Follows sentence example
Oh, he just follows the code and transcribes the letters.
And I'll ensure Brady follows through with his promise to marry you.
From this fundamental difference between the view held by history and that held by jurisprudence, it follows that jurisprudence can tell minutely how in its opinion power should be constituted and what power-- existing immutably outside time--is, but to history's questions about the meaning of the mutations of power in time it can answer nothing.
Yes, I am used to giving orders, orders that everyone follows.
To see how this law follows from Dalton's theory let us consider his diagrams for the molecules of water, ethylene and the oxides of carbon.Advertisement
The physical theory, in its earlier form in The World, and later in the Principles of Philosophy (which the present account follows), rests upon the metaphysical conclusions of the Meditations.
The manner in which the circulation of hot water takes place in the tubes is as follows.
A "methodist" is one who follows a "method," the term being applied not only to the Wesleyan body, but earlier to the Amyraldists, and in the 17th century to certain Roman Catholic apologists.
In the third and longest section, the line starts from a pillar erected in the Perez Rosales pass, near Lake Nahuel-Huapi, and follows the water-parting southward to the highest point of Mt.
The Athenian tradition, which he follows in the main, would naturally seek to obscure their services.Advertisement
In this wider sense the family may be characterized as follows.
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).
The rue de la Marine follows the lines of a Roman street.
The new ship canal from Zeebrugge will not revive the ancient port, as it follows a different route, leaving Damme and Ecluse quite untouched.
And as there is no branch of art in which mechanical improvements, and the consequent change in the nature of technical difficulties, bear so directly upon the possibilities and methods of external effect, it follows that an exclusive preponderance of this view is not without serious disadvantage from the standpoint of general musical culture.Advertisement
Its action was as follows.
That doctrine runs, briefly, as follows.
This follows the precedent set in the accession charter of Henry I.
The cleavage of the ovum follows two types, both seen in Tubularia (Brauer ).
In the first, a cleavage follows each nuclear division; in the second, the nuclei multiply by division a number of times, and then the ovum divides into as many blastomeres as there are nuclei present.Advertisement
Allman  put forward a more detailed view, which was as follows.
It is true he sets out with a transcendent Deity, and follows Plato in viewing the creation of the cosmos as a process of descent from the more to the less perfect according to the distance from the original self-moving agency.
Gassendi, with some deviations, follows Epicurus in his theory of the formation of the world.
The modern highroad follows the ancient line, and remains of the 1 It is important to note how the Romans followed up every victory with a road.
The differentiation of metaxylem follows according to the type of root-stele, and, finally, any stereom there may be is developed.Advertisement
If a root is similarly illuminated, a similar change of direction of growth follows, but in this case the organ grows away from the light.
The causes of disease may be provisionally classified somewhat as follows, but it may he remarked at the outset that no one of these proximal causes, or agents, is ever solely responsible; and it is very easy to err in attributing a diseased condition to any of them, unless the relative importance of primary and subordinate agencies is discoverable.
The Andine sub-region extends from Peru to the Argentine and follows roughly the watershed of the Amazon.
The Magnoliaceous genus Drimys, with a single species in the new world, follows the same track.
Next follows the distribution of plants and animals (biogeography), and finally the distribution of mankind and the various artificial boundaries and redistributions (anthropogeography).Advertisement
It is usual to distinguish between the general coast-line measured from point to point of the headlands disregarding the smaller bays, and the detailed coast-line which takes account of every inflection shown by the map employed, and follows up river entrances to the point where tidal action ceases.
Then follows the rib-bearing portion and then the processus lateralis posterior; this also is the product of ribs, consequently the right and left processes together are equivalent to the xiphoid process or xiphisternum of the mammals.
The most primitive combination, ambiens and A B X Y, is the most common; next follows that of A X Y, meaning the reduction of B, i.e.
But it also follows that, if every extinct and recent bird were known, neither species, nor genera, nor families, nor orders could be defined.
It follows that new groups of Ratitae can no longer be developed since there are no Carinatae living which still retain so many low characters, e.g.Advertisement
The work contains nothing that cannot be learned from Ptolemy, whom he follows in calling the promontory of the Novantae (Mull of Galloway) the most northern point of Britain.
It follows that, if, say, five knots of the line run out in 28 seconds, the ship has gone 5X 47± ft.
The parts of the flower are most frequently arranged in fives, or multiples of fives; for instance, a common arrangement is as follows, - five sepals, succeeded by five petals, ten stamens in two sets of five, and five or fewer carpels; an arrangement in fours is less frequent, while the arrangement in threes, so common in monocotyledons, is rare in dicotyledons.
When this relief has been gained by a series of enactments, a second struggle follows, in which the plebeians win political equality with the patricians.
Matter and force (or energy) are infinite; the conservation of force follows from the imperishability of matter, the ultimate basis of all science.Advertisement
At many points it follows Anselm closely, and, of course, very often " makes light work " of its task.
In 673 Archbishop Theodore divided the East Anglian diocese into two, Elmham being the seat of the northern, Dunwich that of the southern bishop. A long blank follows in the history of this kingdom, until in 792 we find Offa of Mercia slaying iEthelberht, king of East Anglia, who is said to have been his son-in-law.
It follows, therefore, that they have been independently acquired in the course of the evolution of the Coleoptera.
The actual distribution of arable land, forests and meadows, in European Russia and Poland is shown in the following table The land in European Russia and Poland (Caucasia being excluded) is divided amongst the different classes of owners as follows Down to January 1st 1903, the peasants had actually redeemed out of the land allotted to them in 1861 a total of 280,530,516 acres..
Under this principle, rates are reduced where the increase of business which follows such reduction makes the change a profitable one.Advertisement
They are kept relatively high in those cases where the expansion of business which follows a reduction is small, and where such a change is therefore unprofitable.
With increasing altitude vegetation becomes more varied and abundant, until the tree limit is reached; then follows a forest belt, which in the highest mountains is limited above by cold as it is below by aridity.
See " Descent of Ishtar to Hades," Rev. lines 6-10, where universal non-intercourse of sexes follows Ishtar's departure from earth to Hades.
