His face expressed suffering.
She was much too cautious and expressed no interest.
Her entire mood was an-about face from the tentativeness she had expressed that morning.
It simply hadn't been expressed – by either of them.
His eyes expressed approval and the thin lips twitched in what she had grown to accept as a smile - fleeting as it was.
She looked over the car and expressed her approval, but her mind was consumed with guilt.
Cynthia expressed concern that Fred's newly acquired knowledge that the bone fragment was human might jeopardize his court-imposed decree.
And the fact remains that she was taught by a method of teaching language to the deaf the essential principles of which are clearly expressed in Miss Sullivan's letters, written while she was discovering the method and putting it successfully into practice.
She expressed ideas in signs before she learned language.
cerevisiae, is never found wild, but the wine yeasts occur abundantly in the soil of vineyards, and so are always present on the fruit, ready to ferment the expressed juice.
What was expressed by the whole of the count's plump figure, in Marya Dmitrievna found expression only in her more and more beaming face and quivering nose.
Jennifer, ignorant to the significance of the second entrance, expressed little interest in the opening.
The raised eyebrow expressed her disapproval of his sudden appearance in a way that made him want to touch her and remind her that he did what he wanted now.
In this table, unlike Table IV., amplitudes are all expressed as decimals of the mean value of the potential gradient for the corresponding season.
She's not leaving because he expressed disapproval, is she?
Dark hairs were already showing on his upper lip, and his whole face expressed impetuosity and enthusiasm.
Prince Andrew expressed his ideas so clearly and distinctly that it was evident he had reflected on this subject more than once, and he spoke readily and rapidly like a man who has not talked for a long time.
These views were expressed with extraordinary vigour and incisiveness in his Letter from Sydney (1829), published while he was still in prison, but composed with such graphic power that it has been continually quoted as if written on the spot.
When singing, Elisabeth chose music that expressed her feelings for Jackson.
No one expressed any sympathy for Billie and Willie, not even Baratto.
Pascal and other members of Port Royal openly expressed their doubts about the place allowed to God in the system; the adherents of Gassendi met it by resuscitating atoms; and the Aristotelians maintained their substantial forms as of old; the Jesuits argued against the arguments for the being of God, and against the theory of innate ideas; whilst Pierre Daniel Huet (1630-1721), bishop of Avranches, once a Cartesian himself, made a vigorous onslaught on the contempt in which his former comrades held literature and history, and enlarged on the vanity of all human aspirations after rational truth.
The higher the average income of the people (as expressed through per capita GNP), the higher the tax rate.
Instead of piety being expressed simply in a multitude of unrelated individual acts, it expressed itself in group action.
if the results were expressed in absolute measure.
On the 4th of June 1887 the official Vatican organ, the Osservatore Romano, published a letter written by Tosti to the pope conditionally retracting the views expressed in the pamphlet.
No serious mutinies have ever occurred in the Italian army, and the only results of the propaganda were occasional meetings of hoohgans, where Hervist sentiments were expressed and applauded, and a few minor disturbances among reservists unexpectedly called back to the colors.
The tribal feeling may be expressed as friendly within the tribe, courteous to other Andamanese if known, hostile to every stranger, Andamanese or other.
The modern doctrine of evolution or " evolving," as opposed to that of simple creation, has been defined by Prof. James Sully in the 9th edition of this encyclopaedia as a " natural history of the cosmos including organic beings, expressed in physical terms as a mechanical process."
- Of Leibnitz's immediate followers we may mention Lessing, who in his Education of the Human Race brought out the truth of the process of gradual development underlying: human history, even though he expressed this in a form inconsistent with the idea of a spontaneous evolution.
Their natural resemblances and differences are only to be expressed by disposing them as if they were branches springing from a common hypothetical centre.
They were expressed to have not merely appellate but original jurisdiction over causes (iii.
At the Vatican Council, a desire was expressed that he should be a priest (ib.).
This, when fully developed, consists of two parts, but inserted by a single ribbon-like tendon upon the hinder surface of the femur, near the end of its first third; the caudal part, femoro-caudalis, expressed by Garrod by the symbol A, arises from transverse processes of the tail; the iliac part (accessorofemoro-caudal of Garrod, with the symbol B), arises mostly from the outer surface of the postacetabular ilium.
In many birds the insertion is shifted from the femur to the neck of the tibia, in which case the " accessory head " is said to be absent, a condition expressed by Garrod by the symbol X.
discoveries expressed in the new terms of the orders Ciconiiformes and' Charadriiformes.
So large a portion of the Ethiopian subregion lies between the tropics that no surprise need be expressed at the richness of its fauna relatively to that of the last two subregions we have considered.
The relation between the b.h.p. and the torque on the driving-axle is 55 o B.H.P. =Tu., (9) It is usual with steam locomotives to regard the resistance R as including the frictional resistances between the cylinders and the driving-axle, so that the rate at which energy is expended in moving the train is expressed either by the product RV, or by the value of the indicated horse-power, the relation between them being 55 0 I.H.P. =RV (Io) or in terms of the torque 55 0 I.H.P.X€=RVe=TW (II) The individual factors of the product RV may have any value consistent with equation (to) and with certain practical conditions, so that for a given value of the I.H.P. R must decrease if V increases.
Aspinall's results are expressed by the formula S 5+ 50.8 12 r„ =2 -}-0 0278,L where r ro is the resistance in pounds per ton, S is the speed in miles per hour, and L is the length of the train in feet measured over the carriage bodies.
measured horizontally expressed as a percentage, or by the number of feet rising vertically in a mile.
They expressed the opinion that an improvement could be effected enabling the construction of many much-needed lines by an amendment of some of the provisions of the Light Railways Act, and by a reconsideration of the conditions under which financial or other assistance should be granted to such lines by the state and by local authorities.
But among the Jews two other forms of the idea expressed themselves in usages which have been perpetuated in Christianity, and one of which has had a singular importance for the Christian world.
In Isaiah both aspects - divine universal sovereignty and justice, taught by Amos, and divine loving-kindness to Israel and God's claims on His people's allegiance, taught by Hosea - are fully expressed.
I didn't mention his blossoming love life, but expressed concern over his serious problem of nightmares.
Or why they were here in the first place, as they expressed zero interest in the beauty of the area; Ouray's main attraction.
The second earliest dated letter expressed sorrow that the wedding could not take place in Boston and a gift was being shipped separately.
When her son Randy, visiting Bird Song over his Christmas college break, had expressed an interest in the sport, she had a fit.
If her mind wasn't so scattered, she'd have thought it odd he expressed none of the surprise she expected.
According to Alex, Gerald had expressed interest several years ago – when the summer cottage thing was only an idea.
With all that in mind, she was shocked when Alex expressed his impression after Sam left.
The symbols of compounds become very concise, as the number of atoms of one kind in a molecule can be expressed by a sub-index.
Dr Natterer, the chemist of the " Pola " expeditions, has expressed the opinion that the poverty of the pelagic fauna is solely due to the want of circulation in the depths.
During this, her second period, George Sand allowed herself to be the mouthpiece of others - " un echo qui embellissait la voix," as Delatouche expressed it.
In accordance with the expressed desire of the philosopher, his tomb was marked by the figure of a sphere inscribed in a cylinder, the discovery of the relation between the volumes of a sphere and its circumscribing cylinder being regarded by him as his most valuable achievement.
In these he expressed the opinion that the meaning of words was natural, not fixed by man.
We may therefore assume that, in acts of public worship at any rate, prayer and its magico-religious congeners are at all stages resorted to as a "means of grace," even though such grace do not constitute the expressed object of petition.
The gradient or grade of a line is the rate at which it rises or falls, above or below the horizontal, and is expressed by stating either the horizontal distance in which the change of level amounts to r ft., or the amount of change that would occur in some selected distance, such as roo ft., r000 ft.
The earlier usage of the Armenians is expressed in the two following rules recorded against them by a renegade Armenian prelate named Isaac, who in the 8th century went over to the Byzantine church: "Christ did not hand down to us the teaching to celebrate the mystery of the offering of the bread in church, but in an ordinary house, and sitting at a common table.
An astringent fluid, known as shibu, rich in tannin, is expressed from the green fruit and used in various industries.
The binomial theorem is a celebrated theorem, originally due to Sir Isaac Newton, by which any power of a binomial can be expressed as a series.
He expressed surprise that a man of such views as Zwingli should wish brotherly relations with the Wittenberg reformers" (Walker, The Reformation, p. 174).
Her poise expressed both dignity and grace.
His face expressed more satisfaction with himself and those around him, his smile and glance were brighter and more attractive.
Power is the collective will of the people transferred, by expressed or tacit consent, to their chosen rulers.
Until now she would have sworn that he was the one who never expressed his feelings.
But no - if his intentions were ill willed, he would hardly have expressed his interest to an obvious town gossip.
Pasteur found that, when cane sugar was fermented by yeast, 49.4% of carbonic acid and 51.1% of alcohol were produced; with expressed yeast juice cane sugar yields 47% of carbonic acid and 47.7% of alcohol.
The resemblance was so close that Prinsep called the alphabet he was deciphering the Pali alphabet, and the language expressed in it he called the Pali language.
He expressed no emotion, simply dropped his eyes to hers once more.
Even Quinn showed more positive emotion than previously expressed.
