Other cases arise when we consider the continuity of a function.
Absolute continuity of motion is not comprehensible to the human mind.
The Ego he considers not an entity sharply distinguished from the Non-ego, but merely, as it were, a medium of continuity of sensory impressions.
As interruptions of the continuity of nature " (Das Wesen des Christentums, p. 17).
Outside the wall of the oesophagus a vascular space has been detected which is in direct continuity with the longitudinal blood-vessels.
Boundaries, from following lines on which the continuity of the land is interrupted, often necessarily indicate important differences in the conditions of adjoining countries, and of their political and physical relations, yet variations of the elevation of the surface above the sea-level frequently produce effects not less marked.
In both cases it can be shown to be in immediate continuity with the coating of nerve-cells forming part of the longitudinal cords.
His disappearance snapped the chief link with the heroic period, and removed from the helm of state a ruler of large heart, great experience and civil courage, at a moment when elements of continuity were needed and vital problems of internal reorganization had still to be faced.
The Tyrannidae, has evidently been led by the geographical continuity of its soil with that of the Neotropical region, such forms do not occur elsewhere.
The Reformation made no break in the continuity of the school, which had probably existed in the abbey since the 11th century.
So Haggai sees in Zerubbabel the representative of the 5 There is an obvious effort to preserve the continuity of tradition (a) in Ezra ii.
This is especially true of the history of the exilic and post-exilic periods, where the effort is made to preserve the continuity of Israel and the Israelite community (Chronicles - Ezra - Nehemiah).
The recent exploration of a cemetery belonging to the close of the great palace period, and in a greater degree to the age succeeding the catastrophe, has now conclusively shown that there was no real break in the continuity of Minoan culture.
There was no attempt to overwhelm whole empires by pouring into them masses of troops, but commerce was combined with territorial acquisition, and a continuity of European interest secured by the presence of merchants and settlers.
Males in nearly all species appear once a year, when the last female generation, the ovigerous generation, is fertilized, and a few large ova are produced to carry on the continuity of the species over the winter.
Her insular position, continuity of political development and freedom from domestic broils played an important part in bringing about a steady and continuous growth of industry and manufactures for several generations before the modern era.
In most other Mollusca (Anisopleurous Gastropods, Pteropods and Conchifera) there is a want of such continuity; the primitive shell-sac contributes no factor to the permanent shell, or only a very minute FIG.
Such an absolute continuity is sometimes assumed without warrant; but Descartes already recognized that the world was no continuous process, " Tria mirabilia fecit Dominus; res ex nihilo, liberum arbitrium et hominem Deum."
But it is important to bear in mind the continuity of the Crusades - the constant flow of new forces eastward and back again westward; for this alone explains why the Crusades formed a great epoch in civilization, familiarizing, as they did, the West with the East.
Now, owing to the necessary inexactness of measurement, it is impossible to discriminate directly whether any kind of continuous physical quantity possesses the compactness of the series of rationals or the continuity of the series of real numbers.
Similarly, the continuity of space apparently rests upon sheer assumption unsupported by any a priori or experimental grounds.
There are, however, among these border-ranges several breaches of continuity - broad depressions or trenches leading from Lake Balkash and Lake Zaisan to the upper parts of the plateau.
The idea of continuity must in the first instance be introduced from the graphical point of view; arithmetical continuity being impossible without a considerable extension of the idea of number (ï¿½ 65).
Physically its continuity is broken by Monte Urticu and several smaller hills which rise within it, but these are all composed of volcanic rock and are the remains of Tertiary volcanoes.
The Hari-Rud marks the only important break existing in the continuity of the great central water-parting of Asia.
(9th January Deaths t~ 1878) stirred national feeling to an unprecedented Victor depth, and placed the continuity of monarchical in&nmaauel stitutions in Italy upon trial before Europe.
3 Leibnitz's doctrine of continuity necessarily led him in the same direction; and, of the infinite multitude of monads with which he peopled the world, each is supposed to be the focus of an endless process of evolution and involution.
Boveri in fact has put forward the view that the chromosomes are elementary units which maintain an organic continuity and independent existence in the cell.
The mode of formation of the sieve plate is not certainly known; but from the fact that delicate connecting threads of protoplasm are present between the cells from their first development it is probable that it is a special case of the normal protoplasmic continuity, the sieve pores being produced by a secondary enla~gement of the minute openings through which these delicate strands pass.
But the old continuity was not entirely broken; there was a return to earlier conditions, and life moved more freely in its wonted channels.
There is complete present, and probably previous long-existing, geographical continuity in the area over - which they are found.
It is important here to note that Clausilia furnishes us with an exceptional instance of the continuity of the shell or secreted product of the primitive shell - sac with the adult shell.
