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

Thus, the binding energy to contain or trap a particle in a smaller region of space, increases without bound, as the region of space grows smaller.

Thus, the energy required to break any single pair is related to the energy required to break all of the pairs ( or more than just two electrons ).

Thus it can be interpreted without any reference to the zero-point energy ( vacuum energy ) or virtual particles of quantum fields.

Thus, any electromagnetic radiation can " heat " ( in the sense of increase the thermal energy termperature of ) a material, when it is absorbed.

In the field of high-energy particle physics, the fundamental velocity unit is the speed of light c. Thus, dividing energy in eV by the speed of light in vacuum, one can describe the momentum of an electron in units of eV / c.

Thus, it is this semi-empirical formula for bond energy that underlies Pauling electronegativity concept.

Thus, explosives are substances that contain a large amount of energy stored in chemical bonds.

Thus, a piece of iron in its lowest energy state (" unmagnetized ") generally has little or no net magnetic field.

Thus a vast and elaborate house may serve as a sign of conspicuous wealth, whereas a low-profile house built of recycled materials may indicate support of energy conservation.

Thus, if an optical brightener or color enhancer absorbs light energy and emits it through or with the dye, the appearance changes, as the spectrum of light re-emitted to the observer changes.

Thus the engine expended much of its energy in repeatedly heating the cylinder rather than in delivering mechanical force.

Thus, although the joule has the same dimensions as the newton-metre ( 1 J = 1 N · m = 1 kg · m < sup > 2 </ sup >· s < sup >− 2 </ sup >), these units are not interchangeable as the newton-metre ( N · m ) is the unit of torque and joule the unit of energy.

Thus, electrons are found in specific energy levels of an atom, two of which are shown below:

) Thus lighting energy accounts for about four or five million barrels of oil ( equivalent ) per day.

Thus commercial lighting alone consumes about four to five million barrels per day ( equivalent ) of petroleum, in line with the alternate rationale above to estimate U. S. lighting energy consumption.

Thus the psychopathologized individual for Freud was an immature individual, and the goal of psychoanalysis was to bring these fixations to conscious awareness so that the libido energy would be freed up and available for conscious use in some sort of constructive sublimation.

Thus, conservation of four-momentum is Lorentz-invariant and implies conservation of both mass and energy.

Thus, an additional 6 % of the total energy of fission is also released eventually as non-prompt ionizing radiation, and this is about evenly divided between gamma and beta ray energy.

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

Thus, there is freshness not only in the individual movements of the dance but in the shape of their continuity as well.

Thus jazz is transmuted into something holy, the sacred road to integration of being.

Thus the fictional detective is much more than a simple businessman.

Thus the cocktail party would appear to be the ideal system, but there is one weakness.

Thus in both types attention is focused on the community itself, and its phenomenological life.

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

Thus human perception and human volition is the immanent cause of all social change and this most truly when the change reaches the civilizational level.

Thus, circular motion is itself one of the essential characteristics of completely perfect celestial existence.

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

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 science is the savior of mankind, and in this respect Childhood's End only blueprints in greater detail the vision of the future which, though not always so directly stated, has nevertheless been present in the minds of most science-fiction writers.

Thus the copywriter in the world of the space merchants is the person who in earlier ages might have been a lyric poet, the person `` capable of putting together words that stir and move and sing ''.

Thus there is a clearer division of authority, administrative and legislative.

Thus, as a development program is being launched, commitments and obligations must be entered into in a given year which may exceed by twofold or threefold the expenditures to be made in that year.

Thus, the need for the B-70 as a strategic weapon system is doubtful.

Thus technical efficiency is achieved at the expense of actual experience.

Thus, there is an added incentive to stay on the job.

Thus, the Span of its ossification was shortened and the center's ability to `` catch up '' in ossification is demonstrated.

Thus T is not diagonalizable.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

Thus, the study of the solutions to the equation Af is reduced to the study of the space of solutions of a differential equation of the form Af.

Thus in the three-dice example Af, Af, and the independence assumption imply that the probability that the three dice fall ace, not-ace, ace in that order is Af.

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

Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus Af is also continuous at Af, and in a neighborhood of Af which does not contain a tangent point.