Thus, direct comparisons can be drawn with free burning arcs which have been studied in detail during the past years and decades by numerous investigators ( Ref. 3 ).

Thus twenty `` black souls '' were to remain ignorant of their imminent journey to the land of free men.

Thus, natural beryllium bombarded either by alphas or gammas from a suitable radioisotope is a key component of most radioisotope-powered nuclear reaction neutron sources for the laboratory production of free neutrons.

Thus in Austinian terms a moral code can objectively determine what people ought to do, the law can embody whatever norms the legislature decrees to achieve social utility, but every individual remains free to choose what to do.

Thus, a poison that covers surface randomly will tend to reduce the number of uncontaminated large planes but leave proportionally more smaller sites free, thus changing the hydrogenation vs. hydrogenolysis selectivity.

Thus, the molecules are free to flow and their center of mass positions are randomly distributed as in a liquid, but still maintain their long-range directional order.

Thus, a waiver of Miranda rights is voluntary unless the defendant can show that their decision to waive their rights and speak to the police was the product of police misconduct and coercion that overcame the defendant's free will.

( Thus, a song that is in the public domain is free to play on the radio, regardless of who performs it or when it was performed.

This wilful destruction of values and the overcoming of the condition of nihilism by the constructing of new meaning, this active nihilism, could be related to what Nietzsche elsewhere calls a ' free spirit ' or the Übermensch from Thus Spoke Zarathustra and the Antichrist, the model of the strong individual who posits his own values and lives his life as if it were his own work of art.

Thus less energy is needed in the smaller nuclei and the difference to the state before is set free.

Thus Tantra, especially in its nondual forms, rejected the renunciant values of Patañjalian yoga, offering instead a vision of the whole of reality as the self-expression of a single, free and blissful Divine Consciousness under whatever name, whether Śiva or Buddha-nature.

Thus two arrows and in space represent the same free vector if they have the same magnitude and direction: that is, they are equivalent if the quadrilateral ABB ′ A ′ is a parallelogram.

Thus, in traditional use, the term “ free ” was attached to Gibbs free energy, i. e., for systems at constant pressure and temperature, or to Helmholtz free energy, i. e., for systems at constant volume and temperature, to mean ‘ available in the form of useful work .’ With reference to the Gibbs free energy, we add the qualification that it is the energy free for non-volume work.

Thus the unpredictability of the emerging behaviour from deterministic processes leads to a perception of free will, even though free will as an ontological entity does not exist.

Thus, in the long-standing debate on whether free will is compatible with the doctrine of determinism, several philosophers have proposed analyses of the relevant concepts to argue for either compatibilism or incompatibilism.

Thus the principality ruled politically by a prince-bishop could wholly or largely overlap with his diocesan jurisdiction, but not necessarily ; several lost their actual see ( the city itself ), which could obtain the status of free imperial city.

Thus human beings have free will and can choose the path in life that they will take.

Thus, market capitalization is one measure of " float " i. e., share value times an equity aggregate, with free and public being others.

" Thus the emperor proposed a free discussion in council ; the pope required the unqualified acceptance of orthodoxy, and submission to himself as head of Christendom, before he would treat at all.

Thus with regard to the loss of tradition, in the change from order to disorder the metaphysics of change works itself out as a disruption of the individual soul, a change in which man continues as an objective ontological existent, but no longer as a man.

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

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

Thus the unstressed it of it rarely snows here gets its significance from its use with snows: nothing can snow snow but `` it ''.

Thus, during any given year ( A ) if the revenues from the residential service are $7,000,000, ( B ) if the operating expenses imputed to this class of service come to $5,000,000, and ( C ) if the net investment in ( or value of ) the plant and equipment deemed devoted to this service amounts to $30,000,000, the cost analyst will report that residential service, in the aggregate, has yielded a return of $2,000,000 or 6-2/3 per cent.

Thus one line in five from The Iliad and The Odyssey is to be found somewhere else in the two poems.

Thus, when specifically permitted, the operand of a given line on the Autocoder coding sheet may be continued in the operand of from one to four additional lines which immediately follow.

Thus Af denotes the state of the feed to the R-stage process, and Af the state of the product from the last stage.

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, 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, while it remains possible that the Babylonians and/or the Pythagoreans may perhaps have had the magic square of three before the Chinese did, more definite evidence will have to turn up from the Middle East or the Classical World before China can lose her claim to the earliest known magic square by more than a thousand years.

Thus, moral decision must be entirely deduced backward from the likely eventuality ; ;

" Thus Boolos and Jeffrey are saying that an algorithm implies instructions for a process that " creates " output integers from an arbitrary " input " integer or integers that, in theory, can be chosen from 0 to infinity.

Thus the only member churches of the present Anglican Communion existing by the mid-18th century were the Church of England, its closely linked sister church, the Church of Ireland ( which also separated from Roman Catholicism under Henry VIII ) and the Scottish Episcopal Church which for parts of the 17th and 18th centuries was partially underground ( it was suspected of Jacobite sympathies ).

Thus a colonial bishop and colonial diocese was by nature quite a different thing from their counterparts back home.

Thus situated, the mountains make travel from north to south difficult.

Thus, from the human body, the usual form assigned to the Deity, forasmuch as it is written that God created man in his own image, issue the two supporters, Nous and Logos, symbols of the inner sense and the quickening understanding, as typified by the serpents, for the same reason that had induced the old Greeks to assign this reptile for an attribute to Pallas.

Thus we have the story of his riding across a stick ( horse made of stick ) with his children and upon being discovered by a friend desiring that he not mention till he himself were the father of children ; and because of the affection of his son Archidamus ' for Cleonymus, he saved Sphodrias, Cleonymus ' father, from execution for his incursion into the Piraeus, and dishonorable retreat, in 378 BC.

Thus the possibility of re-incorporating Portugal ( up to then Southern Galicia ) into a Kingdom of Portugal and Galicia as before was eliminated and Afonso became sole ruler ( Duke of Portugal ) after demands for independence from the county's church and nobles.

Thus, Afonso continued to distinguish himself by his exploits against the Moors, from whom he wrested Santarém ( see Conquest of Santarém ) and Lisbon in 1147 ( see Siege of Lisbon ).

Thus while Persian-speakers were concentrated on the lower rungs of the work force, managers tended to be brought in from some distance.

Thus, if a two-dimensional array has rows and columns indexed from 1 to 10 and 1 to 20, respectively, then replacing B by B + c < sub > 1 </ sub >-− 3 c < sub > 1 </ sub > will cause them to be renumbered from 0 through 9 and 4 through 23, respectively.