Thus, when the fluid finally does strike the object, it is forced to change its properties -- temperature, density, pressure, and Mach number -- in an extremely violent and irreversible fashion called a shock wave.

Thus the pagan curse was finally dissolved by the arrival of Christianity.

Thus the initial input change circulates along the feedback loop and grows in an avalanche-like manner until finally Q1 switches off and Q2 switches on.

Thus, by the end of the 1st century AD Latin had finally displaced the original Venetic language.

Thus, when the hostilities finally ceased in 1648 with the Treaty of Westphalia, most of Alsace went to France with some towns remaining independent.

Thus Palpatine's New Order was finally brought to an end after 157 years of imperialism which opposed to his 10, 000 year rule that he had promised at its formation.

Thus, all who are truly born again are kept by God the Father for Jesus Christ, and can neither totally nor finally fall from the state of grace, but will persevere in their faith to the end, and be eternally saved.

Thus he lost two crucial days before finally adopting the solution, however obvious, of his predecessor.

Thus, at the end of this phase and at the beginning of the next they are finally in a position to go up against their primary goal.

Thus, Oedipus finally realized in great agony that so many years ago, at the place where the three roads met, he had killed his own father, King Laius, and subsequently married his mother, Jocasta.

Thus, by the end of 1815, the Moselle department had finally the limits that it would keep until 1871.

Thus, the leaders of the big railroads finally learned the source of William Nelson Page's deep pockets.

Thus finally the theme throughout the palace of honouring the Duke reached its apotheosis with completion of his tomb.

Thus, there are different answers even to the question What is the Church ?, which finally is the goal of the ecumenist movement itself.

Thus the Fronde finally resulted in the disempowerment of the territorial aristocracy and the emergence of absolute monarchy.

Thus the unification of the four provinces in the Union of South Africa, the idea of the British Commonwealth of Nations, and, finally, the great whole resulting from the combination of the peoples of the earth in a great league of nations were but a logical progression consistent with his philosophical tenets.

Thus the papyri were finally brought together in Cairo: of the 1945 find, eleven complete books and fragments of two others, ' amounting to well over 1000 written pages ' are preserved there.

Thus, respectable momentum was given to the idea that finally came to fruition, on 17 April 1982, with the proclamation of the Canadian Charter of Rights and Freedoms.

Thus, as God creates, the universe evolves towards higher forms of complexity, consciousness, and finally with humans, personality, because God, who is drawing the universe towards Him, is a person.

Thus he rejected advantageous offers of mediation and alliance made to him, during 1712, by the maritime powers and by Prussia ; and in 1714 he scorned the friendly overtures of Louis XIV of France and the emperor, so that when peace was finally concluded between France and the Empire, at the Congress of Baden, Swedish affairs were, by common consent, left out of consideration.

Thus the controversy finally shifted to a speculative theological question: whether or not it was consonant with Catholic Faith to hold that Christ and the Apostles had no property individually or in common ; and while in the famous dispute at Narbonne in 1321 the inquisitor, John of Belna, claimed that it was heretical, Berengarius of Perpignan declared it a Catholic dogma in perfect accordance with the decretals of Nicholas III and Clement V.

" Thus, despite being negatively affected for at least the previous two decades, it was finally declared endangered in September 2010.

Thus, on July 18, 1966, South Cotabato was finally formed as an independent province raring to push its own development.

Thus the gods and goddesses who had once been the superiors or equals of Yahweh were first made his peers, then subordinate gods, and finally ended as angels in his service.

Thus human perception and human volition is the immanent cause of all social change and this most truly when the change reaches the civilizational level.

Thus, there has come into being a situation in which the state must raise all of its own revenues and, in addition, must give assistance to its local governments.

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

Thus it follows that the secants of **zg are all invariant.

Thus Af where the maximization is over all admissible policies Af, and Af is related to Af by ( 5 ).

Thus creativity may run all the way from making a cake, building a chicken coop, or producing a book, to founding a business, creating a League of Nations or, developing a mature character.

Thus all differences were leveled, and all contrasts erased, in a realm of no distinction, and the harmonious balance of the Lo Shu square could effectively symbolize the world in balanced harmony around a powerful central axis.

Thus we hear of abbots going out to hunt, with their men carrying bows and arrows ; keeping horses, dogs and huntsmen ; and special mention is made of an abbot of Leicester, c. 1360, who was the most skilled of all the nobility in hare hunting.

Thus Christ's atonement is intended for all, but requires faith to be effected.

Thus, almost all positive integers are composite ( not prime ), however there are still an infinite number of primes.

Thus she, through whom salvation was being prepared for all people, would be the first to receive the promised fruit of salvation.

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, in Steiner's view, we can overcome the subject-object divide through inner activity, even though all human experience begins by being conditioned by it.

Thus, anthroposophy considers there to be a being who unifies all religions, and who is not represented by any particular religious faith.

Thus a third style, the " curved lip " style was produced, and all official and third-party cartridges during the console's lifespan were released ( or re-released ) using this style.

Thus, all the antiderivatives of x < sup > 2 </ sup > can be obtained by changing the value of C in F ( x ) = ( x < sup > 3 </ sup >/ 3 ) + C ; where C is an arbitrary constant known as the constant of integration.

Thus there are alignments in all directions which would suggest there is little of astronomical significance, However, ethnohistorical records show that the various directions do have cosmological and astronomical significance with various points in the landscape being significant at different times of the year.

Thus, current expected inflation reflects a weighted average of all past inflation, where the weights get smaller and smaller as we move further in the past.

Thus, the energy required to break any single pair is related to the energy required to break all of the pairs ( or more than just two electrons ).

Thus the electrons stay paired together and resist all kicks, and the electron flow as a whole ( the current through the superconductor ) will not experience resistance.

By a theorem of Gelfand and Naimark, given a B * algebra A there exists a Hilbert space H and an isometric *- homomorphism from A into the algebra B ( H ) of all bounded linear operators on H. Thus every B * algebra is isometrically *- isomorphic to a C *- algebra.

Thus, a player should use Blackwood only when he can ascertain that the partnership holds at least second-round controls in all suits ( kings or, if a suit fit is found, singletons ).

Thus, all carbon isotopes have nearly identical chemical properties because they all have six protons and six electrons, even though carbon atoms may differ in number of neutrons.