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

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

Thus, we have no part, and want none, in current discussions of the relative importance of science, the social studies, the humanities, the creative arts.

Thus in a context in which there has been discussion of snow but mention of local conditions is new, dominant stress will probably be on here in it rarely snows here, but in a context in which there has been discussion of local weather but no mention of snow, dominant stress will probably be on snows.

Thus all differences were leveled, and all contrasts erased, in a realm of no distinction, and the harmonious balance of the Lo Shu square could effectively symbolize the world in balanced harmony around a powerful central axis.

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 the negation of the axiom of choice states that there exists a set of nonempty sets which has no choice function.

" Thus Ambrose refused to be drawn into a false conflict over which particular local church had the " right " liturgical form where there was no substantial problem.

Thus, there is no assault if an ox gores a man.

Thus, during the abdication crisis of 1936, caused by Edward VIII's desire to marry Wallis Simpson, the consent of all realms concerned, along with, in some cases, new acts of parliament, was required in Britain and throughout the British Dominions to allow for Edward's stepping aside and to ensure that if he had any children they would have no claim to the thrones.

Thus, services could be moved to a different machine and, so long as they kept the same service name, there was no need for users to do anything different to continue accessing the service.

Thus, ATP was a simple request / response exchange, with no need to set up or tear down connections.

This latter construal is sometimes expressed by saying " there is no fact of the matter as to whether or not P ." Thus, we may speak of anti-realism with respect to other minds, the past, the future, universals, mathematical entities ( such as natural numbers ), moral categories, the material world, or even thought.

Thus, any transverse velocity of the emitting source plays no part in aberration.

Thus, the theory asserts that the apple is no more than the collection of its properties.

Thus, according to the Bank of England's Boxall and Gallagher ( 1997 ), "... there was virtually no difference between banks and building society ' listed ' interest rates for home finance mortgage lending between 1984 and 1997.

Thus, the molecular formula of ethanol may be written in a paper in conformational, three-dimensional, full two-dimensional ( indicating every bond with no three-dimensional directions ), compressed two-dimensional ( CH < sub > 3 </ sub >– CH < sub > 2 </ sub >– OH ), separating the functional group from another part of the molecule ( C < sub > 2 </ sub > H < sub > 5 </ sub > OH ), or by its atomic constituents ( C < sub > 2 </ sub > H < sub > 6 </ sub > O ), according to what is discussed.

Thus, no two nuclear powers have yet fought a conventional war directly, with the exception of brief skirmishes between for example, China and Russia in the 1969 Sino-Soviet conflict and between India and Pakistan in the 1999 Kargil War.

Thus, he implicitly emphasized that it is God-made (" God has joined together "), " male and female ," lifelong (" let no one separate "), and monogamous (" a man ... his wife ").

Thus no form of justification will rationally warrant our inductive inferences.

Thus miniatures were no longer required for game play, although some players continued to use them as a visual reference.

Thus, a central conclusion of Keynesian economics is that, in some situations, no strong automatic mechanism moves output and employment towards full employment levels.

Thus, the majority of communications can no longer be intercepted by earth stations ; they can only be collected by tapping cables and intercepting line-of-sight microwave signals, which is possible only to a limited extent.

Thus, there should be no need for prices.

For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as its linear momentum,, crossed by its position from the origin, r. Thus, the angular momentum L of a particle with respect to some point of origin is

Thus, at a given angular rate of rotation, a concave surface represents the stable situation, and the more rapid the rotation, the more concave this surface.

Thus the aim developed, to provide a new time scale for astronomical and scientific purposes, to avoid the unpredictable irregularities of the mean solar time scale, and to replace for these purposes Universal Time ( UT ) and any other time scale based on the rotation of the Earth around its axis, such as sidereal time.

Thus there is a three-parameter family of rotations which transform the sphere onto itself, this is the rotation group SO ( 3 ).

Thus, all parts share the same rate of rotation, or the same number of rotations or revolutions per unit of time.

Thus the spinor rotation γ ( ψ ) = γψ ( ordinary quaternionic multiplication ) will rotate the spinor ψ through an angle one-half the measure of the angle of the corresponding vector rotation.

Thus rotation allows increased yields from nutrient availability but also alleviation of allelopathy and competitive weed environments.

Thus the rotation of a rigid body over a fixed axis is referred to as rotational motion.

Thus, as a result of the Earth's rotation, for each successive saros, an eclipse will occur about 8 hours later in the day.

Thus every rotation can be represented uniquely by an orthogonal matrix with unit determinant.

Thus the amplitude of the galaxy rotation curve is related to the galaxy's visible mass.

Thus quaternions are a preferred method for representing spatial rotations – see quaternions and spatial rotation.

Thus while Tycho acknowledged that the daily rising and setting of the sun and stars could be explained by the Earth's rotation, as Copernicus had said, still such a fast motion could not belong to the earth, a body very heavy and dense and opaque, but rather belongs to the sky itself whose form and subtle and constant matter are better suited to a perpetual motion, however fast.

Thus, if a ray of light is passed through a material and reflected back through it, the rotation doubles.

Thus the rotation of the solution will increase from + 18. 7 to an equilibrium value of + 52. 5 as some of the β form is converted to the α form.

Earth's rotation period relative to the fixed stars, called its stellar day by the International Earth Rotation and Reference Systems Service ( IERS ), is seconds of mean solar time ( UT1 ) Earth's rotation period relative to the precessing or moving mean vernal equinox, misnamed its sidereal day, is seconds of mean solar time ( UT1 ) Thus the sidereal day is shorter than the stellar day by about 8. 4 ms.

Thus, tire rotation needs to occur more frequently for front-wheel drive vehicles.

Thus image schemata are rich images, in a sense of the term similar to how the rotation of Shepard and Metzler-like mental images preserves the visual contours of the 2D picture of the 3D object ; in other words image schemata are not strictly 2D pictures, but a rich image-like whole that contain procedural as well as perceptual information about the object as a whole.

Thus we can extract from any 3 × 3 rotation matrix a rotation axis and an angle, and these completely determine the rotation.