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, when the fluid finally does strike the object, it is forced to change its properties -- temperature, density, pressure, and Mach number -- in an extremely violent and irreversible fashion called a shock wave.

For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as its linear momentum,, crossed by its position from the origin, r. Thus, the angular momentum L of a particle with respect to some point of origin is

Thus the Bauhaus style, also known as the International Style, was marked by the absence of ornamentation and by harmony between the function of an object or a building and its design.

Thus a statement of the form is said to be true, under a particular interpretation, if there is some object in the domain of discourse of that interpretation that satisfies the predicate that the interpretation uses to assign meaning to the symbol Phil.

Thus, any real object cannot remain the same, also because of movement of its physical parts ( even much bigger than molecules ).

Thus what we really mean is: " I perceive that ' This object a is red '" and this is an undeniable-by-3rd-party " truth ".

Thus the proof of the existence of a mathematical object is tied to the possibility of its construction.

Thus we can conceive of a “ noumenal ” world ( noumenal meaning " object of thought ") which exists only as a heuristic for our cognitive capacities and not as something directly accessible to experience.

Thus, from the war of nature, from famine and death, the most exalted object which we are capable of conceiving, namely, the production of the higher animals, directly follows.

Thus, by measuring the current-day < sup > 87 </ sup > Sr /< sup > 86 </ sup > Sr ratio ( and often the Nd-Nd ratios as well ) the geological fingerprint of an object or skeleton can be measured, allowing migration patterns to be determined.

Thus the mathematical formulation of the Alcubierre metric does not contradict the conventional claim that the laws of relativity do not allow a slower-than-light object to accelerate to faster-than-light speeds.

Thus, an object starting from rest will attain a velocity of 9. 81 m / s ( 32. 2 ft / s ) after one second, 19. 62 m / s ( 64. 4 ft / s ) after two seconds, and so on, adding 9. 81 m / s ( 32. 2 ft / s ) to each resulting velocity.

Thus, to perform a spell check, a front-to-end iterator would be given a reference to a object.

Thus began a fifteen-year correspondence between Balzac and " the object of sweetest dreams ": Ewelina Hańska.

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, some objects will end in a real reference, and some with the referenced object, and the machine must be able to tell by reading the final cell which one it is.

Thus, the object's hour angle indicates how much sidereal time has passed since the object was on the local meridian.

Thus, in active declarative sentences in English the subject is followed by the main verb which in turn is followed by the object ( SVO ).

Thus a definition reflects the ultimate object of our understanding, and is the foundation of all valid inference.

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

Thus, there is no need for direct contact between the pyrometer and the object, as there is with thermocouples and resistance temperature detectors ( RTDs ).

Thus this dependency-based parse tree acknowledges the subject noun John and the object noun phrase the ball as constituents just like the constituency-based parse tree does.

Thus the speed of the diurnal motion of a celestial object is this cosine times 15 °/ hr

Thus an object can be classified as " invisible to " a person, animal, instrument, etc.

Thus, a " more accessible " object for nostalgia was a " secondary silver age within the last few hundred years "— the Kingdom of Romania's 19th century cultural renaissance.