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sin

sin

sin Sentence Examples

  • His main sin appears to be his poor timing.

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  • It is not a sin to want your child.

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  • Sin is the contradiction of that purpose, and guilt is alienation from the family.

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  • "Ah, what have you done to me?" it still seemed to say, and Prince Andrew felt that something gave way in his soul and that he was guilty of a sin he could neither remedy nor forget.

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  • I've been so focused on sin that I have been...

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  • Ogling a spouse couldn't be a sin – especially when he derived such obvious pleasure from it.

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  • Powers created by worldliness and sin are crumbling, as they well may; "the city of God remaineth!"

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  • Call it a sin of omission.

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  • She has done this deed for so many others, but I can't bear to heap more sin on my blackened soul and kill unborn this result of my Joshua's love.

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  • The fact that sin exists, and that great misery results from it, dawned gradually upon her mind as she understood more and more clearly the lives and experiences of those around her.

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  • It's a sin... outside marriage.

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  • Several indications favour the view of the connexion in the age of Moses between the Yahweh-cult at Sinai and the moon-worship of Babylonian origin to which the name Sinai points (Sin being the Babylonian moon-god).

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  • After the first blush of sin comes its indifference; and from immoral it becomes, as it were, unmoral, and not quite unnecessary to that life which we have made.

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  • If now you married again with the object of bearing children, your sin might be forgiven.

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  • He is appointed watchman to warn men when they sin, and is to be held responsible for the consequences if he fails in this duty.

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  • That is why it is a sin for men like you, Prince, not to serve in these times!

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  • "The sin once committed, there is no more wavering or flinching possible to him, who has fought so hard against the demoniac possession; while she who resigned body and soul to the tempter, almost at a word, remains liable to the influences of religion and remorse."

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  • This element of public confession for sin became more prominent in the days when synagogal worship developed, and prayer took the place of the sacrificial offerings which could only be offered in the Jerusalem temple.

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  • So Josephus saved them from the sin of suicide and gave himself up to the Romans.

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  • It is, of course, true that the ethical conception of sin as violation of righteousness and an act of rebellion against the divine righteous will had been developed since the days of Amos and Isaiah; but, as we have already observed, cultus and prophetic teaching were separated by an immense gulf, and in spite of the reformation of 621 B.C. still remain separated.

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  • The enzymes which act upon glucosides are many; the best known are emul sin and myrosin, which split up respectively amygdalin, the special glucoside of certain plants of the Rosaceae; and sinfgrin, which has a wide distribution among those of the Cruciferae.

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  • Yes; if I have a sin, a great sin, it is hatred of that vile woman! almost shrieked the princess, now quite changed.

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  • A venial sin, for you acted without evil intention.

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  • The icicles are prison bars on our windows, trapping us, prisoners to this life of sin and degradation...

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  • Imagine the overwhelming guilt Rev. Martin must have felt over this terrible sin of his relationship with a prostitute.

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  • " If we clearly see that what we are doing is wrong, it would be impossible for us to sin, so long as we saw it in that light."

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  • The belief was taught in the homogeneity of all living things, in the doctrine of original sin, in the transmigration of souls, in the view that the soul is entombed in the body (v13µa ojia), and that it may gradually attain perfection during connexion with a series of bodies.

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  • It's a sin to speak so.

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  • We are here moving in a realm of ideas prevailing in ancient Israel respecting holiness, uncleanness and sin, which are ceremonial and not ethical; see especially Robertson Smith's Religion of the Semites, 2nd ed., p. 446 foll.

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  • Tennant's Origin and Propagation of Sin (1902) - sin a " bye-product " of a generally good evolution.

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  • Randy has been so good about it—so encour­aging, but even so—I feel like it's a sin to smile, or laugh.

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  • The second governorship of Clive was marked by the transfer of the diwani or financial administration from the Mogul emperor to the Company, and by the enforcement of stringent regulations against the besetting sin of peculation.

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  • Once more, in the doctrine of sin and redemption, the governing idea is God's fatherly purpose for His family.

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  • The family name of the principal branch of this tribe is Abu Sin, and Gedaref, an important town in the centre of the Shukria country, was formerly called Suk Abu Sin.

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  • 1 Calvin suggested that men of known worth should be appointed in different quarters of the city to report to the ministers those persons in their district who lived in open sin; that the ministers should then warn such persons not to come to the communion; and that, if their warnings were unheeded, discipline should be enforced.

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  • In the tenth book of the Republic we find the curious argument that the soul does not perish like the body, because its characteristic evil, sin or wickedness does not kill it as the diseases of the body wear out the bodily life.

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  • Lowe was delighted with this, and promptly translated it into Latin, as follows: "Centinentur hac in fossa Humilis Roberti ossa; Si ad coelum evolabit, Pax in coelo non restabit; Sin in inferis jacebit, Diabolum ejus poenitebit."

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  • SIN, the name of the moon-god in Babylonia and Assyria, also known as Nannar, the "illuminer."

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  • After the defeat of the Abyssinians at Debra Sin in August 1887 Gondar was looted and fired by the dervishes under Abu Anga.

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  • The factors Af (u-v cos i) and Bf (v sin i) give the frictional resistance to sinking, per unit length of the cable, in the direction of the length and transverse to the length respectively.

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  • It was a noble end to what, in spite of its besetting sin of infirmity of moral purpose, was a not ignoble life.

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  • Pain and sin must have been reduced to a minimum by God; though they are so ingrained in the finite that we have to make up our minds even to the endless sin and endless punishments of hell.

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  • The confessions of sin which he introduced descend to minute ritual details and rise to the most exalted aspects of social and spiritual life.

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  • After the defeat of the Abyssinians at Debra Sin in August 1887 Gondar was looted and fired by the dervishes under Abu Anga.

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  • The factors Af (u-v cos i) and Bf (v sin i) give the frictional resistance to sinking, per unit length of the cable, in the direction of the length and transverse to the length respectively.

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  • "I often think, though, perhaps it's a sin," said the princess, "that here lives Count Cyril Vladimirovich Bezukhov so rich, all alone... that tremendous fortune... and what is his life worth?

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  • I'd drench him in sin and guilt.

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  • "It sounds like sin was a very big business," Cynthia offered as she stirred a pot of fish chowder.

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  • God can dumbness keep While Sin creeps grinning through His house of Time.

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  • At this point, abandoning the two fertilized eggs might be a worse sin.

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  • We're going to have a baby, not a sin.

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  • She knew very little of Hannah's friends, except they were all richer than sin.

