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, the alignment of the `` dots '' and `` tips '', respectively, indicate individual variability of the 21 growth centers of each child with respect to the mean values for these boys and girls.

Thus, when more than one distinct form leads to a particular cell in the X-region, a chain of information cells must be created to accommodate the forms, one cell in the chain for each form.

Thus, the efficiency **yt couplers is given by -- Af or approximately 50 percent each.

Thus some provinces contained tribes which detested each other, and to them independence meant an opportunity for war.

Thus arose the first monastic community, consisting of anchorites living each in his own little dwelling, united together under one superior.

Thus, each person of the Trinity is described as uncreated ( increatus ), limitless ( Immensus ), eternal ( æternus ), and omnipotent ( omnipotens ).

Thus, each Spruance-class destroyer originally carried a maximum total of 24 ASROC.

Thus, there are 35 possible basic contracts ( five at each of the seven levels ); 1 being the lowest, followed by 1 etc., up to 7NT, the highest possible bid.

Thus, the broadcast domain is the entire inter-connected layer two network, and the segments connected to each switch / bridge port are each a collision domain.

Thus an understanding of how these two levels relate to each other is needed.

Thus, on a real computer display, each pixel is actually composed of separate red, green, and blue subpixels.

Thus the dynamic characteristic of DHTML is the way it functions while a page is viewed, not in its ability to generate a unique page with each page load.

Thus, the change in slope between each successive point is small, reducing the apparent " jaggedness " of the approximation.

Thus, speakers of two adjacent Inuit dialects would usually be able to understand one another, but speakers from dialects distant from each other on the dialect continuum would have difficulty understanding one another.

Thus, ecosystem processes are driven by the number of species in an ecosystem, the exact nature of each individual species, and the relative abundance organisms within these species.

Thus, churches actually had money-changing tables at which each coin would be examined separately and a token of actual worth given to the layperson so that he or she could be seen by the other parishioners as putting money in the basket during that part of the service.

Thus, medical practitioners would select treatment options for specific cases based on the best research for each patient they treat.

Thus in each term ( endothermic & exothermic ) the prefix refers to where heat goes as the reaction occurs.

Thus, over time we would expect each traditional song to become aesthetically ever more appealing — it would be collectively composed to perfection, as it were, by the community.

Thus, online conversations often involve a variety of assumptions and motives unique to each individual user.

Thus, the eight items of the path are not to be understood as stages, in which each stage is completed before moving on to the next.

Thus, in a sense, there is a different completeness theorem for each deductive system.

Thus, in place of one unchallenged military commander, the province now had five officers, each with command of only a small fraction of the garrison.

Thus, a square and a circle are homeomorphic to each other, but a sphere and a donut are not.