(After Spengel.) being formed afresh on the surface of the visceral hump. It is, then, in this sense that we may speak of primary, secondary and tertiary shells in Mollusca, recognizing the fact that they may be merely phases fused by continuity of growth so as to form but one shell, or that in other cases they may be presented to us as separate individual things, in virtue of the non-development of the later phases, or in virtue of sudden changes in the activity of the mantle-surface causing the shedding FIG.
These posterior brain-lobes, which in all Heteronemertines are in direct continuity of tissue with the upper pair of principal lobes, cease to have this intimate connexion in the Metanemertini; and, although still constituted of (I) a ciliated duct, opening out externally, (2) nervous tissue surrounding it, and (3) histological elements distinctly different from the nervous, and most probably directly derived from the oesophageal outgrowths, they are nevertheless here no longer constantly situated behind the upper brain-lobes and directly connected with them, but are found sometimes behind, sometimes beside and sometimes before the brain-lobes.
The descent of alchemistical doctrine can thus be traced with fair continuity for a thousand years, from the Greeks of Alexandria down to the time when Latin alchemy was firmly established in the West, and began to be written of by historical authors like Albertus Magnus, Roger Bacon and Arnoldus Villanovanus in the 13th century.
But it is not so well understood that slavery discharged important offices in the later social evolution - first, by enabling military action to prevail with the degree of intensity and continuity requisite for the system of incorporation by conquest which was its final destination; and, secondly, by forcing the captives, who with their descendants came to form the majority of the population in the conquering community, to an industrial life, in spite of the antipathy to regular and sustained labour which is deeply rooted in human nature.
Indeed, mathematicians now reserve "continuity" as the term for the latter kind of continuity; the mere property of having an infinite number of terms between any two terms is called "compactness."
The great abstract ideas (considered directly and not merely in tacit use) which have dominated the science were due to them - namely, ratio, irrationality, continuity, the point, the straight line, the plane.
Fortunately the continuity of the organization was maintained, largely through the mediation of the British Government, and the council held its first post-war meeting in London in 1920.
Not only is the coelom thus subdivided, but the enteron (gut, alimentary canal, digestive tube) itself shows indications of three main subsections in continuity with one another: - (I) proboscis-gut (Eicheldarm, stomochord, vide infra); (2) collar-gut (buccal cavity, throat); (3) truncal gut extending from the collar to the vent.
In one family, the Ptychoderidae, the medullary tube of the collar is connected at intermediate points with the epidermis by means of a variable number of unpaired outgrowths from its dorsal wall, generally containing an axial lumen derived from and in continuity with the central canal.
Nor is the argument that they are a visible manifestation of the continuity of the Church anything but a doubleedged weapon; for, as Father Braun pertinently asks, if these be their symbolism, of what was their disuse in the Church of England for nigh on 3 00 years a symbol?
Magnetic induction, like other fluxes such as electrical, thermal or fluid currents, is defined with reference to an area; it satisfies the same conditions of continuity as the electric current does, and in isotropic media it depends on the magnetic force just as the electric current depends on the electromotive force.
This involved not only the geometrical interpretation of negative quantities, but also the idea of continuity; this latter, which is the basis of modern analysis, leading to two separate but allied developments, viz.
One of the most difficult questions for the teacher of algebra is the stage at which, and the extent to which, the ideas of a negative number and of continuity may be introduced.
The first error is to assert that history unfolds in a basically linear fashion, that there is a fundamental continuity between the past, present, and future.
Vienna considers the bases of the proposed treaty so unattainable that not even a continuity of most brilliant successes would secure them, and she doubts the means we have of gaining them.
These are special organs which Lent~eIs interrupt the continuity of the impermeable layer of ordinary cork-cells.
Protoplasmic Continuity.Except in the unicellular plants the cell is not an independent unit.
We cannot suppose that there occurred, at or about the commencement of the 19th century, a breach of historical continuity of such a character that institutions, customs, laws and social conventions were suddenly swept away, the bonds of society loosened, and the state and people of England dissolved into an aggregate of competing individuals.
There may be also a breach of continuity in some depression towards Barkul.
The difficulty is due to the fact that number is naturally not continuous, so that continuity can only be achieved by an artificial development.
This idea of the continuity of species is developed more fully in a remarkable passage (Essay, bk.
It must always be remembered that we are liable (especially in the case of fossilized integuments) to attach an unwarranted interpretation to the mere discontinuity or continuity of the thickened plates of chitinous cuticle on the back of an Arthropod.
The other extreme end closes, but the invaginated endoderm cells remain in continuity with this extremity of the blastopore, and form the " rectal peduncle " or " pedicle of invagination " of Lankester, although the endoderm cells retain no contact with the middle region of the now closed-up blastopore.
Segments are the apertures of the Nervous system rarely atria.C, Perichaeta: the spermathecal pores (Aeolosoma) in continuity are between segments 6 and 7, 7 with epidermis.