limit their sphere unduly.
Eckhart was a distinguished son of the Church; E but in reading his works we feel at once that we have passed into quite a different sphere of thought from that of the churchly mystics; we seem to leave the cloister behind and to breathe a freer atmosphere.Advertisement
In the 9th and 8th centuries B.C. they became the chief power within their sphere and the suzerain of their parent Babylon.
When several rings or circles were combined representing the great circles of the heavens, the instrument became an armillary sphere.
With the earth as centre such a sphere is known as Ptolemaic; with the sun as centre, as Copernican.
With the physiocrats, he believed in an enlightened absolutism, and looked to the king to carry through all reforms. As to the parlements, he opposed all interference on their part in legislation, considering that they had no competency outside the sphere of justice.
In reasserting and amplifying the empirical conclusions of his predecessors, especially in the sphere of ethics, Mill's chief function was the introduction of the humanist element.Advertisement
Then the large cells recommence the process of division and sink into the hollow of the sphere, leaving an elongated groove, the blastopore, on the surface.
The system itself aims in principle at being thoroughly monistic; but, since matter, although created by God out of nothing, was regarded merely as the sphere in which souls are punished and purified, the system is pervaded by a strongly dualistic element.
He was now to further the cause of the republic one and indivisible in the sphere of action.
In the sphere of European diplomacy, no less than in that of French politics, the results of the coup d'etat of Fructidor were momentous.
The effects of the expedition in the sphere of world-politics were equally remarkable and more immediate.
Everything, therefore, portended a change in this sphere, but few persons expected a change so drastic as that which Bonaparte now brought about in the measure of 28 Pluviose, year VIII.
Bonaparte signalized his tenure of power by no very important developments in the sphere of elementary education.
The career of Napoleon, which had lured France far away from the principles of 1789, now brought her back to that starting-point; just as, in the physical sphere, his campaigns from1796-1814had at first enormously swollen her bulk and then subjected her to a shrinkage still more portentous.
They do not appear to have moved on to another sphere, as these nomadic tribes often did when defeated, and were probably gradually absorbed in the surrounding populations.
In Der Kampf urns Dasein am Himmel von Prel endeavoured to apply the Darwinian doctrine of organic evolution not only to the sphere of consciousness but also even more widely as the philosophical principle of the world.
Manchuria was claimed by Russia as her particular sphere of interest towards the close of the 19th century, and in the course of the disturbances of 1900 Russian troops occupied various parts of the country.
In much the same way, at a later date and in a lesser sphere, the closing of the traderoutes by the advance of the Ottoman Turks led traders to endeavour to find new channels, and issued in the rounding of the Cape of Good Hope and the discovery of America.
Distinct from all these courts, if similar in its sphere, is the court which the Italian quarter generally enjoyed in each town under its own consuls - a court privileged to try all but the graver cases, like murder, theft and forgery.
In other spheres the immunities and exemptions of the Church offered a far more serious problem, and especially in the sphere of finance.
Venice had her own reward; a Venetian, Thomas Morosini, became patriarch; and the doge of Venice added "a quarter and a half" of the Eastern empire - chiefly the coasts and the islands - to the sphere of his sway.
Partly as a result of this trade, ever pushing its way farther east, and partly as a result of the Asiatic missions, which were themselves an accompaniment and effect of the Crusades, a third great result of the Crusades came to light in the 13th century - the discovery of the interior of Asia, and an immense accession to the sphere of geography.
When we turn from the sphere of politics to the history of civilization and culture, we find the effects of the Crusades as deeply impressed, if not so definitely marked.
While a new spirit which compares and tolerates thus sprang from the Crusades, the large sphere of new knowledge and experience which they gave brought new material at once for scientific thought and poetic imagination.
The circle in which a sphere is cut by a plane is called a "great circle," when the cutting plane passes through the centre of sphere.
Treating the earth as a sphere, the meridians of longitude are all great circles.
But of all the Hildebrandine statesmen who applied their teacher's ideas within the sphere of a particular national church he was the most successful.
In 1162 he was transferred to a new sphere of action.
None of the coins with Alexander's own image can be shown to have been issued during his reign; the traditional gods of the Greeks still admitted no living man to share their prerogative in this sphere.
Or from the Persian Gulf wares might be taken up the Euphrates and carried across to Antioch; this route lay altogether in the Seleucid sphere.
On the other hand a map drawn on the surface of a sphere representing a terrestrial globe will prove true to nature, for it possesses, in combination, the qualities which the ingenuity of no mathematician has hitherto succeeded in imparting to a projection intended for a map of some extent, namely, equivalence of areas of distances and angles.
The sphere is then coated with plaster or whiting, and when it has been smoothed on a lathe and dried, the lines representing meridians and parallels are drawn upon it.
The map or diagram of which Leonardo Dati in his poem on the Sphere (Della Spera) wrote in 1422 " un T dentre a uno 0 mostra it disegno " (a T within an 0 shows the design) is one of the most persistent types among the circular or wheel maps of the world.
He purified it from the grossly sensual elements of daeva worship, and uplifted the idea of religion to a higher and purer sphere.
He has the supervision of all the state services in his department, which procures the necessary uniformity in the working of the services, each of which is specialized within a narrow sphere.
Under the constitution of the Republic the sphere of individual liberty is large and constitutionally protected against the government.
This convention caused much excitement and irritation in Great Britain, owing to the encroachment of German influence sanctioned by it on territories bordering the Persian Gulf, hitherto considered to fall solely within the sphere of British influence.
Mathieu de Montmorency and Mme Recamier were exiled for the crime of seeing her; and she at last began to think of doing what she ought to have done years before and withdrawing herself entirely from Napoleon's sphere.
By the same treaty France renounced its sphere of influence on the right bank of the Mekong.
The cases of greatest practical importance are those of a sphere (which is an ellipsoid with three equal axes) and an ovoid or prolate ellipsoid of revolution.
Since 7ra'I is the moment of the sphere (=volume X magnetization), it appears from (10) that the magnetized sphere produces the same external effect as a very small magnet of equal moment placed at its centre and magnetized in the same direction; the resultant force therefore is the same as in (14).
For small bodies other than spheres the coefficient will be different, but its sign will always be negative for diamagnetic substances and positive for others; hence the forces acting on any small body will be in the same directions as in the case of a sphere' Directing Couple acting on an Elongated Body.