What immediately follows is on a descending slope with some striking exceptions, e.g.
The oldest of these trunk lines, the Southern Pacific (formerly the Central Pacific), follows the course of the Humboldt and Truckee rivers.Advertisement
The Kennet and Avon Canal, between Reading and the Avon, follows the river closely from Bradford down to Bath, where it enters it by a descent of seven locks.
The malarial cachexia that follows definite attacks of ague consists in a state of ill-defined suffering, associated with a sallow skin, enlarged spleen and liver, and sometimes.
Being thus composed, he is neither able to eat flesh like his father, nor herbs like his mother; therefore he perisheth from inanition"; the moral follows.
Thus by transposition we may write the last equation as follows 2HI =H2+12+12200 cal., and thus express that hydriodic acid when decomposed into its elements evolves 12200 cal.
Their concessions continue to become ever more significant, and all that follows from them should be carefully noticed by those who are impressed by their arguments.
The later phase, which follows on the destruction of the Cnossian palace, and corresponds with the diffused Mycenaean style of mainland Greece and elsewhere, is already partly decadent.
Fielde show that an ant follows her own old track by a scent exercised by the tenth segment of the feeler, recognizes other inmates of her nest by a sense of smell resident in the eleventh segment, is guided to the eggs, maggots and pupae, which she has to tend, by sensation through the eighth and ninth segments, and appreciates the general smell of the nest itself by means of organs in the twelfth segment.
The eastern flank of this tableland follows a line of hills drawn a short distance from the Indus, between the mouth of that river and the Himalaya, about on the 72nd meridian; these hills do not generally exceed 4000 or 5000 ft.
The southern and south-western face follows the coast closely up the Persian Gulf from the mouth of the Indus, and is formed farther west by the mountain scarp, which, rising in many points to 10,000 ft., flanks the Tigris and the Mesopotamian plains, and extends along Kurdistan and Armenia nearly to the 40th meridian; beyond which it turns along the Taurus range, and the north - eastern angle of the Mediterranean.
Although the succession of the periodical winds follows the progress of the seasons as just described, the changes in the wind's direction everywhere take place under the operation of special local influences which often disguise the more general law, and make it difficult to trace.
Then follows a long period in which eastern Europe was mainly occupied in combating Asiatic invasions, and had little opportunity of Europeanizing the East.
Thus converted into an enemy, Gawain urges his uncle to make war on Lancelot, and there follows a desperate struggle between Arthur and the race of Ban.
The second account, which Herodotus follows, is a rationalized version of the first, where the dog is changed into a woman (the wife of the shepherd) named Spako (bitch).
Its situation is most picturesque, on the steep left bank of the river Nidd, which here follows a well-wooded valley, hemmed in by limestone cliffs.
In it the book of husbandry consists of 118 pages, and then follows the Points of Housewifrie, occupying 42 pages more.
As the main object of the act is to obtain records of prices, it follows that only in so far as statements of the prices realized, together with the description of the animals involved, are obtained, is the full advantage of the statute secured.
From the very nature of the records in which we study the town life of the middle ages, it follows that we obtain from them only a onesided view.
From this follows the necessity for the created spirit, after apostasy, error and sin, to return always to its origin in God.
This is devoted to the very distinct and not nearly-allied groups of hornbills and of birds which for want of a better name we must call " Chatterers," and is illustrated, like those works of which a notice immediately follows, by coloured plates, done in what was then considered to be the highest style of art and by the best draughtsmen procurable.
A driving-road from Kongsberg follows a favourite route for travellers through this district, connecting with routes to Sand and Odde on the west coast.
For what follows, with regard to the Church's conversion of guerra into the Holy War, cf.
The frontier line follows the crest of the mountains, three peaks some io,000 or more ft.
This railway follows, N.E.
From this it follows that hot-wire ammeters are generally not capable of giving visible indications below a certain minimum current for each instrument.
Since the current passing through the balance when equilibrium is obtained with a given weight is proportional to the square root of the couple due to this weight, it follows that the current strength when equilibrium is obtained is proportional to the product of the square root of the weight used and the square root of the displacement distance of this weight from its zero position.
The principal street of Luxor follows the line of the ancient avenue.
It follows that p must be greatest at pericentre, where its distance from F is least.
It follows that putting n for the mean motion and T for the period of revolution we shall have in degrees nT=3600.
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.
Representing by P this position, it follows that the area of that portion of the ellipse contained between the radii vectores FB and FP will bear the same ratio to the whole area of the ellipse that t does to T, the time of revolution.
Leake, whom Frazer follows, assumed the Pelasgicum to be a fortified space at the western end of the Acropolis; this view necessitates the assumption that the nine gates were built one within the other, but early antiquity furnishes no instance of such a construction; DOrpfeld believes it to have extended from the grotto of Pan to the sacred precinct of Asclepius.
The Benedictine work follows the old monastic tradition of the direct intercourse of the soul with God.
The great court on the,north side has a lofty cloister round it, so that in many respects it follows the normal type.
A diagnosis covering all the Ratitae (struthio, rhea, casuarius, dromaeus, apteryx and the allied fossils dinornis and aepyornis) would be as follows - (i) terrestrial birds without keel to the sternum, absolutely flightless; (ii) quadrate bone with a single proximal articulating knob; (iii) coracoid and scapula fused together and forming an open angle; (iv) normally without a pygostyle; (v) with an incisura ischiadica; (vi) rhamphotheca compound; (vii) without apteria or bare spaces in the plumage; (viii) with a complete copulatory organ, moved by skeletal muscles.
These three acids yield on heating phenol, identical with the substance started with, and since in the three oxybenzoic acids the hydroxyl groups must occupy positions other than I, it follows that four hydrogen atoms are equal in value.
The formation of this substance readily follows from Kekule's formula, while considerable difficulties are met with when one attempts an explanation based on Ladenburg's representation.
Baeyer pointed out that although benzene derivatives were obtainable from hexamethylene compounds, yet it by no means follows that only hexamethylene compounds need result when benzene compounds are reduced.