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  • (2) The acceleration of the element at the origin is - n 2 sin nt; so that the force which would have to be applied to the parts where the density is D' (instead of D), in order that the waves might pass on undisturbed, is, per unit of volume, (D' - D)n 2 sin nt.

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  • The element of area being 22rr 2 sin 04,, we have f:2 l 2x r2 si n 2 d ?=gam, r so that the energy emitted from T is represented by 87r3 (D, - D) 2 T2 (9) D2 x4' on such a scale that the energy of the primary wave is unity per unit of wave-front area.

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  • The name of Sin's chief sanctuary at Ur was E-gish-shir-gal, "house of the great light"; that at Harran was known as E-khul-khul, "house of joys."

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  • Or it is the doctrine of unfallen man's " natural state " - a doctrine intensified in Protestantism - separating itself from the theologians' grave doctrine of sin.

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  • Some of the Jews had married women of Ashdod, Ammon and Moab, and the impetuous governor indignantly adjured them to desist from a practice which was the historic cause of national sin.

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  • (2) Hebrew has one more sibilant than Arabic or Syriac: thus, as corresponding to s (samekh), s (sin) sh in Hebrew, Arabic has only s (sin) sh, while Syriac has a different pair s (samekh) sh.

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  • sin and Syr.

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  • sin (Syr.

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  • sin.

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  • The sense of sin can hardly be said to enter into these exercises - that is, they are not undertaken as penance for personal transgression.

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  • (Porphyry tells us that Plotinus was unwilling to name his parents or his birthplace, and seemed ashamed of being in the body.) Beyond the uaOap ra, or virtues which purify from sin, lies the further stage of complete identification with God (ovrc w aµaprias Eivac; aXAa 0E6v Elm).

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  • His great sin in the matter of Uriah would have been forgotten but for his repentance: the things at which modern ideas are most offended are not always those that would have given umbrage to early writers.

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  • From this follows the necessity for the created spirit, after apostasy, error and sin, to return always to its origin in God.

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  • Of the names of the planets Estera (Ishtar Venus, also called Ruha d'Qudsha, "holy spirit"), Enba (Nebo, Mercury), Sin (moon), Kewan (Saturn), Bil (Jupiter), and Nirig (Nirgal, Mars) reveal their Babylonian origin; Il or Il Il, the sun, is also known as Kadush and Adunay (the Adonai of the Old Testament); as lord of the planetary spirits his place is in the midst of them; they are the source of all temptation and evil amongst men.

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  • The elliptic lemniscate has for its equation (x 2 +31 2) 2 =a 2 x 2 +b 2 y 2 or r 2 = a 2 cos 2 9 +b 2 sin 20 (a> b).

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  • The hyperbolic lemniscate has for its equation (x2 +y2)2 = a2x2 - b 2 y 2 or r 2 =a 2 cos 2 0 - b 2 sin 2 B.

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  • On the problem of evil and sin it is impossible here to enter; but this must be insisted on, that the miracles of Jesus at least express divine benevolence just under those conditions in which the course of nature obscures it, and are therefore, proper elements in a revelation of grace, of which nature cannot give any evidence.

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  • In the southwest of Manchuria a line of the imperial railways of Northern China gives connexion from Peking, and branches at Kou-pang-tsze to Sin Population.

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  • If G is the acceleration of gravity at the equator and g that at any latitude X, then g= G(IFo�o0513 sin 2 X).

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  • 20, no man is free from sin; vii.

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  • Under the new settlement Athens remained a free and sovereign city - a boon which she repaid by zealous Caesar-worship, for the favours bestowed upon her tended to pauperize her citizens and to foster their besetting sin of calculating flattery.

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  • Its object is to convince a man of sin, of justice and of judgment.

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  • The first week is the foundation, and has to do with the consideration of the end of man, sin, death, judgment and hell.

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  • Having purified the soul from sin and obtained a detestation thereof, the second week treats of the kingdom of Christ, and is meant to lead the soul to make an election of the service of God.

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  • If he says that a subject is to allow himself to be moved and directed, under God, by a superior just as though he were a corpse or as a staff in the hands of an old man, he is also careful to say that the obedience is only due in all things "wherein it cannot be defined (as it is said) that any kind of sin appears."

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  • It was thought that martyrdom would atone for sin, and imprisoned confessors not only issued to the Churches commands which were regarded almost as inspired utterances, but granted pardons in rash profusion to those who had been excommunicated by the regular clergy, a practice which caused Cyprian and his fellow bishops much difficulty.

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  • Then we have sin 2 D =sin a sin zt, and since sin a=sin (90°-1) = cos 1, it follows that sin ID = cos 1 sin it.

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  • Thus, cos D - cos a cos b cos sin a sin b cos D = cos a cos b + sin a sin b cos t = sin 1 sin l' + cos 1 cos l cos t.

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  • Contrary to the Puritan teaching of the time, they insisted on the possibility, in this life, of complete victory over sin.

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  • The writer already sees the Messianic kingdom established, under the sway of which the Gentiles will in due course be saved, Beliar overthrown, sin disappear from the earth, and the righteous dead rise to share fr1 the blessedness of the living.

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  • Up to this time Wesley says he had no notion of inward holiness, but went on "habitually and for the most part very contentedly in some or other known sin, indeed with some intermission and short struggles especially before and after Holy Communion," which he was obliged to attend three times a year.

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  • In 1765 he said it "contains all that I now teach concerning salvation from all sin, and loving God with an undivided heart."

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  • Victory over sin was the goal which he set before all his people.

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  • There shall be no more sin, no more temptation, no more suffering.

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  • They do not attempt a psychological explanation of the origin of human sin; bad thought (yeser ra`, Ecclus.

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  • Reform of this system, and, further, very necessary reforms of the methods of collection of the wines and spirits revenue (which is protection turned upside down, the home-growers being far more heavily taxed than importers), and of the customs (in which almost every possible administrative sin was exemplified), were also undertaken.

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  • But he showed admirable judgment in his choice of subordinates; Robert of Meulan, who died in 1118, and Roger of Salisbury, who survived his master, were statesmen of no common order; and Henry was free from the mania of attending in person to every detail, which was the besetting sin of medieval sovereigns.

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  • His system declared that holiness and sin are free voluntary exercises; that men act freely under the divine agency; that the slightest transgression deserves eternal punishment; that it is through God's mere grace that the penitent believer is pardoned and justified; that, in spite of total depravity, sinners ought to repent; and that regeneration is active, not passive, with the believer.

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  • The sacrament of the most Holy Eucharist shall be freely administered in the two kinds, that is bread and wine, to all the faithful in Christ who are not precluded by mortal sin - according to the word and disposition of Our Saviour.

