In the system adopted in 1905 and since maintained, recurring and non-recurring expenditure were shown separately, the non-recurring expenditure being termed special.
This is the foundation of the use of recurring decimals; thus we can replace = s s = 1 o o /(' - 1 + 0 -)1 by .363636(=36/102 +36/ 104 +3 6 / 106), with an error (in defect) of only 36/(10 6.99).
An application of the method is to the summation of a recurring series, i.e.
(We need not consider a fraction with a non-recurring part).
Such frequently recurring movements introduced new blood.
Meantime, while recurring again and again, as was his custom, to this cardinal difficulty, Mill worked indefatigably in other directions where he saw his way clear.
The words, " rates, taxes, assessments " point to payments of a periodical or recurring character.
Biot, who assisted in the correction of its proof sheets, remarked that it would have extended, had the demonstrations been fully developed, to eight or ten instead of five volumes; and he saw at times the author himself obliged to devote an hour's labour to recovering the dropped links in the chain of reasoning covered by the recurring formula.
The following years were marked by recurring attempts at revolution, but on the whole Venezuela during the period1830-1846was less disturbed than the neighbouring republic owing to the dominating influence of General Paez, who during the whole of that time exercised practically dictatorial power.
`Arib of Cordova made an abridgment, adding the history of the West and continuing the story to about 975.1 Ibn 1Vlashkawaih wrote a history from the creation to 980, with the purpose of drawing the lessons of the story, following Tabari closely, as far as his book is known, and seldom recurring to other sources before the reign of Moqtadir; what follows is his own composition and shows him to be a writer of talent.
The Incas had an elaborate system of state-worship, with a ritual, and frequently recurring festivals.
The explanation of these recurring phenomena is that a great cloud or distended stream of meteors revolves around the sun in a period of 331years, and that one portion of the elliptical orbit intersects that of the earth.
Tree-worship again is a constantly recurring feature, seen, for instance, in the permanently sacred character of the ficus Ruminalis and the caprcus of the Campus Martius, and above all in the oak of luppiter Feretrius, on which the spolia opima were hung after a victory.
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.
And the world of the spirit and the world of nature continue to have this distinction, that the latter moves only in a recurring cycle while the former certainly also makes progress."
It has three entrances on the Plaza, and over its main gateway hangs the " liberty bell " of Mexico, first rung by the humble parish priest Hidalgo, on the night of the 16th of September 1810, to call the people of Dolores to arms, and now rung at midnight on each recurring anniversary by the president himself.
And when such declensions occurred, they soon called forth efforts at reform and revival; indeed these constantly recurring reformmovements are one of the most striking features of Benedictine history, and the great proof of the vitality of the institute throughout the ages.
John Goodricke established in 1782 the periodicity of its change in about 2 d 21 h, and suggested their cause in recurring eclipses by a large dark satellite.
When two notes are not quite in unison the resulting sound is found to alternate between a maximum and minimum of loudness recurring periodically.
The two great recurring " necessities of State," the budget and the authorization of the contingents of army recruits, regularly occupied a large part of the sittings; the budget was generally passed only in instalments in three or six monthly grants, and the Government was forced to adopt the practice of adjourning the obstructive House of Deputies and of providing for indispensable requirements in its absence by emergency decree.
An objective and non-party application of the laws, and equal rights for all nationalities, were in consequence the ever-recurring heads of their programme.
Mexican acquaintance with the signs related only to their secondary function as dies (so to speak) with which to stamp recurring intervals of time.
The usual arrangement by countries has been mainly abandoned in favour of following out each unit as a whole, without recurring to it separately for every locality.
This bond was doubtless preserved by Christian Hellenists, and must have tended to continue their reliance on the Temple services for the forgiveness of their recurring "sins of ignorance" - subsequent to the great initial Messianic forgiveness coming with faith in Jesus.
It is profoundly affecting to contemplate this man, a mere wreck from gout, shrinking from no fatigue, no labour, and no personal sacrifices; disregarding the obstacles and difficulties thrown in his way by cardinals and temporal princes, whose fatal infatuation refused to see the peril which hung above them all; recurring time after time, with all his intellect and energy, to the realization of his scheme; and finally adopting the high-hearted resolve of placing himself at the head of the crusade.
- The increase of plants, so far as the production of new individuals of particular kinds is concerned, is one of the most important and constantly recurring of gardening operations.
In the front row patches of the white arabis, the yellow alyssum, white, yellow, blue, or purple violas, and the purple aubrietia, recurring at intervals of 5 or 6 yards on a border of considerable length, carry the eye forwards and give a balanced kind of finish to the whole.
Disputes had been constantly recurring between Dutch and English traders in the East Indies and elsewhere, and the seeds were already sown of that stern rivalry which was to issue in a series of fiercely contested wars.