According to the law of Avogadro, equal volumes of different gases under the same conditions of temperature and pressure contain equal numbers of molecules; therefore, since the density depends upon the number of molecules present in unit volume, it follows that for a comparison of the densities of gases, the determinations must be made under coincident conditions, or the observations reduced or re-computed for coincident conditions.
The identity of the four valencies of the carbon atom follows from the fact that the heats of combustion of methane, ethane, propane, trimethyl methane, and tetramethyl methane, have a constant difference in the order given, viz.
It follows that the true heat of combustion of carbon, i.e.
It follows that the thermal effects stated above must be equal, i.e.
It follows therefore that two hydrocarbon radicals are bound to the carbon monoxide residue with the same strength as they combine to form a paraffin.
It follows on this theory that all coloured substances contain either of the groupings or the former being a para-quinonoid, the latter an ortho-quinonoid.
It follows immediately the ninth or the fasting-month, Ramadan, occupying the first three days of the tenth month, Shawwal.
In the intervening body of the epistle the writer also follows the regular form of a letter.
If mortification follows, the parts.
Alexander's gold coinage, indeed (possibly not struck till after the invasion of Asia), follows in weight that of Philip's staters; but he seems at once to have adopted for his silver coins (of a smaller denomination than the tetradrachm) the Euboic-Attic standard, instead of the Phoenician, which had been Philip's.
Up to the year 1139 he follows closely the history written by his predecessor, Prior Richard; thenceforward he is an independent though not a very valuable authority.
A simple plan is as follows - draw an outline of the country of which a map is to be produced upon a board; mark all points the altitude of which is known or can be estimated by pins or wires clipped off so as to denote the heights; mark river-courses and suitable profiles by strips of vellum and finally finish your model with the aid of a good map, in clay or wax.
In Strabo's time, (latter half of 1st century B.C.) the principal buildings were as follows, enumerated as they were to be seen from a ship entering the Great Harbour.
Then follows a list of his works, so far as, at that date, they had been composed.
The characters of the genus may be expressed as follows in a more detailed manner.
But the Peckhams' careful observations and experiments show that, with the American wasps, the victims stored in the nests are quite as often dead as alive; that those which are only paralysed live for a varying number of days, some more, some less; that wasp larvae thrive just as well on dead victims, sometimes dried up, sometimes undergoing decomposition, as on living and paralysed prey; that the nerve-centres are not stung with the supposed uniformity; and that in some cases paralysis, in others death, follows when the victims are stung in parts far removed from any nerve-centre.
The boundary line follows the crest of the principal chain or ridge (Riesenkamm), which stretches along the northern side of the group, with an average height of over 4000 ft.
This line is now abandoned in favour of the railway which follows the canal from Suez to Ismailia, and then ascends the Wadi Tumilat to Zagazig, whence branches diverge to Cairo and Alexandria.
Even Leibnitz,' who initiated a more modern point of view, follows the tradition in thus confining the scope of mathematics properly so called, while apparently conceiving it as a department of a yet wider science of reasoning.
The arithmetic of real numbers follows from appropriate definitions of the operations of addition and multiplication.
The addition and multiplication of these "signed" real numbers is suitably defined, and it is proved that the usual arithmetic of such numbers follows.
It follows that a careful scrutiny of the very idea of classes and relations is required.
The other, a narrowgauge line, crosses the Save at Bosna Brod, and follows the Bosna to Serajevo, throwing out branches eastward beyond Dolnja Tuzla, and westward to Jajce and Bugojno.
The principal items of revenue and expenditure are as follows, the figures being taken from the published budget above-mentioned.
The story of the fleece was as follows.
According to Robertson Smith, the development of the various institutions connected with the Passover was as follows.
The greater part of the country is hilly and irregular, though there are considerable plains; but besides Rhodope two other tolerably definite chains intersect it, one of which descends from Haemus to Adrianople, while the other follows the coast of the Euxine at no great distance inland.
It follows, too, that when there is a number of substances, all essential for the elaboration of living material, and when one of these is present in minimal proportion, that one substance rules the production, just as the effective strength of a chain depends on the weakest link.
Fifty miles from its source the river and the Janglam route touch each other, and from that point past Tadum (the first important place on its banks) for another 130 m., the road follows more or less closely the left bank of the river.
A freedom of interchange is thus indicated between the opposite parts of the molecules of salts in solution, and it follows reasonably that with the solution of a single salt, say sodium chloride, continual interchanges go on between the sodium and chlorine parts of the different molecules.
In 1897 the distribution was as follows.
It follows the course of the Amur, again in a succession of villages some 20 m.
Smith, who follows it, suggests "Egypt from 608-605" as an alternative to Assyria (p. 124).
It holds its own, however, when base bullion contains bismuth in appreciable amounts, as in the Pattinson process bismuth follows the lead to be cupelled, while in the Parkes process it remains with the desilverized lead which goes to market, and lead of commerce should contain little bismuth.
The substance of Caesar's account is as follows.
Pascal had already shown how philosophical scepticism might be employed as a bulwark for faith, and Glanvill follows in the same track.
It follows that between two neighbouring magnets, the poles of which are regarded as centres of force, there must always be four forces in action.
A south pole would be urged oppositely to the conventional " direction " of the line; hence it follows that a very small magnetic needle, if placed in the field, would tend to set itself along or tangentially to the line of force passing through its centre, as may be approximately verified if the compass be placed among the filings on the cardboard.
Terminology And Elementary Principles In what follows the C.G.S.
From the equation K=(µ - I)/47r, it follows that the magnetic susceptibility of a vacuum (where µ = I) is o, that of a diamagnetic substance (where, u I) is positive.
It follows that in testing iron for magnetic quality the greatest care must be exercised to guard the specimen against any accidental vibration.
Since, for example, stretching diminishes 'the magnetization of nickel, it follows from theory that the length of a nickel rod should be diminished by magnetization and conversely.
Changes of elasticity are in all cases dependent, not only upon the field, but also upon the tension applied; and, owing to hysteresis, the results are not in general the same when the magnetization follows as when it precedes the application of stress; the latter is held to be the right order.
