Thus, to cite but one example, the Pax Britannica of the nineteenth century, whether with the British navy ruling the seas or with the City of London ruling world finance, was strictly national in motivation, however much other nations ( e.g., the United States ) may have incidentally benefited.

Thus, Margenau remarks: `` A large number of unrelated epicycles was needed to explain the observations, but otherwise the ( Ptolemaic ) system served well and with quantitative precision.

Thus, the Church was born and because of its intrinsic character was soon identified as a conservative institution, determined to resist the forces of change, to identify itself with the political rulers, and to maintain a kind of splendid isolation from the masses.

Thus, when the Russians sent up their first sputnik, American chagrin was human enough, and American determination to put American satellites into orbit was perfectly understandable.

Thus, a finding of conspiracy to restrain trade or attempt to monopolize was excluded from the Court's decision.

Thus, in the last few years, a number of programs which looked very promising at the time their development was commenced have since been completely eliminated.

Thus was invented the single thread sewing machine, which Mr. Gibbs in partnership with Mr. Willcox decided to bring to Brown & Sharpe with the proposal that the small company undertake its manufacture.

Thus it was that Barco, apprehended for mere larceny, now began to suspect that one or another of his murders had been uncovered.

Thus, the energy transferred from the arc to the anode was partly fed back into the arc.

Thus, the dotted line shown in figure 4 was taken as typical for the temperature distribution for all blowing rates.

Thus, the Span of its ossification was shortened and the center's ability to `` catch up '' in ossification is demonstrated.

Thus to has light stress both in that was the conclusion that I came to and in that was the conclusion I came to.

Thus the Congress marks a formal recognition of the political system that was central to world politics for a century.

Thus, in the immemorial way -- in the way of the right hand that knows and the left that does not -- was the stage set for tragedy at Bari.

Thus at the same time that William Henry Harrison was preparing to pacify the aborigines of Indiana Territory and winning fame at the battle of Tippecanoe, Anglo-Saxon settlement made a great leap into the center of the North American continent to the west of the American agricultural frontier.

Thus, when Dartmouth's Winter Carnival -- widely recognized as the greatest, wildest, roaringest college weekend anywhere, any time -- was broadcast over a national television hookup, Prexy John Sloan Dickey appeared on the screen in rugged winter garb, topped off by a tam-o'-shanter which he confessed had been acquired from a Smith girl.

Thus when Premier Khrushchev intimated even before inauguration that he hoped for an early meeting with the new President, Mr. Kennedy was confronted with a delicate problem.

Thus `` America '', the most widely sung of the patriotic songs, was written by a New England Baptist clergyman, Samuel Francis Smith ( 1808-1895 ), while a student in Andover Theological Seminary.

Thus, the Mahayana metaphysic of mystical union for salvation was distilled down to a bare self-seeking, and for this reason, the mystic in Asia did not long remain in isolated contemplation.

Thus there was really an excess of eighteenth-century charm as one of these light-weight pieces followed another on Saturday night.

Thus, the masculine animate infinitive dabhumaksanigalu'ahai, meaning to live, was, in the perfect tense, ksu'u'peli'afo, and, in the future, mai'teipa.

Thus, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be observed.

Thus, the task is to find universal properties that uniquely determine the objects of interest.

Thus if we wish to claim that no-cloning is a uniquely quantum result, some care is necessary in stating the theorem.

Thus rather than " nurture ", behavior geneticists distinguish shared family factors ( i. e., those shared by siblings, making them more similar ) and nonshared factors ( i. e., those that uniquely affect individuals, making siblings different ).

Thus, Kolmogorov introduced a second hypothesis: for very high Reynolds numbers the statistics of small scales are universally and uniquely determined by the viscosity () and the rate of energy dissipation ().

Thus, every element of Dic < sub > n </ sub > can be uniquely written as a < sup > k </ sup > x < sup > j </ sup >, where 0 ≤ k < 2n and j = 0 or 1.

Thus closed system thermodynamics can be used to evaluate functions of state for open systems, but processes specified in terms of heat and work transfer are not physically uniquely defined for open systems.

Thus every rotation can be represented uniquely by an orthogonal matrix with unit determinant.

Thus almost uniquely in Europe, many of the UK's canals remain as they have been since the 18th and 19th century: mostly operated with narrowboats less than 7 feet ( 2. 3 m ) wide and 70 feet ( 23 m ) long ( although in parts of the country slightly larger canals were constructed, called ' broad ' or ' wide ' canals, which could take boats that were wide and long ).

Since any vector v is a linear combination ∑ v < sup > j </ sup > e < sub > j </ sub > of its components, df is uniquely determined by df < sub > p </ sub >( e < sub > j </ sub >) for each j and each p ∈ U, which are just the partial derivatives of f on U. Thus df provides a way of encoding the partial derivatives of f. It can be decoded by noticing that the coordinates x < sup > 1 </ sup >, x < sup > 2 </ sup >,... x < sup > n </ sup > are themselves functions on U, and so define differential 1-forms dx < sup > 1 </ sup >, dx < sup > 2 </ sup >, ..., dx < sup > n </ sup >.