Gabriel was reminded of the many times he'd expressed something human to the goddess he'd loved for thousands of years.
In the potential curves of the diagram the ordinates represent the hourly values expressed - as in Tables II.
The good sense and clearness of the views which he expressed caused attention to be paid to his desire to be again employed in India.
Some see the guarantee, or at least the indication, of infallibility in the consensus of the Church (quod semper, ubique, et ab omnibus) expressed from time to time in general councils; others see it in the special grace conferred upon St Peter and his successors, the bishops of Rome, as heads of the Church; others again see it in the inspired Scriptures, God's Word.
He appeared on the 6th of March before the standing committee of the two Houses to explain his conduct, when he stated that he had come over because he saw danger to the Protestant religion in the king's service, and expressed his willingness to take the Covenant.
The struggle of the Bohemians against Rome continued uninterruptedly, and the position of Podébrad became a very difficult one when the young king Ladislas, who was crowned in 1453, expressed his sympathies for the Roman Church, though he had recognized the compacts and the ancient privileges of Bohemia.
In 1831, from a study of the specific heats of compounds, he formulated "Neumann's law," which expressed in modern language runs: "The molecular heat of a compound is equal to the sum of the atomic heats of its constituents."
He had expressed an opinion that the true art of memory was not to be gained by technical devices, but by a philosophical apprehension of things; and the cardinal de Berulle, the founder of the Congregation of the Oratory, was so struck by the tone of the remarks as to impress upon the speaker the duty of spending his life in the examination of truth.
The magisterial views seem to have prevailed in the professoriate, which formally in March 1642 expressed its disapprobation of the new philosophy as well as of its expositors.
5), and with a supreme significance for the religious life of the people which is expressed in the figure of the living waters issuing from under the threshold of the house (Ezek.
Their peculiar business is expressed by the term" ruling elders."20 II.
The latter, about the time of Elizabeth's succession, expressed his hope that the bishops would become pastors, labourers and watchmen; and that the great riches of bishoprics would be diminished and reduced to mediocrity; that, being delivered from courtly and regal pomp, the bishops might take care of the flock of Christ.
This conception is expressed in George Eliot's lines: ", O, may I join the choir invisible Of those immortal dead who live again In minds made better by their presence: live In pulses stirred to generosity, In deeds of daring rectitude, in scorn For miserable aims that end with self, In thoughts sublime that pierce the night like stars, And with their mild persistence urge man's search To vaster issues."
That this individual life of all of us is not something limited in its temporal expression to the life that now we experience, follows from the very fact that here nothing final or individual is found expressed (pp. 144-146).
Hunter states that the Dravidian tribes were driven southwards in Hindustan, and that the grammatical relations of their dialects are " expressed by suffixes," which is true as to the Australian languages.
There are words for the elementary numbers, one, two, three; but " four " is usually expressed by " two-two."
They resigned their positions as councillors of state, and expressed their grievances personally to Margaret and by letter to the king in Madrid, asking for the dismissal of Granvelle.
na-nun, one; nar, two; and ne', three, or variants of these; all higher arithmetical ideas being expressed by the word kerpn, which means " many."
Although this idea had often been expressed by others, and by Seward himself in his speech of 1848, yet he was severely criticized, and four days later he sought to render this statement innocuous also.
The attitude of Paul toward glossolaly among his converts strikingly resembles Plato's opinion as expressed in the Timaeus, p. 72, of the enthusiastic ecstasies of the ancient µav ns (soothsayer).
The latter play was 1 Some doubt has been expressed as to whether the eggs are extruded or hatched within the body.
Douglas Ogilby (Catalogue of Australian Mammals, p. 1, Sydney, 1902), but expressed the hope "that further inquiries might be made by naturalists in Australia as to the actual finding of such eggs in the burrows, so that this most interesting point might be finally settled."
His principles are expressed in the admirable letter to Andre Fremyot of October 1604.
Francis Bacon expressed his conviction that heat consists of a kind of motion or "brisk agitation" of the particles of matter.
The galvanometer being so adjusted that a current of definite strength through one of the coils gives a definite deflection of the needle, the amount of leakage expressed in terms of the insulation resistance of the wires is given by the formula.
If L and N are the inductances of any two circuits which have a coefficient of mutual inductance M, then M/-/ (LN) is called the coefficient of coupling of the circuits and is generally expressed as a percentage.
The National Telephone Company again applied to parliament for powers to lay wires underground; public discontent with inadequate telephone services was expressed, and at the same time the competition of the telephone with the Post Office telegraph became more manifest.
It also expressed willingness that the companies should have rights of way in the streets.
The London County Council, according to the statement of its comptroller, was disturbed by the hope expressed by the manager of the company, that the holders of the company's ordinary shares would obtain the par value of their shares in 1911.
The emperors real weakness was in Germany, where his subjects openly expressed their discontent.
The European ferment of ideas which preceded the French Revolution expressed itself in men like Alfieri, the fierce denouncer of tyrants, Beccaria, the philosopher of criminal jurisprudence, Volta, the physicist, and numerous political economists of Tuscany.
moral degradation, as expressed in the writings of bonarl.
In the long and important debate upon foreign policy in the Italian Chamber of Deputies (6th to 9th December) the fear was repeatedly expressed lest Bismarck should seek to purchase the support of German Catholics by raising the Roman question.
At the end of May the pope, in an allocution to the cardinals, had spoken of Italy in terms of unusual cordiality, and had expressed a wish for peace.
In Great Britain the curvature is defined by stating the length of the radius, expressed in chains (i chain=66 ft.), in America by stating the angle subtended by a chord ioo ft.
The solidarity of race or family was expressed in the old tradition reflected in Deut.
But Ezekiel expressed the strong reaction which had set in against this belief in its older forms. He denies that the individual ever dies for the sins of the father.
1) and expressed itself as a word of instruction of Yahweh (torah); see Isa.
The ideas of expiation and atonement so prevalent in Ezekiel's scheme, which there find expression in the half-yearly sacrificial celebrations, are expressed in Lev.
These differences have given rise to a supposed multiplicity of species, expressed by the names C. lycaon (Central Europe), C. laniger and C. niger (Tibet), the C. occidentalis, C. nubilus, C. mexicanus, &c., of North America, and the great blackish-brown Alaskan C. pambasileus, the largest of them all.
The great reflecting telescope at Dorpat was manufactured by him, and so great was the skill he attained in the making of lenses for achromatic telescopes that, in a letter to Sir David Brewster, he expressed his willingness to furnish an achromatic glass of 18 in.
He further expressed the belief that the dark lines D of the solar spectrum coincide with the bright lines of the sodium flame.
His repugnance to public life had been strongly expressed to his father in a letter of a very early date, in which he begged that the money which a seat in the House of Commons would cost might be expended in a mode more agreeable to him.
The nebular theory is a noble speculation supported by plausible argument, and the verdict of science on the whole subject cannot be better expressed than in the words of S.
The chief characteristic of the Diptera is expressed in the name of the Order, since, with the exception of certain aberrant and apterous forms, flies possess but a single pair of membranous wings, which are attached to the meso-thorax.
It has been proposed to adopt the joule, with the symbol j, as thermochemical unit for small quantities of heat, large amounts being expressed in terms of the kilojoule, Kj =100o j.
With a touch of vanity he expressed the fear lest "the coolness of fancy that attends advanced years should make me risk the reputation I had acquired."
Later constitutional theory held that the repression of civil discord was also one of the motives for the institution of a dictatorship. Such is the view expressed by Cicero in the De legibus (iii.
The prefaces and notes to both these expressed the view that Holy Scripture is the only rule of doctrine, and that justification is by faith alone.
Thus " the son of the king " is more commonly expressed by b`ra dh`malka or b`reh d`malka than by bar mailed, whereas the latter type would alone be permissible in Hebrew.
The tradition of the mitre as an episcopal ornament has, nevertheless, been continuous in the Church of England, " and that on three lines: (i) heraldic usage; (2) its presence on the head of effigies of bishops, of which a number are extant, of the 16th, 17th, 18th and 19th centuries; (3) its presence in funeral processions, where 1 In Father Braun's opinion, expressed to the writer, this mitre, which was formerly at Sens, belongs probably to the 13th century.
These are unequivocally pantheistic in tone, and the desire of the soul to escape and rest with God is expressed with all the fervour of Eastern poetry.
In yet another incident the Philistines maintained a garrison in Bethlehem, and David expressed a wish for a drink from its well.
- Robertson Smith's later views subsequent to 1877 (when he wrote the article on David for this Encyclopaedia) were expressed partly in the Old Test.
He first thought of becoming a minister at a very early date, if we may believe a story contained in the Memoires of the duchesse d'Abrantes, to the effect that in May 1789 the queen tried to bribe him, but that he refused this and expressed his wish to be a minister.
expressed it, "where a: Presbyterian and myself shall be like Castor and Pollux, the one up and the other down," and to which also a very meagre salary was attached.
The only other algebraical symbol is A for minus; plus being expressed by merely writing terms one after another.
They are not expressed in terms which satisfy our canons of scientific accuracy.
There are few if any conceptions in economics which cannot be expressed in it without depleting the ordinary vocabulary.
