By varying the proportions of copper and zinc, the properties of the brass can be changed, allowing hard and soft brasses.

By varying ability scores, the same system is used for a human hero as a trollish villain.

By varying the air pressure, a flute player can also change the pitch of a note by causing the air in the flute to resonate at a harmonic other than the fundamental frequency without opening or closing any holes.

By varying the snap count, a quarterback forces the defensive players to react to the movement of the offensive players, or risk being called for an offsides or encroachment penalty.

By varying the number of particles added for heterogeneous nucleation and the rate of cooling in a hot-dip process, the spangle can be adjusted from an apparently uniform surface ( crystallites too small to see with the naked eye ) to grains several centimetres wide.

By controlling the voltage applied across the liquid crystal layer in each pixel, light can be allowed to pass through in varying amounts thus constituting different levels of gray.

By varying the parameter r, the following behavior is observed:

By varying the ratio of graphite to clay, the hardness of the graphite rod could also be varied.

By integrating varying delivery streams, hybrids enable pay-TV operators more flexible application deployment, which decreases the cost of launching new services, increases speed to market, and limits disruption for consumers.

By varying the magnetic sail's field strength over the course of its orbit, a magnetic sail can give itself a " perigee kick " raising the altitude of its orbit's apogee.

By adding frame numbers to the frame sync, it is possible to extend the length of the random sequence, by varying the random sequence in accordance with the frame number.

By varying the gun ’ s angle of elevation with respect to the target vacuum chamber, impact angles from 0 ° to 90 ° relative to the gravitational vector are possible.

By extension, the term ' waveform ' also describes the shape of the graph of any varying quantity against time.

By 1835 all six daughters had died of varying causes, two when very young, two as children, the other two as young women: from whooping cough, yellow fever, and complications of childbirth.

By varying the monochromator's wavelength setting, the full spectrum can be measured.

By varying the extent and path of motion, a variety of effects can be obtained, with variable depth of field and different degrees of blurring of " out of plane " structures.

By varying the proportions of the juices, every shade from pink to black can be obtained.

By varying the amount of cream returned, producers can make a variety of low-fat milks to suit their local market.

By varying the pulse rate per LED, the display can approximate levels of brightness.

By varying the-Si-O-chain lengths, side groups, and crosslinking, silicones can be synthesized with a wide variety of properties and compositions.

By varying the angle of incidence and take-off on the crystal, a single X-ray wavelength can be selected.

By layering the highest quality crystals of varying compositions, it enabled the demonstration of the highest quality heterojunction semiconductor laser materials for many years.

By repeatedly sampling the randomly varying signal, a series of random numbers is obtained.

By varying the degree of smoothing, mid-tones between black and white can be created, hence the name mezzo-tinto which is Italian for " half-tone " or " half-painted ".

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 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.