The disposition adopted was one which is found recurring in many sea-fights of the middle ages where a fleet had to fight on the defensive.
Perhaps it was to them that the often recurring title oueb, the pure, should properly be restricted, though strict rules as to personal purity, dress and diet were demanded of all priests.
The most ancient form these exercises took is recorded in the often recurring paragraphs translated in Rhys Davids' Dialogues of the Buddha (i.
And there are numerous instances of the introductory story stating how, and when, and to whom the sutta was enunciated - a sort of narrative framework in which the sutta is set - recurring also.
MARMOT, the vernacular name of a large, thickly built, burrowing Alpine rodent mammal, allied to the squirrels, and typifying the genus Arctomys, of which there are numerous species ranging from the Alps through Asia north of (but including the inner ranges of) the Himalaya, and recurring in North America.
The history, therefore, falls into recurring cycles, each of which begins with religious corruption, followed by chastisement, which continues until Yahweh, in answer to the groans of his oppressed people, raises up a "judge" to deliver Israel, and recall them to the true faith.
They are enveloped in a cloud of religious sanctions, and serve to mark out by their recurring periods the annual round of common life.
Another side is the recurring exhibition of the fact that these witnesses were persecuted only by those whose action should create no bias against the persecuted.
Frequently recurring deficits are, in themselves, a condemnation of the methods under which they are found.
Is of the simplest, consisting only in the arrangement of the discourse in lines of uniform length - usually heptasyllabic (Ephraim's favourite metre) or pentasyllabic. A more complicated arrangement is found in other poems, such as the Carmina Nisibena: these are made up of strophes, each consisting of lines of different lengths according to a settled scheme, with a recurring refrain.
Female; the distinction between its permanent objects, and its occasional or recurring operations; the recognition that behind sudden manifestations of power, like the thunder-storm, there are steady forces and continuous cosmic agencies at work - lead to the gradual rise of the higher deities.
In a state of nature, every recurring severe winter or otherwise unfavourable season weeds out those individuals of tender constitution or imperfect structure which may have got on very well during favourable years, and it is thus that the adaptation of the species to the climate in which it has to exist is kept up. Under domestication the same thing occurs by what C. Darwin has termed "unconscious selection."
His concluding years were mainly spent at Chislehurst, where he had taken up his residence in 1609, and in spite of recurring illnesses he continued to work at material for the improvement of the Britannia and kindred subjects.
If b 2 /a 2, 3 /a 3 ..., the component fractions, as they are called, recur, either from the commencement or from some fixed term, the continued fraction is said to be recurring or periodic. It is obvious that every terminating continued fraction reduces to a commensurable number.
Recurring Simple Continued Fractions.
+ 1/n+ 271+ ., where, after the n th partial quotient, the cycle of partial quotients b 1, b2, ..., b n recur in the same order, is the type of a recurring simple continued fraction.
The second case illustrates a feature of the recurring continued fraction which represents a complete quadratic surd.
If bl, b2, ..., k J is the cycle of recurring quotients, then b n 2a1, b, bn_1, b 2 bn_2, b 3 = bn_3, &c.
In the case of a recurring continued fraction which represents N, where N is an integer, if n is the number of partial quotients in the recurring cycle, and pnr/gnr the nr th convergent, then p 2 nr - Ng2nr = (- I) nr, whence, if n is odd, integral solutions of the indeterminate equation x 2 - Ny 2 = I (the so-called Pellian equation) can be found.
If r be the number of quotients in the recurring cycle, we can by writing down the relations connectin g the successive p's and q's obtain a linear relation connecting p nr +m, t'(n-1)r +m, +m in which the coefficients are all constants.
The higher plateau is devoted almost exclusively to cattleraising, once the principal industry of the state, though recurring seccas have been an insuperable obstacle to its profitable development.
Of this we have recurring examples in pre-exilian Hebrew history.
In spite of chronic unpopularity and recurring persecutions they have spread over nearly all Europe.
In the years 1760-1776 Boston was the most frequently recurring and most important name in British colonial history.
According to him, the myths arose from definite local (especially atmospheric and aquatic) phenomena, and represented the annually recurring processes of nature as the acts of gods and heroes; thus, in Achill (1853), the Trojan War is the winter conflict of the elements in that district.
The theory and development of the simple recurring continued fraction is due to Lagrange.
He listened with weary ears to the ever-recurring sounds, distinguishing the whistle of flying projectiles from the booming of the reports, glanced at the tiresomely familiar faces of the men of the first battalion, and waited.
It is always possible to find the value of the n th convergent to a recurring continued fraction.
Like many Oriental works it is a compilation, as may be illustrated from a comparison of Chronicles with Samuel - Kings, and the representation of the past in the light of the present (as exemplified in Chronicles) is a frequently recurring phenomenon.