Elements sentence example
There's elements to consider.
If all were as it seems, and men made the elements their servants for noble ends!
Initially, we plan to use the Dublin core metadata elements to index the pages on the superjournal web site.
Parkside was nothing more than an innocent battleground for disreputable elements of our society, at war with one another.
Regular observations were made of both elements.Advertisement
We think of things not in the abstract elements of the things themselves, but in connexion with, and in language which presupposes, other things.
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 men of the Left believed themselves subtle enough to retain the confidence and esteem of all foreign powers while coquetting at home with elements which some of these powers had reason to regard with suspicion.
Com posed mainly of elements drawn from the Left, and dependent for a majority upon the support of the subversive groups of the Extreme Left, the formation of this cabinet gave the signal for a vast working-class movement, during which the Socialist party sought to extend its political influence by means of strikes and the organization of labor leagues among agricultural laborers and artisans.
This result was most satisfactory to all the best elements in the country, and great hopes were entertained that the 1909.Advertisement
From them are developed two distinct types of histological elements; the genital cells and the cnidoblasts or mothercells of the nematocysts.
A further stage in evolution is that the muscle-cells lose their connexion with the epithelium and come to lie entirely beneath it, forming a sub-epithelial contractile layer, developed chiefly in the tentacles of the polyp. The of the evolution of the ganglioncells is probably similar; an epithelial cell develops processes of nervous nature from the base, which come into connexion with the bases of the sensory cells, with the muscular cells, and with the similar processes of other nerve-cells; next the nerve-cell loses its connexion with the outer epithelium and becomes a sub-epithelial ganglion-cell which is closely connected with the muscular layer, conveying stimuli from the sensory cells to the contractile elements.
The buds may all become detached after a time and give rise to separate and independent individuals, as in the common Hydra, in which only polyp-individuals are produced and sexual elements From Allman's Gymnoblastic Hydroids, by permission of are developed the Council of the Ray Society.
We can distinguish (I) digestive endoderm, in the stomach, often with special glandular elements; (2) circu-, latory endoderm, in the radial and ring canals; (3) supporting endoderm in the axes of the tentacles and in the endodermlamella; the latter is primitively a double layer of cells, produced by concrescence OC-- = w.?"
Empedocles took an important step in the direction of modern conceptions of physical evolution by teaching that all things arise, not by transformations of some primitive form of matter, but by various combinations of a number of permanent elements.Advertisement
The force which brings the atoms together in the forms of objects is inherent in the elements, and all their motions are necessary.
He is indeed careful to keep right with the orthodox doctrine of creation by saying that he does not believe the world actually arose in this mechanical way out of the three kinds of elements which he here supposes, but that he simply puts out his hypothesis as a mode of conceiving how it might have arisen.
Galen believed in the doctrine of humours originated by Hippocrates, which supposes the condition of the body to depend upon the proper mixture of the four elements, hot, cold, moist and dry, and that drugs possess the same elementary qualities, and that on the principle of contraries one or other was indicated, e.g.
Molybdenum combines with the halogen elements in varying proportions, forming with chlorine a di-, tri-, tetraand penta-chloride, and similar compounds with bromine and iodine.
In later times Orphic theology engaged the attention of Greek philosophersEudemus the Peripatetic, Chrysippus the Stoic, and Proclus the Neoplatonist, but it was an especially favourite study of the grammarians of Alexandria, where it became so intermixed with Egyptian elements that Orpheus came to be looked upon as the founder of mysticism.Advertisement
Here also he wrote Lucinde (1799), an unfinished romance, which is interesting as an attempt to transfer to practical ethics the Romantic demand for complete individual freedom, and Alarcos, a tragedy (1802) in which, without much success, he combined romantic and classical elements.
The war against the castles became a war against the palaces; and the system of government by consuls proved inefficient to control the clashing elements within the state.
On the 15th of November he was assassinated, and as no one was punished for this crime the insolence of the disorderly elements increased, and shots were exchanged with the Swiss Guard.
He ended by dominating the cabinet, but owing to his having negotiated a union of the Right Centre and the Left Centre (the Con nubio) in the conviction that the country needed the moderate elements of both parties, he quarrelled with DAzeglio (who, as an uncompromising conservative, failed to see the value of such a move) and resigned.
In the Jewish speculations of the middle ages may be found curious forms of the doctrine of emanations uniting the Biblical idea of creation with elements drawn from the Persians and the Greeks.Advertisement
As the aerial stem is traced down into the underground rhizome portion, these three mantles die out almost entirelythe central hydrom strand forming the bulk of the cylinder and its elements becoming mixed with thick-walled stereids; at the same time this central hydromstereom strand becomes three-lobed, with deep furrows between the lobes in which the few remaining leptoids run, separated from the central mass by a few starchy cells, the remains of the amylom sheath.
The tracheids or vessels, indifferently called tracheal elements, together with the immediately associated cells (usually amylom in Pteridophytes) constitute the xylem of the plant.
Such a vascular cylinder is called a haplostele, and the axis containing it is said to be haplostelic. In the stele of the root the strands of tracheids along the lines where the xylem touches the pericycle are spiral or annular, and are the xylem elements first formed when the cylinder is developing.
In the very frequent cases where the bundles have considerable individuality, the fibrous pericyclic cap very clearly has a common origin from the same strand of tissue as the vascular elements themselves.
The parenchyma is often arranged in tangential bands between the layers of sievetubes and tracheal elements.
The xylem parenchyma is often found in strands associated with the tracheal elements.
In a few cases some of the tracheids have very thick walls and reduced cavities, functioning as mechanical rather than as waterconducting elements.
The stereom is furnished either by cortical cells or by the tracheal elements, in a few cases by fibres which arc probably homologous with sievetubes.
In some cases special secreting tissues, resin ducts, oil glands, laticiferous tissue, crystal sacs, &c., may be developed among the ordinary secondary vascular elements.
The limit of each years increment of secondary wood, in those plants whose yearly activity is interrupted by a regular winter or dry season, is marked by a more or less distinct line, which is produced by the sharp contrast between the wood formed in the late summer of one year (characterized by the sparseness or small diameter of the tracheal elements, or by the preponderance of fibres, or by a combination of these characters, giving a denseness to the wood) and the loose spring wood of the next year, with its absence of fibres, or its numerous large tracheae.
The living elements die, and the walls of all the cells often become hardened, owing to the deposit in them of special substances.
There is at present also a want of agreement among botanists as to the path which the water takes in the structural elements of the tree, two views being held.
While so many conspicuous Australian elements are wanting in New Zealand, one-eighth of its flora belongs to South American genera.
The direct geographical elements are the arrangement of land and sea (continents and islands standing in sharp contrast) and the vertical relief of the globe, which interposes barriers of a less absolute kind between portions of the same land area or oceanic depression.
The indirect geographical elements, which, as a rule, act with and intensify the direct, are mainly climatic; the prevailing winds, rainfall, mean and extreme temperatures of every locality depending on the arrangement of land and sea and of land forms. Climate thus guided affects the weathering of rocks, and so determines the kind and arrangement of soil.
