Thus, Nauru was left to handle the immense and expensive task of restoring large chunks of land which were destroyed by the mining.

Thus, to cite but one example, the Pax Britannica of the nineteenth century, whether with the British navy ruling the seas or with the City of London ruling world finance, was strictly national in motivation, however much other nations ( e.g., the United States ) may have incidentally benefited.

Thus, paradoxically, the beat writers resort to `` religious '' metaphors: they are in search of mana, the spiritual, the numinous, but not anything connected with formal religion.

Thus the transformation of Adam Smith's ideal entrepreneur into a mythological detective coincides closely with the decline of the real entrepreneur in economic life.

Thus, if corporations are not to run away with us, they must become quasi-governmental institutions, subject to public control and needs.

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, 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 he complains, with considerable justice, that the Tory writers have resorted to libel instead of answering his arguments.

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, 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.

Before them stalked the beadle, proclaiming as he went, `` Thus the Council deals with those who break its laws -- adulterers, thieves, murderers, and lewd persons.

Thus was invented the single thread sewing machine, which Mr. Gibbs in partnership with Mr. Willcox decided to bring to Brown & Sharpe with the proposal that the small company undertake its manufacture.

Thus, when you have prepared your foundation and laid the floor, these can be trucked to the site and erected with a small crew of friends in a weekend.

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, the alignment of the `` dots '' and `` tips '', respectively, indicate individual variability of the 21 growth centers of each child with respect to the mean values for these boys and girls.

Thus cortico-fugal discharges induced by topical application of strychnine to a minute area in the neocortex summate with spikes present in the hypothalamus and cause increased convulsive discharges.

Thus D' and N' commute with any polynomial in T ; ;

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

Thus in Mary wrote an account of the trip first strong stress on Mary marks Mary as the first in a series of people who wrote accounts of the trip, strong stress on wrote marks the writing as the first of a series of actions of Mary's concerned with an account of her trip ( about which she may later have made speeches, for example ), and strong stress on trip makes the trip the first of a series of subjects about which Mary wrote accounts.

Thus, the Commission acted with a sense of social responsibility within the area of its own convictions about the problem of government support to private education.

Thus he wired J. P. Lower and Sons of Denver: `` Have you any percussion hand grenades for throwing in a house or across a well loaded with balls or shrapnel shot??

Thus every part and plane of the picture keeps changing place in relative depth with every other part and plane ; ;

Thus, in the example cited above Fromm rests his whole case on the premise that the workers are being deprived unconsciously, unknowingly, of fulfillment, and then supports this with survey data reporting conscious, experienced frustrations.

Thus, the combined efficiency of the elements replaced by the two fiber plates ( with a combined efficiency of 0.25 ) is 0.043 or about six times less than that of the two fiber plates.

Thus most z / OS customers are either " odd " or " even.

Thus, the DST-I corresponds to the boundary conditions: x < sub > n </ sub > is odd around n =- 1 and odd around n = N ; similarly for X < sub > k </ sub >.

Thus, the number of quadratic residues modulo n cannot exceed n / 2 + 1 ( n even ) or ( n + 1 )/ 2 ( n odd ).

Thus he deployed the young general off with merely a thousand odd troops and a tiny cavalry force.

Thus, the quaternion components are either all integers or all half-integers, depending on whether is even or odd, respectively.

Thus, for example, a real-valued function of a real variable could be even or odd, as could a complex-valued function of a vector variable, and so on.

Furthermore when n is odd, the number of ordinary lines is at least 3n / 4 − C, for some constant C. Thus, the constructions of Böröczky for even and odd ( discussed above ) are best possible.

Thus a super-Poincaré algebra is a Z < sub > 2 </ sub > graded vector space with a graded Lie bracket such that the even part is a Lie algebra containing the Poincaré algebra, and the odd part is built from spinors on which there is an anticommutation relation with values in the even part.

Thus the device that recreates Ryder's costume when he becomes The Creeper also recreates the drugs in his system, explaining the Creeper's odd personality.

Thus one can speak of, say, an odd tensor density of weight + 2 or an even tensor density of weight − 1 / 2.

Thus, the rest of the weight classes are even and odd accordingly.

Thus if n is odd, a cyclic polygon is equiangular if and only if it is regular.

Thus, there may sometimes be confusion about the blade lengths, depending on which shaku value is being assumed when converting to metric or US measurements.

Thus the ancient Rabbis went to great lengths to try and account for the number of the names of God, by claiming that they account for the various aspects of God.

Thus public key systems require longer key lengths than symmetric systems for an equivalent level of security.

Thus there is an infinite list of English phrases ( where each phrase is of finite length, but lengths vary in the list ) that unambiguously define real numbers ; arrange this list by length and then dictionary order, so that the ordering is canonical.

Thus, e < sup > 1 </ sup > and e < sub > 2 </ sub > are perpendicular to each other, as are e < sup > 2 </ sup > and e < sub > 1 </ sub >, and the lengths of e < sup > 1 </ sup > and e < sup > 2 </ sup > normalized against e < sub > 1 </ sub > and e < sub > 2 </ sub >, respectively.

Thus, Ribot's triumph ( correctly by eight and half lengths and not by an official six lengths ) in the race is de facto the largest winning distance.

Thus the lengths of the two segments are.

Thus the entire polynomial is the product of these terms, and according to vector mathematics the angles add ( or subtract, for terms in the denominator ) and lengths multiply ( or divide ).

Thus, it enables one to calculate the lengths of curves on the surface and the areas of regions on the surface.

Thus finding more repeated strings narrows down the possible lengths of the keyword, since we can take the greatest common divisor of all the distances.

Thus a 30 year mortgage is transformed into bonds of various lengths suitable for various investors with various goals.

Thus prefix code with lengths can be constructed for all source symbols.

Thus, in order to establish the convergence of the finite-difference approximation, it is necessary to use other methods, which in turn could imply further limitations on the length of the time step and / or the lengths of the spatial intervals.

Thus, Blowfish and RC5 are block cipher algorithms whose design specifically allowed for several key lengths, and who cannot therefore be said to have any particular strength with respect to brute force key search.