Nasir Lek's message and the urgent representations of Firdousi's friends had the desired effect; and Mahmud not only expressed his intention of offering full reparation to the poet, but put his enemy Maimandi to death.
The most famous outcome of his inquiries is the law known as Weber's or Fechner's law which may be expressed as follows:- "In order that the intensity of a sensation may increase in arithmetical progression, the stimulus must increase in geometrical progression."
She also provoked a dangerous enemy in John Knox by her expressed contempt for a letter which he had written to her, but the first revolt against her authority arose from an attempt to establish a standing army.
The lakes of Albano and Nemi were probably formed by volcanic explosions at the margin of the great crater; though a view has also been expressed that the basins are the result of subsidence.
(I) An indigenous script expressed in characters of which only a very small percentage are identical, or even obviously connected, with those of any other script.
Carrying on the work from the anatomical point at which he had left it, correcting his errors, and utilizing to the fullest extent the observations of Keyserling and Blasius, to which reference has already been made, Muller, though hampered by mistaken notions of which he seems to have been unable to rid himself, propounded a scheme for the classification of this group, the general truth of which has been admitted by all his successors, based, as the title of his treatise expressed, on the hitherto unknown different types of the vocal organs in the Passerines.
The theory of the government, a theory expressed throughout the whole commercial career of the republic, the theory which made Venice a rigidly protective state, was that the Levant trade belonged solely to Venice and her citizens.
In May 1533 he expressed approval of Henry VIII.'s marriage with Anne Boleyn in a sermon preached before the king.
The area of the complete curve is 2a 2, and the length of any arc may be expressed in the form f(1 - x 4) - i dx, an elliptic integral sometimes termed the lemniscatic integral.
Any signification of a desire to terminate the tenancy, whether expressed as " notice " or not, will bring it to an end.
The Conveyancing Act 1881 provides that, as regards conveyances subsequent to 1881, unless a contrary intention is expressed, a lease of " land " is to be deemed to include all buildings, fixtures, easements, &c., appertaining to it; and, if there are houses or other buildings on the land demised, all out-houses, erections, &c., are to pass with the lease of the land.
Expressed both absolutely and as percentages of the price averaged from the 1st of October to the 31st of July, the range of movement, standard deviation, and mean weekly movement calculated between the times mentioned above (October 1st to July 31st), after diminishing significantly for some years after the later 'sixties, have risen appreciably on the whole of late years.
In this table measurements of price movements stated both absolutely and as percentages of price levels are given, because authorities have expressed doubts as to whether the former or the latter might be expected to remain constant, other things being equal, when price rose.
The sole piece of evidence, from which probable conclusions may be drawn, is that three separate measurements of price fluctuations over some forty years reveal a growing unsteadiness of late, whether they be expressed absolutely or as percentages of price.
Mr. Harding's inaugural address, and his first message to Congress, delivered in person on April 12, voiced his desire to return to " normalcy," as he expressed it.
But he expressed himself warmly in favour of active cooperation with other nations of the world, and by accepting the invitation to participate in interAllied councils indicated that he would avoid a policy of isolation.
Bergman (1784) Charles Hatchett (1798) and others also expressed views with regard to the constitution and origin of bitumens.
But new deposits are continually being exploited, and there may be others as yet unknown, which would entirely alter any view that might be expressed at the present time in regard to the probable duration of the world's supply of oil and gas.
As early as 1804, Humboldt expressed the opinion that petroleum was produced by distillation from deep-seated strata, and Karl Reichenbach in 1834, suggested that it was derived from the action of heat on the turpentine of pine-trees, whilst Brunet, in 1838, adumbrated a similar theory of origin on the ground of certain laboratory experiments.
The predominance of the nobility in this way became as characteristic of feudalism in the Latin kingdom of Jerusalem as the supremacy of the crown was of contemporary feudalism in England; and that predominance expressed itself in the position and powers of the high court, in which the ultimate sovereignty resided.
The truth of the matter, however, has been expressed by Cervantes, through the mouth of the Canon in Don Quixote: " There is no doubt there was such a man as the Cid, but much doubt whether he achieved what is attributed to him."
A somewhat different criticism must be passed on the Facetiae, a collection of humorous and indecent tales expressed in such Latinity as Poggio could command.
7); its positive assertion is not in accord with the doubt expressed in iii.
This disagreement comes largely from the attempts made to find definitely expressed Greek philosophical dogmas in the book; such formulas it has not, but the general air of Greek reflection seems unmistakable.
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.
A fifth element is the position of the pericentre, which may be expressed by its angular distance XFN from the ascending node.
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.
Thus he based Judaism on love, not on knowledge; love was the bond between God and man, and man's fundamental duty was love as expressed in obedience to God's will.
The laws of chemical combination were solved, in a measure, by John Dalton, and the solution expressed as Dalton's " atomic theory."
the views therein expressed were ignored both by their own and the succeeding generation.
The same views were expressed by Cannizzaro, and also by A.
The distribution of weight in chemical change is readily expressed in the form of equations by the aid of these symbols; the equation 2HC1+Zn =ZnCl2+H2, for example, is to be read as meaning that from 73 parts of hydrochloric acid and 65 parts of zinc, 136 parts of zinc chloride and 2 parts of hydrogen are produced.
Two cases then arise: (I) the properties may be expressed as linear functions of the composition, the terminal values being identical with those obtained for the individual components, and there being a break in the curve corresponding to the absence of mixed crystals; or (2) similar to (I) except that different values must be assigned to the terminal values in order to preserve collinearity.
If we wish to know what Wagner means, we must fight our way through his drama to his music; and we must not expect to find that each phrase in the mouth of the actor corresponds word for note with the music. That sort of correspondence Wagner leaves to his imitators; and his views on " Leit-motifhunting," as expressed in his prose writings and conversation, are contemptuously tolerant.
No doubt of the Pauline authorship was expressed in ancient times; nor is there any lack of early use by writers who make no direct quotation, to raise doubts as to the genuineness of the epistle.
The influence of Schleiermacher, whose pupil Leonhard Usteri in his Entwickelung der paulinischen Lehrbegriffs (1824) expressed strong doubts as to Ephesians, carried weight.
One has hitherto supposed that he was related to the Mediterraneans, the race to which the Bronze Age Greeks and Italians belonged; but this supposed connexion may well break down in the matter of skull form, as the Hittite skull, like that of the modern Anatolian, probably inclined to be brachycephalic. whereas that of the Mediterranean inclined in the other direction, And now the Bohemian Assyriologist Prof. Hrozny has brought forward evidence s that the cuneiform script adopted by the Hittites from the Mesopotamians expressed an Indo-European tongue, nearly akin to Latin!
Whether the national hieroglyphic system of the Hittites expressed the same Indo-European language as, according to Hrozny, their cuneiform does, we do not know, as further attempts to elucidate it made by Campbell Thompson 11 and Cowley," while in themselves very interesting experiments, do not seem to take us further than previous attempts by Sayce and others.
This altitude was expressed in isbas or inches each equivalent to 1° 42' 50".
This freedom of the will is clearly expressed in Yasna, 31, I I: "Since thou, 0 Mazda, didst at the first create our being and our consciences in accordance with thy mind, and didst create our understanding and our life together with the body, and works and words in which man according to his own will can frame his confession, the liar and the truth-speaker alike lay hold of the word, the knowing and the ignorant each after his own heart and understanding.
In the Titanotheroidea the dentition may be expressed by the formula i: oru, ci, p T 4,, my.
The characters of the genus may be expressed as follows in a more detailed manner.
The individualistic view is expressed in xv.
He had not based his case against the Transvaal on the letter of the Conventions, and regarded the employment of the word "suzerainty" merely as an "etymological question," but he realized keenly that the spectacle of thousands of British subjects in the Transvaal in the condition of "helots" (as he expressed it) was undermining the prestige of Great Britain throughout South Africa, and he called for "some striking proof" of the intention of the British government not to be ousted from its predominant position.
Sceptical views are expressed in Job, Prov.
By the treaty of Paris, signed on the 10th of December, Spain " relinquished " the island to the United States in trust for its inhabitants; the temporary character of American occupation being recognized throughout the treaty, in accord with the terms of the American declaration of war, in which the United States disclaimed any intention to control the island except for its pacification, and expressed the determination to leave the island thereupon to the control of its people.
The definitions of the finite ordinals can be expressed without use of the corresponding cardinals, so there is no essential priority of cardinals to ordinals.
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.
Lord Aberdeen made no secret of his dislike for the Turks, and openly expressed his disbelief in the reality of their reforms; and in January 1853 the tsar, in conversation with Sir Hamilton Seymour, the British ambassador at St Petersburg, spoke of the Ottoman Empire as " the Sick Man," and renewed the proposals for a partition made in 1844.
As the diplomatic crisis approached, spies were sent into Prussia, and simultaneously with the orders for preliminary concentration the marshals received private instructions, the pith of which cannot be better expressed than in the following two quotations from Napoleon's correspondence: " Mon intention est de concentrer toutes mes forces sur l'extremite de ma droite en laissant tout l'espace entre le Rhin et Bamberg entierement degarni, de maniere a avoir pres de 200,000 hommes reunis sur un meme champ de bataille; mes premieres marches menacent le coeur de la monarchie prussienne " (No.