Plant life, utilizing solar light to combine the inorganic elements of water, soil and air into living substance, is the basis of all animal life.
The so-called alkaline earth-metals are the elements beryllium, magnesium, calcium, strontium and barium.
This pad varies much; it is morphologically the homologue of the pair of basiventral elements which by their lateral extension give origin to the corresponding ribs.
The traditions would seem to point to the institution of new principles in the religion of Yahweh, and would associate with it not merely Moses but those foreign elements which are subsequently found in Israel and Judah.
His son Moses, who died about the end of the 13th century, translated the rest of Maimonides, much of Averroes, the lesser Canon of Avicenna, Euclid's Elements (from the Arabic version), Ibn al-Jazzar's Viaticum, medical works of IIunain ben Isaac (Johannitius) and Razi (Rhazes), besides works of less-known Arabic authors.
In biology conception is the coalescence of the male and female generative elements, producing pregnancy.
In correcting the elements of Delambre's solar tables he had been led to suspect an inequality overlooked by their constructor.
In each case the Arab or the Norman was the kernel, the centre round which all other elements gathered and which gave its character to the whole.
In the end something like a Sicilian nation did arise; but it arose rather by the dying out of several of the elements in the country, the Norman element among them, than by any such fusion as took place in England.
Out of these elements the Saracens of Sicily had formed a noble and beautiful style, grand and simple in its construction, rich and graceful in its characteristic detail.
At Bari, Trani and Bitonto we see a style in which Italian and strictly Norman elements are really mingled.
Sulphur also combines directly with most of the elements to form sulphides.
It reacts most energetically with many organic compounds, removing the elements of water in many cases and leaving a carbonized mass.
It combines directly with many elements and compounds and frequently acts as energetic oxidizing agent.
One of his most important works was the Elements de Philosophic published in 1759, in which he discussed the principles and methods of the different sciences.
Alembert was much interested in music both as a science and as an art, and wrote Elements de musique theorique et pratique (1779), which was based upon the system of P. Rameau with important modifications and differences.
The primary distinctions between these branches have been increased during the last nine centuries by their contact with different nationalities - the Great Russians absorbing Finnish elements, the Little Russians undergoing an admixture of Turkish blood, and the White Russians submitting to Lithuanian influence.
The more moderate elements found a rallying cry in the manifesto of October, took the name of " the Party of 17 October," and became known as " Octobrists."
For other areas we have often no description of the procedure at all, but merely the briefest outline of the actual process of slaughter, and we are ignorant whether the form of the rite is in reality simple (either from a loss of primitive elements or from never having advanced beyond the stage at which we find it), or whether the absence of detail is due to the inattention or lack of interest of the observer.
The sacrifices of sacralization and desacralization mentioned above find their analogues in the Hindu scheme of the rite; sacralization and desacralization, sometimes performed by means of subsidiary sacrifices, are the essential elements of the preparation for sacrifice and the subsequent lustration.
The innumerable theories which were framed as to the precise nature of the offering and as to the precise change in the elements all implied that conception of it.
He took stern measures against the revolutionary elements in southern Italy, and his new cabinet was essentially military and conservative.
For Amos and Isaiah were able to single out those loftier spiritual and ethical elements which lay implicit in Mosaism and to lift them into their due place of prominence.
The Deutero-Isaiah closes a great prophetic succession, which begins with Amos, continues in Isaiah in even greater splendour with the added elements of hope and Messianic expectation, and receives further accession in Jeremiah with his special teaching on inward spiritual and personal religion which constituted the new covenant of divine grace.
The fetters of nationalism were to be broken, and the Hebrew religion in its essential spiritual elements was to become the heritage of all humanity.
The elements he had to deal with could not be welded together.
Even before authentic history begins, the elements of religion and society had already crystallized into a solid coherent structure which was to persist without essential modification.
From a variety of independent reasons one is forced to conclude that, whatever historical elements they may contain, the stories of this remote past represent the form which tradition had taken in a very much later age.
Many of the elements lie outside questions of time and place and are almost immemorial.
In Elephantine, as in Nippur, the legal usages show that similar elements of Babylonio-Assyrian culture prevailed, and the evidence from two such widely separated fields is instructive for conditions in Palestine itself.3 20.
In him culminates the Jewish expression of the Spanish-Moorish culture; his writings had an influence on European scholasticism and contributed significant elements to the philosophy of Spinoza.
On account of the prejudices of her mother, who did not desire her to know more than was necessary for being useful in the family, she received in youth only the first elements of education.
Art was still by no means extinct, and its forms and decorative elements are simply later derivatives of the great palace style.
As to the character of the invading elements that hastened its close, and the date of their incursions, contemporary Egyptian monuments afford the best clue.
For example, the priests are not to be chosen by the people; penitents are not to be present at ordinations (lest they should hear the failings of candidates discussed); bishops are to be appointed by the metropolitan and his suffragan; sub-deacons may not distribute the elements of the Eucharist; clerics are forbidden to leave a diocese without the bishop's permission.
In either case it is of course open to anyone to maintain that the apparent completeness of synthesis really rests on the subtle intrusion of elements of feeling into the rational process.
Japan appears to have been formerly inhabited by the Ainus, who have traditions of an older but unknown population, but was invaded in prehistoric times by a race akin to the Koreans, which was possibly mingled with Malay elements after occupying the southern part of the islands.
Both China and Japan have felt through Buddhism the influence of Indian art, which contains at least two elements - one indigenous and the other Greco-Persian.
These excerpts, however, have been so pieced together, that it is often impossible to separate them with precision, and to distinguish accurately between earlier and later elements.
David was not only a great captain, he was a national hero in whom all the noblest elements of the Hebrew genius were combined.
The commercial importance of the town dates from the second half of the r9th century; in 1870 its population had risen to 38,000, and after it was brought into railway connexion with Kharkov and Voronezh, and thus with the fertile provinces of south and south-east Russia, the increase was still more rapid, the number reaching 56,047 in 1885, and 58,928 in 1900 - Greeks, Jews, Armenians and West-Europeans being important elements.
A third account omits all the apocryphal elements in the story and says that Agrippa was assassinated by the Romans, who objected to his growing power.
Most of these were simple records of patient and laborious analytical operations, and it is perhaps surprising that among all the substances he analysed he only detected two new elements - beryllium (1798) in beryl and chromium (1797) in a red lead ore from Siberia.
But it lacked the elements of true greatness.
The rebellious elements allied themselves instinctively with the Poles, who thus found the absorption of the greater part of the lands of the Order an easy task.
It brought Ladislaus little immediate gain; but it stimulated the elements of unrest in Prussia to fresh activity.
The higher parts of the plains, which are deeply trenched by the upper tributaries of the rivers, are inhabited by various Caucasian races - Kabardians and Cherkesses (Circassians) in the west, Ossetes in the middle, and several tribal elements from Daghestan, described under the general name of Chechens, in the east.