If a hollow sphere 7 of which the outer radius is R and the inner radius r is placed in a uniform field Ho, the field inside will also be uniform and in the same direction as Ho, and its value will be approximately 3 i - R 3 For a cylinder placed with its axis at right angles to the lines of force, 2 = Ho (41) 2 +4(-2)(i - R2) These expressions show that the thicker the screen and the greater its permeability o, the more effectual will be the shielding action.
An electrically neutral atom is believed to be constituted in part, or perhaps entirely, of a definite number of electrons in rapid motion within a " sphere of uniform positive electrification " not yet explained.
The relation of reason and faith remains external, and certain doctrines - an increasing number as times goes on - are withdrawn from the sphere of reason.
But the further progress of Scholastic thought consisted in a withdrawal of doctrine after doctrine from the possibility of rational proof and their relegation to the sphere of faith.
Robert Grosseteste, important in the sphere of ecclesiastical politics, has been already mentioned as active in procuring translations of Aristotle from the Greek.
The monotheistic influence of Aristotle and his Arabian commentators shows itself in Albert and Aquinas, at the outset, in the definitive fashion in which the " mysteries " y sof the Trinity and the Incarnation are henceforth detached from the sphere of rational or philosophical theology.
Gauss in particular employed it in the calculation of the magnetic potential of the earth, and it received new light from Clerk Maxwell's interpretation of harmonics with reference to poles on the sphere.
Archimedes' problem of dividing a sphere by a plane into two segments having a prescribed ratio,was first expressed as a cubic equation by Al Mahani, and the first solution was given by Abu Gafar al Hazin.
We imagine a wave-front divided o x Q into elementary rings or zones - often named after Huygens, but better after Fresnelby spheres described round P (the point at which the aggregate effect is to be estimated), the first sphere, touching the plane at 0, with a radius equal to PO, and the succeeding spheres with radii increasing at each step by IX.
In these instruments the lines are ruled upon a spherical surface of speculum metal, and mark the intersections of the surface by a system of parallel and equidistant planes, o; of which the middle member passes through the centre of the sphere.
The geometrical theory first requires a consideration of the path of a ray of light falling upon a transparent sphere.
Of the total amount of light falling on such a sphere, part is reflected or scattered at the incident surface, so rendering the drop visible, while a part will enter the drop. Confining our attention to a ray entering in a principal plane, we will determine its deviation, i.e.
Other important contributors to this sphere of literature were Isho' bar Nan (t827/8), John bar Zo`bi (beginning of the 13th century), Jacob bar Shakko (f1241), and the great Nestorian scholar `Abadisho' (f 1318).
The retention by women in Europe of the tropical garb can be explained by the fact that her sphere has been mainly confined to the house, and her life has been less active than that of man; consequently the adoption of the arctic dress has been in her case less necessary.
If in regard to France his policy appeared to lack suavity and circumspection, it must be remembered that the French republic was then engaged in active anti-Italian schemes and was working, both at the Vatican and in the sphere of colonial politics, to create a situation that should compel Italy to bow to French exigencies and to abandon the Triple Alliance.
In times past it has been the habit to look upon its sphere Connexion as lying really within that of practical medicine, and with human medicine more particularly; as something Biology.
If the striking conceptions of Paul Ehrlich and Emil Fischer continue to prove as fertile in inspiring and directing research as at present they seem to be, another wide sphere of.
If we consult the medical works even of the middle of the 19th century we shall find that, in the light of the present time, accurate knowledge in this sphere, whether clinical, pathological or therapeutical, could scarcely be said to exist.
In the sphere of physiology and in the interpretation of associated arterial diseases much obscurity still remains; as, for instance, concerning the nature of the toxic substances which produce those bilateral changes in the kidneys which we call Bright's disease, and bring about the "uraemia" which is characteristic of it.
A full account of the process of blowing crown-glass will be found in all older books and articles on the subject, so that it need only be mentioned here that the glass, instead of being blown into a cylinder, is blown into a flattened sphere, which is caused to burst at the point opposite the pipe and is then, by the rapid spinning of the glass in front of a very hot furnace-opening, caused to expand into a flat disk of large diameter.
A small sphere of the fluid, if frozen suddenly, would retain this angular velocity.
Irrotational Motion in General.-Liquid originally at rest in a singly-connected space cannot be set in motion by a field of force due to a single-valued potential function; any motion set up in the liquid must be due to a movement of the boundary, and the motion will be irrotational; for any small spherical element of the liquid may be considered a smooth solid sphere for a moment, and the normal pressure of the surrounding liquid cannot impart to it any rotation.
Thus, for example, with = 4Uy 2 (r 2 a 2 -I), r2 = x2 +y 2, (13) for the space inside the sphere r=a, compared with the value of, i' in § 34 (13) for the space outside, there is no discontinuity of the velocity in crossing the surface.
Inside the sphere d I d'd rd?
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'.
A distribution of sources and doublets over a moving surface will enable an expression to be obtained for the velocity function of a body moving in the presence of a fixed sphere, or inside it.
On completing his legal studies he entered the service of the state in 1837; and after holding a series of minor posts was transferred in 1848 to the ministry of commerce, which was to be the sphere of his real life's work.
Some of the religious gilds supported schools, or helped to maintain roads, bridges and town-walls, or even came, in course of time, to be closely connected with the government of the borough; but, as a rule, they were simply private societies with a limited sphere of activity.
Thus with every creation of a craft fraternity the gild merchant was weakened and its sphere of activity was diminished, though the new bodies were subsidiary to the older and larger fraternity.
When these various unions of dealers and of craftsmen embraced all the trades and branches of production in the town, little or no vitality remained in the old gild merchant; it ceased to have an independent sphere of activity.
This delimitation places the whole of southern Arabia, east of this line, within the British sphere of influence, which thus includes the district surrounding Aden (q.v.), the Hadramut and Oman with its dependencies.
A few new members were admitted, mainly from the westernmost sphere of Hanseatic influence, but membership was refused to some important applicants.
The Hanseatic embargo against Bruges from 1451 to 14J7, its later war and embargo against England, the Turkish advance closing the Italian Black Sea trade with southern Russia, all were utilized by Nuremberg and its fellows to secure a landtrade outside the sphere of Hanseatic influence.
But a decline of its importance, similar to that within the larger sphere which it influenced prior to 1859, has continued uninterruptedly within the Habsburg dominions up to the present day.