This symbolism is expressed in the words used, at least since the 10th century, by the consecrator in delivering the pastoral staff at the consecration of a bishop and the benediction of an abbot.
Thirty years after the Ridsdale judgment, the ritual confusion in the Church of England was worse than ever, and the old ideal expressed in the Acts of Uniformity had given place to a desire to sanctify with some sort of authority the parochial "uses" which had grown up. In this respect the dominant opinion in the Church, intent on compromise, seems to have been expressed in the Report presented in 1908 to the convocation of the province of Canterbury by the sub-committee of five bishops appointed to investigate the matter, namely, that under the Ornaments Rubric the vestments prescribed in the first Prayer Book of Edward VI.
Frederick expressed the desire to make the personal acquaintance of his conqueror; and Charles X.
This phenomenon he explained as a "repulsion from radiation," and he expressed his discovery in the statement that in a vessel exhausted of air a body tends to move away from another body hotter than itself.
He expressed himself plainly during the canvass on the questions of slavery and the bank, at the same time voting, perhaps with a touch of bravado, for a bill offered in 1836 to subject abolition literature in the mails to the laws of the several states.
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.
If al, a2, ...a, n be the roots of f=o, (1, R2, -Ai the roots of 0=o, the condition that some root of 0 =o may qq cause f to vanish is clearly R s, 5 =f (01)f (N2) ï¿½ ï¿½;f (Nn) = 0; so that Rf,q5 is the resultant of f and and expressed as a function of the roots, it is of degree m in each root 13, and of degree n in each root a, and also a symmetric function alike of the roots a and of the roots 1 3; hence, expressed in terms of the coefficients, it is homogeneous and of degree n in the coefficients of f, and homogeneous and of degree m in the coefficients of 4..
Now by the theory of symmetric functions, any symmetric functions of the mn values which satisfy the two equations, can be expressed in terms of the coefficient of those equations.
Hence, finally, the resultant is expressed in terms of the coefficients of the three equations, and since it is at once seen to be of degree mn in the coefficient of the third equation, by symmetry it must be of degrees np and pm in the coefficients of the first and second equations respectively.
The partitions with one bipart correspond to the sums of powers in the single system or unipartite theory; they are readily expressed in terms of the elementary functions.
= (A11+A22)n by the substitutions 51 = A l, E1+ï¿½1 2, 52 = A2E1+ï¿½2E2, the umbrae Al, A2 are expressed in terms of the umbrae al, a 2 by the formulae A l = Alai +A2a2, A2 = ï¿½la1 +ï¿½2a2ï¿½ We gather that A1, A2 are transformed to a l, a 2 in such wise that the determinant of transformation reads by rows as the original determinant reads by columns, and that the modulus of the transformation is, as before, (A / .c).
is expressed in terms of new quantities X, Y, Z, ...
is expressed in terms of other new quantities X', Y', Z', ....
+ ï¿½ï¿½ï¿½, Z = v16+v2%/+v3" +ï¿½ï¿½ï¿½, wherein it should be noticed that new quantities are expressed in terms of the old, as regards the latter set, and not vice versa."
If u, a quantic in x, y, z, ..., be expressed in terms of new variables X, Y, Z ...; and if, n,, ..., be quantities contragredient to x, y, z, ...; there are found to exist functions of, n, ?, ..., and of the coefficients in u, which need, at most, be multiplied by powers of the modulus to be made equal to the same functions of E, H, Z, ...
Sylvester showed that the quintic might, in general, be expressed as the sum of three fifth powers, viz.
Now, evidently, the third transvectant of f, expressed in this form, with the cubic pxgxrx is zero, and hence from a property of the covariant j we must have j = pxgxrx; showing that the linear forms involved are the linear factors of j.
The general equation of degree 5 cannot be solved algebraically, but the roots can be expressed by means of elliptic modular functions.
When a z and the invariants B and C all vanish, either A or j must vanish; in the former case j is a perfect cube, its Hessian vanishing, and further f contains j as a factor; in the latter case, if p x, ax be the linear factors of i, f can be expressed as (pa) 5 f =cip2+c2ay; if both A and j vanish i also vanishes identically, and so also does f.
In general the coefficient, of any product A n A m A 7, 3 ..., will have, as coefficient, a seminvariant which, when expressed by partitions, will have as leading partition (preceding in dictionary order all others) the partition (Tr1lr2lr3ï¿½..).
Solving the equation by the Ordinary Theory Of Linear Partial Differential Equations, We Obtain P Q 1 Independent Solutions, Of Which P Appertain To S2Au = 0, Q To 12 B U =0; The Remaining One Is Ab =Aobl A 1 Bo, The Leading Coefficient Of The Jacobian Of The Two Forms. This Constitutes An Algebraically Complete System, And, In Terms Of Its Members, All Seminvariants Can Be Rationally Expressed.
The number of different symbols a, b, c,...denotes the the covariants are homogeneous, but not in general isobaric functions, of the coefficients of the original form or forms. Of the above general form of covariant there are important transformations due to the symbolic identities: - (ï¿½b) 2 2)2 = a b - a b; (xï¿½ = as a consequence any even power of a determinant factor may be expressed in terms of the other symbolic factors, and any uneven power may be expressed as the product of its first power and a function of the other symbolic factors.
to make an attempt to reconcile the church with the republic. He invited the officers of the Mediterranean squadron to lunch at Algiers, and, practically renouncing his monarchical sympathies, to which he clung as long as the comte de Chambord was alive, expressed his support of the republic, and emphasized it by having the Marseillaise played by a band of his Peres Blanes.
He had there collected twenty-six relations or stories of the same description as that of the drum, in order to establish, by a series of facts, the opinion which he had expressed in his Philosophical Considerations.
In astronomical practice the masses of the planets are commonly expressed as fractions of the mass of the sun, the latter being taken as unity.
If m, and m 2 are the strengths of two poles, d the distance between them expressed in centimetres, and f the force in dynes, f=ml m2/d2 (I) The force is one of attraction or repulsion, according as the sign of the product m l m 2 is negative or positive.
The opposite and parallel forces acting on the poles are always equal, a fact which is sometimes expressed by the statement that the total magnetism of a magnet is zero.
If the coil has the form of a ring of mean radius r, the length will be 21rr, and the field inside the coil may be expressed as H = 2ni/r.
The closed figure a c d e a is variously called a hysteresis curve or diagram or loop. The area f HdB enclosed by it represents the work done in carrying a cubic centimetre of the iron through the corresponding magnetic cycle; expressed in ergs this work is I HdB.
After pointing out that, since the magnetization of the metal is the quantity really concerned, W is more appropriately expressed in terms of I, the magnetic moment per unit of volume, than of B, he suggests an experiment to determine whether the mechanical work required to effect the complete magnetic reversal i Phil.
The standard induction in reference to determinations of hysteresis is generally taken as 2500, while the loss is expressed in watts per lb at a frequency of ioo double reversals, or cycles, per second.
In many experiments, however, different inductions and frequencies are employed, and the hysteresis-loss is often expressed as ergs per cubic centimetre per cycle and sometimes as horse-power per ton.
In order to save arithmetical labour it is convenient to be provided with conversion factors for reducing variously expressed results to the standard form.
F=27r12+HI expressed as dynes per square centimetre.
The strength of the field is proportional to the swing of the galvanometer-needle, and, when the galvanometer is calibrated, can be expressed in C.G.S.
When the saturation value of I has been reached, the relation of magnetic induction to magnetic force may be expressed by B = H +constant.
This is at once evident when the tractive force due to magnetization is expressed as 27rI 2 -}-HI.
Ann., 1880, 11, 399) that in weak fields the relation of the magnetization I to the magnetizing force H is approximately expressed by an equation of the form I =aH +bH2, or K=I/H =a+bH, whence it appears that within the limits of Baur's experiments the magnetization curve is a parabola, and the susceptibility curve an inclined straight line, x being therefore a known function of H.
The whole of the rod will therefore be subject to a compressive longitudinal stress P, the associated contraction R, expressed as a fraction of the original length, being R = P/M = (B 2 -H2)/87-M, where M is Young's modulus.
The following table gives some of their results, the specific resistance of the bismuth being expressed in C.G.S.
the Westminster, a decided judgment is passed on them, that, they are not " to be any otherwise approved or made use of than other human writings," a milder verdict is expressed regarding them in many other quarters, e.g.
The limitation scheme he opposed, on the ground that monarchy under the conditions expressed in it would be an absurdity.
Instead of following the motion of each individual part of a material system, he showed that, if we determine its configuration by a sufficient number of variables, whose number is that of the degrees of freedom to move (there being as many equations as the system has degrees of freedom), the kinetic and potential energies of the system can be expressed in terms of these, and the differential equations of motion thence deduced by simple differentiation.
The religious significance of the plague of drought and locusts is expressed in ch.
Maret accompanied Napoleon through most of his campaigns, including that of 1809; and at its close he expressed himself in favour of the marriage alliance with the archduchess Marie Louise of Austria, which took place in 181o.
It is understood, unless otherwise expressed, that the judgment shall be in accordance with the law by which civilized nations have agreed to be bound, whenever such law is applicable.
The Brazilian deputies on arriving in Lisbon expressed dissatisfaction with the Cortes for having begun the framing of the constitution before their arrival, for Brazil could not be treated as a secondary part of the monarchy.
