Thus, for positronium, its reduced mass only differs from the rest mass of the electron by a factor of 2.

Thus, they found the length of 1 ° of meridian to be 111. 8 km ( 115. 1 km ), which differs from the actual value by 850 metres.

Thus, the reactance differs with the rate of change, and is a constant only for circuits under alternating current of constant frequency.

Thus, in spherical geometry angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects ; for example, the sum of the interior angles of a triangle exceeds 180 degrees.

Thus, he wrote: " if 0 is interpreted as falsehood, 1 as truth, and other numbers in the interval 0-1 as the degrees of probability corresponding to various possibilities, a many-valued logic is obtained which is expansion of three-valued logic and differs from the latter in certain details.

Thus, the only way that one crime differs from another is in the backgrounds and characteristics of its perpetrators.

Thus, Cowdery's account, containing a single vision, differs from Smith's 1832 account, which contains two separate visions, one in 1821 prompted by religious confusion ( the First Vision ) and a separate one regarding the plates on September 22, 1822.

Thus, the second anointing differs from the " first anointing " ( part of the Endowment ceremony ) in that, the first anointing promises blessings in the afterlife contingent on the patron's faithfulness, the Second Anointing actually bestows those blessings.

Thus, practice in the Eastern Catholic Churches of Byzantine Rite is identical with that described above for the Churches that constitute the Eastern Orthodox Church, but differs from that of, for instance, the Syro-Malabar Catholic Church or the Latin Church.

Thus, the format of the output differs considerably among Unix implementations.

Thus they could be created by some mechanism that differs from the mare-forming flows.

Thus the methodology of international trade economics differs little from that of the remainder of economics.

Thus the title Baron Stanley of Alderley, in the County of Chester differs in format from Baron Stanley, of Bickerstaffe in the County Palatine of Lancaster only by the placement of the comma: the former title is Baron Stanley of Alderley whilst the latter is Baron Stanley.

Thus, the beech marten differs from most other European mustelids of the Quaternary, as all other species ( save for the European mink ) appeared during the Middle Pleistocene.

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.

Thus, recently-allocated serial numbers may duplicate very old serial numbers, but not other recently-allocated serial numbers.

Thus, screen update commands need only be sent once and this allows the use of a slower data connection, typically serial — a feature very well adapted to computer terminal use in 1960s and 1970s computing.

Thus, the intensity of many lighting instruments are often altered with a single fade, especially with newer digital control systems like DMX, which uses a serial data stream to control up to 512 dimmers or other compatible fixtures, via a single twisted pair of wires.

Thus, it was recognized that the judge, through his action to deny the earlier motion to dismiss, had ultimately prevented a serial killer from going free.