He wrote also Elements de metaphysique (1724), a "French Grammar on a new plan," and a number of historical essays.
Mill remarks that the uncertainty hanging over the very elements of moral and social philosophy proves that the means of arriving at the truth in those sciences are not yet properly understood.
The standard of life of the ordinary well-to-do middle class in England, for example, includes not only food, clothing and shelter of a kind different in many respects from that of a similar class in other countries and of other classes in England, but a highly complicated mechanism, both public and private, for ministering to these primary needs, habits of social intercourse, educational and sanitary organization, recreative arrangements and many other elements.
But it is doubtful whether the most complete investigation would ever enable us to include all the elements of the standard of life in a money estimate.
In the investigation of past times, the incommensurate elements of well-being are so numerous that merely money estimates are frequently misleading.
The detorted visceral commissure shows a tendency to the concentration of all its elements round the oesophagus, so that except in the Bullomorpha and in Aplysia the whole nervous system is aggregated in the cephalic region, either dorsally or ventrally.
To us, indeed, his conception of the universe, like that of Philo, seems a strange medley, and one may be at a loss to conceive how he could bring together such heterogeneous elements; but there is no reason to doubt that the harmony of all the essential parts of his system was obvious enough to himself.
He is, moreover, a judicious critic. The union of these four elements gives character to his theology, and in a certain degree to all subsequent theology.
Very many accepted these terms, rallied to the First Consul with more or less sincerity; and their return to France to strengthen the conservative elements in French society.
But the Arsacid kingdom never was a truly national state; with the Scythian and Parthian elements were united some elements of Greek civilization.
They crushed a civilization already hard hit; and it took two or three centuries for the artistic spirit, instinct in the Aegean area, and probably preserved in suspended animation by the survival of Aegean racial elements, to blossom anew.
Certain elements present themselves in feeling which seem stubbornly to resist any attempt to explain them in terms of thought.
Into these regions descended Hibil the brilliant, in the power of Mana rabba, just as in the Manichaean mythology the "primal man," armed with the elements of the king of light, descends to a contest with the primal devil.
The thoracic segments, as seen in an early stage of the ventral plate, display in a well-marked manner the essential elements of the insect segment.
These elements are a central piece or sternite, 12 and a lateral field on each side bearing the leg-rudi 1s ment.
The very elements now began to fight against the perishing but still unconquered host.
Of the foreign-born population these elements constituted respectively 35.6, 24 o, 7.6, 7 o, 6.7 and 5.3%.
Its characteristic civilization grew out of a mixture of various elements, Arabic, Aramaic, Greek and Roman.
A tenant is not responsible, under such a covenant, for deterioration due to diminution in value caused by lapse of time or by the elements.
The products of cotton seed have become important elements in the national industry of the United States.
Possessing soil, climate and apparently all the requisite elements from nature for the production of cotton to an almost boundless extent, and of a 1 Approximately.
As regards the first point, it is now generally held that miracles are exceptions to the order of nature as known in our common experience; and as regards the second, that miracles are constituent elements in the divine revelation, deeds which display, the divine character and purpose; but they are signs and not merely seals of truth.
On the problem of evil and sin it is impossible here to enter; but this must be insisted on, that the miracles of Jesus at least express divine benevolence just under those conditions in which the course of nature obscures it, and are therefore, proper elements in a revelation of grace, of which nature cannot give any evidence.
Various elements in the Republican party, nevertheless, had stoutly opposed their appointment, so that the President's choice showed that he was prepared to exert his independence of party managers and to insist upon administrative efficiency.
The principal elements are found in various combinations, the hydrocarbons of the Pennsylvania oils being mainly paraffins (q.v.), while those of Caucasian petroleum belong for the most part to the naphthenes, isomeric with the olefines (q.v.).
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.
At the council of Tours (1054) he found a protector in the papal legate, the famous Hildebrand, who, satisfied himself with the fact that Berengar did not deny the real presence of Christ in the sacramental elements, succeeded in persuading the assembly to be content with a general confession from him that the bread and wine, after consecration, were the body and blood of the Lord, without requiring him to define how.
Philosophical sanction and explanation of this belief was then found by bringing it into relation with the theory of the prima materia, which was identical in all bodies but received its actual form by the adjunction of qualities expressed by the Aristotelian elements - earth, air, fire and water.
The prima materia was early identified with mercury, not ordinary mercury, but the " mercury of the philosophers," which was the essence or soul of mercury, freed from the four Aristotelian elements - earth, air, fire and water - or rather from the qualities which they represent.
Though an alchemist, Boyle, in his Sceptical Chemist (1661), cast doubts on the " experiments whereby vulgar Spagyrists are wont to endeavour to evince their salt, sulphur and mercury to be the true principles of things," and advanced towards the conception of chemical elements as those constituents of matter which cannot be further decomposed.
The Old Testament depicts the history of the people as a series of acts of apostasy alternating with subsequent penitence and return to Yahweh, and the question whether this gives effect to actual conditions depends upon the precise character of the elements of Yahweh worship brought by the Israelites into Palestine.
Two elements define the position of the plane passing through the attracting centre in which the orbit lies.
Hence the number of independent elements assigned to a planet or other body moving around the sun is commonly six.
In these cases therefore the mean distance and mean motion are regarded as different elements, and the whole number of the latter is seven.
The process by which the position of a planet at any time is determined from its elements may now be conceived as follows The epoch of passage through pericentre being given, let t be the interval of time between this epoch and that for which the position of the body is required.
To form a conception of this problem it is to be noted that since the position of the body in space can be computed from the six elements of the orbit at any time we may ideally conceive the coordinates of the body to be algebraically expressed as functions of the six elements and of the time.
Then by solving these equations, regarding the six elements as unknown quantities, the values of the latter may be computed.
Instead of the six ideal equations just described we have to combine a number of equations of various forms containing other quantities than the elements.
As soon as he had learnt the elements of reading and writing, he was sent as a page to the court of Ferdinand and Isabella; afterwards, until his twenty-sixth year, he took service with Antonio Maurique, duke of Nagera, and followed the career of arms. He was free in his relations with women, gambled and fought; but he also gave indications of that courage, constancy and prudence which marked his after life.
Under the name of "Anti-Masons" able leaders united those who were discontented with existing political conditions, and the fact that William Wirt, their choice for the presidency in 1832, was not only a Mason but even defended the Order in a speech before the convention that nominated him, indicates that simple opposition to Masonry soon became a minor factor in holding together the various elements of which the party was composed.
But whether he lived or not, and whenever he lived, it is certain that many mythical elements are contained in his story.
How certain it is that the Robin Hood story attracted to it and appropriated other elements is illustrated by its subsequent history - its history after the 14th century.
In 1513 the arrival of its first bishop, who later also exercised the function of general inquisitor, added one more to the discordant elements ruling the island.
