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, an enemy would probably use this weapon for attack on static population centers such as large cities.

Thus in the presence of large quantum computers an n-bit key can provide at least n / 2 bits of security.

Thus, a poison that covers surface randomly will tend to reduce the number of uncontaminated large planes but leave proportionally more smaller sites free, thus changing the hydrogenation vs. hydrogenolysis selectivity.

Thus the interior of a metal is filled up with a large number of unattached electrons that travel aimlessly around like a crowd of displaced persons.

In particular, one should think of the condition number as being ( very roughly ) the rate at which the solution, x, will change with respect to a change in b. Thus, if the condition number is large, even a small error in b may cause a large error in x.

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

Thus, from an evolutionary perspective men may have had more to gain from a large increase in resources than women have had, which may be one explanation for why men, and especially poor men, tend to gamble more than women.

Thus, a high GWP correlates with a large infrared absorption and a long atmospheric lifetime.

Thus, actual address space utilization rates will be small in IPv6, but network management and routing efficiency is improved by the large subnet space and hierarchical route aggregation.

Thus, although the composition of the group is slightly different in each instance, the large majority of men present are always close neighbors.

Thus, according to Keynesian theory, some individually-rational microeconomic-level actions such as not investing savings in the goods and services produced by the economy, if taken collectively by a large proportion of individuals and firms, can lead to outcomes, wherein the economy operates below its potential output and growth rate.

Thus, Islamic architecture started witnessing the introduction of such structures as domes and large, arched entrances, referred to as iwans.

Thus the Mary Rose was subject to salvage from the sixteenth century and later, but a very large amount of material, buried in the sediments, remained to be found by maritime archaeologists of the twentieth century.

Thus, the mergers were not done to see large efficiency gains, they were in fact done because that was the trend at the time.

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

Thus, at a general level, there is a large degree of uniformity amongst all Orthodox Jews.

Thus, there is a correlation between the results of measurements performed on entangled pairs, and this correlation is observed even though the entangled pair may have been separated by arbitrarily large distances.

Thus for a large or very distributed company that requires multiple PBXs, users can receive the same services across the network and be unaware of the switch that their telephone is connected to.

Thus, first slavery and then serfdom gradually decreased in Europe as the population grew, but were reintroduced in the Americas and in Russia as large areas of new land with few people became available.

Thus, in the very large cases, the HTSC cost can not be offset by simply reducing the coil size at a higher magnetic field.

Thus, the party's platforms and rhetoric critique any corporate influence and control over government, media, and American society at large.

Thus, a few volts ' difference at the grid would make a large change in the plate current and could lead to a much larger voltage change at the plate ; the result was voltage and power amplification.

Thus in the absence of the minimum wage law unskilled workers would be paid approximately the same amount.

Thus each shell of a given thickness will produce the same net amount of light regardless of how far away it is.

Thus there are two unknowns ( albedo and size ), which can be determined by two independent measurements ( of the amount of reflected light and emitted infrared heat radiation ).

Thus the variance is a measure of the amount of variation of the values of that variable, taking account of all possible values and their probabilities or weightings ( not just the extremes which give the range ).

Thus, the vocoder dramatically reduces the amount of information needed to store speech, from a complete recording to a series of numbers.

Thus the velocity can be measured from the amount of redshift ( or blueshift ) of the star's spectrum.

Thus cutting a cake, where taking a larger piece reduces the amount of cake available for others, is a zero – sum game if all participants value each unit of cake equally ( see marginal utility ).

Its change is equal to the amount of reversible work done on, or obtainable from, a system at constant T. Thus its appellation " work content ", and the designation A from Arbeit, the German word for work.

Thus, it is the proportionality factor that relates the molar mass of an entity, i. e., the mass per amount of substance, to the mass of said entity.

Thus over months-to-years, the net ( integrated ) amount of force is substantial, and is thought to be sufficient to speed interplanetary probes to velocities that could traverse the Earth-Pluto distance in 1 / 2 to 1 / 4 the time of a chemically accelerated vessel.

There is no sustained, mature analysis of the notion ..." Thus, some critics object, it would be acceptable to torture one person if this would produce an amount of happiness in other people outweighing the unhappiness of the tortured individual.

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.

Thus phytoplankton are responsible for much of the oxygen present in the Earth's atmosphere – half of the total amount produced by all plant life.

Thus, in the above example, after an increase and decrease of percent, the final amount, $ 198, was 10 % of 10 %, or 1 %, less than the initial amount of $ 200.

Thus, astronomers measure the amount of light produced by an object as a function of time ( the light curve ).

Thus, as with all heat pumps, the Coefficient of Performance ( amount of thermal energy moved per unit of input work required ) decreases with increasing temperature difference.

: Thus, in Bergsland & Vogt ( 1962 ), the authors make an impressive demonstration, on the basis of actual language data verifiable by extra-linguistic sources, that the " rate of change " for Icelandic constituted around 4 % per millennium, whereas for closely connected Riksmal ( Literary Norwegian ) it would amount to as much as 20 %.

Thus, if a company is sued for monopolizing a market and the jury concludes the conduct resulted in consumers ' being overcharged $ 200, 000, that amount will automatically be tripled, so the injured consumers will receive $ 600, 000.

Thus, the plate will contain enzyme in proportion to the amount of secondary antibody bound to the plate.

Thus, tuning was a relatively slow operation, and composers had to allow a reasonable amount of time for players to change notes if they were called to tune in the middle of a work.

Thus, unless the quantity of newsprint used each year worldwide declines to reflect the lost fiber, a certain amount of new ( virgin ) fiber is required each year globally, even if the individual newsprint mill may continue to use 100 % recycled fiber.