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 using the 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 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.

By this standard, it is determined that where two stations operating on the same frequency are involved, objectionable interference from station A exists at any point within the service area of station B where station A's signal is of an intensity one-twentieth or more of the strength of station B's signal at that point.

By this time Henri's entire chest-back-lat-shoulder area is pumped-up to almost bursting point, and Claude takes time to do a bit more pectoral-front deltoid shaping work.

By 800 B.C. the Aegean was an area of common tongue and of common culture.

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 1971, 12 percent of the total area of South Vietnam had been sprayed with defoliating chemicals, at an average concentration of 13 times the recommended USDA application rate for domestic use.

By 1971, 12 percent of the total area of South Vietnam had been sprayed with defoliating chemicals, at an average concentration of 13 times the recommended USDA application rate for domestic use.

By the late 1960s, the area of LAFTA had a population of 220 million and produced about $ 90 billion of goods and services annually.

By 667, the Afghan area was under invasion by the Arabs but in 683 Kabul revolted and completely routed the invading army which was led by the Governor of Seistan.

By the 18th century, the area from Sambas to Berau were tributaries to the Banjar Kingdom, but this eventually shrunk to the size of what is now South Kalimantan as a result of agreements with the Dutch.

By the late 1950s, the once-prosperous port area of downtown Manhattan was occupied by a number of dilapidated shipping piers, casualties of the rise of container shipping which drove sea traffic to Port Elizabeth, New Jersey.

By the 1970s the area was notorious for street robberies and drug dealing.

Boroughs proliferated in the suburban areas of the larger cities: By the 1980s there were 19 boroughs and three cities in the area that is now the City of Auckland.

By 1080, a huge area had been lost to the Empire, and the Turks were within striking distance of Constantinople.

By area of extent, it was one of the largest empires ever in history.

By far the largest of the SSSIs is called Cheddar Complex and covers of the gorge, caves and the surrounding area.

By 2002, the cross had been rebuilt and the area around it was redesigned to protect and enhance its appearance.

By the time Allen reached his teens, the area, while still a difficult area in which to make a living, began to resemble a town, with wood-frame houses beginning to replace the rough cabins of the early settlers.

By 1769 the situation in the Grants had deteriorated to the point where surveyors and other figures of New York authority were being physically threatened and driven from the area.

By suppressing the inhibition of neurons by external factors, the targeted area of the brain may be reactivated and thereby recruited to compensate for lost function.

By 1916 Shepard started working for the Intelligence Department sketching the combat area within the view of his battery position.

By the first century BC Germanic languages had become prevalent, and the inhabitants were called Belgæ while the area was the coastal district of Gallia Belgica, the most northeastern province of the Roman Empire at its height.

By the late evening of 12 April most of the major southern parts and all the western area of the city had been occupied by the Germans, who cleared the city house by house, street by street.

By the 3rd century, the Goths ruled a vast area north of the Black Sea from where they either through crossing the lower Danube or traveling by sea, raided the Balkan Peninsula and Anatolia as far as Cyprus.

By now Glasnevin was an area for families of distinction-in spite of a comment attributed to the Protestant Archbishop King of Dublin that " when any couple had a mind to be wicked, they would retire to Glasnevin ".