But it was hardly adapted to teach a people utterly without political experience the essential elements of self-government.
His name is best known for the share he had in the periodic classification of the elements.
His book on Die modernen Theorien der Chemie, which was first published in Breslau in 1864, contains a discussion of relations between the atomic weights and the properties of the elements.
His idea was to combine the more conservative elements of both sections in favour of a settlement which would concede the Southern view on two questions, the Northern view on two, and balance the fifth.
The fundamental chemical classification of matter, on the other hand, recognizes two groups of substances, namely, elements, which are substances not admitting of analysis into other substances, and compounds, which do admit of analysis into simpler substances and also of synthesis from simpler substances.
Here is treated the history of descriptive inorganic chemistry; reference should be made to the articles on the separate elements for an account of their preparation, properties, &c.
In the view of some alchemists, the ultimate principles of matter were Aristotle's four elements; the proximate constituents were a " sulphur " and a " mercury," the father and mother of the metals; gold was supposed to have attained to the perfection of its nature by passing in succession through the forms of lead, brass and silver; gold and silver were held to contain very pure red sulphur and white quicksilver, whereas in the other metals these materials were coarser and of a different colour.
At the same time he clarified the conception of elements and compounds, rejecting the older notions, the four elements of the " vulgar Peripateticks " and the three principles of the " vulgar Stagyrists," and defining an element as a substance incapable of decomposition, and a compound as composed of two or more elements.
To him is also due a rigorous examination of the nature of elements and compounds; he held the same views that were laid down by Boyle, and with the same prophetic foresight predicted that some of the elements which he himself accepted might be eventually found to be compounds.
Berzelius, who, fired with enthusiasm by the original theory of Dalton and the law of multiple proportions, determined the equivalents of combining ratios of many elements in an enormous number of compounds.2 He prosecuted his labours in this field for thirty years; as proof of his industry it may be mentioned that as early as 1818 he had determined the combining ratios of about two thousand simple and compound substances.
The denotation of elements by symbols had been practised by the alchemists, and it is interesting to note that the symbols allotted to the well-known elements are identical with the astrological symbols of the sun and the other members of the solar system.
Hassenfratz and Adet, who assigned to each element a symbol, and to each compound a sign which should record the elements present and their relative quantities.
Straight lines and semicircles were utilized for the non-metallic elements, carbon, nitrogen, phosphorus and sulphur!
Compounds were denoted by joining the symbols of the components, and by varying the manner of joining compounds of the same elements were distinguished The symbol V was used to denote a liquid, and a vertical line to denote a gas.
If two compounds combined, the + signs of the free compounds were discarded, and the number of atoms denoted by an Arabic index placed after the elements, and from these modified symbols the symbol of the new compound was derived in the same manner as simple compounds were built up from their elements.
Berzelius objected to the hypothesis that if two elements form only one compound, then the atoms combine one and one; and although he agreed theory.
While successfully investigating the solid elements and their compounds gravimetrically, Berzelius was guilty of several inconsistencies in his views on gases.
From a study of the free elements Cannizzaro showed that an element may have more than one molecular weight; for example, the molecular weight of sulphur varied with the temperature.
We have seen how its utilization in the " structure theory " permitted great clarification, and attempts were not wanting for the deduction of analogies or a periodicity between elements.
Carbon was joined with silicon, zirconium and titanium, while boron, being trivalent, was relegated to another group. A general classification of elements, however, was not realized by Frankland, nor even by Odling, who had also investigated the question from the valency standpoint.
The solution came abOut by arranging the elements in the order of their atomic weights, tempering the arrangement with the results deduced from the theory of valencies and experimental observations.
But when the properties of the elements are carefully contrasted together it is found that no strict line of demarcation can be drawn dividing them into two classes; and if they are arranged in a series, those which are most closely allied in properties being placed next to each other, it is observed that there is a more or less regular alteration in properties from term to term in the series.
Those elements which are disengaged at the negative pole are termed electro-positive, or positive, or basylous elements, whilst those disengaged at the positive pole are termed electro-negative, or negative, or chlorous elements.
But the difference between these two classes of elements is one of degree only, and they gradually merge into each other; moreover the electric relations of elements are not absolute, but vary according to the state of combination in which they exist, so that it is just as impossible to divide the elements into two classes according to this property as it is to separate them into two distinct classes of metals and non-metals.
Elements which readily enter into reaction with each other, and which develop a large amount of heat on combination, are said to have a powerful affinity for each other.
The tendency of positive elements to unite with positive elements, or of negative elements to unite with negative elements, is much less than that of positive elements to unite with negative elements, and the greater the difference in properties between two elements the more powerful is their affinity for each other.
Hydrogen and oxygen are, therefore, of very opposite natures, and this is well illustrated by the circumstance that oxygen combines, with very few exceptions, with all the remaining elements, whilst compounds of only a limited number with hydrogen have been obtained.
Com pounds .-A chemical compound contains two or more elements; consequently it should be possible to analyse it, i.e.
In general, a compound has properties markedly different from those of the elements of which it is composed.
When the same two elements combine together to form more than one compound, the different masses of one of the elements which unite with a constant mass of the other, bear a simple ratio to one another.
The masses of different elements which combine separately with one and the same mass of another element, are either the same as, or simple multiples of, the masses of these different elements which combine with each other.
If more than one compound be formed from the same two elements,, the difference is shown by prefixing such words as mono-, di-, tri-, sesqui-, per-, sub-, &c., to the last part of the name, or the suffixes -ous and -ic may be appended to the name of the first element.
Usually, when the symbols of the elements are written or printed with a figure to the right, it is understood that this indicates a molecule of the element, the symbol alone representing an atom.
Before explaining these formulae it will be necessary, however, to consider the differences in combining power exhibited by the various elements.
In explanation of these facts it is supposed that each element has a certain number of " units of affinity," which may be entirely, or only in part, engaged when it enters into combination with other elements; and in those cases in which the entire number of units of affinity are not engaged by other elements, it is supposed that those which are thus disengaged neutralize each other, as it were.
Compounds in which all the units of affinity of the contained elements are engaged are said to be saturated, whilst those in which the affinities of the contained elements are not all engaged by other elements are said to be unsaturated.
According to this view, it is necessary to assume that, in all unsaturated compounds, two, or some even number of affinities are disengaged; and also that all elements which combine with an even number of monad atoms cannot combine with an odd number, and vice versa, - in other words, that the number of units of affinity active in the case of any given element must be always either an even or an odd number, and that it cannot be at one time an even and at another an odd number.
The number of units of affinity active in the case of any particular element is largely dependent, however, upon the nature of the element or elements with which it is associated.
It is often convenient to regard compounds as formed upon certain types; alcohol, for example, may be said to be a compound formed upon the water type, that is to say, a compound formed from water by displacing one of the atoms of hydrogen by the group of elements C 2 H 5, thus - H C2H5 O H O H Water Alcohol.