Leaving that question for consideration in connexion with the systematic statement of the characters of the various groups of Arachnida which follows on p. 475, it is well now to consider the following question, viz., seeing that Limulus and Scorpio are such highly developed and specialized forms, and that they seem to constitute as it were the first and second steps in the series of recognized Arachnida - what do we know, or what are we led to suppose with regard to the more primitive Arachnida from which the Eurypterines and Limulus and Scorpio have sprung ?
Since this surplusage is in turn derived from the Septuagint, from which the old Latin version was translated, it thus follows that the difference between the Protestant and the Roman Catholic Old Testament is, roughly speaking, traceable to the difference between the Palestinian and the Alexandrian canons of the Old Testament.
From the latter it follows that in the Acts of Paul the death of Peter was recounted.
In Spain, on the other hand, the title of conde, the earlier history of which follows much the same development as in France, is still of much social value, mainly owing to the fact that the rule of primogeniture exists, and that, a large fee being payable to the state on succession to a title, it is necessarily associated with some degree of wealth.
The boundary with Colombia, fixed by treaty of April 24, 1907, follows the lower rim of the Amazon basin, as defined by Brazil.
The form (m+n)A=mA+nA follows at once from the fact that A is the unit with which we are dealing.
The ordinary method of representation is as follows.
The following are some particular cases; the proof usually follows the lines already indicated.
The argument involves the theorem that, if 0 is a positive quantity less than I, 0 t can be made as small as we please by taking t large enough; this follows from the fact that tlog 0 can be made as large (numerically) as we please.
If A 1 = X a i e i, B i = /if i e i, the distributive law of multiplication is preserved by assuming A1B1=E(a0 i 3)eiej; it follows that A 1 B 1 = - B 1 A 1, and that A l 2 = o.
He follows the methods of Diophantus; his work on indeterminate equations has no resemblance to the Indian methods, and contains nothing that cannot be gathered from Diophantus.
So far as the northern boundary follows the Oxus stream, under the northern slopes of the Hindu Kush, it is only separated by the length of these slopes (some 8 or 10 m.) from the southern boundary along the crest.
Wotton follows Aristotle 1 in the division of animals into the Enaema and the Anaema, and in fact in the recognition of all the groups above given, adding only one large group to those recognized by Aristotle under the Anaema, modifica- namely, the group of Zoophyta, in which Wotton includes the Holothuriae, Star-Fishes, Medusae, Sea-Anemones and Sponges.
The matter strictly relates to the consideration of the " causes of variation," and is as follows.
In the part covered by the books of the Bible Josephus follows them, and that mainly, if not entirely as they are translated into Greek by the Seventy (the Septuagint version).
Roughly sketched, his argument is as follows.
The northern edge of the plateau follows an irregular line from somewhat north of Mafeking on the west to the Mauchberg on the east.
Since the value of µ for water is about, it follows that n must be at least unity for a rainbow to be formed; there is obviously no theoretical limit to the value of n, and hence rainbows of higher orders are possible.
It seems, in short, to have originally formed the preface to the small group of prophecies which now follows it, viz.
From this it follows that nothing beyond myself exists; for what is experience is its (the self's) states."
Terence justifies this practice by that of the older poets, Naevius, Plautus, Ennius, whose careless freedom he follows in preference to the "obscura diligentia" of his detractor.
Disease as an entity - as something to which all living matter is subject - is what the pathologist has to recognize and to investigate, and the practical application of the knowledge thus acquired follows as a natural consequence.
If the injury be a small incised wound through the skin and subcutaneous tissues without any septic contamination, there usually follows a minimum of reaction on the part of the tissues.
In a given case of anasarca due to a cause acting generally, it will be found that the liquid of the pleural cavity always contains the highest percentage of proteid, that of the peritoneal cavity comes next, that of the cerebral ventricles follows this, and the liquid of the subcutaneous areolar tissue contains the lowest.
En-lil is associated with the ancient city of Nippur, and since En-lil with the determinative for "land" or "district" is a common method of writing the name of the city, it follows, apart from other evidence, that En-lil was originally the patron deity of Nippur.
To the east of the gorge the wall still follows the edge of low cliffs of the, coast, and continues to do so all along the east side of Achradina 1 The date of the fragment of city wall immediately to the north-east of the so-called palaestra is uncertain; it is therefore doubtful whether it can belong to this system of defences (Lupus, pp. 308, 331).
It follows from what has been said that prognosis, or the art of foretelling the course and event of the disease, was a strong point with the Hippocratic physicians.
It almost follows from the nature of the case that the great task of Boerhaave's life, a synthesis of ancient and modern medicine, and the work in which this is chiefly contained, his.
The explanation of the meteoric splendour of the Brunonian system in other countries seems to be as follows.
Waller (1816-1870), who tracked the line of nervous strands by experimental sections, and showed that when particular strands are cut off from their nutritive centres the consequent degeneration follows the line of the separated strands.
It follows the new direction for about 20 m., but at Bingen it again turns to the north and begins a completely new stage of its career, entering a narrow valley in which the enclosing rocky hills abut so closely on the river as often barely to leave room for the road and railway on either bank; during this portion of its course the speed of the current at a normal state of the water exceeds 6 m.
The modern highroad follows the ancient line, and some of the original bridges still exist.
The Thames follows a devious course through London, and the fine embankments on its north side, nowhere continuing uninterruptedly for more than 2 m., do not form important thoroughfares, with the exception of the Victoria Embankment.
The bridges in order above London Bridge are as follows, railway-bridges being bracketed - Southwark, (Cannon Street), (Blackfriars), Blackfriars, Waterloo, (Hungerford - with a footway), Westminster, Lambeth, Vauxhall, (Grosvenor), Victoria, Albert, Battersea, (Battersea), Wandsworth, (Putney), Putney and Hammersmith.
The railways whose systems are mainly or wholly confined within the metropolitan area are as follows.
It follows, therefore, that the main streets also are not in line with the Roman ways, except perhaps in a few instances.
As a result of its relatively great depth there are seldom any great fluctuations of level in this lake due to wind disturbance, but the lake follows the general rule of the Great Lakes (q.v.) of seasonal and annual variation.