Of other common types of condenser, we may notice the "spiral" or "worm" type, which consists of a glass, copper or tin worm enclosed in a vessel in which water circulates; and the ball condenser, which consists of two concentric spheres, the vapour passing through the inner sphere and water circulating in the space between this and the outer (in another form the vapour circulates in a shell, on the outside and inside of which water circulates).
Assuming that Yahweh was primitively a nature god, scholars in the 19th century discussed the question over what sphere of nature he originally presided.
Like the gods, the cult heroes were supposed to exercise an influence on human affairs, though not to the same extent, their sphere of action being confined to their own localities.
The system for which the Positive Philosophy is alleged to have been the scientific preparation contains a Polity and a Religion; a complete arrangement of life in all its aspects, giving a wider sphere to Intellect, Energy and Feeling than could be found in any of the previous organic types, - Greek, Roman or Catholic-feudal.
With this may be compared a passage in the Ursprung der Sprache, where there is a curious adumbration of Spencer's idea that intelligence, as distinguished from instinct, arises from a growing complexity of action, or, to use Herder's words, from the substitution of a more for a less contracted sphere.
These men, living in the past, paid little attention to the great popular movement, which seemed to be quite outside their social and artistic sphere and scarcely worthy of cultured criticism.
From God emanates a divine sphere, which appears in the spiritual world as a sun, and from this spiritual sun again proceeds the sun of the natural world.
She wrote and lectured on women's education and in behalf of better primary schools, and radically opposed woman suffrage and college education for women, holding woman's sphere to be domestic. The National Board of Popular Education, a charitable society which she founded, sent hundreds of women as teachers into the South and West.
Some of these criticisms are rather beside the mark, but were all true, they would not impair his essential greatness, which lay in another sphere.
He returned resolved to devote the rest of his days to rousing the Church to her duty in the sphere of foreign missions, but his health was now broken, and his old energy flagged.
A very small sphere is said then to possess a charge of one electrostatic unit of quantity, when it repels another similar and similarly electrified body with a force of one dyne, the centres being at a distance of one centimetre, provided that the spheres are in vacuo or immersed in some insulator, the dielectric constant of which is' taken as unity.
Cavendish proved it by enclosing a metal sphere in two hemispheres of thin metal held on insulating supports.
If the sphere is charged and then the jacketing hemispheres fitted on it and removed, the sphere is found to be perfectly discharged.
The thinnest possible spherical shell of metal, such as a sphere of insulator coated with gold-leaf, behaves as a conductor for static charge just as if it were a sphere of solid metal.
The electric density on the sphere being uniform, the quantities of electricity on these areas are proportional to the areas, and if the electric force varies inversely as the square of the distance, the forces exerted by these two surface charges at the point in question are proportional to the solid angle of the little cone.
Hence we see that if the whole surface of the sphere is divided into pairs of elements by cones described through any interior point, the resultant force at that point must consist of the sum of pairs of equal and opposite forces, and is therefore zero.
If, however, we employ a hollow sphere and let the stem pass through a hole in the side larger than itself, and attach the end to the interior of the sphere, then leakage cannot take place.
Thus, consider a sphere uniformly charged with Q units of positive electricity.
The quantity of electricity which must be given to the sphere to raise it to unit potential is therefore R electrostatic units.
Thus the distribution of electricity on a sphere in free space must be uniform, and all parts of the charge are at an equal distance R from the centre.
Since of a the capacity C is the ratio of charge to potential, the sphere.
Let R 1 be the radius of the inner sphere, R2 the inside radius of the outer sphere, and R2 the outside radius of the outer spherical shell.
In each case we have C = a when e= 0, and the ellipsoid thus becomes a sphere.
This last result shows that the capacity of a thin disk is 2/7r =1/1.571 of that of a sphere of the same radius.
Hence the potential V at the centre of the inner sphere is given by V =Q/R1 - Q/R2+Q/R3.
If the outer shell is connected to the earth, the charge +Q on it disappears, and we have the capacity C of the inner sphere given by C= I /R 1 - I /R2=(R2 - R1) R1R2 (II).
It is worth noting that if we have a charged sphere we can perfectly discharge it by introducing it into the interior of another hollow insulated conductor and making contact.
The small sphere then becomes part of the interior of the other and loses all charge.
The unit of electrostatic capacity is therefore that of a sphere of I cm.
Thus for instance the capacity in free space of a sphere 2 metres in diameter would be 100/900,000 = 1/9000 of a microfarad.
The electrical capacity of the whole earth considered as a sphere is about 800 microfarads.
He constructed two equal condensers, each consisting of a metal ball enclosed in a hollow metal sphere, and he provided also certain hemispherical shells of shellac, sulphur, glass, resin, &c., which he could so place in one condenser between the ball and enclosing sphere that it formed a condenser with solid dielectric. He then determined the ratio of the capacities of the two condensers, one with air and the other with the solid dielectric. This gave the dielectric constant K of the material.
It has been shown above that the potential due to a charge of q units placed on a very small sphere, commonly called a point-charge, at any distance x is q/x.
Let a very small sphere be described round the source, and let the strength of the source be defined as the total flow per second through the surface of this small sphere.
The electric force due to a point-charge q at a distance r is defined to be q/r 2, and the total flux or induction through the sphere of radius r is therefore 41rq.
The same reasoning can be applied to determine the electrical image of a point-charge of positive electricity in a spherical surface, and therefore the distribution of induced electricity over a metal sphere connected to earth produced by a point-charge near it.
Suppose then we remove the negative point-charge, and let the sphere be supposed to become conductive and be connected to earth.
But this first national kingdom within the sphere of Greek culture could not ultimately live between the surge of the Northern barbarians and the Roman power.
The "powers" (numina, not dei), which thus become the objects of worship, are spirits specialized in function and limited in sphere.
They are not conceived of in any anthropomorphic form, their sex even may often be indeterminate ("sive mas, sive femina" is the constantly recurring formula of prayer), but the sphere of action of each is clearly marked and an appeal to a spirit outside his own special sphere would never even be thought of.
Just as there is a faculty which apprehends beauty in the sphere of art, so there is in the sphere of ethics a faculty which determines the value of actions.
She extended her sphere of influence throughout the coast-lands of the western gulf; by the settle meat of numerous colonies in N.W.