Thus, according to the Cutlerites, whereas the church can never exist without the priesthood ( a belief held by practically all other Latter Day Saint churches ), the priesthood can exist on earth without the church ( a uniquely Cutlerite belief ), as it did between 1829 and 1830.

Thus, the first two results appeared to establish 11 dimensions uniquely, the third result appeared to specify the theory, and the last result explained why the observed universe appears to be four-dimensional.

Thus, during the Nazi invasion and occupation of Kalmykia in 1942, German forces uniquely found volunteers among the Kalmyks for the Kalmykian Voluntary Cavalry Corps, which killed many Soviet partisans.

Thus subverting Harley's theory that mapping is uniquely a source of power for the powerful.

Thus, as it uniquely illustrates the articles ' discussion of the artist's representation of the subjects, it is not replaceable by the public domain image.

Thus an inhabitant of Brazil should have become known in Portuguese as a Brasiliano (" Brazilian "), but uniquely among Portuguese demonyms they are instead referenced as a Brasileiro (" Braziler ").

The Cantor – Bendixson theorem states that closed sets of a Polish space X have the perfect set property in a particularly strong form ; any closed set C may be written uniquely as the disjoint union of a perfect set P and a countable set S. Thus it follows that every closed subset of a Polish space has the perfect set property.

Thus, as he saw it ( in Comparative Studies in Vaishnavism and Christianity ), Vaishnavism and Christianity were two distinct religious traditions, each with its own uniquely rich tradition of historical exegesis that spanned two millennia and could in no way be seen as being phases in the development of ( a Eurocentric ) human civilization, as one leading to another in a pattern of cause and effect.

Thus, during the abdication crisis of 1936, caused by Edward VIII's desire to marry Wallis Simpson, the consent of all realms concerned, along with, in some cases, new acts of parliament, was required in Britain and throughout the British Dominions to allow for Edward's stepping aside and to ensure that if he had any children they would have no claim to the thrones.

Thus the dragoon regiments of the Imperial German Army wore the pickelhaube ( spiked helmet ) of the same design as those of the infantry and the British dragoons wore scarlet tunics, In other respects however dragoons had adopted the same tactics, roles and equipment as other branches of the cavalry and the distinction had become simply one of traditional titles.

Thus, Egypt was by Ottoman law de jure a province of that empire, but de facto was part of the British Empire.

Thus, the 11th edition is " dedicated by Permission to His Majesty George the Fifth, King of Great Britain and Ireland and of the British Dominions beyond the Seas, Emperor of India, and to William Howard Taft, President of the United States of America.

Thus in A v United Kingdom, the Court dismissed a claim that a derogation lodged by the British government in response to the September 11 attacks was invalid, but went on to find that measures taken by the United Kingdom under that derogation were disproportionate .< ref >

Thus, although Scots were only 10 per cent of the British population, they made up 15 per cent of the national armed forces and eventually accounted for 20 per cent of the dead.

Thus as a result of the three Carnatic Wars, the British East India Company gained exclusive control over the entire Carnatic region of India.

Thus, the third phase of the war ( roughly August 1920 – July 1921 ) involved the IRA taking on a greatly expanded British force, moving away from attacking well defended barracks and instead using ambush tactics.

Thus encouraged, the encircling regiments remained in place, maintaining continual pressure, until weakened British dispositions enabled the host to make a final surge forward.

Thus a cash dispenser ( British English ) as well as and automatic teller machine or ATM in ( American English ) while belonging to speakers of different dialect would be understood by both American and British dialect speakers.

Thus the British Navy captured New Amsterdam ( New York ) in 1664.

Thus, Peel affirmed a convention of the constitution that promotes stability in the British system: the Parliament of the day must respect the settlement of constitutional issues made by previous Parliaments.

Thus, in the last half of the 19th century, it was clear that the British treated the Tawang Tract as part of Tibet.

Thus Britain had both a formal Empire based on British rule and an informal one based on the British pound.

Thus, American and British actors were easily able to collaborate with German directors and cast-members on films made in Germany ( for example, the collaborations of Georg Pabst and Louise Brooks ).

Thus in Puget Sound itself, the names given by Wilkes are common and Spanish names rare, while the reverse is true for the San Juan and Gulf Islands ( although the Spanish did not explore Puget Sound as thoroughly as the British and Americans, resulting in fewer Spanish names to start with ).

Thus, Afghanistan's foreign minister commented that Afghanistan was a democratic but not yet socialist republic, while a member of the People's Democratic Party of Afghanistan's Politburo predicted that " Afghanistan will not see socialism in my lifetime " in an interview with a British journalist in 1981.

Thus a British assault on Sullivan's Island was driven off and Clinton then abandoned his attempts to capture the city.

Thus the British " sterling " was 92. 5 % pure silver ; the base metal added ( and thus the pure silver retained by the government mint ) was ( less costs ) the profit, the seigniorage.

Thus the inhabitants are of mixed heritage, but of predominantly British ancestry.

Thus at the time of Edward VIII's Abdication, the prevailing view – formulated by George VI himself – was that the former king had reverted to the rank of HRH, his right as the son of a British sovereign.