In the political part of his system Ferguson follows Montesquieu, and pleads the cause of well-regulated liberty and free government.
At a time when the Cartesian system of vortices universally prevailed, he found it necessary to investigate that hypothesis, and in the course of his investigations he showed that the velocity of any stratum of the vortex is an arithmetical mean between the velocities of the strata which enclose it; and from this it evidently follows that the velocity of a filament of water moving in a pipe is an arithmetical mean between the velocities of the filaments which surround it.
It follows that when the fluid has come to rest, the tangential stress in any plane in its interior must vanish, and the stress must be entirely normal to the plane.
This fundamental principle of hydrostatics follows at once from the principle of the normality of fluid pressure implied in the definition of a fluid in § 4.
It follows that the pressure of a fluid requires to be calculated in one direction only, chosen as the simplest direction for convenience.
The circulation being always zero round a small plane curve passing through the axis of spin in vortical motion, it follows conversely that a vortex filament is composed always of the same fluid particles; and since the circulation round a cross-section of a vortex filament is constant, not changing with the time, it follows from the previous kinematical theorem that aw is constant for all time, and the same for every cross-section of the vortex filament.
It then follows that d-mannose is represented by No.
Hence it follows that the " optical " formulae of the acids derived from two pentoses having the configuration given above will be C02H - 0 - C02H CO 2 H + 0 - C02H, and that consequently only one of the acids will be optically active.
It follows from the manner in which l-idose is produced that its configuration is CH 2 (OH) + - - +COH.
It follows a generally easterly course, roughly parallel with that of the Dee, and a few miles to the south of it, falling into the North Sea close to Old Aberdeen, after a run of 82 m.
What follows is rather a perfection of details in the direction of logical completeness.
The northern edge of this great desert follows.
A second type of Arabian historiography is that in which an author combines the different traditions about one occurrence into one continuous narrative, but prefixes a statement as to the lines of authorities used and states which of them he mainly follows.
This position follows logically from the theory of English law that all offences are breaches of the king's peace.
This second girdle of fortifications was known as the Lines (Linien), and a second wide boulevard (GÃ¼rtel-Strasse) follows their course round the city.
The line adopted starts from Lake Suches, the source of a small river of that name flowing into the north of Lake Titicaca, crosses the Cordillera by the Palomani to the Tambopata river, follows that stream to the mouth of the Lanza, thence crosses to the source of the Heath river, which forms the dividing line down to its junction with the Madre de Dios, descends that river to the mouth of the Torosmonas, thence in a straight line north-westerly to the intersection of the Tahu.amanu river by the 69th meridian, and thence north on that meridian to the Brazilian frontier.
A dissolved in B and B dissolved in A, since both of these solutions emit vapours of the same composition (this follows since the same vapour must be in equilibrium with both solutions, for if it were not so a cyclic system contradicting the second law of thermodynamics would be realizable).
Thence it follows the valley of the Adige to Trent (35 m.) and on to Verona (562 m.) - in all 1742 m.
As the meteors have been numerously visible in five or six successive years it follows they must be pretty densely distributed along a considerable arc of their orbit.
It also follows that, as some of the meteors are seen annually, they must be scattered around the whole orbit.
The phylum is subdivided as follows.
It is as follows.
Comte's principle of classification is that the dependence and order of scientific study follows the dependence of the phenomena.
It follows that the crowning science of the hierarchy, dealing with the phenomena of human society, will remain longest under the influence of theological dogmas and abstract figments, and will be the last to pass into the positive stage.
In both cases the romance follows the prose rendering of Borron's Joseph of Arimathea and Merlin, and precedes a Mort Artus, thus forming part of a complete cycle.
If experience develops incompatibility of temper or some other mutually repellent characteristic, separation follows as a matter of course.
The threads extend only to the outlines of each figure, and it follows that every part of the pattern has a rim of minute holes like pierced lines separating postage stamps in a sheet, the effect being that the design seems to hang suspended it1 the groundlinked into it, as the Japanese term implies.i A specimen of this nature recently manufactured by Kawashimas weavers measured 20 ft.
Behind these enlarged poison-fangs follows a series of smaller, solid FIG.
The animal body, if it be composed of many cells, follows a different architectural plan; the compact nature of its food, and the yielding nature of its cell-walls, result in a form of structure consisting essentially of tubular or spherical masses of cells arranged concentrically round the food-cavity.
It follows that the drug is an antipyretic, and it is hence largely used in fevers as a means of reducing the temperature.
It follows that alcohol is a food in fever, and its value in this regard is greatly increased by the fact that it requires no primary digestion, but passes without changes, and without needing change, to the tissues which are to use it.
From this fact it follows that we can shield any conductor entirely from external influence by other "charged conductors by enclosing it in a metal case.
For by the definition of potential it follows that the electric force in any direction at any point is measured by the space rate of change of potential in that direction or E = + dVldx.
Accordingly, since the total solid angle round a point is 47r, it follows that the total flux through the closed surface due to the single point charge q is 41rq, and what is true for one point charge is true for any collection forming a total charge Q of any form.
Every tube of electric force must therefore begin and end on electrified surfaces of opposite sign, and the quantities of positive and negative electricity on its two ends are equal, since the force E just outside an electrified surface is normal to it and equal to a/41r, where a is the surface density; and since we have just proved that for the ends of a tube of force EdS = E 1 dS', it follows that adS = a'dS', or Q = Q', where Q and Q' are the quantities of electricity on the ends of the tube of force.
Accordingly, since every tube sent out from a charged conductor must end somewhere on another charge of opposite sign, it follows that the two electricities always exist in equal quantity, and that it is impossible to create any quantity of one kind without creating an equal quantity of the opposite sign.
Since the potential of a conductor is defined to be the work required to move a unit of positive electricity from the surface of the earth or from an infinite distance from all electricity to the surface of the conductor, it follows that the work done in putting a small charge dq into a conductor at a potential v is v dq.
If then we put a negative point-charge -qr/d at B, it follows that the spherical surface will be a zero potential surface, for q rq 1 (24).