Changes of the first and second kind, according to our views of the constitution of molecules, are probably of very rare occurrence; in fact, chemical action appears almost always to involve the occurrence of both these kinds of change, for, as already pointed out, we must assume that the molecules of hydrogen, oxygen and several other elements are diatomic, or that they consist of two atoms. Indeed, it appears probable that with few exceptions the elements are all compounds of similar atoms united together by one or more units of affinity, according to their valencies.
If this be the case, however, it is evident that there is no real distinction between the reactions which take place when two elements combine together and when an element in a compound is displaced by another.
This difference in behaviour of the three elements, chlorine, bromine and iodine, which in many respects exhibit considerable resemblance, may be explained in the following manner.
We may suppose that in the formation of gaseous hydrochloric acid from gaseous chlorine and hydrogen, according to the equation H2 +C1 2 = HCI+HC1, a certain amount of energy is expended in separating the atoms of hydrogen in the hydrogen molecule, and the atoms of chlorine in the chlorine molecule, from each other; but that heat is developed by the combination of the hydrogen atoms with the chlorine atoms, and that, as more energy is developed by the union of the atoms of hydrogen and chlorine than is expended in separating the hydrogen atoms from each other and the chlorine atoms from one another, the result of the action of the two elements upon each other is the development of heat, - the amount finally developed in the reaction being the difference between that absorbed in decomposing the elementary molecules and that developed by the combination of the atoms of chlorine and hydrogen.
Lastly, in the production of gaseous hydriodic acid from hydrogen and solid iodine H2 - 1 - 12=HI+HI, so much energy is expended in the decomposition of the hydrogen and iodine molecules and in the conversion of the iodine into the gaseous condition, that the heat which it may be supposed is developed by the combination of the hydrogen and iodine atoms is insufficient to balance the expenditure, and the final result is therefore negative; hence it is necessary in forming hydriodic acid from its elements to apply heat continuously.
Inorganic Chemistry Inorganic chemistry is concerned with the descriptive study o f the elements and their compounds, except those of carbon.
Reference should be made to the separate articles on the different elements and the more important compounds for their preparation, properties and uses.
Cleve, the first to make a really thorough study of these elements and their compounds.
The beginning of the 19th century witnessed the discovery of certain powerful methods for the analysis of compounds and the isolation of elements.
Berzelius's investigation of the action of the electric current on salts clearly demonstrated the invaluable assistance that electrolysis could render to the isolator of elements; and the adoption of this method by Sir Humphry Davy for the analysis of the hydrates of the metals of the alkalis and alkaline earths, and the results which he thus achieved, established its potency.
The success which attended his experiments in the case of silicon led him to apply it to the isolation of other elements.
Balard completed for many years Berzelius's group of " halogen " elements; the remaining member, fluorine, notwithstanding many attempts, remained unisolated until 1886, when Henri Moissan obtained it by the electrolysis of potassium fluoride dissolved in hydrofluoric acid.
Chemically related to vanadium are the two elements tantalum and columbium or niobium.
Nilson, and subsequently (1904) by Hall, rendered notable additions to our knowledge of these elements and their compounds.
Since their day many chemists have entered the lists, new and powerful methods of research have been devised, and several new elements definitely characterized.
In the separation of the constituents of the complex mixture of oxides obtained from the " rare earth " minerals, the methods generally forced upon chemists are those of fractional precipitation or crystallization; the striking resemblances of the compounds of these elements rarely admitting of a complete separation by simple precipitation and filtration.
Other elements predicted and characterized by Mendeleeff which have been since realized are gallium, discovered in 1875, and germanium, discovered in 1885 by Clemens Winkler.
He established the existence of two new elements, samarium and gadolinium, since investigated more especially by Cleve, to whom most of our knowledge on this subject is due.
In addition to the rare elements mentioned above, there are a score or so more whose existence is doubtful.
After having been somewhat neglected for the greater attractions and wider field presented by organic chemistry, the study of the elements and their inorganic compounds is now' rapidly coming into favour; new investigators are continually entering the lists; the beaten paths are being retraversed and new ramifications pursued.
Theoretical speculations were revived by Lavoisier, who, having explained the nature of combustion and determined methods for analysing compounds, concluded that vegetable substances ordinarily contained carbon, hydrogen and oxygen, while animal substances generally contained, in addition to these elements, nitrogen, and sometimes phosphorus and sulphur.
Berzelius, in 1813 and 1814, by improved methods of analysis, established that the Daltonian laws of combination held in both the inorganic and organic kingdoms; and he adopted the view of Lavoisier that organic compounds were oxides of compound radicals, and therefore necessarily contained at least three elements - carbon, hydrogen and oxygen.
Dumas went no further that thus epitomizing his observations; and the next development was made in 1836 by Auguste Laurent, who, having amplified and discussed the applicability of Dumas' views, promulgated his Nucleus Theory, which assumed the existence of " original nuclei or radicals " (radicaux or noyaux fondamentaux) composed of carbon and hydrogen, and " derived nuclei " (radicaux or noyaux derives) formed from the original nuclei by the substitution of hydrogen or the addition of other elements, and having properties closely related to the primary nuclei.
The brilliant researches of Frankland on the organo-metallic compounds, and his consequent doctrine of saturation capacity or valency of elements and radicals, relieved Kolbe's views of all obscurity.
Of these, undoubtedly the simplest are the ethers (q.v.), formed by the elimination of the elements of water between two molecules of the same alcohol, " simple ethers," or of different alcohols, " mixed ethers."
In fact, the analogy between the alkyl groups and metallic elements forms a convenient basis from which to consider many derivatives.
Considering derivatives primarily concerned with transformations of the hydroxyl group, we may regard our typical acid as a fusion of a radical R CO - (named acetyl, propionyl, butyl, &c., generally according to the name of the hydrocarbon containing the same number of carbon atoms) and a hydroxyl group. By replacing the hydroxyl group by a halogen, acid-haloids result; by the elimination of the elements of water between two molecules, acid-anhydrides, which may be oxidized to acid-peroxides; by replacing the hydroxyl group by the group. SH, thio-acids; by replacing it by the amino group, acid-amides (q.v.); by replacing it by the group - NH NH2, acid-hydrazides.
Similar considerations will apply to rings containing other elements besides carbon.
It has already been stated that benzene derivatives may be regarded as formed by the replacement of hydrogen atoms by other elements or radicals in exactly the same manner as in the aliphatic series.
A larger and more important series of condensations may be grouped together as resulting from the elimination of the elements of water between carbonyl (CO) and methylene (CH 2) groups.
From the fact that reduction products containing either one or two double linkages behave exactly as unsaturated aliphatic compounds, being readily reduced or oxidized, and combining with the halogen elements and haloid acids, it seems probable that in benzenoid compounds the fourth valencies are symmetrically distributed in such a manner as to induce a peculiar stability in the molecule.
The elements which go to form heterocyclic rings, in addition to carbon, are oxygen, sulphur, selenium and nitrogen.