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  • the sale of tithes, the taking of a fee for confession, absolution, marriage or burial, the concealment of one in mortal sin or the reconcilement of an impenitent for the sake of gain, and the doing homage for spiritualities.

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  • Thus what have been called seminvariants are not all of them invariants for the general substitution, but are invariants for the particular substitution xl = X11 + J-s12, X 2 = 112 Again, in plane geometry, the most general equations of substitution which change from old axes inclined at w to new axes inclined at w' =13 - a, and inclined at angles a, l3 to the old axis of x, without change of origin, are x-sin(wa)X+sin(w -/3)Y sin w sin ' _sin ax y sin w a transformation of modulus sin w' sin w' The theory of invariants originated in the discussion, by George Boole, of this system so important in geometry.

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  • Of the quadratic axe+2bxy+cy2, he discovered the two invariants ac-b 2, a-2b cos w+c, and it may be verified that, if the transformed of the quadratic be AX2=2BXY+CY2, sin w 2 AC -B 2 =) (ac-b2), sin w A-2B cos w'+C = (sin w'1 2(a - 2bcosw+c).

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  • sin w The fundamental fact that he discovered was the invariance of 2 COS w xy+y 2, viz.

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  • We have cos w' = cos w = o and the substitution x 1 =cos OX, -sin 0(2 x 2 = sin OX i +cos 6X2, with modulus unity.

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  • If the senses of rotation be opposite we have the skew orthogonal substitution x1 =cos0Xi+sinOX2r x 2 = sin °Xicos OX2r of modulus -1.

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  • In both cases ddl and dal are cogredient with xl and x 2; for, in the case of direct substitution, dxi = cost dX i - sin 00-(2, ad2 =sin B dX i +cos O dX 2, and for skew substitution dai = cos B dX i +sin 0d2, c-&-- 2 n d =sin -coseax2.

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  • sin/3 + sin Consider the binary n Ee.

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  • (aixi+a2x2)"`=4, and the direct stitution xi = XXi -, LX2, X2 =, hX replacing cos 0, sin 0 respectively.

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  • These were huge digests of all that popes, councils, primitive fathers had decided on every kind of question pertaining to the confessional - what exactly is a sin, what kind of questions the priests must ask, under what conditions he could give absolution.

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  • This made it a grave sin in the priest to refuse absolution, whenever there was some good reason for giving it even when there were other and better reasons for refusing it.

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  • 3) by F, and its components parallel to the co-ordinate axes by X and Y, we have X= - ax = M(3 cos' 0 - I), Y= - y = M (3 sin 0 cos 0.

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  • If F T is the force along r and F t that along t at right angles to r, F r =X cos 0+ Y sin 0=M 2 cos 0, F t = - X sin 0+ Y cos 0 = - r 3 sin 0.

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  • If a small magnet of moment M is placed in the sensibly uniform field H due to a distant magnet, the couple tending to turn the small magnet upon an axis at right angles to the magnet and to the force is MH sin 0, (17) where 0 is the angle between the axis of the magnet and the direction of the force.

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  • It can be deduced from (17), (12) and (13) that the couple on S'N' due to SN, and tending to increase 4), is MM' (sin 0 cos 4-2 sin 4) cos 0)/r'.

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  • (18) This vanishes if sin 0 cos 4)=2 sin 4 cos 0, i.e.

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  • The components X, Y, parallel and perpendicular to r, of the force between the two magnets SN and S'N' are X =3MM'(sin 0 sin 4)-2 cos 0 cos 4)/r 4, (21) Y=3MM'(sin 0 cos 4-{-sin 4 cos 0)/r 4 .

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  • If P is the weight of the magnet, l the length of each of the two threads, 2a the distance between their upper points of attachment, and 2b that between the lower points, then, approximately, MH = P(ab/l) sin 0.

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  • Let 0 be the angle which the standard magnet M makes with the meridian, then M'/R = sin 0, and M/R = cos 0, whence M' = M tan 0.

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  • He presupposes a nation of Yahweh-worshippers, whose religion has its centre in the temple and priesthood of Zion, which is indeed conscious of sin, and needs forgiveness and an outpouring of the Spirit, but is not visibly divided, as the kingdom of Judah was.

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  • The impressiveness and the stimulating power of the mystic ceremonies, the consciousness of being the privileged possessor of the secret wisdom of the ancients, the sense of purification from sin, and the expectation of a better life where there was to be compensation for the sufferings of this world - were all strong appeals to human nature.

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  • From that time Conselheiro was a victim of remorse, and to expiate his sin became a missionary in the sertao or interior of Brazil among the wild Jagunco people.

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  • If the primary wave at 0 be cos kat, the effect of the secondary wave proceeding from the element dS at Q is dS 1 dS - p cos k(at - p+ 4 A) = - -- sin k(at - p).

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  • If dS =27rxdx, we have for the whole effect 27r œ sin k(at - p)x dx, f P ' or, since xdx = pdp, k = 27r/A, - k fr' sin k(at - p)dp= [- cos k(at - p)]°° r.

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  • The amplitude of the light at any point in the axis, when plane waves are incident perpendicularly upon an annular aperture, is, as above, cos k(at-r 1)-cos k(at-r 2) =2 sin kat sin k(r1-r2), r2, r i being the distances of the outer and inner boundaries from the point in question.

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  • The second and third factors of (3) being each of the form sin 2u/u2, we have to examine the character of this function.

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  • The maxima occur when u=tan u, (4), and then sin 2 u/u 2 = cos 2 u (5).

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  • 15, p. 315) to determine the absolute intensity of a secondary wave, may be at once effected by means of the known formula isin 2 u f sin u du = du =7-.

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  • In the direction (suppose horizontal) for which n=o, /f=sin 0, the phases of the secondary waves range over a complete period when sin 0 =X/a, and, since all parts of the horizontal aperture are equally effective, there is in this direction a complete compensation and consequent absence of illumination.

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  • When sin 0 = 2A/a, the phases range one and a half periods, and there is revival of illumination.

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  • In like manner we may find the illumination in any other direction, and it is obvious that it vanishes when sin 0 is any multiple of A/a.

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  • 3), representing the value of the function sin 2 u/u 2 from u=o to u=271.

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  • (2), where S = ff sin(px+gy)dx dy,.

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  • This integral is the Bessel's function of order unity, defined by J,(z) n (z cos 0) sin 24 d4)..