It follows from the first law that the intrinsic energy of a substance in a given state must always be the same, or that the change of E in any transformation must depend only on the initial and final states, and not on the path or process.
The same result follows if the work W =RT log e ?'
A similar expression for the variation of the specific heat S at constant pressure is obtained from the second expression in (8), by taking p and 0 as independent variables; but it follows more directly from a consideration of the variation of the function (E+pv).
This is geometrically obvious from the form of the area representing the function on the indicator diagram, and also follows directly from the first law.
In the case of ferrous sulphate, prepared by dissolving iron in dilute sulphuric acid, the reaction follows the equation AuCl 3 +3FeS04 = FeC13-I-Fe2(S04)3+Au.
The effect on themselves was what usually follows in such circumstances.
The rise and progress of the movement were as follows.
It follows that the words " holy Church " were contained in the Roman Creed.'
From this principle, it follows (I) that the distinction between right and wrong is part of the constitution of human nature; (2) that morality stands apart from theology, and the moral qualities of actions are determined apart from the arbitrary will of God; (3) that the ultimate test of an action is its tendency to promote the general harmony or welfare; (4) that appetite and reason concur in the determination of action; and (5) that the moralist is not concerned to solve the problem of freewill and determinism.
From Miranda to Mora the Bilbao-Tarragona railway follows the course of the Ebro along the right bank.
Livy in general adheres to the epoch of Cato, though he sometimes follows that of Fabius Pictor.
Cicero follows the account of Varro, which is also in general adopted by Pliny.
Dionysius of Halicarnassus follows Cato.
To reduce the civil dates of the Armenians to the Christian era, proceed as follows.
As has been said, he closely follows Moray's version reported by de Silva in July 1567.
It was argued by Andrew Lang that Wood was likely to show these letters to Lennox; and that as Lennox follows Moray's version of Mary's long and murderous letter, and does not follow Letter II., the murderous letter (a forgery) was then part of the dossier of Mary's accusers.
It follows that Lennox possessed Crawford's written notes of the Darnley and Mary conversations.
Here is proof positive that Crawford does not copy Letter but gives Darnley's words as reported to him by Darnley - words that Darnley was proud of, - while Mary, returning on the second day of writing to the topic, does not quote Darnley's brave words, but merely contrasts his speaking "very bravely at the beginning" with his pitiful and craven later submission; "he has ever the tear in his eye," with what follows.
In the forms of his words he generally follows Attic usage.
The main facts of his life are usually given as follows.
A small commentary (no date) by Anderson Scott follows in some measure the lines laid down in Bousset and Porter.
Accordingly later exegetes 1 hold that the seventh in each series is unfolded in the series of seven that follows.
Spitta takes verse 6 to be an addition of the redactor, which describes proleptically what follows, while Gunkel sees in 6 and 7-16 parallel accounts.
It is to be observed that our author follows the apocalyptic scheme of two judgments which is first attested about ioo B.C. The first judgment precedes the establishment of the temporary Messianic kingdom, as here in xix.
From the preceding sections it follows that we cannot ascribe a strict literary unity to the book.
The relative advantages of the different methods may be generally stated as follows.
Zimmer follows previous critics in rejecting the Prologus maior (§§ 1, 2), the Capitula, or table of contents, and part of the Mirabilia which form the concluding section.
The Cher itself becomes navigable when it receives the Arnon and Yevre, and the communications of the department are greatly facilitated by the Canal du Berry, which traverses it from east to west, the lateral canal of the Loire, which follows the left bank of that river, and the canal of the Sauldre.
It follows that no revealed religion, so far as matter or substance is concerned, can contain anything beyond this law; nor can any fact in the world of experience be recognized by us as supernatural.
All that has been expounded follows if the ego comes to consciousness.
It follows that the average distance apart of the molecules in the gaseous state is roughly ten times as great as in the solid or liquid state, and hence that in the gaseous state the molecules are at distances apart which are large compared with their linear dimensions.
Since the volume at constant pressure is exactly proportional to the absolute temperature, it follows that the coefficients of expansion of all gases ought, to within the limits of error introduced by the assumptions on which we are working, to have the same value 1/273.
From Dulong and Petit's law that Cm is the same for all elements, it follows that n+3 must be the same for all atoms. Moreover, the value of Cm shows that n+3 must be equal to six.
Thence it crosses that lake in a straight line and afterwards the Ruwenzori to its highest point, Margherita peak, whence it follows the Lamia River to its junction with the Semliki.
The Grand Junction canal follows its course, and gives the town extensive water-communications.
From this it follows that ultimate or absolute reality is to be sought not beyond the region of experience, but in the fullest and most harmonious statement of the facts of our experience.
Then it follows the Spree for 12 m., and at Gross Tranke (121 ft.) passes out and goes.
In his family tree of HomoAmericanus Keane follows out such a plan, placing the chief linguistic family names on the main limbs, North American on one side, and South American on the other.
The necessity for sights follows directly on investigation of the forces acting on a projectile during flight.
Then follows the Lord's Prayer, almost exactly as in St Matthew, with a brief doxology - "for Thine is the power and the glory for ever."
In ethics Diihring follows Comte in making sympathy the foundation of morality.
It follows that the subfamily typified by this species, in which are included the gazelles, is the one to which alone the term antelopes should be applied if it were employed in a restricted and definable sense.
By the end of May he had placed his forces as follows to protect his empire.
Wellington and Blucher were disposed as follows in the early days of June (Map I.).
This order follows, in fact, the historical order of development of the subject.
By considering the circle as the limit of a polygon, it follows that the formulae (iii) and (v) of § 26 hold for a right circular cylinder and a right circular cone; i.e.
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.
It follows from §§ 48 and 51 that, if V is a solid figure extending from a plane K to a parallel plane L, and if the area of every cross-section parallel to these planes is a quadratic function of the distance of the section from a fixed plane parallel to them, Simpson's formula may be applied to find the volume of the solid.
In what follows it will be assumed that the conditions of continuity (which imply the continuity not only of u but also of some of its differential coefficients) are satisfied, subject to the small errors in the values of u actually given; the limits of these errors being known.