In the beginning of his reign he adopted a prudent policy of amity with his two most powerful neighbours, the emperors of the East and West, but the death of Manuel in 1180 gave Hungary once more a free hand in the affairs of the Balkan Peninsula, her natural sphere of influence.
One of them, "John Fisher," who had his sphere at Oxford, succeeded in making a convert of young Chillingworth, and prevailed upon him to go to the Jesuit college at Douai.
His originality consists in having extended the positive intelligence of his century from the sphere of contemporary politics and special interests to man at large regarded as a political being.
English exiles were welcomed at his court; he was mainly instrumental in restoring Eardwulf to the throne of Northumbria in 80 9; and Einhard includes the Scots within the sphere of his influence.
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.
Only in the sphere of practical reason, where the intelligible nature prescribed to itself its own laws, was there the possibility of systematic deduction from a single principle.
Even in the practical sphere, however, Fichte found that the contradiction, insoluble to cognition, was not completely suppressed, and he was thus driven to the higher view, which is explicitly stated in the later writings though not, it must be confessed, with the precision and scientific clearness of the Wissenschaftslehre.
By the agreement of the 1st of July 1890, between the British and German governments, and by agreements concluded between Germany and Portugal in 1886 and 1894, and Germany and the Congo Free State in 1884 and later dates, the German sphere of influence attained its present area.
Wissmann remained in the country until 1891 as commissioner, and later (1895-1896) was for eighteen months governor of the colony - as the German sphere had been constituted by proclamation (1st of January 1897).
Debarred from election to the second National Assembly (known as the Legislative) by the self-denying ordinance passed by the "constituents," Talleyrand, at the close of 1791, sought to enter the sphere of diplomacy for which his mental qualities and his clerical training furnished him with an admirable equipment.
His abilities were inconsiderable, his character weak, and he was qualified neither for the ordinary administration of public business nor for the higher sphere of statesmanship, and was entirely destitute of that experience which sometimes fills the place of natural aptitude.
To the north, Lutheran influence had spread into Denmark; Sweden and Norway were also brought within its sphere.
In expounding these ideas Socrates limited himself to the sphere of practice.
The hope that a passage through to the Spice Islands would be found near existing Spanish settlements was now given up. One was sought farther south, and in November 1520 Ferdinand Magellan passed through the strait which bears his name and sailed across the Pacific. At last the existence of a continent divided by a vast stretch of ocean from Asia, and mostly lying within the sphere of influence assigned to Spain by the pope, was revealed to the world.
Two foreign settlements within the English sphere - the Dutch colony of New Netherland, now New York, and the Swedish settlement on the Delaware - were absorbed by the growing English element.
But Canada is bound only by a voluntary allegiance, Guiana is unimportant, and in the West Indian islands, where the independence of Hayti and the loss of Cuba and Porto Rico by Spain have diminished the European sphere, European dominion is only a survival of the colonial epoch.
Their sphere of influence included not only the cross-roads, but the whole neighbouring district of the town and country in which they were situated.
Perceiving the difficulty of the Socratic dictum he endeavoured to give to the word "knowledge" a definite content by divorcing it absolutely from the sphere of sense and experience, and confining it to a sort of transcendental dialectic or logic. The Eleatic unity is Goodness, and is beyond the sphere of sensible apprehension.
A collection of circles such as is the armillary sphere, if each circle were fitted with a view-tube, might be considered a complete astrolabe.
As the sphere of the census operations in Canada has been gradually spreading from the small beginnings on the east coast to the immense territories of the north-west, so, in the island continent, colonization, first concentrated in the south-east, has extended along the coasts and thence into the interior, except in the northern region.
On each occasion new areas had to be brought within the sphere of enumeration, whilst the necessity for the use in the wilder tracts of a schedule simpler in its demands than the standard, grew less as the country got more accustomed to the inquiry, and the efficiency of the administrative agency increased.
This formula applies to such figures as the cone, the sphere, the ellipsoid and the prismoid.
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.
But in working out the consequences of this view Say is not free from obscurities and inconsistencies; and by his comprehension of these immaterial products within the domain of economics he is confirmed in the error of regarding that science as filling the whole sphere which really belongs to sociology.
If we take one of these spheres a distance from the source very great as compared with a single wave-length, and draw a radius to a point on the sphere, then for some little way round that point the sphere may be regarded as a plane perpendicular to the radius or the line of propagation.
He aided practical efforts, however, for extending the sphere of woman's employments.
The peace negotiations were opened at Portsmouth, New Hampshire, on the 9th of August, and by the end of the month the belligerents had agreed as to the main points at issue, that Russia should cede the half of Saghalien, annexed in 1875, surrender her lease of the Kwangtung peninsula and Port Arthur, evacuate Manchuria and recognize Japan's sphere of influence in Korea.
Every point is equidistant from a fixed point within the surface; this point is the "centre," the constant distance the "radius," and any line through the centre and intersecting the sphere is a "diameter."
The shortest distance between two points on a sphere is the arc of the great circle containing the points.
The determination of the shortest distance between two small circles on a sphere is given in the article Variations, Calculus Of.
The solid enclosed by a small circle and the radii vectores from the centre of the sphere is a "spherical sector"; and the solid contained between two spherical sectors standing on copolar small circles is a "spherical cone."
The geometry of the sphere was studied by the Greeks; Euclid, in book xii.
To Zenodorus (c. 200100 B.C.) is due the important problem in maxima and minima that for a given surface the sphere is the solid of maximum volume.
In analytical geometry, the equation to the sphere takes the forms x 2 +y 2 +z 2 =a 2, and r=a, the first applying to rectangular Cartesian co-ordinates, the second to polar, the origin being in both cases at the centre of the sphere.
A sphere can therefore be described so as to satisfy four given conditions.
Two spheres intersect in a plane, and the equation to a system of spheres which intersect in a common circle is x 2 + y 2 + z 2 +2Ax -fD = o, in which A varies from sphere to sphere, and D is constant for all the spheres, the plane yz being the plane of intersection, and the axis of x the line of centres.
The investigation of triangles and other figures drawn upon the surface of a sphere is all-important in the sciences of astronomy, geodesy and geography.
In "geodesy," and the cognate subject "figure of the earth," the matter of greatest moment with regard to the sphere is the determination of the area of triangles drawn on the surface of a sphere - the so-called "spherical triangles"; this is a branch of trigonometry, and is studied under the name of spherical trigonometry.
In mathematical geography the problem of representing the surface of a sphere on a plane is of fundamental importance; this subject is treated in the article MAP.
