Consider the case of two concentric spheres, a solid one enclosed in a hollow one.
Capacity of two concentric spheres, of two coaxial cylinders and of two parallel planes.
Yet, allpowerful in their individual spheres of action, they can influence the fortunes of men and can enter into relations with them.
Only in the highest spheres did all these schemes, crossings, and interminglings appear to be a true reflection of what had to happen.
The shapes of these ferruginous sandstones are very fantastic - tubes, hollow spheres, plates, &c., being common.
No material advance was made on Ptolemy's instrument until Tycho Brahe, whose elaborate armillary spheres passing into astrolabes are figured in his Astronjmiae Instauratae Mechanica.
The dioceses were now mapped out into several archdeaconries (archidiaconatus), which corresponded with the political divisions of the countries; and these defined spheres, in accordance with the prevailing feudal tendencies of the age, gradually came to be regarded as independent centres of jurisdiction.'
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.
Related to the tetrahedron are two spheres which have received much attention.
The hydrosphere is one of the four spheres of the earth.
It is the same thought which collected in the cosmic space the divided masses into spheres, and combined these to solar systems; the same which caused the weather-beaten dust on the surface of our metallic planet to spring forth into living forms."
Justinian has a clearer perception of the demarcation between the spheres of spiritual and temporal law.
Some Churches still continued the three weeks' fast, but by the middle of the 5th century most of these divergences had ceased and the usages of Antioch-Constantinople and Rome-Alexandria had become stereotyped in their respective spheres of influence.
It is, in fact, "a procedure whereby communication is established between the sacred and profane spheres by a victim, that is to say by an object destroyed in the course of the ceremony."
It leaves the Hindu Kush near the Dorah Pass at the head of one of the minor Chitral affluents, and passing south-west divides Kafiristan from Chitral and Bajour, separates the sections of the Mohmands who are within the respective spheres of Afghan and British sovereignty, and crosses the Peshawar-Kabul route at Lundi-Khana.
The summingup of divine powers manifested in the universe in a threefold division represents an outcome of speculation in the schools attached to the temples of Babylonia, but the selection of Anu, Bel and Ea for the three representatives of the three spheres recognized, is due to the importance which, for one reason or the other, the centres in which Anu, Bel and Ea were worshipped had acquired in the popular mind.
In the first of these spheres the victory of Marengo (14th of June 1800) was of special importance, as it consolidated the reputation of Bonaparte at a time when republican opposition was gathering strength.
Strong generals were needed in the separate divisions of the empire, and these, as has always been the case in Eastern empires, made themselves independent in their spheres of command, because there was no organization to keep them together under a single control.
In other spheres the immunities and exemptions of the Church offered a far more serious problem, and especially in the sphere of finance.
In remembrance of these victims of popular wrath Jalal-uddin founded the order of the Maulawi (in Turkish Mevlevi) dervishes, famous for their piety as well as for their peculiar garb of mourning, their music and their mystic dance (sama), which is the outward representation of the circling movement of the spheres, and the inward symbol of the circling movement of the soul caused by the vibrations of a Sufi's fervent love to God.
Money was also struck in their own name by the cities in the several dynasties' spheres of power, but in most cases only bronze or small silver for local use.
During 1884, 1885, 1886 treaties guaranteeing British protection were concluded with various Somali tribes and in 1888 the limits of the British and French spheres were defined, all claims to British jurisdiction in the Gulf of Tajura and the islands of Musha and Bab being abandoned.
He governs the visible world, preserves the harmony and guides the revolutions of all the spheres, and is the captain of all the myriads of angelic beings.
The good he did was limited to the spheres of public works and police; in other respects his rule was a pernicious influence for Cuba.
In their natural condition the marekanite spheres are doubly refracting, but when they have been heated and very slowly cooled they lose this property and no longer exhibit any tendency to sudden disintegration.
The battle of Thapsus in 46 made the Romans definitely masters of Numidia, and the spheres of administration were clearly marked out.
The potential due to a single pole of strength m at the distance r from the pole is V = m/ r, (7) the equipotential surfaces being spheres of which the pole is the centre and the lines of force radii.
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.
When the fluids inside a particle were mixed together, the particle was neutral; when they were more or less completely separated, the particle became magnetized to an intensity depending upon the magnetic force applied; the whole body therefore consisted of a number of little spheres having north and south poles, each of which exerted an elementary action at a distance.