In ethics Gioja follows Bentham generally, and his large treatise Del merito e delle recompense (1818) is a clear and systematic view of social ethics from the utilitarian principle.
The West Shore railway, which follows closely the route of the New York Central & Hudson River, was also the result of a consolidation, completed in 1881, of several shorter lines.
This road, although its name of the Pilgrims' Way has for long confined it to the road by which the pilgrims came to Canterbury from Winchester, follows a far older track.
As AB returns from EF towards CD the layer of air next to it follows it as if it D E F were pulled back by AB.
It further follows, as in the analogous case of light, that there is a certain angle termed the critical angle, whose sine is found by dividing the less by the greater velocity, such that all rays of sound meeting the surface separating two different bodies will not pass onward, but suffer total reflection back into the first body, if the.
The engine follows up any wave that it has sent forward, and so crowds up the succeeding waves into a less distance than if it remained at rest.
Since U=n X where U is the velocity of sound, X the wave-length, and n the frequency, it follows that the forward frequency is greater than the backward frequency.
Since the forces called into play by an extension or compression of the material are proportional to the cross-section, it follows that if we consider any case and then another case in which, with the same longitudinal disturbance, the cross-section is doubled, the force in the second case is doubled as well as the mass to be moved.
Ordinarily when a bell is struck the impulse primarily excites the radial motion, and the tangential motion follows as a matter of course.
When a finger-glass (an inverted bell), is excited by passing the finger round the circumference, the tangential motion is primarily excited and the radial follows it.
The third mode of production of combination tones, the production in the medium itself, follows from the varying velocity of different parts of the wave, as investigated at the beginning of this article.
In this direction the principal buildings are the Wolfendahl church, a massive Doric building of the Dutch (1749); the splendid Roman Catholic cathedral of St Lucia (completed in 1904); and St Thomas's College (1851), which follows the lines of an English public school.
The main range of the Rockies follows the boundary line between Montana and Idaho west and north-west from Yellowstone Park in Wyoming to Ravalli county, then turns eastnorth-east to Lewis and Clark county, and from there extends' north-north-west into Canada.
It follows from Quesnay's theoretic views that the one thing deserving the solicitude of the practical economist and the statesman is the increase of the net product; and he infers also what Smith afterwards affirmed, on not quite the same ground, that the interest of the landowner is "strictly and indissolubly connected with the general interest of the society."
To the west of this stream and almost parallel with it is the James or Dakota river, which rises in North Dakota and follows a general course southward until it joins the Missouri river near Yankton.
Silver follows gold in importance, but the other minerals met with, including gypsum, mica, petroleum, natural gas, granite, marble and tin are not found in paying quantities.
It follows, to be sure,.
From Okla the canal follows the high land between the Khari-nadi and the Jumna, and finally joins the Banganga river about 20 m.
The main watershed follows a tortuous course which crosses the mountainous belt just north of New river in Virginia; south of this the rivers head in the Blue Ridge, cross the higher Unakas, receive important tributaries from the Great Valley, and traversing the Cumberland Plateau in spreading gorges, escape by way of the Cumberland and Tennessee rivers to the Ohio and Mississippi, and thus to the Gulf of Mexico; in the central section the rivers, rising in or beyond the Valley Ridges, flow through great gorges (water gaps) to the Great Valley, and by southeasterly courses across the Blue Ridge to tidal estuaries penetrating the coastal plain; in the northern section the water-parting lies on the inland side of the mountainous belt, the main lines of drainage running from north to south.
A good deal of salt is produced in a line which closely follows the railway.
The rainfall follows the valleys of the Mu and the Irrawaddy, and leaves the rest of the district comparatively dry.
It follows that the number of the revolutions the mercury makes in a given time is proportional to the quantity of electricity which is passed through the meter.
From this point he follows closely the Brut of Wace.
The interval corresponding to the octave being divided into seven equal parts, each about 14 semitone, it follows that Siamese music sounds strange in Western ears.
The subject of the sentence precedes the verb and the object follows it.
The possessive pronoun follows the object.
The adverb usually follows the verb.
It examines the plant in its earliest state of development, and follows it through all its stages of progress until it attains maturity.
It follows that the density of the aether must exceed io 18, and its elastic modulus must exceed Io 3, which is only about io s of the modulus of rigidity of glass.
It follows that, while in the traditional Church, with its claim to an unbroken descent from a divine original, the individual is subordinate to the Church, in the " free churches " the Church is in a certain sense secondary to the individual.
It follows from the above argument that, from the period of the Reformation onward, no historical account of the Christian Church as a whole, and considered as a definite institution, is possible.
Dillmann's analysis is as follows.
In his " tesmoynages de nostre imbecillite " he follows in the main the lines of the ancients, and he sums up with a lucid statement of the two great arguments in which the sceptical thought of every age resumes itself - the impossibility of verifying our faculties, and the relativity of all impressions.
It follows (1) that past and future pleasure have no real existence for us, and (2) that among present pleasures there is no distinction of kind, but only of intensity.
The Saetersdal railway follows that valley north to Byglandsfiord (48 m.), whence a good road continues to Viken i Valle at the head of the valley.
In fundamental principles he follows almost entirely Locke and Pufendorf; but he works out with great skill the theory of moral obligation, referring it to the command or will of God.
The author follows Ascham in protesting.
The Psalms were written mostly by David, but " some of them after the return from the captivity, as the 137th 1 In what follows the actual quotations are from his English work; some of the summaries take account of the brief expansions in his later Latin version.
Von Soden's analysis of numbers, contents and date may be tabulated as follows, but it must be remembered that it reckons many small fragments as separate MSS., especially in the earlier centuries.
He therefore conceived the idea that perhaps both texts were Lucan, and represented two recensions by the original writer, and he reconstructed the history as follows.
Granted the philosophical basis, the criticism practised upon the New Testament by Paulus and Strauss follows almost automatically.
The former are represented by Harnack, the latter by Wieseler, whom Lightfoot follows.
Investigation, then, of that part of the bookof Acts which follows the death of Agrippa, recorded in chap. xii.
