The calculation of the expressions in brackets may be simplified by taking the pairs in terms from the outside; by finding the successive differences of uo + um, ill + um_l, ..., or of uI u i +umi, ..
Thus the figure represents a section the (ideally simplified) uni verse cut perpendicular to C P' D the planes AB and CD between which the stars are contained, 1 This number is the 3/2th power of the ratio of the brightness of stars differing by a unit magnitude.
He sometimes altered and contorted the facts; he very often unduly simplified his problems; he was very apt when he had proved a favourite opinion true to infer it to be the whole truth.
Analysis showed that all the required sounds could be conveyed with 47 syllables, and having selected the ideographs that corresponded .to those sounds, they reduced them, first, to forms called hiragana, and, secondly, to still more simplified forms called katakana.
The question is greatly simplified when two of the principal moments are equal, say A=B.
In this work Jacob ben Asher codified Rabbinic law on ethics and ritual, and it remained a standard work of reference until it was edited with a commentary by Joseph Qaro, who afterwards simplified the code into the more popular Shulhan Aruch.
A simplified exposition has been given by Horace Lamb (Prot.
These equations may be simplified slightly, using the equation of continuity (5) § for dpu dpu 2 dpuv dpuw dt dx + dy + dz =p Cat +uax+vay+waz?
The geometry of the rectangular hyperbola is simplified by the fact that its principal axes are equal.
The process is simplified by writing down the general formula first and then substituting the values of u.
In fresh-water Hydromedusae the life-cycle is usually secondarily simplified, but in marine forms the life-cycle may be extremely complicated, and a given species often passes in the course of its history through widely different forms adapted to different habitats and modes of life.
It is quite possible that some of these medusae will be found to be truly hypogenetic, that is to say, with a life-cycle secondarily simplified by suppression of metagenesis.
These courts were convenient, since it was the custom to appoint delegates resident in the neighbourhood, and the power of sub-delegation, general or limited, simplified questions of distance.
The interesting little Rhodope veranyii, which has no odontophore, has been associated by systematists both with these simplified Opisthobranchs and with Rhabdocoel Planarians.
He regulated and simplified the whole system of taxation, encouraged agriculture by differential duties in favour of the farmers, and promoted trade by a systematic improvement of the ways of communication.
Some of Laplace's results in the theory of probabilities are simplified in S.
He introduced the terms multinomial, trinomial, quadrinomial, &c., and considerably simplified the notation for decimals.
Yugoslavia's relations with Albania, though simplified by this decision, have been affected by the Albanian counterclaim to Pee, Djakovo and the plain of Kosovo, where since the middle of last century the Albanian element had grown steadily stronger at the expense of the Serbs.
Finance In addition to the provisions that have been mentioned above (Section VII.), the London Government Act 1899 simplified administration in two respects.
The task of the chronologer was thus simplified and reduced to a study and comparison of dates in a few leading systems.
Passing through found its task much simplified, and before nightfall had carried the Hindenburg reserve line on practically the whole of its front, taking a further Boo men and 20 guns in its advance.
The third form is the outflow or reversing thermometer, first introduced by Aime, who used a very inconvenient form in the Mediterranean in 1841-1845, but greatly improved and simplified by Negretti and Zambra in 1875.
The introduction of these special methods has considerably simplified the problem of sinking through water-bearing strata.
There is no unreduced material, and the process is considerably simplified, while less expensive plant is required.
The position was simplified when, in 1220, Albert van Cuyck, the last of the hereditary burgraves, sold his rights to the bishop. These ecclesiastical princes were churchmen in little but name, and their desire to be absolute rulers found itself confronted by the determination of the burghers to secure greater independence.
The complexity of administrative areas, though far less than in England, was simplified, and the census compilation proportionately facilitated, by the passing of the Local Government Act for Scotland, in 1889.
The calculation of this last expression is simplified by noticing that we are only concerned with the mutual ratios of Xo, X 1, ...
In the second half of the 17th century the rules of grammar and rhetoric were simplified, and the time withdrawn from the practice of composition (especially verse composition) transferred to the explanation and the study of authors.
Other reforms. followed in quick succession during the next five or six years: army and navy organization, a new judicial administration on the French model, a new penal code and a greatly simplified system of civil and criminal procedure, an elaborate scheme of local self-government for the rural districts and the large towns, with elective assemblies possessing a restricted right of taxation, and a new rural and municipal police under the direction of the minister of the interior.
Copernicus (1473-1543) employed the same system, and greatly simplified the application of it, especially by regarding the earth as rotating and the sun as the centre of the solar system.
The deliberations follow a simplified procedure, which is founded more on equity than on the more strictly legal forms, and decisions are given in the shortest possible form, in answer to carefully formulated questions or dubia.
Five classes according to population, the powers being concentrated and simplified by degrees in the case of the smaller cities, and reaching a maximum of separation and completeness in class 1, i.e.
If there is this tendency to adopt too as a basis instead of to, the teaching of decimals might sometimes be simplified by proceeding from percentages to percentages of percentages, i.e.
In calculating an average it should be observed that the addition of any numerical quantity (positive or negative) to each of the measurements produces the addition of the same quantity to the average, so that the calculation may often be simplified by taking some particular measurement as a new zero from which to measure.
The introduction of steel construction has simplified many details of architectural treatment, such as projections for cornices, bay windows and galleries.
Plato further simplified the form, and reduced it to pure argumentative conversation, while leaving intact the amusing element of character-drawing.
Schewiakoff, simplified from a coloured plate in Morphologisches Jahrbuch, xv., r889, by permission of Wilhelm Engelmann.
(From Gegenbaur.) Much simplified from a coloured plate in Results of the " Albatross" Expedition, Museum of Comparative Zoology, Cambridge, Mass., U.S.A.
(pope 1073-1085), too, simplified the liturgy as performed at the Roman court, and gave his abridgment the name of Breviary, which thus came to denote a work which from another point of view might be called a Plenary, involving as it did the collection of several works into one.
The services were at the same time simplified and shortened, and the use of the whole Psalter every week (which had become a mere theory in the Roman Breviary, owing to its frequent supersession by saints' day services) was made a reality.
To apply the equations (11) to the case of the top we start with the expression (15) of 22 for the kinetic energy, the simplified form (i) of 20 being for the present purpose inadmissible, since it is essential that the generalized co-ordinates employed should be competent to specify the position of every particle.
He explained and simplified the process of obtaining phosphorus from urine, and made some admirable observations on phosphoric acid; but though he noted the increase in weight that attends the conversion of phosphorus into phosphoric acid he was content to remain an adherent of the phlogistic doctrine.