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, finally, all sin and pain would disappear and men would live to the age of 1, 000 years in happiness and peace, and after death enjoy a blessed immortality in the spirit world.

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, there is freshness not only in the individual movements of the dance but in the shape of their continuity as well.

Thus jazz is transmuted into something holy, the sacred road to integration of being.

Thus the fictional detective is much more than a simple businessman.

Thus the cocktail party would appear to be the ideal system, but there is one weakness.

Thus in both types attention is focused on the community itself, and its phenomenological life.

Thus, it is no mystical intuition, but an analyzable conception to say that man and his tradition can `` fall out of existence ''.

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, circular motion is itself one of the essential characteristics of completely perfect celestial existence.

Thus, in no ordinary sense of ' simplicity ' is the Ptolemaic theory simpler than the Copernican.

Thus Burns's `` My love is like a red, red rose '' and Hopkins' `` The thunder-purple sea-beach, plumed purple of Thunder '' although clearly intelligible in content, hardly present ideas of the sort with which we are here concerned.

Thus science is the savior of mankind, and in this respect Childhood's End only blueprints in greater detail the vision of the future which, though not always so directly stated, has nevertheless been present in the minds of most science-fiction writers.

Thus the copywriter in the world of the space merchants is the person who in earlier ages might have been a lyric poet, the person `` capable of putting together words that stir and move and sing ''.

Thus there is a clearer division of authority, administrative and legislative.

Thus, as a development program is being launched, commitments and obligations must be entered into in a given year which may exceed by twofold or threefold the expenditures to be made in that year.

Thus, the need for the B-70 as a strategic weapon system is doubtful.

Thus technical efficiency is achieved at the expense of actual experience.

Thus, there is an added incentive to stay on the job.

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

Thus T is not diagonalizable.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

Thus, the study of the solutions to the equation Af is reduced to the study of the space of solutions of a differential equation of the form Af.

Thus in the three-dice example Af, Af, and the independence assumption imply that the probability that the three dice fall ace, not-ace, ace in that order is Af.

Thus we do not score the number of bull's-eyes, and the random variable is not the number of successes.

Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus Af is also continuous at Af, and in a neighborhood of Af which does not contain a tangent point.