Closely related to the flame-colorations, we have to notice the great services rendered by the spectroscope to the detection of elements.
Potassium gives a blue-violet flame which may be masked by the colorations due to sodium, calcium and other elements.
Other elements do not interfere with this method.
The flame coloration may give information as to which elements are present.
It is unnecessary here to dwell on the precautions which can only be conveniently acquired by experience; a sound appreciation of analytical methods is only possible after the reactions and characters of individual substances have been studied, and we therefore refer the reader to the articles on the particular elements and compounds for more information on this subject.
The elements which play important parts in organic compounds are carbon, hydrogen, nitrogen, chlorine, bromine, iodine, sulphur, phosphorus and oxygen.
We shall here consider the qualitative and quantitative determination of these elements.
The most direct manner in which to test any property for additive relations is to determine the property for a number of elements, and then investigate whether these values hold for the elements in combination.
Want of data for the elements, however, restricts this method to narrow limits, and hence an indirect method is necessary.
These values hold fairly well when compared with the experimental values determined from other compounds, and also with the molecular volumes of the elements themselves.
The relation between the atomic volumes and the atomic weights of the solid elements exhibits the periodicity which generally characterizes the elements.
Specific Heat and Composition.-The nature and experimental determination of specific heats are discussed in the article Calorimetry; here will be discussed the relations existing between the heat capacities of elements and compounds.
Their observations on the solid elements led to a remarkable generalization, now known as Dulong and Petit's law.
This states that " the atomic heat (the product of the atomic weight and specific heat) of all elements is a constant quantity."
He regarded these anomalies as solely due to the chemical nature of the elements, and ignored or regarded as insignificant such factors as the state of aggregation and change of specific heat with temperature.
The specific heat of a compound may, in general, be calculated from the specific heats of its constituent elements.
Conversely, if the specific heats of a compound and its constituent elements, except one, be known, then the unknown atomic heat is readily deducible.
Atomic refractions may be obtained either directly, by investigating the various elements, or indirectly, by considering differences in the molecular refractions of related compounds.
It is found, however, that the same element has not always the same atomic refraction, the difference being due to the nature of the elements which saturate its valencies.
It has been shown that certain elements and groups exercise morphotropic effects when substituted in a compound; it may happen that the effects due to two or more groups are nearly equivalent, and consequently the resulting crystal forms are nearly identical.
Mitscherlich, in the case of the acid phosphate and acid arsenate of potassium, KH 2 P(As)04, who adopted the term isomorphism, and regarded phosphorus and arsenic as isomorphously related elements.
Other isomorphously related elements and groups were soon perceived, and it has been shown that elements so related are also related chemically.
Isomorphism is most clearly discerned between elements of analogous chemical properties; and from the wide generality of such observations attempts have been made to form a classification of elements based on isomorphous replacements.
For a detailed comparison of the isomorphous relations of the elements the reader is referred to P. von Groth, Chemical Crystallography.
The bare conception of such art as this shows how perfect is the unity between the different elements in Wagner's later musicdrama.
How to equate this foreign civilizing race from Asia with the Semitic elements in the ancient Egyptian speech we do not yet know.
Seleniumand tellurium-ultramarine, in which these elements replace the sulphur, have also been prepared.
The Bulgars of the Volga were of Turkish origin, but may have assimilated Finnish and, later, Slavonian elements.
The existence of these Christian elements in the text misled nearly every scholar for the past four hundred years into believing that the book itself was a Christian apocryph.
He explained not only the gods but also the heroes Agamemnon, Achilles, Hector, as representing primary elements and natural phenomena.
He purified it from the grossly sensual elements of daeva worship, and uplifted the idea of religion to a higher and purer sphere.
The red matter proves to be the remains of wine, not of blood; and the conclusion of the ablest archaeologists is that the vessels were placed where they are found, after the eucharistic celebration or agape on 'the day of the funeral or its anniversary, and contained remains of the consecrated elements as a kind of religious charm.
Its ten Sephiroth are made up of the grosser elements of the former three worlds; they consist of material substance limited by space and perceptible to the senses in a multiplicity of forms. This world is subject to constant changes and corruption, and is the dwelling of the evil spirits.
In its present form the law shows plainly the Latin and English elements.
The selection of the topics of mathematical inquiry among the infinite variety open to it has been guided by the useful applications, and indeed the abstract theory has only recently been disentangled from the empirical elements connected with these applications.
Under the general heading "Algebra and Theory of Numbers" occur the subheadings "Elements of Algebra," with the topics rational polynomials, permutations, &c., partitions, probabilities; "Linear Substitutions," with the topics determinants, &c., linear substitutions, general theory of quantics; "Theory of Algebraic Equations," with the topics existence of roots, separation of and approximation to, theory of Galois, &c. "Theory of Numbers," with the topics congruences, quadratic residues, prime numbers, particular irrational and transcendental numbers.
Under the general heading "Analysis" occur the subheadings "Foundations of Analysis," with the topics theory of functions of real variables, series and other infinite processes, principles and elements of the differential and of the integral calculus, definite integrals, and calculus of variations; "Theory of Functions of Complex Variables," with the topics functions of one variable and of several variables; "Algebraic Functions and their Integrals," with the topics algebraic functions of one and of several variables, elliptic functions and single theta functions, Abelian integrals; "Other Special Functions," with the topics Euler's, Legendre's, Bessel's and automorphic functions; "Differential Equations," with the topics existence theorems, methods of solution, general theory; "Differential Forms and Differential Invariants," with the topics differential forms, including Pfaffians, transformation of differential forms, including tangential (or contact) transformations, differential invariants; "Analytical Methods connected with Physical Subjects," with the topics harmonic analysis, Fourier's series, the differential equations of applied mathematics, Dirichlet's problem; "Difference Equations and Functional Equations," with the topics recurring series, solution of equations of finite differences and functional equations.
After pointing out the immense difficulties which he had had to encounter owing to the absence of any regular accounts, and above all of any of " those statistics which constitute the soul, indeed the very life of a public administration," and that it was therefore impossible for him to pretend that he had been able to free himself altogether from the effects of the past, the minister continues, " every time we have endeavoured to have recourse to the previous elements of appreciation, we found ourselves faced by the chaos which characterized former years.
He was no more successful than Piri or his successor Murad in fighting the elements and the Portuguese in the Persian Gulf; but he was happier in his fate.
The deserters from Cicala's army, distributed in armed bands throughout Asia Minor, had become centres round which all the elements of discontent gathered, and formed the mainstay of the Jellali sectaries who, at this time, rose in insurrection and ravaged Anatolia.
Janissaries and the suppression of the quasi-indepen dent power of the derebeys had removed the worst disturbing elements; the government had been centralized; a series of enactments had endeavoured to secure economy in the administration, to curb the abuses of official power, and ensure the impartiality of justice; and the sultan had even expressed his personal belief in the principle of the equality of all, Mussulman and non-Mussulman, before the law.