This theory is clearly stated by Cranmer: " In the New Testament he that is appointed bishop or priest needed no consecration, by the Scripture, for election or appointment thereto is sufficient."2 This view, widely held among modern scholars, has strong support in the fact that the words used for ordination in the first three centuries (xaporov€ v, xaOcvTav€CV, «Afpova9at, constituere, ordinare) also expressed appointment to civil office.
The governor expressed his views to the prime minister that the Natal government ought to give the British government every support, and Colonel Hime replied that their support would be given, but at the same time he feared the consequences to Natal if, after all, the British govern m ent should draw back.
The fact that the channels of thought during the middle ages were determined in this way is usually expressed by saying that reason in the middle age is subject to authority.
And accordingly it gave rise to the three great doctrines which divided the medieval schools: Realism of the Platonic type, embodied in the formula universalia ante rein; Realism of the Aristotelian type, universalia in re; and Nominalism, including Conceptualism, expressed by the phrase universalia post rem, and also claiming to be based upon the Peripatetic doctrine.
The views which he expressed in his commentary on the pseudo-Boetian treatise, De Trinitate, are certainly much more important than the mediatizing systems already referred to.
difference of opinion as to his system, some, like Ritter and Erdmann, regarding it as a moderate form of Realism - a return indeed to the position of Aristotle - while others, like Cousin, Remusat, Haureau and Ueberweg, consider it to be essentially Nominalistic, only more prudently and perhaps less consistently expressed than was the case with Roscellinus.
The chief characteristic of this criticism is well expressed in the name bestowed on Duns by his contemporaries - Doctor subtilis.
These statesmen expressed in general terms their approval of his purpose, but he went entirely on his own account, clothed at first with no official authority.
Matthian system, desired, as they expressed it, " a king whose beard they could hold in their fists," and they found a monarch after their own heart in Wladislaus Jagiello, since 1471 king of Bohemia, who as Wladislaus II.
The visible signs of this contemptuous point of view were (1) the suspension of the august dignity of palatine, which, after the death of Tamas Nadasdy, " the great palatine," in 1562, was left vacant for many years; (2) the abolition or attenuation of all the ancient Hungarian court dignitaries; (3) the degradation of the capital, Pressburg, into a mere provincial town; and (4) the more and more openly expressed determination to govern Hungary from Vienna by means of foreigners, principally German or Czech.
The grammatical forms are expressed, as in Turkish, by means of affixes modulated according to the high or low vowel power of the root or chief syllables of the word to which they are appended-the former being represented by e, o, S, ii, i l l, the latter by a, d, o, 6, u, it; the sounds e, i, i are regarded as neutral.
The long-sought cause of the "great inequality" of Jupiter and Saturn was found in the near approach to commensurability of their mean motions; it was demonstrated in two elegant theorems, independently of any except the most general considerations as to mass, that the mutual action of the planets could never largely affect the eccentricities and inclinations of their orbits; and the singular peculiarities detected by him in the Jovian system were expressed in the so-called "laws of Laplace."
The theory of probabilities, which Laplace described as common sense expressed in mathematical language, engaged his attention from its importance in physics and astronomy; and he applied his theory, not only to the ordinary problems of chances, but also to the inquiry into the causes of phenomena, vital statistics and future events.
Expressed Equations.-The simplest forms of arithmetical equation arise out of abbreviated solutions of particular problems. In accordance with ï¿½ 15, it is desirable that our statements should be statements of equality of quantities rather than of numbers; and it is convenient in the early stages to have a distinctive notation, e.g.
combine the separate quantities or numbers expressed in terms of x as unit into a single quantity or number so expressed, obtaining sx =10.
(iv.) If P and Q can be expressed in the forms pL and qL, where p and q are integers, R will be equal to (p-kq)L, which is both less than pL and less than qL.
It can be shown by the above reasoning that this can be expressed as a series of terms containing descending powers of n, the first term being nr+1/(r+I).
Considered in this way, the relations between the coefficients of the powers of x in a series may sometimes be expressed by a formal equality involving the series as a whole.
This is expressed by saying that the sequence converges to (x+h)" as its limit; it may be stated concisely in any of the three ways, (x+h) n =lim(x"+n(1)xn-lh+....+ n(T)xn-rhr+ï¿½ï¿½.),(x+h)n =lim Sr, Sr. (x+h)n.
a number which cannot be expressed as the ratio of two integers.
Finally, there is a law of absorption expressed by a+ab = a.
If B 1 = E(3e, there is a law of addition expressed by A1+B1 = (a, +ï¿½ei =B1+Ai; this law of addition is associative as well as commutative.
Various special algebras (for example, quaternions) may be expressed in the notation of the algebra of matrices.
Archimedes' problem of dividing a sphere by a plane into two segments having a prescribed ratio,was first expressed as a cubic equation by Al Mahani, and the first solution was given by Abu Gafar al Hazin.
It further expressed its inability to believe that the Powers wished to impose " a treaty concluded unknown to it by third parties, and whose clauses have never been communicated to it."
Before proceeding to special cases it may be well to call attention to some general properties of the solution expressed by (2) (see Bridge, Phil.
At the focal point (E =o, n = o) all the secondary waves agree in phase, and the intensity is easily expressed, whatever be the form of the aperture.
Analytically expressed ff+ co x I 2 d dn=ff dxdy= A (9) We have seen that Io (the intensity at the focal point) was equal to A 2 /X 2 f2.
If r, or z, be infinite, Jo(z), J 1 (z) vanish, and the whole illumination is expressed by 71-R 2, in accordance with the general principle.
If the angular interval between the components of a double star were equal to twice that expressed in equation (15) above, the central disks of the diffraction patterns would be just in contact.
If 2R be the diameter of the objectglass and D the distance of the object, the angle subtended by AP is E/D, and the angular resolving power is given by X/2 D sin a = X/2 R (3) This method of derivation (substantially due to Helmholtz) makes it obvious that there is no essential difference of principle between the two cases, although the results are conveniently stated in different forms. In the case of the telescope we have to deal with a linear measure of aperture and an angular limit of resolution, whereas in the case of the microscope the limit of resolution is linear, and it is expressed in terms of angular aperture.
If 8 and 4' denote the angles with the normal made by the incident and diffracted rays, the formula (5) still holds, and, if the deviation be reckoned from the direction of the regularly reflected rays, it is expressed as before by (0+0), and is a minimum when 8 = 0, that is, when the diffracted rays return upon the course of the incident rays.
In the present application 4' is not necessarily equal to; but if P correspond to a line upon the grating, the difference of retardations for consecutive positions of P, so far as expressed by the term of the first order, will be equal to mX (m integral), and therefore without influence, provided v (sin 0-sin0') = nzX (11), where a denotes the constant interval between the planes containing the lines.
The intensity I 2, the quantity with which we are principally concerned, may thus (be expressed I 2 = 3 fcos27rv 2 .dv} 2 2 t 2 These integrals, taken from v =o, are (known as Fresnel's integrals; we will denote them by C and S, so that C = fo cos 27rv 2 .dv, S = fjsinv 2 .dv.
The law of diminution when V is moderately large is easily expressed with the aid of the series (16), (17) for G, H.
The intensity may be expressed by 12= (2+Cv) 2 +(2+Sv) 2 and the maxima and minima occur when dC dS (z+Cv)a`j+(2+Sv)dV=0, whence sin rV 2 +cos27rV 2 =G..
The intensity of light is, however, more usually expressed in terms of the actual displacement in the plane of the wave.
Its connexion with a is expressed by a =c4'/dr; so that TZ sin 05 e'(at - kr) 47b 2 where the factor e int is restored.
Retaining only the real part of (16), we find, as the result of a local application of force equal to DTZ cos nt (17), the disturbance expressed by TZ sin 4, cos(nt - kr) ?
The best evidence in favour of the step is to be found in the publicly expressed views of the state's own president, Burgers, already quoted.
So keenly were the Midlothian speeches appreciated by the Boers that the Boer committee wrote a letter of thanks to Gladstone, and expressed the hope that should a change in the government of Great Britain occur, " the injustice done to the Transvaal might find redress."
(Clarendon Press, 1896), the same hostility to Peter is expressed.
The word is of Armenian formation and signifies a son of Paulik or of little Paul; the termination -ik must here have originally expressed scorn and contempt.
In Babylonia Naram-Sin in the guise of a god wears the pointed helmet and two great horns distinctive of the deities.3 This relationship between the gods and their human representatives is variously expressed.
The reason is obvious, and the principle could be variously expressed.
This particular product was insoluble in a mixture of ether and alcohol, and its composition could be expressed by the term tri-nitrocellulose.
Soc., 1901, 23, p. 527), who, assuming the formula C24H4 6 O 20 for cellulose, showed how the nitrocelluloses described by different chemists may be expressed by the formula C24H4,..-z020(N02)s, where x has the values 4, 5, 6, ...
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.
When Virchow wrote, in 1850, " every animal presents itself as a sum of vital unities, every one of which manifests all the characteristics of life," he expressed a doctrine whose sway since then has practically been uninterrupted.