It splits into two parts east of the Philippines, one division flowing northwards as the Kuro Siwo or Black Stream, the analogue of the Gulf Stream, to feed a drift circulation which follows the winds of the North Pacific, and finally forms the Californian Current flowing southwards along the American coast.
Part of this rejoins the North Equatorial Current, and part probably forms the variable Mexican Current, which follows the coasts of Mexico and California close to the land.
From Toulouse to Agen the main canal follows the right bank of the Garonne, crossing the Tarn on an aqueduct at Moissac, while another magnificent aqueduct of twenty-three arches carries it at Agen from the right to the left bank of the river.
It follows exactly the curve of the mainland, and is continued into Panama, under the name of the Cordillera de Chiriqui.
The process in its final and highest development was as follows.
From the above it follows that P=4.5407857 kg.
Since the soul in its longings reaches forth beyond all sensible things, beyond the world of ideas even, it follows that the highest being must be something supra-rational.
It follows very simply from the definition of a logarithm that logo b X logo a, = 1, logo m =log.
It follows from this property of the function that we cannot have for log x a series which shall be convergent for all values of x, as is the case with sin x and cos x, for such a series could only represent a uniform function, and in fact the equation log(I +x) =x -",, x2 +3x 3 -4x 4 + is true only when the analytical modulus of x is less than unity.
The name logarithm is derived from the words X6 7 wv hp426s, the number of the ratios, and the way of regarding a logarithm which justifies the name may be explained as follows.
His method of finding the logarithms of the small primes, which consists in taking a great number of continued geometric means between unity and the given primes, may be described as follows.
The polyphyletic law was early demonstrated among invertebrates by Neumayr (1889) when he showed that the ammonite genus Phylloceras follows not one but five distinct lines of evolution of unequal duration.
It by no means follows, however, from this incontrovertible evidence that the acquisition either of the jaw or of the lateral fins had not been in itself an extremely gradual process.
The scholastic then follows the ordinary course of an undergraduate at a university.
It is an arbitrary line and follows only two natural lines of demarcation - the Suchiate river from the Pacific coast to its source, and the Chixoy and Usumacinta rivers from near the 16th parallel N.W.
Inside the present sandy coast is a peculiar tide-water channel called the Rio Lagartos, which follows almost the whole northern shore, with occasional openings or bocas, connecting with the open sea.
Then follows the creation, when the creators said " Earth," and the earth was formed like a cloud or a fog, and the mountains appeared like lobsters from the water, cypress and pine covered the hills and valleys, and their forests were peopled with beasts and birds, but these could not speak the name of their creators, but could only chatter and croak.
Cavite is the terminus of a railway which follows the shore of the bay from Manila.
The distribution of the two communions still closely follows the lines of the settlement at the peace of Westphalia.
The less trustworthy history of the Flatey Book makes Biarni Heriulfsson in 985 discover Helluland (Labrador?) as well as other western lands which he does not explore, not even permitting his men to land; while Leif Ericsson follows up Biarni's discoveries, begins the exploration of Helluland, Markland and Vinland, and realizes some of the charms of the last named, where he winters.
In any case of potential difference measurement it is essential not to disturb the potential difference being measured; hence it follows that in electrokinetic voltmeters the wire connecting the two points of which the potential difference is to be measured must be of very high resistance.
It follows that the very words and discourses are his flesh and blood, of which he that constantly partakes, nourished as it were upon heavenly bread, will partake of the heavenly life.
Such a reaction can only take place if the addition of the alkyl group takes place on the nitrogen atom of the isonitrile, from which it follows that the nitrogen atom must be trivalent and consequently the carbon atom divalent.
The Chiapas follows a similar course.
From this it follows that religious knowledge involves the knowledge of nature and her elements, and that redemption consists in a physical process of freeing the element of light from the darkness.
The historical relation of Mani to Christianity is then as follows.
The horizontal strata of the plateau present equal ease or difficulty of erosion in any direction; the streams and the submature valleys of the plateau therefore ramify in every direction, thus presenting a pattern that has been called insequent, because it follows no apparent control.
Farther south, as far as the entrance of the Ohio, the Mississippi follows a rock-walled valley 300 to 400 ft.
The succession of formations in that state is as follows Upper Ordovician (or J and Indiana).
In the decade1890-1900the increase of the South exceeded slightly that of the North for the same period owing to the rapid development in recent years of the Southern states west of the Mississippi, which only the Western group, has exceeded since 1870.1 In general the increase of the two sections every 1000 in the South was as follows from 1790 to 1900
All it does is to declare that a conflict exists between two laws of different degrees of authority, whence it necessarily follows that the weaker law is extinct.
The equation x 2 +y 2 =o denotes a pair of perpendicular imaginary lines; it follows, therefore, that circles always intersect in two imaginary points at infinity along these lines, and since the terms x 2 +y 2 occur in the equation of every circle, it is seen that all circles pass through two fixed points at infinity.
A further deduction from the principle of continuity follows by considering the intersections of concentric circles.
Since PD = PD', it follows that AB =AB'.
Since the area of a circle equals that of the rectilineal triangle whose base has the same length as the circumference and whose altitude equals the radius (Archimedes, KIKXou A ir, prop.i), it follows that, if a straight line could be drawn equal in length to the circumference, the required square could be found by an ordinary Euclidean construction; also, it is evident that, conversely, if a square equal in area to the circle could be obtained it would be possible to draw a straight line equal to the circumference.
If this be applied to the right-hand side of the identity m m m 2 m2 tan-=- - n n -3n-5n" it follows that the tangent of every arc commensurable with the radius is irrational, so that, as a particular case, an arc of 45 having its tangent rational, must be incommensurable with the radius; that is to say, 3r/4 is an incommensurable number."
For in such a construction every point of the figure is obtained by the intersection of two straight lines, a straight line and a circle, or two circles; and as this implies that, when a unit of length is introduced, numbers employed, and the problem transformed into one of algebraic geometry, the equations to be solved can only be of the first or second degree, it follows that the equation to which we must be finally led is a rational equation of even degree.