Thus, a child's Skeletal Age `` dots '' may be classified as `` advanced '' when they appear above the middle curve, `` moderate '' when they appear immediately above or below the middle curve, and `` delayed '' when they appear below the lower curve.

Thus, the white middle and lower classes are arrayed against the Negro middle and lower classes.

Thus, every chlorine is in the middle of a cube formed by caesium atoms and every caesium is in the middle of a cube formed by chlorine.

Thus, middle C would be heard as the note B < sub > 3 </ sub > just below it, and so on.

Thus, only those who could afford such weaponry fought as hoplites ; as with the Roman Republican army it was the middle classes who formed the bulk of the infantry.

Thus, while there was a good measure of debate in the Early Church over the New Testament canon, the major writings are claimed to have been accepted by almost all Christians by the middle of the 3rd century.

Thus, according to the law of non-contradiction, " not p " must be false, and so, according to the law of the excluded middle, p is true.

Thus, in the middle of 1929 he accepted Paul Tillich's offer to present an Habilitation on Kierkegaard, which Adorno eventually submitted under the title The Construction of the Aesthetic.

Thus, skete life has elements of both solitude and community, and for this reason is called the " middle way ".

Thus two tooth cattle are marked on the wither, four tooth on the middle of the back and six tooth on their high bone ( near tail ).

Thus a movement grew amongst the middle class Criollo and Mestizo classes.

Thus ( Leviticus 8: 23 ) is the middle verse in the Pentateuch ; all the names of Divinity mentioned in connection with Abraham are holy except ( Genesis 18: 3 ); ten passages in the Pentateuch are dotted ; three times the Pentateuch has the spelling לא where the reading is לו.

Thus the antipodes of France are in the middle of the water hemisphere in the South Pacific.

Thus, tuning was a relatively slow operation, and composers had to allow a reasonable amount of time for players to change notes if they were called to tune in the middle of a work.

Thus zero appears in the middle, with the positive numbers to the right and the negative numbers to the left.

Thus, having recovered his stature, in the middle of the year he was sent by the princes to invite Kerbogha to settle all differences by a duel which the Emir subsequently declined ; and in 1099 he appears as treasurer of the alms at the siege of Arqa ( March ), and as leader of the supplicatory processions around the walls of Jerusalem before it fell and later within Jerusalem which preceded the Crusaders ' miraculous victory at the Battle of Ascalon ( August ).

Thus the first name is the personal name, the middle name is the father's name and the last name is the family name.

Thus there was some antagonism between the Jewish apostles Peter, James and John, and Paul the " Apostle to the Gentiles ", and this struggle continued down to the middle of the 2nd century.

Thus, the term " synod " as used by the ELCA refers to middle level administrative districts in different regions of the United States ( example: Illinois Synod of the ELCA ), whereas in the case of LCMS, WELS, and ELS, " synod " refers to the entire church body.

Thus, the formal instruction of law as a course of study did not commence until the middle of the 19th century.

Thus, since a point at an intersection is surrounded by more intensity than a point at the middle of a line, the intersection appears darker due to the increased inhibition.

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

Thus the multiplicity of Af for a given T must be an even number.

Thus, casework involving a limited number of interviews is still to be regarded in terms of the quality of service rendered rather than of the quantity of time expended.

Thus a number of operations of the order of Af are required.

Thus a simple count of the number of distinct symbols is an important clue to the nature of an unknown script.

Thus although most species in the order are herbaceous, some no more than 15 cm high, there are a number of climbers ( e. g. some species of Asparagus ), as well as several genera forming trees ( e. g. Agave, Cordyline, Yucca, Dracaena ), some of which can exceed 10 m in height.

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

The evaluation order does not affect the value of such expressions, and it can be shown that the same holds for expressions containing any number of operations .< ref > Thus, when is associative, the evaluation order can be left unspecified without causing ambiguity, by omitting the parentheses and writing simply:

If a description of s, d ( s ), is of minimal length ( i. e. it uses the fewest number of characters ), it is called a minimal description of s. Thus, the length of d ( s ) ( i. e. the number of characters in the description ) is the Kolmogorov complexity of s, written K ( s ).

In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R. Thus A is endowed with binary operations of addition and multiplication satisfying a number of axioms, including associativity of multiplication and distributivity, as well as compatible multiplication by the elements of the field K or the ring R.

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, in the mid-1990s the army sought to reduce the number of active-duty generals.

Thus the discovery report by the Berkeley group reads: " It is suggested that element 97 be given the name berkelium ( symbol Bk ) after the city of Berkeley in a manner similar to that used in naming its chemical homologue terbium ( atomic number 65 ) whose name was derived from the town of Ytterby, Sweden, where the rare earth minerals were first found.

Thus, a single " rule ," like mapping every real number x to x < sup > 2 </ sup >, can lead to distinct functions and, depending on whether the images under that rule are understood to be reals or, more restrictively, non-negative reals.

Thus, a PICMG backplane can provide any number and any mix of ISA, PCI, PCI-X, and PCI-e slots, limited only by the ability of the SBC to interface to and drive those slots.

Thus, a number of Allied soldiers received the Bronze Star Medal in World War II, as well as U. N. soldiers in the Korean War, Vietnamese and allied forces in the Vietnam War, and coalition forces in recent military operations such as the Gulf War, Operation Enduring Freedom and the Iraq War.

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.

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 if one chooses an infinite number of points in the closed unit interval, some of those points must get arbitrarily close to some real number in that space.