If further selection be made from the large body of miscellaneous poems, the comic poem on the physician Andro Kennedy may stand out as one of the best contributions to medieval Goliardic literature; The Two Mariit Wemen and the Wedo, as one of the richest and most effective pastiches in the older alliterative style, then used by the Scottish Chaucerians for burlesque purposes; Done is a battell on the Dragon Blak, for religious feeling expressed in melodious verse; and the well-known Lament for the Makaris.
- Contemporary with the school of medical humanists, but little influenced by them, lived in Germany a man of strange genius, of whose character and importance the most opposite opinions have been expressed.
The love-sick mood and romantic temperament of the young Irishman found congenial soil in the wild surroundings of unexplored Canadian forests, and the enthusiasm thus engendered for the "natural" life of savagery may have been already fortified by study of Rousseau's writings, for which at a later period Lord Edward expressed his admiration.
Various authors of the ante-Nicene period have expressed themselves as distinctly unfavourable to its religious, though not of course to its domestic, use.
Green expressed the same opinion in The Making of England (p. Ioi).
Thus, at every complete stroke of the piston, the air in the vessel or receiver was diminished by that fraction of itself which is expressed by the ratio of the volume of the available cylindrical space above the outward opening valve to the whole volume of receiver, nozzle and cylinder.
An American writer has expressed his satisf action that the day-labourer can now have on his table at a nominal price glass dishes of elaborate design, which only an expert can distinguish from hand-cut crystal.
A bounding surface is such that there is no flow of fluid across it, as expressed by equation (6).
If at any points of a vortex line the cross-section ABC, A'B'C' is drawn of the vortex filament, joined by the vortex line AA', then, since the flow in AA' is taken in opposite directions in the complete circuit ABC AA'B'C' A'A, the resultant flow in AA' cancels, and the circulation in ABC, A'B'C' is the same; this is expressed by saying that at all points of a vortex filament wa is constant where a is the cross-section of the filament and w the resultant spin (W.
.,' d x 2 dy e d z2' (10) which is expressed .
Expressed as a differential relation, with the value of c-TKL ai,G+2 (a 2 +A) a d ?
A torsion of the ellipsoidal surface will give rise to a velocity function of the form 4)--- where SZ can be expressed by the elliptic integrals in a similar manner, since dX/P3.
Conversely, if the kinetic energy T is expressed as a quadratic function of x, x x3, y1, y2, y3, the components of momentum, the partial differential coefficient with respect to a momentum component will give the component of velocity to correspond.
Thus if T is expressed as a quadratic function of U, V, W, P, Q, R, the components of momentum corresponding are dT dT dT (I) = dU + x2=dV, x3 =dW, dT dT dT Yi dp' dQ' y3=dR; but when it is expressed as a quadratic function of xi, 'x2, x3, yi, Y2, Y3, U = d, V= dx, ' w= ax dT Q_ dT dT dy 1 dy2 dy The second system of expression was chosen by Clebsch and adopted by Halphen in his Fonctions elliptiques; and thence the dynamical equations follow X = dt x2 dy +x3 d Y = ..., Z ..., (3) = dt1 -y2?y - '2dx3+x3 ' M =..
are the components of a constant vector having a fixed direction; while (4) shows that the vector resultant of y, y, y moves as if subject to a couple of components x Wx V, x Ux W, x V-x U, (Io) and the resultant couple is therefore perpendicular to F, the resultant of x, x, x, so that the component along OF is constant, as expressed by (iii).
Consider, for example, a submarine boat under water; the inertia is different for axial and broadside motion, and may be represented by (1) c 1 =W+W'a, c2=W+W'/3' where a, R are numerical factors depending on the external shape; and if the C.G is moving with velocity V at an angle 4) with the axis, so that the axial and broadside component of velocity is u = V cos 0, v =V sin 4), the total momentum F of the medium, represented by the vector OF at an angle 0 with the axis, will have components, expressed in sec. Ib, F cos 0 =c 1 - = (W +W'a) V cos 43, F sin 0 = c 2.11 = (W +W'/3) V sin 4) .
the precedin investigation, the liquid stops dead when the body is brought to rest and when the body is in motion the surrounding liquid moves in uniform manner with respect to axes fixed in the body, and the force experienced by the body from the pressure of the liquid on it surface is the opposite of that required to change the motion of the liquid; this has been expressed by the dynamical equations give above.
The book treats of the Messiah and the Messianic kingdom, the woes of Israel in the past and the destruction of Jerusalem in the present, as well as of theological questions relating to original sin, free will, works, &c. The views expressed on several of these subjects are often conflicting.
But though Christianity was in spirit the descendant of ancient Jewish prophecy, it was no less truly the child of that Judaism which had expressed its highest aspirations and ideals in pseudepigraphic and apocalyptic literature.
The value of sugar-canes at a given plantation or central factory would at first sight appear to vary directly as the amount of saccharine contained in the juice expressed from them varies, Sugar-canes.
It shows the greatest quantity of juice that may be expressed from canes, according to the different proportions of fibre they contain, but without employing maceration or imbibition, to which processes reference is made hereafter.
conveniently made of diameter which will give the cylindrical portion sufficient capacity to hold the juice expressed from the cane-mill in one hour.
The juice is then drawn off and pumped up to one of the double-bottomed defecators and redefecated, or, where juice-heaters have been used instead of defecators, the scums from the separators or subsiders are heated and forced through filter presses, the juice expressed going to the evaporators and the scum cakes formed in the filter presses to the fields as manure.
A process for purifying and decolorizing the juice expressed from beetroots by the addition of a small quantity of manganate of lime (20 to 50 grammes per hectolitre of juice), under the influence of an electric current, was worked with considerable success in a sugar factory in the department of Seine-et-Marne in the year 1900-1901.
Bergne reported on the 27th of July 1907 to Sir Edward Grey that " The permanent session had met in special session on the 25th of July, to consider the suggestion of His Britannic Majesty's government to the effect that, if Great Britain could be relieved from the obligation to enforce the penal provisions of the convention, they would be prepared not to give notice on the 1st of September next of their intention to withdraw on the 1st of September 1908 a notice which they would otherwise feel bound to give at the appointed time "; and he added that " At this meeting, a very general desire was expressed that, in these circumstances, arrangements should, if possible, be made which would permit Great Britain to remain a party to the Sugar Convention."
After his release Prynne further expressed his feelings in defence of advowsons and patrons, an attack on the Quakers (1655), and in a pamphlet against the admission of the Jews to England (A Short Demurrer to the Jews) issued in 1656.
In one family (Ligulidae) the segmentation is only expressed in the metameric distribution of the generative organs and the worm is externally unisegmental.
Historians have expressed divergent views regarding the early relations of the craftsmen and their fraternities to the gild merchant.
The leaves, when stripped from the stalks, are made into rolls and subjected to great pressure, which is released daily to allow the leaves to absorb their expressed juice.
Of these migrations, however, history knows nothing, nor are they expressed in literature.
A Catholic commentator of the 16th century, Hieronymus ab Oleastro, seems to have been the first to connect the name " Jehova " with howah interpreting it contritio, sive pernicies (destruction of the Egyptians and Canaanites); Daumer, adopting the same etymology, took it in a more general sense: Yahweh, as well as Shaddai, meant " Destroyer," and fitly expressed the nature of the terrible god whom he identified with Moloch.
In 1869 the government of Santo Domingo (or the Dominican Republic) expressed a wish for annexation by the United States, and such a step was favoured Washington, comprising wholesale frauds on the public revenue, awakened lively disgust.
Mill had suggested to Comte that he should write articles for the English periodicals, and expressed his own willingness to translate any such articles from the French.
It is hardly possible, however, to share the admiration expressed by some of Comte's disciples for his style.
When quite young he expressed a wish to become a minister of the gospel, but his aspirations were discouraged by the local clergyman.
In reply to a question in the House of Commons, Lord Palmerston accepted and adopted Gladstone's statement, expressed keen sympathy with the cause which he had espoused, and sent a copy of his letter to the queen's representative at every court of Europe.
The process of evolution from the indeterminate to the determinate is often expressed as a progress from the universal to the particular.
And when in 1890 he began to gather together the miscellaneous essays and papers written during a period of sixty years, he expressed the hope that, though " they could lay no claim to logical consistency," they might yet show " beneath the varying complexion of their thought some intelligible moral continuity," " leading in the end to a view of life more coherent and less defective than was presented at the beginning."
Theory and The Study of Religion, and, in some measure, of The Seat of Authority in Religion."' These books expressed his mature thought, and may be said to contain, in what he conceived as a final form, the speculative achievements of his life.
Concerning the virtues of truth and probity, extremely conflicting opinions have been expressed.
The position is well expressed in the Scotch Confession (1559).
In some of the cases the question has been raised how far the doctrine of the church could be ascertained by reference to the opinions generally expressed by divines belonging to its communion.
In elliptic integrals, the amplitude is the limit of integration when the integral is expressed in the form f 4) 1% I - N 2 sin e 4) d4.
The idea had already been expressed by E.
He is the chief tragic poet of the revolutionary period, and as Camille Desmoulins expressed it, he decorated Melpomene with the tricolour cockade.
He settled in Leipzig as a journalist; but the democratic views expressed in some essays and the volumes of poems Glocke and Kanone (1481) and Irdische Phantasien (1842) led to his expulsion from Saxony in 1846.