Cobden had married in 1840 Miss Catherine Anne Williams, a Welsh lady, and left five surviving daughters, of whom Mrs Cobden-Unwin (wife of the publisher Mr Fisher Unwin), Mrs Walter Sickert (wife of the painter) and Mrs Cobden-Sanderson (wife of the well-known artist in bookbinding), afterwards became prominent in various spheres, and inherited their father's political interest.
The Governments of Belgrade and Zagreb were to retain their former spheres until a constituent assembly, elected by universal suffrage, could draw up a new constitution.
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.
To these may be added a very short disquisition on the same subject addressed to Adalbold, and a similar one, on one of his own spheres, addressed to Constantine, abbot of Micy.
Contrary, however, to the experience of others, he has never found that the attraction-spheres play an important part in direct cell-division, or, indeed, that they exert any influence whatever upon the mechanism of the process.
Where pigment was present within the cells (sarcoma), the attraction-spheres were represented by quite clear unpigmented areas, sometimes with a centrosome in their midst.
Seldom has it happened, since the discovery of the law of gravity, that so profound an impression has been made upon the scientific world at large as by the revelation of the part played by germ-life in nature; seldom has any discovery been fraught with such momentous issues in so many spheres of science and industry.
In foreign affairs, the conclusion of a treaty with Russia for delimiting the British and Russian spheres of influence in the Middle East laid the foundations of entirely new relations between the British and Russian governments.
Between two concentric spheres, with a 2 +A = r 2, a2+A1=a12, A=B =C =a3/3r3, a 3 a 3 a3 _ a3 Cb _1U x r 3 a13 Y'=2 Uy2 r3 3 a13 .
The method of electrical images will enable the stream function, )' to be inferred from a distribution of doublets, finite in number when the surface is composed of two spheres intersecting at an angle 7r/m, where m is an integer (R.
Thus for m =2, the spheres are orthogonal, and it can be verified that a13 a2 3 aY3 i f /' = ZU (I - 13 - 7.2 3 + 3) ' (8) where a l, a2, a =a l a 2 /J (a 1 2 +a 2 2) is the radius of the spheres and their circle of intersection, and r 1, r 2, r the distances of a point from their centres.
Two equal spheres, intersecting at 120°, will require - I U j x _ a 3 a4(a 7 2 x) a3 a4(a+2x)] (II) 2 - _ 2 y a 271 3 271 +2Y2 3 2720 ' with a similar expression for cylinders; so that the plane x=o may be introduced as a boundary, cutting the surface at 60°.
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).
After the return of Columbus and his supposed demonstration that the Indies could be reached by sailing west, disputes might obviously arise between the two powers as to their respective "spheres of influence."
The waves from a source surrounded by a uniform medium at rest spread out as spheres with the source as centre.
This treatise is in two books, dedicated to Dositheus, and deals with the dimensions of spheres, cones, "solid rhombi" and cylinders, all demonstrated in a strictly geometrical method.
In 1526 he was sent out in command of an expedition fitted out for the purpose of determining by astronomical observations the exact line of demarcation, under the treaty of Tordesillas, between the colonizing spheres of Spain and Portugal, and of conveying settlers to the Moluccas.
We are not here concerned with understandings as to " spheres of influence," or with arrangements such as the AngloRussian Convention of 1907 concerning Persia.
Armillary spheres occur in many old sculptures, paintings and engravings; and from these sources we know that they were made for suspension, for resting on the ground or on a table, for holding by a short handle, or either for holding or for resting on a stand.
Bonaparte's selection gave general satisfaction, as also did the personnel of the Council of State (divided into five sections for the chief spheres of government) and of the other organs of state.
- In recent times the positive bent of modern knowledge and methods in other spheres of science and thought, and especially in biology, has influenced medicine profoundly.
As regards pulmonary disease, pneumonia has passed more and more definitely into the category of the infections: the modes of invasion of the lungs and pleura by tuberculosis has been more and more accurately followed; and the treatment of these diseases, in the spheres both of prevention and of cure, has undergone a radical change.
If the two small conducting spheres are placed with centres at a distance d centimetres, and immersed in an insulator of dielectric constant K, and carry charges of Q and Q' electrostatic units respectively, measured as above described, then the mechanical force between them is equal to QQ'/Kd 2 dynes.