We thus see that the American and the European-Asiatic elements of the flora are nearly equivalent; and if the flora of Arctic North America were better known, the number of plants common to America might be still more enlarged.5 In the south, a few goats, sheep, oxen and pigs have been introduced.
Rice, dried fish, beans, pepper and oxen are the chief elements in the export trade of the country, which is in the hands of Chinese.
Iron shipments from the Mesabi and Vermilion ranges, cereals from the Northwest, fruits and vegetables from the Pacific coast, and Oriental products obtained via the great northern railways, are also elements of great importance in the state's commerce.
The dorsal skeletal elements of the thorax and of the anterior six abdominal segments unite with the wing-cases to form a large respiratory chamber, containing five pairs of tracheal gills, with lateral slits for the inflow and a posterior orifice for the outflow of water.
The volume of the hydrogen was about double that of the oxygen, and, since this is the ratio in which these elements are combined in water, it was concluded that the process con sisted essentially in the decomposition of water.
In 1807 he decomposed potash and soda, previously considered to be elements, by passing the current from a powerful battery through the moistened solids, and thus isolated the metals potassium and sodium.
The globules in the latex are liquid, and the phenomenon of coagulation would seem to consist in the passage of this liquid into solid caoutchouc through the kind of change known as polymerization or condensation, in which a liquid passes into solid without alteration of composition or by condensation with the elimination of the elements of water.
The effect may, however, also be due to chemical change known as condensation, and be accompanied by the elimination of the elements of water.
On the other hand, it is not too much to say that, from the end of 1759 to the end of 1761, the unshakable firmness of the Russian empress was the one constraining political force which held together the heterogeneous, incessantly jarring elements of the anti-Prussian combination.
This result he considered to be due, not to any removal of impurities, but to an actual splitting-up of the yttrium molecule into its constituents, and he ventured to draw the provisional conclusion that the so-called simple bodies are in reality compound molecules, at the same time suggesting that all the elements have been produced by a process of evolution from one primordial stuff or "protyle."
Similarly we have a development proceeding according to the elements contained in any row or in any column, viz.
Every factor common to all the elements of a row or of a column is obviously a factor of the determinant, and may be taken outside the determinant brackets.
Hence the product determinant has the principal diagonal elements each equal to A and the remaining elements zero.
It was observed above that the square of a determinant when expressed as a determinant of the same order is such that its elements have the property expressed by aik = aki.
We may therefore form an orthogonal transformation in association with every skew determinant which has its leading diagonal elements unity, for the Zn(n-I) quantities b are clearly arbitrary.
The philosophy of history, by which Hebrew prophets could read a deep moral significance into national disaster and turn the flank of resistless attack, became one of the most important elements in the nation's faith.
The heat is then raised in (relative) absence of air, when the two elements named unite into sulphur-dioxide, while a regulus of molten lead remains.
Their respective followers, and more especially cultured laymen, lacking the capacity for original work, seeking for a solution in some kind of compromise, and possibly failing to grasp the essentials of the controversy, take refuge in a combination of those elements in the opposing systems which seem to afford a sound practical theory.
Thus it might be argued that there can be no logical combination of elements from Christian ethics, with its divine sanction, and purely intuitional or evolutionary ethical theories, where the sanction is essentially different in quality.
He came strongly under the influence of the pietists, particularly of Spener, and there was a mystic vein in his thought; but other elements of his nature were too powerful to allow him to attach himself wholly to that party.
Theodore obtained the elements of knowledge in the schools of the district, which were open during the winter months only.
From the meridian observations of the same planets made for the purpose of controlling the elements of motion of the planets Auwers found it = 8.806".
The determination of the solar parallax through the parallactic inequality of the moon's motion also involves two elements - one of observation, the other of purely mathematical theory.
If a series of such elements, all equally and longitudinally magnetized, were placed end to end with their unlike poles in contact, the external action of the filament thus formed would be reduced to that of the two extreme poles.
The first column contains the symbols of the various elements which were added to the iron, and the second the percentage proportion in which each element was present; the sample containing 0.03% of carbon was a specimen of the best commercial iron, the values obtained for it being given for comparison.
It appears that the elements at about the middle of each row are the most strongly paramagnetic; towards the ends of a row the susceptibility decreases, and ultimately becomes negative.
The values assigned to the atomic susceptibilities of most of the known elements are appended.
For Frederick William the position of leader of Germany now meant the employment of the military force of Prussia to crush the scattered elements of revolution that survived the collapse of the national movement.
Palamnaeus indus, de Geer, to show the arrangement of the coxae of the limbs, the sternal elements, genital plate and pectens.
Opisthosoma consisting of only ten somites, which have no tergal and sternal elements, the prae-genital somite contracted to form a " waist," as in the Pedipalpi; the last three narrowed to form a A B prae-1 2345 6789 io I I111I IV V VI gen Opisttaosoma Prosoma FIG.
Sternal elements of prosoma almost entirely absent, traces of a prosternum and metasternum alone remaining.
Sternal elements much reduced.
E, Lateral view of the whole body and two 1st appendages, showing the fusion of the dorsal elements of the prosoma into a single plate, and of those of the opisthosoma into an imperfectly segmented plate continuous with that of the prosoma.
The bulk of these in due course underwent transformation either complete or partial, but there was always a residuum of incongruous and inconsistent elements existing side by side with the essential truths of Christianity.
Recently Schubert has sought to derive the elements which are found in the Petrine Gospel, but not in the canonical gospels, from the original Ada Pilati, while Zahn exactly reverses the relation of these two works.
Here with his five brothers and sisters Riemann spent his boyhood and received, chiefly from his father, the elements of his education.
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 calculus of variations lay undeveloped in Euler's mode of treating isoperimetrical problems. The fruitful method, again, of the variation of elements was introduced by Euler, but adopted and perfected by Lagrange, who first recognized its supreme importance to the analytical investigation of the planetary movements.
Joel's eschatological picture appears indeed to be largely a combination of elements from older unfulfilled prophecies.
From Light came Heat and Fluidity; these three together with Space make up the elements out of which all things are constructed.
It is usually found associated with tantalum, the chief minerals containing these two elements being tantalite, columbite, fergusonite and yttrotantalite; it is also a constituent of pyrochlor, euxenite and samarskite.
In the absence of these more respectable elements, the government fell into the hands of a gang of military adventurers and unscrupulous politicians, whose only object was to exploit the national resources for their own benefit.
Nergal is called the "raging king," the "furious one," and the like, and by a play upon his name - separated into' three elements Ne-urugal "lord of the great dwelling" - his position at the head of the nether-world pantheon is indicated.
On the other hand, there are elements in the poem which show that it is not entirely the work of a poor crowder; and these (notably references to historical and literary authorities, and occasional reminiscences of the literary tricks of the Scots Chaucerian school) have inclined some to the view that the text, as we have it, is an edited version of the minstrel's rough song story.
The universal consists of the non-different elements or attributes in the separate individuals, which alone exist substantially.