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  • Trans., 1834) in his original investigation of the diffraction of a circular object-glass, and readily obtained from (6), is z z 3 25 27 J1(z) = 2 2 2.4 + 2 2.4 2.6 2 2.4 2.6 2.8 + When z is great, we may employ the semi-convergent series Ji(s) = A/ (7, .- z)sin (z-17r) 1+3 8 1 ' 6 (z) 2 3.5.7.9.1.3.5 5 () 3 1 3.5.7.1 1 3 cos(z - ?r) 8 ' z (z) 3.5.7.9.11.1.3.5.7 1 5 + 8.16.24.32.40 (z

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  • Thus, if x = p cos 4), y= p sin 0, C =11 cos px dx dy =f o rt 2 ' T cos (pp cos 0) pdp do.

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  • When z is great, the descending series (io) gives i 2J 1 (z) = 2 sin (z1 7r) 22; (2) z so that the places of maxima and minima occur at equal intervals.

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  • Now since AP is very small, AL' - PL'= AP sin a, where a is the angular semi-aperture L'AB.

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  • In like manner PL - AL has the same value, so that PL - PL' = 2AP sin a.

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  • Calling the refractive index µ, we have as the critical value of e=2Xo/ µ sin a, (1).

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  • The denominator sin a is the quantity well known (after Abbe) as the " numerical aperture."

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  • 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.

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  • (7) If B m denote the brightness of the mth lateral image, and Bo that the central image, we have amp 'cosx' dx= a d (1) (-) m7r B.: Bo= a+d am?r sin' a4 d (1).

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  • hen d =a the general formula becomes sin' Zm7r Bm: B = (3), showing that, when m is even, B m vanishes, and that, when m is odd, B m: B =1/m272.

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  • 6), and the diffracted rays make an angle ¢ (upon the same side), the relative retardation from each element of width (a+d) to the next is (a+d) (sin 9 +sin op); and this is the quantity which is to be equated to mX.

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  • Thus sin e +sin 0=2 sin 2(0+x) cos 2(0-0) = mX/(a +d) (5).

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  • To find the former, we have, if OAQ=4), AOP=w, QP 2 =u 2 +4a 2 sin 2 2w - 4au sin la) sin (2w-4)) = (u +a sin 4) sin w) 2 -a 2 sin 2 4)sin 2 c0+4a sin 2 2w(a-u cos 0).

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  • But if we now suppose that Q lies on the circle u= a cos 0, the middle term vanishes, and we get, correct as far as w4, QP= (u+a sin 4) sin w) 1 ' 3 1 {- a sin2c?sin4w V 4u so that QP - u=asin0sinw -Ft asin¢tanOsin 4 w..

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  • (9), in which it is to be noticed that the adjustment necessary to secure the disappearance of sin 2w is sufficient also to destroy the term in sin' w.

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  • A similar expression can be found for Q'P - Q"A; and thus, if Q' A =v, Q' AO = where v =a cos (0", we get - - -AQ' = a sin w (sin 4 -sink") - - 8a sin 4 w(sin cktan 4 + sin 'tan cl)').

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  • 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.

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  • For this purpose Rowland places the eye-piece at 0, so that 0 =o, and then by (11) the value of '" in the m th spectrum is o- sin $' = tmX.

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  • If w now relate to the edge of the grating, on which there are altogether n lines, no- = 2a sin w, and the value of the last term in (I o) becomes no- sin 3w sin O'tan 0', - 1 1 - 6 mnX sin' w tan 0'.

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  • f + 1 sin k a - f+ " dxdy = - 2 1h sin n k ?.

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  • If we put for shortness 7 for the quantity under the last circular function in (I), the expressions (i), (2) may be put under the forms u sin T, v sin (T - a) respectively; and, if I be the intensity, I will be measured by the sum of the squares of the coefficients of sin T and cos T in the expression u sin T +v sin (T - a), so that I =u 2 +v 2 +2uv cos a, which becomes on putting for u, v, and a their values, and putting f =Q .

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  • The constant multiplier is of no especial interest so that we may take as applicable to the image of a line 0 I = z 2 sin e A f 1+cos ` - 271 - Eh).

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  • In the second term if we observe that cos {p'+ 27rh/Af)E} =cos{p' - g,E} = cos p cos g, +sin p sin giE, we see that the second part vanishes when integrated, and that the remaining integral is of the form w = f +.0 sin z h, cos where h,=7rh/Af, g,=a-27Th/Af.

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  • v sin ?i, where a is the grating-interval and 43, the obliquity, the closeness of the grouping increasing with the number of intervals.

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  • By separation of real and imaginary parts, C =M cos 27rv 2 +N sin 27rv2 1 S =M sin 27rv 2 - N cos 27rv2 where 35+357.9 N _ 7rv 3 7r 3 v 7 + 1.3 1.3.5.7 1.3.5.7.9.11 These series are convergent for all values of v, but are practically useful only when v is small .

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  • dx ru i-x) C-Fi S= „ 7 o?I x o 1 fGO dx eu(ti-x) - 1 2Jo x i - x Thus, if we take _ 1 `°el 1 ('°° e uxdx G 7r12 Jo 1+ x 2 ' H 7r-N/2Jo -Vx.(1-i-x2)' C = 2-G cos u+ H sin u, S =1---G sin u-H cos u.

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  • (19), 1 abA) ' ' we may write 12= (cos 27rv 2 .dv) 2 + (f sin zirv 2 .dv) 2 (20), or, according to our previous notation, 12 = (2 - C 2 +(z - Sv)2= G2 +H2 Now in the integrals represented by G and H every element diminishes as V increases from zero.

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  • 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..

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  • 19, where, according to the definition (5) of C, S, x =i v cos 27rv 2 .dv, y = f v sin ?7rv 2 .dv..

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  • For dx=cos airv 2 .dv, dy= sin 271-v2.dv; so that s = f (dx 2 +dy 2) =v, (30), 0= tan1 (dyldx) =171-v 2 (31).

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  • Then the displacement at 0 will take place in a direction perpendicular to 0 1 0, and lying in the plane Z0 1 0; and, if 1' be the displacement at 0, reckoned positive in the direction nearest to that in which the incident vibrations are reckoned positive, = 4?y (1 +cos 0) sin 4 f' (bt - r).

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  • f(bt - x) =c sin 2 i n: (bt - x).

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  • we shall have '2y (1 +cos e)sin cos 2?

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  • The occurrence of sin 4 as a factor in (6) shows that the relative intensities of the primary light and of that diffracted in the direction B depend upon the condition of the former as regards polarization.

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  • 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.

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  • 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) ?

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  • - 47rb 2 ' The occurrence of sin 4 shows that there is no disturbance radiated in the direction of the force, a feature which might have been anticipated from considerations of symmetry.

