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 using the formula

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 connecting outward light to inward light, via an interaction point, this equation stands for the whole ' light transport ' — all the movement of light — in a scene.

By a proper choice of coordinate system, the ellipse can be described by the canonical implicit equation

By eliminating ρ and J, using Maxwell's equations, and manipulating using the theorems of vector calculus, this form of the equation can be used to derive the Maxwell stress tensor σ, in turn this can be combined with the Poynting vector S to obtain the electromagnetic stress-energy tensor T used in general relativity.

By interchanging the roles of x and y one obtains the corresponding equation of a parabola with a vertical axis as

By assuming that light actually consisted of discrete energy packets, Einstein wrote an equation for the photoelectric effect that agreed with experimental results.

By solving this equation, one arrives at the " equations of motion " of the field.

By using the London equation, one can obtain the dependence of the magnetic field inside the superconductor on the distance to the surface.

By the radiation pressure equation σT < sup > 4 </ sup >/ c ; the sun-facing photon pressure is 3. 61 µPa ( 3. 6 N / km², 2. 08 lbf / mi² ).

By finding the derivative of the equation while assuming that y is a constant, the slope of ƒ at the point is found to be:

By using the definition of an average, this equation states that when the acceleration is constant average velocity times time equals displacement.

By analogy, the magnetic equation is an inductive current involving spin.

By putting the measured period T, and the measured distance between the pivot blades L, into the period equation ( 1 ), g could be calculated very accurately.

By implicit differentiation, one can show that all branches of W satisfy the differential equation

By Late Antiquity, some Gnostic and Neoplatonist thinkers had expanded this syncretic equation to include Aion, Adonis, Attis, Mithras and other gods of the mystery religions.

By 1928 Dirac deduced his equation from the first successful unified combination of special relativity and quantum mechanics to the electron-the Dirac equation.

By contrast the inverse heat equation, deducing a previous distribution of temperature from final data is not well-posed in that the solution is highly sensitive to changes in the final data.

By the Kelvin – Stokes theorem, this equation can also be written in a " differential form ".

By examining Laplace's equation in spherical coordinates, Thomson and Tait recovered Laplace's spherical harmonics.

By separation of variables, two differential equations result by imposing Laplace's equation:

By combining the beamwidth equation with the gain equation, the relation is:

By quantizing this, we get the non-relativistic Schrödinger equation for a free particle,