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, energy is no longer released when such nuclei are made by fusion ; instead, energy is absorbed in such processes.

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

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 his calculations should have required an additional year, ending in 1967.

Thus it has been alleged that many credentes would eventually receive the consolamentum as death drew near — performing the ritual of liberation at a moment when the heavy obligations of purity required of Perfecti would be temporally short.

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

Thus, they required that the Estates be arranged as in 1614.

Thus, numerical mathematical methods are required, even to solve the system of one nucleus and two electrons.

Thus the tonewheel assembly generates 91 frequencies, which are all that are required for the entire organ.

Thus, the state required service from both the old and the new nobility, primarily in the military.

Thus, the Holy Alliance needed Russia to supply the required armies.

Thus, he saw private property as both essential to liberty and a road to tyranny, the former when it resulted from labour and was required for labour and the latter when it resulted in exploitation ( profit, interest, rent, tax ).

Thus, reflection in a resonant cavity is usually required for a laser, but is not absolutely necessary.

Thus ingot casting, foundry techniques, blast furnace extraction, and electrolytic extraction are all part of the required knowledge of a metallurgist / engineer.

Thus, while dialectical methods are necessary to find truth in theoretical matters, rhetorical methods are required in practical matters such as adjudicating somebody's guilt or innocence when charged in a court of law, or adjudicating a prudent course of action to be taken in a deliberative assembly.

Thus to calculate the stoichiometry by mass, the number of molecules required for each reactant is expressed in moles and multiplied by the molar mass of each to give the mass of each reactant per mole of reaction.

Thus, many modern pumps have a molecular drag stage such as a Holweck or Gaede mechanism near the exhaust to reduce the size of backing pump required.

Thus, it is easy to convert from a vector file to a range of bitmap / raster file formats but it is much more difficult to go in the opposite direction, especially if subsequent editing of the vector picture is required.

Thus no special modifications are required to be made to operating systems which would otherwise not know about them.

Thus such studies undermine the broad consensus required for good science by excluding certain people, and so proving themselves in the end to be unscientific.

Thus, according to Coule, an Alcubierre Drive is required in order to build an Alcubierre Drive.

Thus, Electronic Support provides a source of information required for decisions involving Electronic Protection ( EP ), Electronic Attack ( EA ), avoidance, targeting, and other tactical employment of forces.

Thus, a proactive and comprehensive approach to HD is required for US's response.

Thus the amount of the test substance required to produce the same biological effect as a given quantity the unit of a standard preparation is compared and the potency of the unknown is expressed as a % of that of the standard by employing a simple formula.