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  • We will now apply (18) to the investigation of a law of secondary disturbance, when a primary wave = sin (nt - kx) (19) is supposed to be broken up in passing the plane x = o.

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  • According to (18), the effect of the force acting at dS parallel to OZ, and of amount equal to 2b2kD dS cos nt, will be a disturbance - dS sin cos (nt - kr) (20), regard being had to (12).

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  • The proportionality of the secondary disturbance to sin 43 is common to the present law and to that given by Stokes, but here there is no dependence upon the angle 0 between the primary and secondary rays.

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  • The occurrence of factors such as sin 4), or 2 (1cos 0), in the expression of the secondary wave has no influence upon the result of the integration, the effects of all the elements for which the factors differ appreciably from unity being destroyed by mutual interference.

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  • Now, both the Korahite and Asaphic groups of psalms are remarkable that they hardly contain any recognition of present sin on the part of the community of Jewish faith - though they do confess the sin of Israel in the past - but are exercised with the observation that prosperity does not follow righteousness either in the case of the individual (xlix., lxxiii.) or in that of the nation, which suffers notwithstanding its loyalty to God, or even on account thereof (xliv., lxxix.).

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  • Malachi, Ezra and Nehemiah, like Haggai and Zechariah, are still very far from holding that the sin of Israel lies all in the past.

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  • Since the angles of incidence and refraction are connected by the relation sin i=µ sin r (Snell's Law), µ being the index of refraction of the medium, then the problem may be stated as follows: to determine the value of the angle i which makes D = 2 (i - r) +n (7r - 2r) a maximum or minimum, in which i and r are connected by the relation sin i =µ sin r, µ being a constant.

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  • They no doubt deferred the baptism which is death to sin, perhaps because, like the Cathars, they held post-baptismal sin to be unforgivable.

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  • The Key of Truth regards the water as a washing of the body, and sees in the rite no opus operatum, but an essentially spiritual rite in which "the king releases certain rulers a from the prison of sin, the Son calls them to himself and comforts them with great words, and the Holy Spirit of the king forthwith comes and crowns them, and dwells in them for ever."

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  • the moon-god Sin) it has a kind of straight brim which gives it a certain resemblance to a low-crowned " bowler."

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  • 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.

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  • His extraordinary thinness is commemorated, among other things, by the very poor but well-known epigram attributed to Young, and identifying him at once with "Satan, Death and Sin."

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  • of the area A, f f xdxdy = o, ffydxdy = 0, (6) R = p hA, (7) xhA = - cos a f f x 2 dA - sin affxydA, fxydA, (8) yhA = - cos a ff xydA - sin ail y 2 dA.

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  • (9) Turning the axes to make them coincide with the principal axes of the area A, thus making f f xydA = o, xh = - a 2 cos a, y h = - b 2 sin a, (io) where ffx2dA=Aa2, ffy 2 dA= Ab 2, (II) a and b denoting the semi-axes of the momental ellipse of the area.

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  • The varying direction of the inclining couple Pc may be realized by swinging the weight P from a crane on the ship, in a circle of radius c. But if the weight P was lowered on the ship from a crane on shore, the vessel would sink bodily a distance P/wA if P was deposited over F; but deposited anywhere else, say over Q on the water-line area, the ship would turn about a line the antipolar of Q with respect to the confocal ellipse, parallel to FF', at a distance FK from F FK= (k2-hV/A)/FQ sin QFF' (2) through an angle 0 or a slope of one in m, given by P sin B= m wA FK - W'Ak 2V hV FQ sin QFF', (3) where k denotes the radius of gyration about FF' of the water-line area.

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  • Taking the axis of x for an instant in the normal through a point on the surface H = constant, this makes u = o, = o; and in steady motion the equations reduce to dH/dv=2q-2wn = 2gco sin e, (4) where B is the angle between the stream line and vortex line; and this holds for their projection on any plane to which dv is drawn perpendicular.

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  • For example, a pair of equal opposite vortices, moving on a line parallel to a plane boundary, will have a corresponding pair of images, forming a rectangle of vortices, and the path of a vortex will be the Cotes' spiral r sin 20 = 2a, or x-2+y-2=a-2; (io) this is therefore the path of a single vortex in a right-angled corner; and generally.

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  • if the angle of the corner is jr/n, the path is the Cotes' spiral r sin n0=na.

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  • (22) Conjugate functions can be employed also for the motion of liquid in a thin sheet between two concentric spherical surfaces; the components of velocity along the meridian and parallel in colatitude 0 and longitude A can be written d¢_ i _ d4, I dip _ dy (13) d8 sin - 0 dX' sin 0 dX de' and then = F (tan O.

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  • Consider the motion given by w=U(z+a2/z), (I) 4,=U(r+- r) cos 0= U + a1x, so that (2) = U (r-)sin 0= U(i -¢) y.

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  • Then 4, =o over the cylinder r = a, which may be considered a fixed post; and a stream line past it along which 4, = Uc, a constant, is the curve (r - ¢2) sin 0=c, (x2 + y2) (y - c) - a 2 y = o, (3) a cubic curve (C3).

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  • If the liquid is reduced to rest at infinity by the superposition of an opposite stream given by w = - Uz, we are left with w = Ua2/z, (6) =U(a 2 /r) cos 0= Ua2x/(x2+y2), (7) 4, = -U(a 2 /r) sin 0= -Ua2y/( x2+y2), (8) giving the motion due to the passage of the cylinder r=a with velocity U through the origin 0 in the direction Ox.

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  • Along the path of a particle, defined by the of (3), _ c) sine 2e, - x 2 + y2 = y a 2 ' (Io) sin B' de' _ 2y-c dy 2 ds ds' on the radius of curvature is 4a 2 /(ylc), which shows that the curve is an Elastica or Lintearia.

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  • When the cylinder r =a is moved with velocity U and r =b with velocity U 1 along Ox, = U b e - a,1 r +0 cos 0 - U ib2 - 2 a, (r +Q 2 ') cos 0, = - U be a2 a2 (b 2 - r) sin 0 - Uib2 b1)a, (r - ¢2 sin 0; b and similarly, with velocity components V and V 1 along Oy a 2 b2 ?= Vb,_a,(r+r) sin g -Vi b, b2 a, (r+ 2) sin 0, (17) = V b, a2 a, (b2 r) cos 0+Vi b, b, a, (r- ¢ 2) cos h; (18) and then for the resultant motion z 2zz w= (U 2 + V2)b2a a2U+Vi +b a b a2 U z Vi -(U12+V12) b2 z a2b2 Ui +VIi b 2 - a 2 U1 +Vii b 2 - a 2 z The resultant impulse of the liquid on the cylinder is given by the component, over r=a (§ 36), X =f p4 cos 0.ad0 =7rpa 2 (U b z 2 + a 2 Uib.2bz a2); (20) and over r =b Xi= fp?