The epoch-making events which occurred in England, while he was at Oxford profoundly interested him, and coinciding with the Revolution in Denmark, which threw open a career to the middle classes, convinced him that his proper sphere was politics.
Next follow chapters on the literary renaissance of the nation, its progress in art, mathematics, chemistry and natural science; the magnificent development of agriculture, modern industry, commerce and finance; and in particular its flourishing selfgovernment, " which will be exercised in the fullest freedom," and in which " the communal organization embodies in the highest degree the conception of self-government " (p. 234), and " the independent sphere of activity unlimited in its fundamental principle " (p. 235) in that " State control is exercised seldom and discreetly " (p. 236).
Finally, the communes had self-government within their own sphere.
Since Ultramontanism cannot hope to realise its political ambitions unless it succeeds in controlling the intellectual and religious life of Catholic Christendom, it attempts to extend its sphere of influence in all directions over culture, science, education, literature and the forms taken by devotion.
Just as in Protestant countries there has often been an amalgamation of evangelical belief with national feeling, to the great gain of both, Catholics demand that Catholicism shall enter into the sphere of their national interests, and that the activities of the Catholic Church should rest on a national basis.
The state has become independent of the Church, legislates on its own sole authority, and has recognized as falling within its own proper sphere the civilizing agencies and social questions formerly reserved for the Church.
His services in the diplomatic sphere were more important.
Ptolemy, who himself chiefly used the " Claws " (XnXai), speaks of it as a distinctively Chaldaean sign; 2 and it occurs as an extrazodiacal asterism in the Chinese sphere.
Of the zodiac in its true sense of a partitioned belt of the sphere there was no aboriginal knowledge on the American continent.
The assertion, paradoxical at first sight, that the twenty-eight " hostelries " of the Chinese sphere had nothing to do with the moon's daily motion, seems to convey the actual fact.
Meanwhile the Spanish government was considering whether the Moluccas did not fall within the Spanish sphere of influence as defined by the Treaty of Tordesillas in 1494; and in August 1519 an expedition commanded by Ferdinand Magellan sailed from Seville to seek a westward passage to the archipelago.
Further disputes occurred from time to time, and in 1542 a Spanish fleet came into conflict with the Portuguese off Amboyna; but after 1529 the supremacy of each power in its own sphere was never seriously endangered.
By this treaty the Dutch were given almost entire freedom of action in Sumatra, while the Malay Peninsula was recognized as within the British sphere of influence.
He was intended for the priesthood and entered the seminary of Floreffe, but his energies claimed a more active sphere.
On the accession of Nicholas I., Arakcheev, thoroughly broken in health, gradually restricted his immense sphere of activity, and on the 26th of April 1826, resigned all his offices and retired to Carlsbad.
Theirs were not the everyday experiences of ordinary men, but of men lifted out of themselves and transported into a higher sphere.
He too concluded that the temporal power is independent of the spiritual, and is even justified in invading the sphere of the latter in cases of necessity.
Since 1890 Air has been included in the French sphere of influence in West Africa.
Legendre's second memoir was communicated to the Academie in 1784, and relates to the conditions of equilibrium of a mass of rotating fluid in the form of a figure of revolution which does not deviate much from a sphere.
On examining more minutely the course of the development, it is found that the ovum goes through the usual process of cleavage, always total and regular in this group, and so gives rise to a hollow sphere or ovoid with the wall composed of a single layer of cells, and containing a spacious cavity, the blastocoele or segmentation-cavity.
It is true we find many thinkers who' deny the competency of reason when it ventures in any way beyond the sphere of experience, and such men are not unfrequently called sceptics.
Philosophical truth, as deduced from the teaching of Aristotle, it was said, directly contradicts the teaching of the church, which determines truth in theology; but the contradiction leaves the authority of the latter unimpaired in its own sphere.
For criticism not only limits our knowledge to a certain sphere, but denies that our knowledge within that sphere is real; we never know things as they actually are, but only as they appear to us.
In the patronage of learning and in the exercise of authority over the morals and education of youth Laud was in his proper sphere, many valuable reforms at Oxford being due to his activity, including the codification of the statutes, the statute by which public examinations were rendered obligatory for university degrees, and the ordinance for the election of proctors, the revival of the college system, of moral and religious discipline and order, and of academic dress.
In this sphere Absalon proved himself equally great.
The attempts at penetration into the extreme south, abandoned after the massacre by Tuareg of a mission sent in 1881, under Colonel Paul Flatters, to study the question of railway communication with Senegal, were begun again in 1890, in which year the British government recognized the western Sahara as within the French sphere.
In 1842 the French had formally annexed the Marquesas Islands; and subsequently extended their sphere, as shown in the table at the outset of this article, both in the east of Polynesia and in the south of Melanesia.
By ignoring the free poetical form of prophecy, and still more by ignoring the fact that the prophetic pictures of the ideal future of Israel could not be literally fulfilled after the fall of the ancient state had entirely changed the sphere in which the problems of true religion had to be worked out, it was possible to find a great mass of unfulfilled prophecy which might form the basis of eschatological constructions.
Even as professor of Greek he had given great prominence in his lectures to the study of the Scriptures; but he found a much more congenial sphere when, in 1698, he was appointed to the chair of theology.
An institution was founded in 1780 under the name of the Bible Society, but as its sphere was restricted to soldiers and seamen the title was afterwards changed to the Naval and Military Bible Society.
The highest sphere of knowledge - the supra-rational - as well as the very possibility of knowledge, must depend on divine communications - that is, on revelations.
But the spiritual development had shot far ahead of the political; even the Stoa occupied a height far beyond the reach of anything in the political sphere.
Yet the influence of Neoplatonism on the history of our ethical culture is immeasurable, above all because it begot the consciousness that the only blessedness which can satisfy the heart must be sought higher even than the sphere of reason.
The second stage is occupied with the gradual rise and ultimate ascendancy of another system founded on the idea of the right of the individual to an unimpeded sphere for the exercise of his economic activity.
In his lectures he excluded mental philosophy and included the whole sphere of moral obligation, dealing with man's duty to God and to his fellow-men in the light of Christian teaching.
In 1891 the northern frontier of the protectorate was extended to its present boundaries, and the whole of it placed P P under the administration of a resident commissioner, a protest being made at the time by the British South Africa Company on the ground that the protectorate was included in the sphere of their charter.
