Suggest the following twenty-first-century amendment: By moving the term `` Republic '' to lower case, substituting the modern phrase, `` move ahead '' for the stodgy `` keep '', and by using the Postmaster's name on every envelope ( in caps, of course, with the `` in spite '' as faded as possible ), the slogan cannot fail.

By using the appropriate version any one of these factors can be determined for any combination of the other three.

By using instruments of gradually increasing size, the vagina is gently, and with minimum pain at each stage, taught to yield to an object of the appropriate shape.

By 1827 Laplace was using least

By comparing the form of several yupanas, researchers found that calculations were based using the Fibonacci sequence 1, 1, 2, 3, 5 and powers of 10, 20 and 40 as place values for the different fields in the instrument.

By night, an aardwolf can consume up to 200, 000 harvester termites using its sticky, long tongue.

By using the palette to mask the top area of the display and taking care about when it changes mode it can shift the continuous graphics at the bottom of the display down in two pixel increments because the internal display counter is not incremented on blank scanlines during non-continuous graphics modes.

By the Roman period brass was being deliberately produced from metallic copper and zinc minerals using the cementation process and variations on this method continued until the mid 19th century.

By comparison to biotechnology, bioengineering is generally thought of as a related field with its emphasis more on higher systems approaches ( not necessarily altering or using biological materials directly ) for interfacing with and utilizing living things.

By the late 1920s, New York writers other than Fitz Gerald were starting to use " Big Apple " and were using it outside of a horse-racing context.

By the mid-1980s at least 500 courses in business ethics reached 40, 000 students, using some twenty textbooks and at least ten casebooks along supported by professional societies, centers and journals of business ethics.

By 1000 BC ancient civilizations were using technologies that formed the basis of the various branches of chemistry such as ; extracting metal from their ores, making pottery and glazes, fermenting beer and wine, making pigments for cosmetics and painting, extracting chemicals from plants for medicine and perfume, making cheese, dying cloth, tanning leather, rendering fat into soap, making glass, and making alloys like bronze.

By using custom formatting and load / save routines ( sometimes included in third-party DOSes, see below ), all of the mechanically possible 40 tracks could be used.

By the early 1990s, the performance of microprocessor-based computers reached the point that real-time generation of computer music using more general programs and algorithms became possible.

By using the commutator as a Lie bracket, every associative algebra can be turned into a Lie algebra.

By a strange twist of their respective fates, this foursome ends up partnering together, using their unique talents to become a ragtag team of bounty hunters, although their fortunes as such are at best mixed.

By 1970, a calculator could be made using just a few chips of low power consumption, allowing portable models powered from rechargeable batteries.

By reducing the number of tracks used ( and thus the capacity ), Commodore could further reduce cost-in contrast to the double-density drives used e. g. in IBM PCs of the day which saved 180 KB on one side ( by using a 40-track format ).

By the time of the Vietnam War, IDs spelled out the broad religious choices such as PROTESTANT and CATHOLIC, rather than using initials, and also began to show individual denominations such as " METHODIST " or " BAPTIST.

By 1695 he was back in England, now formally using the name " Defoe ", and serving as a " commissioner of the glass duty ", responsible for collecting taxes on bottles.

By contrast, non-digital ( or analog ) systems represent information using a continuous function.

By using doublespeak in advertisements, aspirin production rose by almost 50 percent from over 23 million pounds in 1960 to over 35 million pounds in 1970.

By the 12th to 13th centuries A. D., monks were preparing illuminated manuscripts on vellum and parchment in monasteries throughout Europe and were using lead styli to draw lines for their writings and for the outlines for their illuminations.

By direct substitution, the solution to this equation can be readily shown to be the scalar Green's function, which in the spherical coordinate system ( and using the physics time convention ) is:

By varying the formula, this curve may be moved forward or backward along the coordinates to produce any desired compression strength / density ratio.

By the continuous formula,

By doing this to the formula above, we find:

By using logarithmic identities to transform the formula, the multiplications can be expressed as a sum and the power as a multiplication.

By sorting formulas according to the number of atoms of each element present in the formula according to these rules, with differences in earlier elements or numbers being treated as more significant than differences in any later element or number — like sorting text strings into lexicographical order — it is possible to collate chemical formulas into what is known as Hill system order.

By degrees, however, Justinian came to understand that the formula at issue not only appeared orthodox, but might also serve as a conciliatory measure toward the Monophysites, and he made a vain attempt to do this in the religious conference with the followers of Severus of Antioch, in 533.

By the end of the 5th dynasty, the formula in all tombs becomes " An offering the king gives and Osiris ".

By most accounts, Coca-Cola was India's leading soft drink until 1977 when it left India after a new government ordered The Coca-Cola Company to turn over its secret formula for Coke and dilute its stake in its Indian unit as required by the Foreign Exchange Regulation Act ( FERA ).

By contrast, ext2 and other Berkeley FFS-like file systems of that time simply used a fixed formula for computing inode locations, hence limiting the number of files they may contain.

By the same formula we can find the geostationary-type orbit of an object in relation to Mars ( this type of orbit above is referred to as an areostationary orbit if it is above Mars ).

The canonical model is a model of L, as every L-MCS contains all theorems of L. By Zorn's lemma, each L-consistent set is contained in an L-MCS, in particular every formula unprovable in L has a counterexample in the canonical model.

By comparison, prediction in frequentist statistics often involves finding an optimum point estimate of the parameter ( s ) — e. g. by maximum likelihood or maximum a posteriori estimation ( MAP ) — and then plugging this estimate into the formula for the distribution of a data point.

By using this formula as distance, Euclidean space ( or even any inner product space ) becomes a metric space.

By the time of Diocletian, however, this two-stage process had largely disappeared, and the Praetor would either hear the whole case in person or appoint a delegate ( a iudex pedaneus ), taking steps for the enforcement of the decision ; the formula was replaced by an informal system of pleadings.

By convention, the formula is always true, regardless of the formula P ( x ); see vacuous truth.

By mid-century, Robert Wallace acquired the formula for nickel silver and established with Samuel Simpson, R. Wallace & Company the forerunner of Wallace Silversmiths.

By repeated applications of the half-angle formula

By Euler's formula the number of faces (' F '), vertices ( V ), and edges ( E ) of any convex polyhedron are related by the formula " F + V-E "

By Heron's formula, the area of the triangle is

By choosing a = 0, this formula gives both an integral and a series representation for a function that interpolates the harmonic numbers and extends a definition to the complex plane.

By substituting this formula for current into one or both factors of current in Joule's law, the power dissipated can be written in the equivalent forms:

By inserting different prices into the formula, you will obtain a number of break even points, one for each possible price charged.