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  • Taking two planes x = =b, and considering the increase of momentum in the liquid between them, due to the entry and exit of liquid momentum, the increase across dy in the direction Oy, due to elements at P and P' at opposite ends of the diameter PP', is pdy (U - Ua 2 r2 cos 20 +mr i sin 0) (Ua 2 r 2 sin 2 0+mr 1 cos 0) + pdy (- U+Ua 2 r 2 cos 2 0 +mr1 sin 0) (Ua 2 r 2 sin 2 0 -mr 1 cos 0) =2pdymUr '(cos 0 -a 2 r 2 cos 30), (8) and with b tan r =b sec this is 2pmUdo(i -a 2 b2 cos 30 cos 0), (9) and integrating between the limits 0 = 27r, the resultant, as before, is 27rpmU.

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  • Consider the streaming motion given by w =m =a+si, (5) 4=m ch (n -a)cos(-0), p=m sh(n-a)sin(-13).

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  • Over any ellipse n, moving with components U and V of velocity, =i+Uy-Vx=[msh(n-a) cos (3+Ucshn] sin k -[msh(n-a) sin (3+Vcchn] cos h; (7) so that ' =o, if U c sh n cos R, V = c ch n sin a, (8) m sh(n - a) m sh(n - a).

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  • An ellipse interior to n = a will move in a direction opposite to the exterior current; and when n = o, U = oo, but V = (m/c) sh a sin 13.

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  • The resultant hydrostatic thrust across any diametral plane of the cylinder will be modified, but the only term in the loss of head which exerts a resultant thrust on the whole cylinder is 2mU sin Olga, and its thrust is 27rpmU absolute units in the direction Cy, to be counteracted by a support at the centre C; the liquid is streaming past r=a with velocity U reversed, and the cylinder is surrounded by a vortex.

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  • Similarly, the streaming velocity V reversed will give rise to a thrust 27rpmV in the direction xC. Now if the cylinder is released, and the components U and V are reversed so as to become the velocity of the cylinder with respect +m /a) 2 - U2 The components of the liquid velocity q, in the direction of the normal of the ellipse n and hyperbola t, are -mJi sh(n--a)cos(r-a),mJ2 ch(n-a) sin (E-a).

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  • Next consider the motion given by = m ch 2(77a)sin 2E, tii= -m sh 2(na)cos 2E; (I) in which > ' =o over the ellipse a, and =1'+IR(x2+y2) =[ -m sh 2(7 7 -a)+4Rc 2 ]cos 4Rc2 ch 2n, (2) which is constant over the ellipse n if 4Rc 2.

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  • The velocity of a liquid particle is thus (a 2 - b 2)/(a 2 +b 2) of what it would be if the liquid was frozen and rotating bodily with the ellipse; and so the effective angular inertia of the liquid is (a 2 -b 2) 2 /(a 2 +b 2) 2 of the solid; and the effective radius of gyration, solid and liquid, is given by k 2 = 4 (a 2 2), and 4 (a 2 For the liquid in the interspace between a and n, m ch 2(0-a) sin 2E 4) 1 4Rc 2 sh 2n sin 2E (a2_ b2)I(a2+ b2) = I/th 2 (na)th 2n; (8) and the effective k 2 of the liquid is reduced to 4c 2 /th 2 (n-a)sh 2n, (9) which becomes 4c 2 /sh 2n = s (a 2 - b 2)/ab, when a =00, and the liquid surrounds the ellipse n to infinity.

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  • x+yi =c1,1 [sin(+ 7 ni)] (17) i ' =Qc sh((n-a)sin((E-,6) (18) 'will give motion streaming past the fixed cylinder n = a, and dividing along t =43; and then x 2 -3/ 2 = c 2 sin ch n, 2xy = c 2 cos sh n.

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  • The polar equation of the cross-section being rI cos 19 =al, or r + x = 2a, (3) the conditions are satisfied by = Ur sin g -2Uairi sin IB = 2Uri sin 10(14 cos 18a'), (4) 1J/ =2Uairi sin IO = -U1/ [2a(r-x)], (5) w =-2Uaiz1, (6) and the resistance of the liquid is 2lrpaV2/2g.

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  • Similarly, with the function (19) (2n+ I) 3 ch (2n+ I) ITrb/a' (2) Changing to polar coordinates, x =r cos 0, y = r sin 0, the equation (2) becomes, with cos 0 =µ, r'd + (I -µ 2)-d µ = 2 ?-r3 sin 0, (8) of which a solution, when = o, is = (Ar'+) _(Ari_1+) y2,, ?

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  • For instance, with n = I in equation (9), the relative stream function is obtained for a sphere of radius a, by making it, y' =1y+2Uy 2 = 2U(r 2 -a 3 /r) sin?

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  • 0, 1, = -ZUa 3 sin e B/r; (13) and then =Ux(I+1a3/r2), 4=ZUa 3 cos 0/r2, -d r = Ua3 cos B, -d9=ZUa3 sin 0, so that, if the direction of motion makes an angle >G with Ox, tan (4y-0) =Z tan 0, tan =3 tan 0/(2-tan 2 e).

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  • (16) Along the path of a liquid particle 4)' is constant, and putting it equal to 2Uc2, (r 2 - a 3 /r) sin 2 0 = c 2, sin 2 0 = c2r/(r3 - a3), (17) the polar equation; or y 2 = c2r3/(r3 - a 3), r3 = a3y2 /(y2._ c2), (18) a curve of the 10th degree (C10).

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  • In the absolute path in space cos Ili = (2 - 3 sin 2 6)/1/ (4-sin 2 6), and sin 3 B = (y 3 -c 2 y)/a 3, (19) which leads to no simple relation.

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  • The velocity past the surface of the sphere is dC r sin 0 dy 2U (2r+ a 2) r sin g z U sin e, when r =a; (20) so that the loss of head is (!

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  • sin e 0 - i) U 2 /2g, having a maximum a U 2 /2g, (21) which must be less than the head at infinite distance to avoid cavitation at the surface of the sphere.

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  • Put S2 1 =12 cos 4, 12 2 = -12 sin 4, d4 d52 1 dS22 Y a2+c2 122 7Ti = 71 22 CL2- c2(121+5221)J, a2 +c2 do a2+c2 + 4c2 z dt a'-c2 (a2+,c2)2 M+2c2(a2-c2 N-{-a2+c2 2 Ý_a 2 +c 2 (' 4c2 .?"d za 2 -c 2 c2)2 2'J Z M+ -c2) which, as Z is a quadratic function of i 2, are non-elliptic so also for; G, where =co cos, G, 7 7 = - sin 4.