If we restrict attention to these non-different elements, the individual becomes for us the species, the genus, &c.; everything depends on the point of view from which we regard it.
But as the immigrants were of very different foreign nationalities, the country became a collection of heterogeneous ethnical elements, amid which the ruling Magyar race formed only a minority.
Thus, at the outset, the most heterogeneous elements were to be found both on the Left and Right.
Moreover, by refusing the royal terms, the Coalition had forced the crown into an alliance with the extreme democratic elements in the state.
Its result, had it passed, would have been to strengthen the representation of the Magyar and German elements, to reduce that of the Slovaks, and almost to destroy that of the Rumans and other non-Magyar races whose educational status was low.
The Uralian travels of Anthony Reguly (1843-1845), and the philological labours of Paul Hunfalvy and Joseph Budenz, may be said to have established it, and no doubt has been thrown on it by recent research, though most authorities regard the Magyars as of mixed origin physically and combining Turkish with Finno-Ugric elements.
It was followed by a series of profound investigations, in which Lagrange and Laplace alternately surpassed and supplemented each other in assigning limits of variation to the several elements of the planetary orbits.
The device known as the method of least squares, for reducing numerous equations of condition to the number of unknown quantities to be determined, had been adopted as a practically convenient rule by Gauss and Legendre; but Laplace first treated it as a problem in probabilities, and proved by an intricate and difficult course of reasoning that it was also the most advantageous, the mean of the probabilities of error in the determination of the elements being thereby reduced to a minimum.
Suppose that there are a number of arrangements of r terms or elements, the first of which a is always either A or not-A, the second b is B or not-B, the third c is C or not-C, and so on.
The only known type of algebra which does not contain arithmetical elements is substantially due to George Boole.
Euclid's Elements were first translated in the reign of Harun-al-Rashid (786-809), and revised by the order of Mamun.
The modern Roman Catholic Church is episcopal, for it preserves the bishops, whose potestas ordinis not even the pope can exercise until he has been duly consecrated; but the bishops as such are now but subordinate elements in a system for which "Episcopacy" is certainly no longer an appropriate term.
This was opposed by Trumbie and all the more progressive elements in the new State, who realized that the claim to Skutari knocked the bottom out of the whole Yugoslav case against Italy and Austria.
If round the origin of waves an ideal closed surface be drawn, the whole action of the waves in the region beyond may be regarded as due to the motion continually propagated across the various elements of this surface.
By the principle of superposition the whole effect may be found by integration of the partial effects due to each element of the surface, the other elements remaining at rest.
The phase of the resultant is midway between those of the extreme elements, that is to say, a quarter of a period behind that due to the element at the centre of the circle.
The utility of the curve depends upon the fact that the elements of arc represent, in amplitude and phase, the component vibrations due to the corresponding portions of the primary wave-front.
The dominance from the Yenisei to the Carpathians of a distinct style of art which, whatever its original elements may have been, seems to have taken shape as far east as the Yenisei basin is an additional argument in favour of a certain movement of population from the far north-east towards the south Russian steppes.
These, as has been seen, spoke a cognate dialect, and the tombs which belong to their period show exactly the same culture with Greek and Siberian elements.
The body of the state was now purged of all elements which would not blindly carry out the policy of the Committee.
Marignac's name is well known for the careful and exact determinations of atomic weights which he carried out for twenty-eight of the elements.
But when we look at the Elohim psalms more nearly, we see that they contain two distinct elements, Davidic psalms and psalms ascribed to the Levitical choirs (sons of Korah, Asaph).
The white population is broadly divisible into the British and Dutch elements, the percentage of other whites in 1904 being but 8.6.
There is reason to believe that carbonic acid is always one of these waste products, while the others contain the remainder of the carbon, the nitrogen, the hydrogen and the other elements which may enter into the composition of the protoplasm.
The new matter taken in to make good this constant loss is either a ready-formed protoplasmic material, supplied by some other living being, or it consists of the elements of protoplasm, united together in simpler combinations, which consequently have to be built up into protoplasm by the agency of the living matter itself.
The new form takes on the characters of that from which it arose; exhibits the same power of propagating itself by means of an offshoot; and, sooner or later, like its predecessor, ceases to live, and is resolved into more highly oxidated compounds of its elements.
The other important works of Fontenelle are his Elements de la geometrie de l'infini (1727) and his Apologie des tourbillons (1752).
The chief elements of the native diet are rice, fish and poultry; vegetables and pork are also eaten.
The seventy decrees of the council begin with a confession of faith directed against the Cathari and Waldenses, which is significant if only for the mention of a transubstantiation of the elements in the Lord's Supper.
He held a prominent place in the New School branch of the Presbyterians, to which he adhered on the division of the denomination in 1837; he had been tried (but not convicted) for heresy in 1836, the charge being particularly against the views expressed by him in Notes on Romans (1835) of the imputation of the sin of Adam, original sin and the atonement; the bitterness stirred up by this trial contributed towards widening the breach between the conservative and the progressive elements in the church.
Influenced by the prevailing philosophy of the day, they interpreted the phenomena of disease through its lights, and endeavoured from time to time to reduce the study of pathology to philosophical order when the very elements of philosophical order were wanting.
It is largely to researches on the bone marrow that we owe our present knowledge of the origin and the classification of the different cellular elements of the blood, both erythrocytes or red corpuscles, and the series of granular leucocytes or white corpuscles.
If the demand be for the red cells owing to loss from haemorrhage or any of the anaemias, the fatty marrow is rapidly replaced by cellular elements; this is mainly an active proliferation of the nucleated red cells, and gives rise to the erythroblastic type of marrow.
The term hypertrophy is used when the individual tissue elements become bigger to meet the demands of greater functional activity; hyperplasia, if there is an increase in the number of these elements; and pseudo-hypertrophy, when the specific tissue element is largely replaced by another tissue.
The tissues of the part become disorganized or destroyed, and their place is taken by the mass of warring cellular elements now recognized as pus.
These phagocytic cells carry out the complete removal of all the injured warring elements and the damaged tissues of the part.
Lying between the fibrin mass and the healthy tissues is a zone of injured and degenerated tissue elements, the result of the trauma.
The separated cells become intermingled with other tissue elements amongst which they lie dormant with their inherent power of proliferation in abeyance.
He holds that new growths arise, both before birth or at any subsequent period of life, by the separation of cells or clumps of cells from their normal position, and that in health there is a balance between the various tissues and tissue elements regulated by what he calls the " tissue-tension " of the part, i.e.
From whatever cause the resisting power of the tissue elements is thus weakened, the invasion of other tissue elements is then allowed to take place.
These being freed from the normal inhibiting power of the neighbouring elements, multiply and go on to the formation of a new growth.
Not only is this true of epithelial cells, but - the connective tissuecells of the supporting structure of cancerous growth, after repeated transplantation, may become so altered that a gradual evolution of apparently normal connective tissue into sarcomatous elements takes place, these giving rise to " mixed tumours."