He bought and resided at the estate of La Source near Orleans, studied philosophy, criticized the chronology of the Bible, and was visited amongst others by Voltaire, who expressed unbounded admiration for his learning and politeness.
One or two of the circle of Catullus survived into that age; but an entirely new spirit came over the literature of the new period, and it is by new men, educated indeed under the same literary influences, but living in an altered world and belonging originally to a different order in the state, that the new spirit was expressed.
The Latin hexameter, which in Ennius and Lucretius was the organ of the more dignified and majestic emotions, became in his hands the most perfect measure in which the softer and more luxurious sentiment of nature has been expressed.
Virgil in a supreme degree, and Horace, Propertius and Ovid in a less degree, had expressed in their poetry the romance of the past.
In all these biographies there is internal evidence of confusion; many of the incidents related are elsewhere told of other persons, and certain of them are quite irreconcilable with his character, so far as it can be judged of from his writings and from the opinions expressed of him by his contemporaries; we may safely reject, for instance, the legends that he set fire to the library of the Temple of Health at Cnidos, in order to destroy the evidence of plagiarism, and that he refused to visit Persia at the request of Artaxerxes Longimanus, during a pestilential epidemic, on the ground that he would in so doing be assisting an enemy.
Faraday expressed this fact by saying that no absolute electric charge could be given to matter.
But an artistic temperament was hardly that required of a king of Prussia on the eve of the Revolution; and Frederick the Great, who had employed him in various services - notably in an abortive confidential mission to the court of Russia in 1 780 - openly expressed his misgivings as to the character of the prince and his surroundings.
(I) in which E 0 represents the quantity of energy originally present in the body, and all the quantities are supposed, as usual, to be expressed in mechanical units.
This is mathematically expressed by the statement that dE is an exact differential of a function of the co-ordinates defining the state of the body, which can be integrated between limits without reference to the relation representing the path along which the variations are taken.
(9) These must be expressed as functions of v and 0, which is theoretically possible if the values of s, p, and dp/do are known.
This coefficient is sometimes called the " angular coefficient," and may be regarded as a measure of the deviations from Boyle's law, 'which may be most simply expressed at moderate pressures by formulating the variation of the angular coefficient with temperature.
The final state of the substance, when equilibrium has been restored, may be deduced from this condition, if the energy can be expressed in terms of the co-ordinates.
Assuming the function G to be expressed in terms of p and 0, this condition represents the relation between p and 0 corresponding to equilibrium between the two states, which is the solution of the relation (v" - v')dp/dO=L/D, (5).
(39) dG"/dp (D const) =v, dJ"/dv (0 const) = p. (40) And all the properties of the substance may be expressed in terms of G or J and their partial differential coefficients.
The values of the corresponding functions for the liquid or solid cannot be accurately expressed, as the theoretical variation of the specific heat is unknown, but if we take the specific heat at constant pressure s to be approximately constant, and observe the small residual variation dh of the total heat, we may write F'=s'D+dh+B'.
The two deeds are similar, and the impression left by them is expressed in David's last charges to Solomon (i Kings ii.).
On account of the dissatisfaction expressed indirectly at the result of the contest, he retired from the service in February 1705.
The relative amount of gold in an alloy is expressed in two ways: (1) as " fineness," i.e.
Some of Cyril's personal preferences expressed in his catechetical lectures find expression, e.g.
Eastern theologians expressed the mysterious relationship of the Holy Spirit to the Father and the Son in such phrases as " Who proceedeth from the Father and receiveth from the Son," rightly making the Godhead of the Father the foundation and primary source of the eternally derived Godhead of the Son and the Spirit.
The famous theses which Luther nailed to the door of the church at Wittenberg in 1517 cannot be called a confession, but they expressed a protest which could not rest there.
These cities were inclined to follow Zwingli in his sacramental teaching which was more fully expressed in the Confession of Basel (1534) and the First Helvetic Confession (1536).
Calvin's views were expressed in the Gallican Confession, containing forty articles, which was drawn up in 1559, and was presented both to Francis II.
Aloes is the expressed juice of the leaves of the plant.
Events which greatly affected the physical condition of the human race, or were of a nature to make a deep impression on the minds of the rude inhabitants of the earth, might be vaguely transmitted through several ages by traditional narrative; but intervals of time, expressed by abstract numbers, and these constantly varying besides, would soon escape the memory.
They are frequently, however, of very great use in fixing dates that have been otherwise imperfectly expressed, and consequently form important elements of chronology.
In referring dates expressed by Olympiads to our era, or the contrary, we must therefore distinguish two cases.
Dates expressed according to this era are reduced to the common era by subtracting 5502, up to the Alexandrian year 57 86 inclusive, and after that year by subtracting 5492; but if the date belongs to one of the four last months of the Christian year, we must subtract 5503 till the year 5786, and 5493 after that year.
Dates expressed according to this era occur only on a few medals, and in the acts of certain councils.
To reduce a date expressed in this reckoning to the Julian date, add 551 years, and the days elapsed from the 1st of January to the 10th of August, both inclusive, of the year 552 - that is to say (since 552 is a leap year), 223 days.
Many of the Massachusetts revolutionary documents, including the famous "Massachusetts Resolves" and the circular letter to the legislatures of the other colonies, are from his pen; but owing to the fact that he usually acted as clerk to the House of Representatives and to the several committees of which he was a member, documents were written by him which expressed the ideas of the committee as a whole.
On the 24th of December they marched to Lenthall's house, and expressed their sorrow.
But the pursuit of the English fleet was feeble, and the retreat of the Dutch was ably covered by Cornelius van Tromp, son of Martin Tromp. Much scandal was caused by the mysterious circumstances in which an order to shorten sail was given in the English flagship, and doubts were expressed of the courage of the duke of York.
The relative densities of gases are usually expressed in terms of the standard gas under the same conditions.
(16.6 C.); a reason for this is that the gallon of water is defined by statute as weighing Io lb at 62° F., and hence the densities so expressed admit of the ready conversion of volumes to weights.
His creed, and the whole gist of his argument, is expressed in a single sentence, "I am fully assured that God does not, and therefore that men ought not to, require any more of any man than this, to believe the Scripture to be God's word, and to endeavour to find the true sense of it, and to live according to it."
The arrival of the emperor had been awaited in the capital with an impatience which is expressed by Pliny and by Martial.'
He thus, in the course of his official business, gradually acquired principles and settled ways of thinking which he afterwards expressed in writing.
More than once, in letters to his friend Vettori, no less than in the pages of the Principe, Machiavelli afterwards expressed his belief that Cesare Borgia's behaviour in the conquest of provinces, the cementing of a new state out of scattered elements, and the dealing with false friends or doubtful allies, was worthy of all commendation and of scrupulous imitation.
The two works form one coherent body of opinion, not systematically expressed, it is true, but based on the same principles, involving the same conclusions, and directed to the same philosophical end.
Writing to Vettori in 1513, he had expressed his eager wish to "roll stones" in their service; and this desire was now gratified.
The "service of God and his majesty" was the formula which expressed the belief of the sovereign and his subjects.
It must be remembered, however, that when Dollond expressed preference for this third type he had not then invented the achromatic object-glass.
Calvin replied (r3th February 1546) in a letter now lost; in which, he says, he expressed himself " plus durement que ma coustume ne porte."
The fifteen condemnatory clauses, prefacing the sentence at Geneva, set forth in detail that he was guilty of heresies, blasphemously expressed, against the foundation of the Christian religion.
The advantage of the new definition lies in the fact that the estimation of the chlorine (or rather of the total halogen expressed as chlorine) is sufficient to determine the salinity by a very simple operation.
On the continent of Europe it has been more usual to take both at 17.5° C. (63.5° F.), which is expressed as " Si 7: ", but for pyknometer work in all countries where the sample is cooled to 32° F.
The relations between the various conditions are set forth in the following equations where 0-o signifies the specific gravity of the sea-water in question at o° C., the standard at 4° being taken as 1000, S the salinity and Cl the chlorine, both expressed in parts by weight per mille.
fn2 It has been pointed out by Alexander Wylie that Kushluk was son of a powerful king of the Naimans, whose name Ta-Yang-Khan is precisely" Great King John "as nearly as that could be expressed in Chinese.
The power of a motor is measured by the rate at which it works, and this is expressed by Tw =T 60N in foot-pounds per second.
This ultimate view is expressed throughout the lectures (in the Nachgel.
Being next asked to make an unqualified submission to the council, he expressed himself as unable to do so, while stating his willingness to amend his teaching wherever it had been shown to be false.
If the system is supposed to obey the conservation of energy and to move solely under its own internal forces, the changes in the co-ordinates and momenta can be found from the Hamiltonian equations aE aE qr = 49 - 1 57., gr where q r denotes dg r ldt, &c., and E is the total energy expressed as a function of pi, qi,.
Ideas identical with the modern ones were expressed by John Mayow in his Tractatus quinque medico-physici (1674), but his death in 1679 undoubtedly accounts for the neglect of his suggestions by his contemporaries.
Talleyrand, despite the weakness of his own position (he was as yet little more than the chief clerk of his department), soon came to a good understanding with the general, and secretly expressed to him his satisfaction at the terms which the latter dictated at Campo Formio (17th of October 1797).