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  • Uniplanar motion alone is so far amenable to analysis; the velocity function 4 and stream function 1G are given as conjugate functions of the coordinates x, y by w=f(z), where z= x +yi, w=4-Plg, and then dw dod,y az = dx + i ax - -u+vi; so that, with u = q cos B, v = q sin B, the function - Q dw u_vi=g22(u-}-vi) = Q(cos 8+i sin 8), gives f' as a vector representing the reciprocal of the velocity in direction and magnitude, in terms of some standard velocity Q.

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  • If there are more B corners than one, either on xA or x'A', the expression for i is the product of corresponding factors, such as in (5) Restricting the attention to a single corner B, a = n(cos no +i sin 110) _ (b-a'.0-a) +1!

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  • (b-a.0-a) (6) (Q) AI (a-a .0b) ch n2= ch log (Q) n cos 114+i sh log (9) re sin n9 = 2(r+ fi n) = b - a ' ju -a (7) a-a' l u-b nf2 = sh log (cos nO +1 ch log (" sin 110 =2(?"

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  • 2n u (a -b.b -a')' not requiring the integration of (II) and (12) If 0=a across the end J J' of the jet, where u = oo, q= Q, b-a' a-b ch 7/2,=cos na = I, , sh 162 = i sin na = i,, a - a a-a Then a-a'+(a+a) cos 2na-[a+a'+(a-a) cos 2najcos 2110 (a-a') sin' 2na X cos 211a - cos 2110 Along the wall AB, cos nO =o, sin n0= I, a> u> b, ch n2= i sh log (q) n= i?

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  • m _ c Q du dO dt - rrqu 2r qu AB _ Q du L bq (u -a') +V (b -a')1,l (a -u)11/ndu) L 1,1 (a-a/),,1 (u-b), f u Along the wall Bx, cos n0 =I, sin n0 =o, b >u>o ch nSt = ch log () n=, , fb-a?, ?

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  • 5, I ch S2 = u a, sh C2= ' u (I) (I and along the jet APJ, oo > u=aerslc>a, sh S2=i sin 0 =iu=ie zrs/o, (2) PM sin 0 ds = f e ds = 1 = 1 sin 0, (3) cos 272a - cos 2n0 = 2Q - ?ib L a b2 s i n' 27ta u-b A (a- (u -a.u -b') sin 2110 - 2 a-a .u-b  ?l (u -a.u -a') = s in 2na u-b 2n b) A (ab.ba') p l u -bJ (u -a.u -a') sh nS2=i sin 110=i then the radius sin 2170 (30) A', cos nO= i, sin n0=o, n 1 ' b-a' ch nS2= ch log (9) = Va -a' n shnS2= shlog (Q) q _ o> u>a'.

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  • Along the jet surface A'J', q = Q, b-a' ch nSl= cos 110= a-a la - b sh nft=i sin nO=i a'>u=a'erl"> -oo, giving the intrinsic equation.

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  • (I) Over the jet surface 4'=m, q=Q, u=-e rr,lm= -berslc, ch SZ=cos n0= e>rsle+I, shS2 =i sin ins =tan ds 2n (3) e2 =tan nO, - c dB sin 2,10' For a jet impinging normally on an infinite plane, as in fig.

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  • b a-b (7) cos = a, sin na = 1j a, nd along the free surface APJ, q =Q, 4) =o, u =e-.

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  • u -b' Along a jet surface, q=Q, and ch S2= cos 0 =cos a-i sin2a(a-a')/(u-b), (5) if 0 =-a at the source x of the jet xB, where u = co; and supposing 0=0,13 at the end of the streams where u =j, j', u-b i sin 2 a u - j cos 0-cos /3 i a -a cos a sin a -cos 0' aa' - 2 (cos a -cos (3) (cos a-cos 0)' u-j' 1 2 cos 0-cos, (6) a -a' - 2 S i n a (cos a -cos (3') (cos a -cos B)' and 4' being constant along a stream line d4 - dw ds _d8 d4 _ dw du du du' d- -dud0' 7rQ ds_ it ds (cos a-cos /3) (cos a -cos (3') sin 0 m+m' dB c d0 - (cos a-cos B) (cos 0-cos /3) (cos 0 -cos /3')' _ sin 0 cos a-cos 13 sin 0 - cos a-cos B + cos 0-cos (3' cos 0-cos 13 cos a -cos $ sin 6 cos (3-cos /3' cos 0-cos 0" giving the intrinsic equation of the surface of a jet, with proper attention to the sign.

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  • From A to B, a>u >b, 0=0, ch S2= ch log Q=cos a-i sin 2a a-b I sh S2= sh log Q= I (a u-b-a/) s i n a Q = (u-b) cos a-2(a-a') sin 2 a+1,/ (a-u.u- a')sin a (8) u-b ds _ ds d4 _ Q dw Q du - Q d 4) du q du (u-b) cos a-2(a- a') sin 2 a (a-u.0 - a') sin a (9) it j- -j' AB _f a(2b - a - a')(u-b)-2(a-b)(b-a')+2V (a - b.

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  • 8 (2) (4) e, rs /c e ns/c + I' (2) cos n0= cos na-N e' 31 ' - cos'na' cos 2 na sin2n0 (8) sin 2 n0 - sin2na' he intrinsic equation, the other free surface A'P'J' being given by e m /?

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  • - cos 2 na sin2ng s (9) sin 2 na - sin2n0 Putting n =I gives the case of a stream of finite breadth disturbed y a transverse plane, a particular case of Fig.

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  • Trans., 1890); the solution is given by ch nS2=sn w, shnS2=i cn w (II) so that, round the boundary of the polygon, ik = K', sin n8 =o; and on the surface of the vortex 1P= o, q = Q, and cos n8=sn4p,nB= Zit -am sic, (12) the intrinsic equation of the curve.

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  • Introducing Euler's angles 0, c15, x1= F sin 0 sin 0, x 2 =F sin 0 cos 0, xl+x 2 i =iF sin 0e_, x 3 = F cos 0; sin o t=P sin 4+Q cos 0, dT F sin 2 0d l - dy l + dy 2x = (qx1+ryi)xl +(qx2+ry2)x2 = q (x1 2 +x2 2) +r (xiyi +x2y2) = qF 2 sin 2 0-Fr (FG - x 3 y 3), (16) _Ft (FG _x 323 Frdx3 (17) F x3 X3 elliptic integrals of the third kind.