This stage of religion is well illustrated by the Red Indian custom of offering sacrifice to certain rocks, or whirlpools, or to the indwelling spirits connected with them; the rite is only performed in the neighbourhood of the object, it is an incident of a canoe or other voyage, and is not intended to secure any benefits beyond a safe passage past the object in question; the spirit to be propitiated has a purely local sphere of influence, and powers of a very limited nature.
But his thoughts were already working in a higher sphere.
The Keplerian like the Pythagorean cosmos was threefold, consisting of the centre, or sun, the surface, represented by the sphere of the fixed stars, and the intermediate space, filled with ethereal matter.
The Gaulish invaders appeared in Asia Minor in 278-277 B.C. They numbered 20,000, of which only one-half were fighting men, the rest being doubtless women and children; and not long after their arrival we find them divided into three tribes, Trocmi, Tolistobogii and Tectosages, each of which claimed a separate sphere of operations.
Julius Caesar extended the sphere of the Roman municipal system by his enfranchisement of Cisalpine Gaul, and the consequent inclusion of all the towns of that region in the category of municipia.
Under such circumstances ethics becomes a doctrine of abstinence in regard to all elements which have their source within the sphere of darkness.
Speaking generally, it is chiefly in the sphere of special or private legislation that state legislatures have shown their weak side, and incurred, in many states, the distrust of the people.
This authority corresponds to and is coextensive with the sphere of the Federal government.
Beyond that sphere its authority stops, and state authority, unless inhibited by the Federal Constitution, begins.
Thus the country from ocean to ocean is covered by a network of committees1 each having a sphere of action corresponding to some election area, whether a Federal area or a state area.
In astronomy, the "celestial equator" is the name given to the great circle in which the plane of the terrestrial equator intersects the celestial sphere; it is consequently equidistant from the celestial poles.
Although he was classed in Canada as a Liberal, his tendencies would in England have been considered strongly conservative; an individualist rather than a collectivist, he opposed the intrusion of the state into the sphere of private enterprise, and showed no sympathy with the movement for state operation of railways, telegraphs and telephones, or with any kindred proposal looking to the extension of the obligations of the central government.
Nature's boundary is the outer sphere of the fixed stars, which is eternally moved day after day in a uniform circle round the earth.
In astronomy the horizon is that great circle of the sphere the plane of which is at right angles to the direction of the plumb line.
By invagination one portion of this sphere becomes tucked into the other - as in the preparation of a woven night-cap for the head.
B, 0.1e of the two smaller spheres is reunited to the larger sphere.
Not yet thirty-five years old, he had proved himself a master in the sphere of Indian statesmanship and diplomacy as on the field of battle.
Hewitt has also attacked the problem by brominating the oxyazobenzenes, and has shown that when the hydrobromic acid produced in the reaction is allowed to remain in the system, a brombenzene-azo-phenol is formed, whilst if it be removed (by the addition of sodium acetate) bromination takes place in the phenolic nucleus; consequently the presence of the mineral acid gives the azo compound a pseudo-quinonoid character, which it does not possess if the mineral acid be removed from the sphere of the reaction.
It thought that danger of international irritation might be removed by each power making a declaration respecting the " sphere of interest " in China to which it laid claim.
When James Bradley and Samuel Molyneux entered this sphere of astronomical research in 1725, there consequently prevailed much uncertainty as to whether stellar parallaxes had been observed or not; and it was with the intention of definitely answering this question that these astronomers erected a large telescope at the house of the latter at Kew.
But beyond the sphere of irrigation, where the land is dependent on the rainfall, there is much rough stony ground broken by great fissures cut by flood-water from the border hills.
If the medium which contains the vibration is divided into a sphere equal to k times the molecular vibration outside of which the effects of these molecules may be averaged up, so that its Roy.
Proposition 30 describes the construction of a curve of double curvature called by Pappus the helix on a sphere; it is described by a point moving uniformly along the arc of a great circle, which itself turns about its diameter uniformly, the point describing a quadrant and the great circle a complete revolution in the same time.
Incidentally Pappus describes the thirteen other polyhedra bounded by equilateral and equiangular but not similar polygons, discovered by Archimedes, and finds, by a method recalling that of Archimedes, the surface and volume of a sphere.
This half-success in a subordinate sphere was, however, so far from coinciding with his aspirations that he had again, in the winter of 1821, begun to turn his attention towards missionary labour in the East, when the possibility of fulfilling the dream of his life was suddenly revealed to him by an invitation from the Caledonian church, Hatton Garden, London, to "make trial and proof" of his gifts before the "remnant of the congregation which held together."
The invocation of a powerful name over a thing or person brings him or it within its sphere of influence, and actually communicates thereto the demoniac or supernatural power wielded by the owner of the name.
The great feudatories did not even respect the lives of the royal family, for Andrew was recalled from a futile attempt to reconquer Galicia (which really lay beyond the Hungarian sphere of influence), through the murder of his first wife Gertrude of Meran (September 24, 1213), by rebellious nobles jealous of the influence of her relatives.
Thus, according to him, in the first place reason forms a cosmological " ideal " of a multitude of simple units related; secondly, it forms a psychological " ideal " of a multitude of wills, or substance-generating activities, which communicate with one another by ideas so that will causes ideas in will, while together they constitute a collective will, and it goes on to form the moral ideal of humanity (das sittliche Menschheitsideal); and, thirdly, it forms an ontological " ideal " of God as ground of this moral " ideal," and therewith of all being as means to this end, and an " ideal " of God as world-will, of which the world is development, and in which individual wills participate each in its sphere.
The choice of the pope had been almost entirely removed from the sphere of secular influence, and especially from that of the German king.
In short, it was in the sphere of French interests much more than in that of the general interests of Latin Christendom that the activities of these popes were exerted.
In the sphere of art he left an enduring monument in the Renaissance town of Pienza which he built.
A spherical angle is a particular dihedral angle; it is the angle between two intersecting arcs on a sphere, and is measured by the angle between the planes containing the arcs and the centre of the sphere.
Each of them, then, has supreme authority within its own sphere, while the official responsibility belongs to the pope, just as in all governments it is the government that is responsible for the acts of its departments.
Its sphere was very wide; it administered all non-European countries, except Latin America and the old colonies of the Catholic countries of Europe; in Europe it had also charge of the United Kingdom and the Balkan States.
