Thus, Alfred Sherwood Romer proposed it served as a snorkel, Martin Wilfarth that it was an attachment for a mobile proboscis used as a breathing tube or for food gathering, Charles M. Sternberg that it served as an airtrap to keep water out of the lungs, and Ned Colbert that it served as an air reservoir for prolonged stays underwater.

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 total of entropy of the room plus the entropy of the environment increases, in agreement with the second law of thermodynamics.

Thus the stopping voltage increases.

Thus, it is likely that the worst-case running time for any algorithm for the TSP increases exponentially with the number of cities.

where θ is the angle between the vectors Ω < sub > P </ sub > and L. Thus, if the gyroscope's spin slows down ( for example, due to friction ), its angular momentum decreases and so the rate of precession increases.

Thus the screening current changes direction every time the flux increases by half integer multiples of.

Thus, according to the theory, affirmative action hurts its intended beneficiaries, because it increases their dropout rate.

Thus, increases in the prices of assets held over the period, conventionally referred to as holding gains, are, conceptually, profits.

" Thus for example " smoking increases mortality risk by a factor of just 1. 6, while social isolation does so by a factor of 2. 0 ... suggest an added value to self-help groups such as Alcoholics Anonymous as surrogate communities.

Thus the speed of sound increases with the stiffness ( the resistance of an elastic body to deformation by an applied force ) of the material, and decreases with the density.

Thus, what happens physically is that the energy level of the bottom of the conduction band of body " A " ( and, hence, the whole band structure of body " A ") moves up in energy, relative to the Fermi level of the Earth, as the temperature of body " A " increases.

Thus the liftoff mass requirement increases exponentially with an increase in the required delta-v of the spacecraft.

Thus channel capacity increases linearly by increasing the channel's bandwidth to the maximum value available, or ( in a fixed-channel bandwidth ) by increasing the signal power exponentially.

Thus negative mood increases helpfulness because helping others can reduce one's own bad feelings.

Thus, although the viscosity still decreases as temperature increases, these synthetic motor oils have a higher viscosity index over the traditional petroleum base.

Thus the chemical potential of HA decreases and the sum of the chemical potentials of H < sup >+</ sup > and A < sup >-</ sup > increases.

Thus, the level of oxygen in the blood decreases, and the level of carbon dioxide increases.

Thus as the distance from a point source increases, the spherical wavefronts become flatter and closer to plane waves, which are perfectly collimated.

Thus, increases engine power losses.

Thus as sensitivity increases, a screening program will cost more, or be able to screen a smaller number of women.

Thus, as the number of energy states increases, the energy of the system will be spread among more and more states, thereby increasing the entropy of the system.

Thus, contrary to intuition, the number of k-point lines expected from random chance increases much more than linearly with the size of the area considered.

Thus removing the tumor alone without additional treatment greatly increases the risk that another cancer will form in that testicle.

Thus, MRT increases in absolute size as one moves from the top left of the PPF to the bottom right of the PPF.

Thus in theory, if law enforcement officials decline to offer a Miranda warning to an individual in their custody, they may still interrogate that person and act upon the knowledge gained, but may not use that person's statements to incriminate him or her in a criminal trial.

Thus, Seder participants recall the slavery that reigned during the first half of the night by eating matzo ( the " poor person's bread "), maror ( bitter herbs which symbolize the bitterness of slavery ), and charoset ( a sweet paste representing the mortar which the Jewish slaves used to cement bricks ).

Thus a person's class situation is basically his market situation.

Thus it is advised that the rescuer approach with a buoyant object, or from behind, twisting the person's arm on the back to restrict movement.

Thus astrologers believe that the ascendant signifies a person's awakening consciousness, in the same way that the Sun's appearance on the eastern horizon signifies the dawn of a new day.

Thus, a person's mind cannot be the true cause of his hand's moving, nor can a physical wound be the true cause of mental anguish.

Thus, the term apparatchik, or " agent of the apparatus " was usually the best possible description of the person's profession and occupation.

Thus, if a person's addiction is extinguished and he is then presented with a stimulus that has been associated with the drug in the past, a craving for that drug reappears.

Thus, a person's full attitude can only be understood in terms of what other positions he / she finds acceptable ( or not ) in addition to his / her own stand.

Thus, finding a person's behavior / beliefs reprehensible when they pose no threat of harm to oneself or others, is incompatible with unconditional positive regard.

Thus, God affects the person's environment, even to its atoms, and for those souls who reincarnate, produces the appropriate rebirth body, all in order that the person might have the karmically appropriate experiences.

Thus, God affects the person's environment, even to its atoms, and for those souls who reincarnate, produces the appropriate rebirth body, all in order that the person might have the karmically appropriate experiences.

Thus, when Wesley speaks of " Tradition ," he does not merely refer to ancient Church Tradition and the writings of the great theologians and Church Fathers of days past, but also of the immediate and present theological influences which contribute to a person's understanding of God and of Christian theology.

Thus, using another person's username or identifier ( ID ) and password without proper authority to access data or a program, or to alter, delete, copy or move a program or data, or simply to output a program or data to a screen or printer, or to impersonate that other person using e-mail, online chat, web or other services, constitute the offence.

Thus, service providers have an obligation to be aware of the seemingly unrelated factors that can impact a person's life experience and response to the service and to adapt their methods accordingly.

Thus, as with the case of delirium, the minor degrees of pathological confusion cannot be diagnosed without knowledge of a person's " baseline ", or normal, level of mental functioning.

Thus a person's bodily life is as much a public affair as are the lives of animals.