The recognition of this fact is expressed, at the present day, by the division of the Sporozoa into several well-defined orders, which are grouped in two main divisions, each containing more or less closely related forms. One of these groups consists of the Gregarines, Coccidia and Haer_aosporidia (qq.v.).
When the World War broke out, in spite of his Triplicist policy he openly expressed himself in favour of Italian neutrality, and on Italy's entry into the war he was careful not to compromise himself with Giolitti's attitude.
This Plato expressed in the myth of the Sun, but the garment of mythology in which Plato clothed his idealism, beautiful as it is in itself and full of suggestion, covered an essential weakness.
If there be any truth in this suggestion it seems likely that the last word of idealism, like the first, will prove to be that the type of the highest reality is to be sought for not in any fixed Parmenidean circle of achieved being but in an ideal of good which while never fully expressed under the form of time can never become actual and so fulfil itself under any other.
For almost two years after the outbreak of the World War he urged strict neutrality, but in 1918 publicly expressed regret for this attitude.
The thought life of the American aborigines is expressed in their practical knowledge and their lore.
The fragments of Pacuvius quoted by Cicero in illustration or enforcement of his own ethical teaching appeal, by the fortitude, dignity, and magnanimity of the sentiment expressed in them, to what was noblest in the Roman temperament.
The Holy See, much dependent at that time on its Swiss mercenaries in the pursuit of its secular ends, expressed no resentment on this occasion.
Zwingli's theological views are expressed succinctly in the sixtyseven theses published at Zurich in 1523, and at greater length in the First Helvetic Confession, compiled in 1536 by a number of his disciples.'
This tendency was largely due to a doubt whether the Federal government under the Constitution possessed the power to initiate general statistical inquiries, a doubt well expressed in the 9th edition of the Encyclopaedia Britannica by Francis A.
But an area or a volume cannot generally be measured by successive applications of the unit of area or volume; intermediate processes are necessary, the result of which is expressed by a formula.
(a) The formula may involve numbers or ratios which cannot be expressed exactly in the ordinary notation.
- In § 23 the area of a right trapezium has been expressed in terms of the base and the two sides; and in § 34 the area of a somewhat similar figure, the top having been replaced by an arc of a parabola, has been expressed in terms of its base and of three lengths which may be regarded as the sides of two separate figures of which it is composed.
Formulae giving the area of a trapezette should in general also be expressed so as to state the value of the mean ordinate (§§ 12 (v), 15, 19).
In the case of the briquette the position of the foot of the ordinate u is expressed by co-ordinates x, y, referred to a pair of axes parallel to a pair of sides of the base of the briquette.
If the area of the cross-section, in every position, is known in terms of its distance from one of the bounding planes, or from a fixed plane A parallel to them, the volume of the solid can be expressed in terms of the area of a trapezette.
The volume of a briquette can be found in this way if the area of the section by any principal plane can be expressed in terms of the distance of this plane from a fixed plane of the same set.
The top is then a parabola whose axis is at right angles to the base; and the area can therefore (§ 34) be expressed in terms of the two bounding ordinates and the midordinate.
It follows that, by taking two ordinates in a certain position with regard to the bounding ordinates, the area of any parabolic trapezette whose top passes through their extremities can be expressed in terms of these ordinates and of the breadth of the trapezette.
This is a particular case of a general theorem, due to Gauss, that, if u is an algebraical function of x of degree 2p or 2p + I, the area can be expressed in terms of p -}- i ordinates taken in suitable positions.
If u is an algebraical function of x of degree not exceeding p, and if the area of a trapezette, for which the ordinate v is of degree not exceeding p+q, may be expressed by a formula Aovo-1--yivi+..
To extend these methods to a briquette, where the ordinate u is an algebraical function of x and y, the axes of x and of y being parallel to the sides of the base, we consider that the area of a section at distance x from the plane x = o is expressed in terms of the ordinates in which it intersects the series of planes, parallel to y=o, through the given ordinates of the briquette (§ 44); and that the area of the section is then represented by the ordinate of a trapezette.
The volume of a frustum of a cone, for instance, can be expressed in terms of certain magnitudes by a certain formula; but not only will there be some error in the measurement of these magnitudes, but there is not any material figure which is an exact cone.
If, as is usually the case, the ordinate throughout each strip of the trapezette can be expressed approximately as an algebraical function of the abscissa, the application of the integral calculus gives the area of the figure.
The - - 4X + g tangential area may be expressed in terms of chordal areas.
Some of the formulae obtained by the above methods can be expressed more simply in terms of chordal or tangential areas taken in various ways.
The legitimacy of this assumption, and of the further assumption which enables the area of the new figure to be expressed by an approximate formula instead of by an exact formula, must be verified in every case by reference to the actual differences.
We have therefore B in the first place to see whether the difference can be expressed in terms of the directions of the tangents.
= x0 To apply these, the differential coefficients have to be expressed in terms of differences.
Even where u is an explicit function of x, so that f x udx may be expressed in terms of x, it is often more convenient, for construction of a table of values of such an integral, to use finite-difference formulae.
The formulae may be used for extending the accuracy of tables, in cases where, if v represents the quantity tabulated, hdv/dx or h 2 d 2 v /dx 2 can be conveniently expressed in terms of v and x to a greater degree of accuracy than it could be found from the table.
17), has expressed itself in varying degrees at different times, according as conditions were favourable or the reverse.
Hence the resistance of the insulator can be ascertained, since it is expressed in ohms by the ratio of the voltage of the battery in volts to the current through the C C galvanometer in amperes.
The doctrine of monotheism was formally expressed in the period immediately before and during the Exile, in Deuteronomy" and Isaiah; and at the same time we find angels prominent in Ezekiel who, as a prophet of the Exile, may have been influenced by the hierarchy of supernatural beings in the Babylonian religion, and perhaps even by the angelology of Zoroastrianism."
Algebraically expressed, if x and y be the required mean proportionals and a, 2a, the lines, we have a: x :: x: y :: y : 2a, from which it follows that x = 2a3.
The relation between integral numbers of months and years expressed by Meton's rule therefore deviates only two hours from the truth.
He is inspired with the dislike and jealousy of governments so often felt and expressed by thinkers formed in the social atmosphere of the 18th century.
We have c3 and u expressed in terms of the original length dx and the displacement dy so that we must y put dE= (dx+dy = (I +dy/dx)dx, and U dy p = .l o (w+pu t) I dx.
In other words, " atheism " has been used generally by the orthodox adherents of one religion, or even of a single sect, for all beliefs which are different or even differently expressed.
In May 1899 President Steyn suggested the conference at Bloemfontein between President Kruger and Sir Alfred Milner, but this act, if it expressed a genuine desire for reconciliation, was too late.
His expressed intention was to fight no battle until superiority in numbers was on his side.
It was his frankly expressed wish to be nominated and elected president in 1904, and he was nominated unanimously by the Republican National Convention at Chicago, and was elected in November of that year by the largest popular majority ever given to any candidate in any presidential election.
The hopelessly vicious policemen hated him, but no man ever had a stronger personal hold upon the great body of the honest officers - a hold which existed long after he left the police department, and was frequently expressed by members of the force as he passed through the city streets.
In his Nobel address he said: "In any community of any size the authority of the courts rests upon actual potential force; on the existence of a police or on the knowledge that the able-bodied men of the country are both ready and willing to see that the decrees of judicial and legislative bodies are put into effect;" and he expressed the opinion that until a recognized international supreme court was firmly established, every nation must be prepared to defend itself, and when it was established all the nations must be prepared to maintain its decrees against any recalcitrant nation.
In numerous speeches and addresses he expressed his belief in a strong colonial government, but a government administered for the benefit of the people under its control and not for the profit of the people at home.
He expressed his own judgment of his success as a public man by saying that it was not due to any special gifts or genius, but to the fact that by patience and laborious persistence he had developed ordinary qualities to a more than ordinary degree.
Different views are here expressed.
This was the conception expressed by Bossuet, "Tout l'etat est en la personne du prince," or in Louis XIV.'s saying, "L'etat c'est moi."
The same theory is often expressed by saying that the majority in a community, or a particular group, in fact, rules (Guizot, Representative Government, i.
We find the same expressed by many German jurists, i.e.
Even the fact that he has expressed an opinion on matters in dispute will not of itself disqualify him (Halliday v.
The Arbitration Act 1889 provides that a submission, unless a contrary intention is expressed in it, is irrevocable except by leave of the court or a judge, and is to have the same effect in all respects as if it had been made an order of court.
The statutory definition of the grounds of reduction was intended, however, merely to put an end to the practice which had previously obtained of reviewing awards on their merits, and it does not prevent the courts from setting aside an award where the arbitrator has exceeded his jurisdiction, or disregarded any one of the expressed conditions of the submission, or been guilty of misconduct.
The integration can be performed when M is expressed in terms of x.
Abt Vogler, however, makes reservations in his praise, condemning his philosophical principles as too much in sympathy with those of Fox, which had already been expressed by P. Vallotti.
The verdict of history upon his reign is best expressed in his own words - "I have done nothing which should prevent me from laying down my power, and living in safety as a private man."
The Upper House agreed, but expressed its misgivings as to such a polyglot report of proceedings.
Thus, too, even at the present time, the opinion is very clearly expressed in Ultramontane quarters that, in the event of the state issuing laws contravening those of nature or of the Church, obedience must be refused.