Equilibrium requires that the available energy and therefore the area of contact should be a minimum, as is demonstrated in Plateau's beautiful experiment, where a large drop of oil is placed in a liquid of equal density and a perfect sphere is formed.
This may consist of a glass sphere of 50 litres' capacity, into the neck of which, presented downwards, the necessary tubes are fitted.
The upper Congo region opened up by Livingstone and Stanley has been a favourite sphere for what are known as " faith societies," e.g.
It is possible - even probable, if we accept the theory that he had already 2 been there with Barnabas - that Alexandria was his final sphere of work, as the earliest tradition on the point implies (the Latin Prologue, and Eusebius as above, probably after Julius Africanus in the early 3rd century), and as was widely assumed in the 4th century.
Andreas Gordon (1712-1751) of Erfurt, a Scotch Benedictine monk, first used a glass cylinder in place of a sphere.
In this sphere Gregory manifested rare capacity.
The British government was forced to interfere, more especially as the country, by international agreement, had been included in the British sphere of influence.
The Cour de Cassation has a peculiar judicial sphere.
The friar's sphere of work is normally outside his convent, and he works and influences directly and as an individual.
Because a force exists, capable, if unchecked, of producing certain results, it does not follow that those results are imminent or even possible in the sphere of experience.
The appointment, which had hitherto been reserved for ecclesiastics of marked ability as scholars or administrators, excited much comment; but it was undoubtedly popular, and this popularity was confirmed when it was realized that the bishop intended to carry on in his new sphere the democratic traditions of his East End activities.
To those who hold that all intellectual exercise outside the sphere of religion is impious or that all intellectual exercise inside that sphere is futile, he must remain an enigma.
The sphere of the state authority embraced most of the powers of government, except, for instance, those relating to foreign affairs, army and navy, inter-state commerce, coinage a.nd the tariff; the powers of the central government were specified in the fundamental law.
So, in the sphere of human action, Epicurus would allow of no absolutely controlling necessity.
Mr Roosevelt brought the whole subject before Congress in his message of the 3rd of December 1901, and thereby started what seemed likely to be a new sphere of Federal initiative and control.
In particular it had in view persons of culture, as most apt to be swayed by the philosophical tendencies in the sphere of religion prevalent in that age, the age of neoPlatonism.
In the sphere of material power the repulse of Xerxes and the extension of Athenian or Spartan supremacy in the eastern Mediterranean were large facts patent to the most obtuse.
But the developments within the Hellenic sphere itself were also of great consequence for its Expansion outwards.
But by far the most signal borrowing is in the sphere of art.
On the other hand, even where the creative originality of Rome was most pronounced, as in the sphere of Law, there were elements of Hellenic origin.
To secure British political influence, and to preserve a possible field for future development, the Niger Company had negotiated treaties with some of the most important of these rulers, and the nominal extension of the company's territories was carried over the whole sphere of influence thus secured.
They receive the support of the government within the limits of their recognized sphere of action.
In that sphere of activity, therefore, the Egyptian government might do as it thought fit.
As a dramatist, pure and simple, his bird-like instinct of song carried him too often into a sphere too exalted for the stage; but he has written nothing that is not stamped with the exquisite quality of distinction.
It is somewhat remarkable that, although Justinian is so much more familiar to us by his legislation than by anything else, this sphere of his imperial labour is hardly referred to by any of the contemporary historians, and then only with censure.
The necessity for such a phrase as "Anglican Communion," first used in the 19th century, marked at once the immense development of the Anglican Church in modern times and the change which has taken place in the traditional conceptions of its character and sphere.
The Sunnites, who accept the orthodox tradition (Sunna) as well as the Koran as a source of theologico-juristic doctrines, predominate in Arabia, the Turkish Empire, the north of Africa, Turkestan, Afghanistan and the Mahommedan parts of India and the east of Asia; the Shi`ites have their main seat in Persia, where their confession is the state religion, but are also scattered over the whole sphere of Islam, especially in India and the regions bordering on Persia, except among the nomad Tatars, who are all nominally Sunnite.
In Turkey, and above all in Egypt, it has been found necessary greatly to limit the sphere and influence of the canonical jurists and to introduce institutions nearer to Western legal usage.
Fischer has further established the fact that the peripheral mass, which is a hollow sphere in spherical cells, and either a hollow cylinder or barrel-shaped body in filamentous forms, must be regarded as the single chromatophore of the Cyanophyceous cell.
These aggregations or colonies, as they are termed, may attached to muddy surfaces by rhizoids; Caulerpa, on the other, assume the form of a plate, a ring, a solid sphere, a hollow sphere, presents a remarkable instance of the way in which much the same a perforate sphere, a closed net, or a simple or branched filament.
The organization of the Christian church in the Roman empire following very closely the lines of the civil administration (see Church History), the word diocese, in its ecclesiastical sense, was at first applied to the sphere of jurisdiction, not of a bishop, but of a metropolitan.'
His sphere of influence was the nocturnal heavens, thunderstorms at night being attributed to him, those by day to Jupiter.
Meanwhile Henry had been developing a serious interest in politics, and he could brook no superior in whatever sphere he wished to shine.
The secular importance of Henry's activity has been somewhat obscured by his achievements in the sphere of ecclesiastical politics; but no small part of his energies was devoted to the task of expanding the royal authority at the expense of temporal competitors.
It committed William to conditions which might readily produce a great naval war with Spain, for Paterson's real design was to establish an entrepot in Panama, at Darien, within the undeniable sphere of Spanish influence.
This statement, that the Christians of the 3rd and 4th centuries were in the habit of visiting Jerusalem for prayer, proves that the non-Christian conception of the religious pilgrimage had already entered the sphere of Christian thought.
And it cannot be disproved, for it lies in a sphere beyond the reach of human inquiry.
So far as Hungary was concerned, Budapest in 1867 at once became the favoured rival of Vienna, with the important additional advantage that it had no such competitors within its own sphere as Vienna had in the Austrian provincial capitals.
This is, however, an application of categories from a field where the conditions are finite to a sphere in which the circumstances are infinite."
But as with Aristotle so with Hegel - beyond the ethical and political sphere rises the world of absolute spirit in art, religion and philosophy.
This construction assumes that the sun describes daily a small circle about the pole of the celestial sphere, and ignores any diurnal variation in the declination.
The Greeks discovered that if a line be divided in extreme and mean proportion, then the whole line and the greater segment are the lengths of the edge of a cube and dodecahedron inscriptible in the same sphere.