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  • well as of the body from the vector OF to O'F' requires an impulse couple, tending to increase the angle F00', of magnitude, in sec. foot-pounds F.00'.sin FOO'=FVt sin (0-0), (4) equivalent to an incessant couple N=FV sin (0-0) = (F sin 0 cos 0-F cos 0 sin ¢)V = (c 2 -c i) (V /g) sin 0 cos 4) =W'(13-a)uv/g (5) This N is the couple in foot-pounds changing the momentum of the medium, the momentum of the body alone remaining the same; the medium reacts on the body with the same couple N in the opposite direction, tending when c 2 -c 1 is positive to set the body broadside to the advance.

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  • 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) .

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  • For the body alone the resultant of the components of momentum W V -cos andW V sin 0 is W V -sec. lb, acting along 00', and so is unaltered.

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  • the moment of inertia of the body about the axis, denoted by But if is the moment of inertia of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o.

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  • As the ring is moved from 0 to 0' in time t, with velocity Q, and angular velocity R, the components of liquid momentum change from aM'U +E and SM'V along Ox and Oy to aM'U'+ and /3M'V' along O'x' and O'y', (I) the axis of the ring changing from Ox to O'x'; and U = Q cos 0, V = Q sin 0, U' =Q cos (o - Rt), V' =Q sin (0 - Rt), (2) so that the increase of the components of momentum, X 1, Y 1, and N1, linear and angular, are X 1 = (aM'U'+ 0 cos Rt - aM'U - - 1 3M'V' sin Rt =(a - (3)M'Q sin_(0 - Rt) sin Rt - ver Rt (3) Y 1 = (aM'U'+) sin Rt-[-13M'V' cos Rt - (3M'V = (a - (3) M'Q cos (0 - Rt) sin Rt +t sin RT, N1=[ - (aM'U'+E) sin (0 - Rt)+ 1 3M'V' cos (o - Rt)]OO' = [- (a - 1 3) M'Q cos (o - Rt) sin (o - Rt) - sin (o - Rt) ]Qt.

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  • X i /t=(a - (3)M'QR sin 0= (a - (3)M'VR, (6) Y=It.

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  • ZI /t = - (a - s) M'Q 2 sine cos ° - EQ sin() =[ - (a - (3)M'U+E]V (8) Now suppose the cylinder is free; the additional forces acting on the body are the components of kinetic reaction of the liquid - aM' (Ç_vR), - (3M' (-- E -FUR), - EC' dR, (9) so that its equations of motion are M (Ç - vR) _ - aM' (_vR) - (a - $) M'VR, (io) M (Ç+uR) = - OM' (dV+U R) - (a - ()M'UR - R, '(II) C dR = dR + (a - Q)M'UV+0V; (12) and putting as before M+aM'=ci, M+13M' = c2, C+EC'=C3, ci dU - c2VR=o, dV +(c1U+E)R=o, c 3 dR - (c 1 U+ - c 2 U)V =o; showing the modification of the equations of plane motion, due to the component E of the circulation.

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  • The integral of (14) and (15) may be written ciU+E=Fcoso, c 2 V= - Fsino, dx F cost o F sinz o 71 = U cos o - V sin o = cl + c c ic os o, chi = U sine +V coso= (F - F) sin cos o - l sino, (19) c i 2 2 2 sin o cos o - l ?

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  • sin o= F dl, (20) C3 do F2 h _ F2 cos 2 o F 2 sin z o F dt y - V C G c +2 c1 coso+H]; (21) 1 z so that cos 0 and y is an elliptic function of the time.

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  • Another son was high-priest of the city of Tutu, and in the name of his daughter, Lipus-Eaum, a priestess of Sin some ur dynasty.

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  • Copper Vot1 Sin, King Of Larsa.

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  • The last king of Assyria was probably the brother of Assur-etil-ilani, Sin - sar - iskun (Sin-sarra-uzur), who seems to have been the Sarakos (Saracus) of Berossus.

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  • The moon-god Sin is written by a sign which has the force of " thirty," and is a distinct reference to the monthly course of the planet; or the name is written by two signs to be pronounced EN-ZU, which describe the god as the " lord of wisdom."

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  • 1) and treat of the sin of the angels that led to the flood, and of their temporal and eternal punishment.

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  • 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.

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  • It is possible for a regenerate man to live without sin.

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  • brings the prophet a new sense of sin as essentially a matter of the heart, and an awakened conscience as before the " glory of God," the Creator and Upholder of all things.

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  • But, while Samaria is summarily dismissed, the sin of Judah is analysed at length in chs.

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  • At last the power and influence of the spirits of darkness, with whom man associates himself by his sin, became so great that the existence of the human race was threatened, and Jehovah was necessitated to descend into nature to restore the connexion between Himself and man.

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  • The romantic school was supported by Sin Otetchestva (1812), " Son of the Fatherland," united in 1825 to the Severnoi Arkhiv (1822), which dwindled and came to an end soon after 1839.

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  • 451 affirmed "that Christ is true God and true man, according to His Godhead begotten from eternity and like the Father in everything, only without sin; and that after His incarnation the unity of the person consists in two natures which are conjoined without confusion, and without change, but also without rending and without separation."

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  • 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.

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  • Its preaching is practical and direct, asseverating the reality of Sin, "the everlasting punishment of the wicked," and Redemption.

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  • It ex pounded in terse and significant teaching the doctrine (1) of God, (2) of original sin, (3) of the Son of God, (4) of justification..

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  • It deals with the Bible as the final appeal in controversy, the doctrines of God, man, sin, the Incarnation, the Resurrection of our Lord Jesus Christ, " both the Son of man and the Son of God," the work of the Holy Spirit, justification by faith, the perpetual obligation of Baptism and the Lord's Supper, final judgment, the law of Christian fellowship. The same principles have been lucidly stated in the Evangelical Free Church catechism.

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  • Sin; 9.

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  • He knows that the great object of all my preaching and writing was to convert men from sin.

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  • The church key reminds him that "it is my sin that locks his handes," and the stones of the floor are patience and humility, while the cement that binds them together is love and.

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  • Of in Jesus Christ the Saviour, who delivers from the bondage of sin by his life, doctrine and death; in the operation of the Holy Ghost; in a holy, universal, Christian church; in forgiveness of sins and the life everlasting.

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  • The latter enunciated the following rule: " If a bishop or priest be living in mortal sin, then he neither ordains, nor consecrates, nor baptizes."

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  • The Cathars even held it necessary, in case a bishop fell into mortal sin, to repeat his ba p tisms and ordinations, for they had been vitiated by his sins.

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