Thus, if corporations are not to run away with us, they must become quasi-governmental institutions, subject to public control and needs.

Thus Af if and only if Af.

Thus F satisfies Af if and only if F has the form Af.

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, if public pressure sets the effective limit to the price that the industry may charge, this pressure is itself a function of the wage rate.

Thus, during any given year ( A ) if the revenues from the residential service are $7,000,000, ( B ) if the operating expenses imputed to this class of service come to $5,000,000, and ( C ) if the net investment in ( or value of ) the plant and equipment deemed devoted to this service amounts to $30,000,000, the cost analyst will report that residential service, in the aggregate, has yielded a return of $2,000,000 or 6-2/3 per cent.

Thus if the gyro and platform-controller combination maintains the platform with zero angular deviation about the **yf axis, the system can be rotated with an angular velocity Af if a torque is supplied to the gyro output axis Aj.

Thus, if one accelerometer is properly aligned, the other is also.

Thus, if we are to observe American folklore in the twentieth century, we will do well to establish the relationships between folklore, nationalism and imperialism at the outset.

Thus, red wine must, if possible, never be disturbed or shaken ; ;

Thus, if what is at issue is whether `` All S is P '', it is indifferent whether `` Some S is not P '' or `` No S is P '', since in either case the judgment in question is false.

Thus most Affidavits now require to be Apostilled if used for cross border issues.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

Thus throwing a rock at someone for the purpose of hitting him is a battery if the rock in fact strikes the person and is an assault if the rock misses.

Thus, a court officer taking possession of goods under a court order may use force if reasonably necessary.

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

Thus, if P is a program in L < sub > 2 </ sub > which is a minimal description of s, then InterpretLanguage ( P ) returns the string s. The length of this description of s is the sum of

Thus, if every historian were to claim that there was a solar eclipse in the year 1600, then though we might at first naively regard that as in violation of natural laws, we'd come to accept it as a fact.

Thus, in general, elementary light optical effects, light scatter, and electron scatter determine the obtainable resolution limit.

Thus optical amplification, and laser operation, can take place at a frequency of ν < sub > 32 </ sub > ( E < sub > 3 </ sub >- E < sub > 2 </ sub > = hν < sub > 32 </ sub >).

Thus, the cost of transmitting a bit over an optical network decreases by half every nine months.

Thus it concerns the interaction between the electromagnetic ( optical ) and the electrical ( electronic ) states of materials.

Thus, sensitive detection of specific optical frequencies necessitates optical heterodyne detection, in which two different ( close-by ) wavelengths of light illuminate the detector so that the oscillating electrical output corresponds to the difference between their frequencies.

Thus, if a wave is traveling through several different media, then the optical path length of each medium can be added to find the total optical path length.

Thus, an optical fiber or a copper cable is a transmission medium.

Thus Jansky suspected that the hiss originated well beyond the Earth's atmosphere, and by comparing his observations with optical astronomical maps, Jansky concluded that the radiation was coming from the Milky Way Galaxy and was strongest in the direction of the center of the galaxy, in the constellation of Sagittarius.

Thus, a legacy switch system can be easily " converted " to allow wavelength multiplexed transport over a fiber simply by judicious choice of transceiver wavelengths, combined with an inexpensive passive optical multiplexing device.

Porro prism designs have the added benefit of folding the optical path so that the physical length of the binoculars is less than the focal length of the objective and wider spacing of the objectives gives a better sensation of depth. Thus, the size of binoculars are reduced.

Thus there is not the same direct relation between magnetic optical activity and molecular stereochemistry which would be expected, because it is found in natural optical activity.

Thus, the ground was made for biological experiments with optical trapping.

Thus they show strong optical continuum emission, broad and narrow emission lines, and strong X-ray emission, together with nuclear and often extended radio emission.

Thus, plasmons are collective oscillations of the free electron gas density, for example, at optical frequencies.

Thus, excluding the transmission equipment upgrades, the cost of transmitting a bit over an optical network decreases by half every nine months.

Thus the optical system may contain no nonlinear materials nor active devices ( except possibly, extremely linear active devices ).

Thus, the ( powder ) " grain size " found by laser granulometry can be different from the " grain size " ( or, rather, crystallite size ) found by X-ray diffraction ( e. g. Scherrer method ), by optical microscopy under polarised light, or by scanning electron microscopy ( backscattered electrons ).

Thus, if the size of the quantum dot is small enough that the quantum confinement effects dominate ( typically less than 10 nm ), the electronic and optical properties change, and the fluorescent wavelength is determined by the size.

Thus an optical cavity, also known as a resonator, is a cavity with walls that reflect electromagnetic waves ( light ).

Thus in 1857 he went to Peru in order to determine the magnetic equator ; in 1861 – 1862 and 1864, he studied telluric absorption in the solar spectrum in Italy and Switzerland ; in 1867 he carried out optical and magnetic experiments at the Azores ; he successfully observed both transits of Venus, that of 1874 in Japan, that of 1882 at Oran in Algeria ; and he took part in a long series of solar eclipse-expeditions, e. g. to Trani ( 1867 ), Guntur ( 1868 ), Algiers ( 1870 ), Siam ( 1875 ), the Caroline Islands ( 1883 ), and to Alcosebre in Spain ( 1905 ).

Thus, its nearly flat spectrum on the top with steep sides is due to the effect of optical thickness on the bremsstrahlung spectrum.

Thus, when ClearType sacrifices color accuracy in order to increase luminance detail, the overall effect — as seen by human eyes — should be an improvement for most people.

Thus, two of the three color channels for each sensor must be interpolated and a so-called N-megapixel camera that produces an N-megapixel image provides only one-third of the information that an image of the same size could get from a scanner.

Thus, certain color contrasts may look fuzzier than others, depending on the allocation of the primary colors ( green has twice as many elements as red or blue in the Bayer arrangement ).

Thus the color falls into neither category " red " nor " yellow ", but these are the only categories available to us as we sort the apples.

Thus an RGB value does not define the same color across devices without some kind of color management.

Thus another name for this color is extreme violet.

Thus, this color name has been in use since 1912.

( Thus the mnemonics " queen gets her color ", or " queen on color ", or " queen on her own color ".

Thus, although all people perceive visible radiation the same way, in terms of a continuum of color, people who speak different languages slice up this continuum into discrete colors in different ways.

Thus juvenile blood ( which looks like wet extracts appearing on the skin ) is being transformed into richer blood, having the color of mature wine.

Thus the study of racism can be seen, at least superficially, as the study of the ways that people with a certain skin color and cultural background are systematically mistreated by society at large.

Thus it was entirely possible that models introduced in the ' 50s could be fitted with four different wheel types during the span of their inclusion in the series — or even more, since there were further variations ( e. g. knobby or smooth ) besides the color or material.

Thus the relatively small amount of network color programming, combined with the high cost of color television sets, meant that as late as 1964 only 3. 1 percent of television households in the U. S. had a color set.

Thus the NTSC color subcarrier ended up as 3. 57954545 MHz ( actually 315 / 88 MHz ), the line scan frequency as 15734. 27 Hz and the frame rate 29. 97 Hz ( exactly 30 / 1. 001 Hz ).

Thus, except in sunlight, the color of clothing makes little difference as regards warmth ; likewise, paint color of houses makes little difference to warmth except when the painted part is sunlit.

Thus, Palominos can be considered a color breed.

Thus there are usually only a few words, in large print, and a humorous or arresting image in brilliant color.

Thus, subsequent authors usually considered the supposed P. a. cottoni a semi-melanistic color morph, and recognized an allopatric division between the subspecies as listed above.