A great deal of work is done in this way, though this sphere has also been invaded by the draw presses, whose output would seem incredible to those not familiar with the work.
In thick plates it is not attempted by hand, but pressing is done between dies, or segments of the sphere are prepared separately and riveted together.
He returned to office in April 1885 as foreign minister in the Brisson cabinet, and retained that post when, in January 1886, he succeeded to the premiership. He came into power with an ambitious programme of internal reform; but except that he settled the question of the exiled pretenders, his successes were won chiefly in the sphere of colonial extension.
He, therefore, abandoned the purely intellectual sphere and proposed an inquiry into the data given by the senses, from which he held that all true knowledge really comes.
Thus the problem of the "thing-initself" is dismissed from the inquiry, and philosophy is limited to the sphere of pure thought.
In 1869 the Russian government had assured Lord Clarendon that they regarded Afghanistan as completely outside the sphere of their influence; and in 1872 the boundary line of Afghanistan on the north-west had been settled between England and Russia so far eastward as Lake Victoria.
In the course of the next six months there was much desultory skirmishing between the tribes and the British troops, who defeated various attempts to dislodge them from the positions that had been taken up; but the sphere of British military operations was not materially extended.
Russia, on her part, recognized Afghanistan as outside her sphere of influence.
But he was no soldier, and he was destined in that sphere to encounter the " heaven-born genius " of Clive.
If it cannot be said that any of these missions were fruitful in permanent results, at least they introduced the English to a new set of diplomatic relations, and widened the sphere of their influence.
Also, if the axis is made to revolve at half the apparent diurnal motion of the stars, the image of the celestial sphere, viewed by reflection from such a moving mirror, will appear at rest at every point - hence the name coelostat applied to the apparatus.
Adrar is within the French sphere of influence.
The assumption of a protectorate over another state, or of a sphere of influence, is not strictly annexation, the latter implying the complete displacement in the annexed territory of the government or state by which it was previously ruled.
Annexation may be the consequence of a voluntary cession from one state to another, or of conversion from a protectorate or sphere of influence, or of mere occupation in uncivilized regions, or of conquest.
Even when we reach the New Testament period, we have not passed entirely beyond the sphere of BabylonianAssyrian influences.
We should learn perhaps the distribution and luminosities of the stars within a sphere of radius sixty light years (corresponding to a parallax of about 0.05"), but of the structure of the million-fold greater system of stars, lying be y ond this limit, yet visible in our telescopes, we should learn nothing except by analogy.
It is only when some of the stars considered are more remote and lie outside this sphere (but of course between the two planes) that there is a galactic crowding.
They are accordingly within the sphere of radius SP (fig.), and consequently are equally numerous in every direction.
Thus we see that the effect of limiting the magnitude to 3.5 is that the hydrogen stars are now practically all within the sphere SP, and it is only the helium stars, whose absolute luminosity is still greater, that are more widely distributed.
It is said, for example, that Clarke made virtue consist in conformity to the relations of things universally, although the whole tenor of his argument shows him to have had in view conformity to such relations only as belong to the sphere of moral agency.
The local monarchy of the manorial lords was fast giving way to a central power which maintained its laws, the circuits of its judges, the fiscal claims of its exchequer, the police interference of its civil officers all through the country, and, by prevailing over the franchises of manorial lords, gave shape to a vast dominion of legal equality and legal protection, in which the forces of commercial exchange, of contract, of social intercourse, found a ready and welcome sphere of action.
The sphere of the dukes was never rigidly fixed, and their commission was sometimes permanent, sometimes temporary.
In the sphere of the concrete sciences where law obtains only ws Eiri To 7roX6 this ideal of science can clearly find only a relative satisfaction with large reserves.
But much more it belongs to his transformation of the epistemological problem, and to the suggestiveness of his philosophy as a whole for an advance in the direction of a speculative construction which should be able to cancel all Kant's surds, and in particular vindicate a " ground of the unity of the supersensible which lies back of nature with that which the concept of freedom implies in the sphere of practice," I which is what Kant finally asserts.
Being deeply stirred by the best ideas of the Revolutionary epoch, he found a more congenial sphere for the display of his great powers in his new position.
Especially were the Messianic hopes forgotten or transferred to a transcendent sphere beyond death.
In details also the conclusions of modern science are rejected, as for example the origin of man from lower species, and, in a different sphere, the conclusions of experts as to the origins of the Bible.
In quite a different way a still more influential school seeks essential Christianity in the sphere of the ethical life.
The treaty in 1847 put an end once for all to the hopes which the Dutch had cherished of including the whole island in their dominions, but it served also to stimulate their efforts to consolidate their power within the sphere already subjected to their influence.
The treaty transferring the Danish West Indies to the United States (1917) contained a clause recognizing Denmark's right to extend her economic and pojitical sphere over the whole of Greenland.
Beneath the Rete, in a hollow, are four thin brass discs, called Tables or Climates, engraved with projections of the sphere for different latitudes.
The line of the equinoxes is the imaginary diameter of the celestial sphere which joins them.
In the purely intellectual sphere it is certainly true that the recovery of the antique world was of great importance; that it made possible genuine criticism by presenting new points of contrast and opening up fields that led away from theological quibbles.
Now suppose that a body receives first a positive rotation a about OA, and secondly a positive rotation e3 about OB; and let A, B be the intersections of these axes with a sphere described about 0 as centre.
The composition of finite rotations about parallel axes is, a particular case of the preceding; the radius of the sphere is now infinite, and the triangles are plane.
Take, for example, the case of a sphere rolling on a plane; and let the axes Ox, Oy be drawn through the centre parallel to the plane, so that the equation of the latter is 1=cf.
Again, since the point of the sphere which is in contact with the plane is instantaneously at rest, we have the geometrical relations u+qa=0, v+pa=o, W0, (20) by (12).
The acceleration of the centre is therefore the same as if the plane were smooth and the mass of the sphere were increased by C/a.
Thus the centre of a sphere rolling under gravity on a plane of inclination a describes a parabola with an acceleration g sin a/(I+C/Ma)
Take next the case of a sphere rolling on a fixed spherical surface.
Let a be the radius of the rolling sphere, c that of the spherical surface which is the locus of its centre, and let x, y, I be the co-ordinates of this centre relative to axes through 0, the centre of the fixed sphere.