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 comparing Arithmetic and Geometric mean of numbers

By comparing the length and intensity of various methods of therapies, it was proven that intensity is a better predictor of recovery than the method of therapy used.

By comparing different embryonic stages of different vertebrate species, he formulated the Recapitulation theory.

By comparing the parts of the genome that are not under natural selection and which therefore accumulate mutations at a fairly steady rate, it is possible to reconstruct a genetic tree incorporating the entire human species since the last shared ancestor.

By comparing mitochondrial DNA which is inherited only from the mother, geneticists have concluded that the last female common ancestor whose genetic marker is found in all modern humans, the so-called mitochondrial Eve, must have lived around 200, 000 years ago.

By comparing the genome compositions between genomes, scientists can better understand the evolutionary history of a given genome.

By comparing the relative positions of the moon and Mars with their anticipated positions, Vespucci was able to crudely deduce his longitude.

Soon however, Marl's records became more sample heavy, as can be seen by comparing the MC Shan LPs Down By Law ( 1987 ) and Born to be Wild ( 1988 ); the rhythms less electronic, with drum samples and patterns becoming more prominent.

By comparing the different natural languages, scholars hope to learn something about the nature of human intelligence and the innate biases and constraints that shape natural language, which are sometimes called universal grammar.

By comparing the times of the eclipses, the difference in longitude of Paris to Uranienborg was calculated.

By comparing the photographic plates of the Pleiades cluster taken in 1918 with images taken in 1943, van Maanen was able to identify those stars that had a proper motion similar to the mean motion of the cluster, and were therefore more likely to be members.

By comparing skulls of different ethnic groups it supposedly allowed for ranking of races from least to most evolved.

By measuring the frequency of the returned signal and comparing that with the original, the difference can be easily measured.

By comparing the spectra of stars such as Sirius to the Sun, they found differences in the strength and number of their absorption lines — the dark lines in a stellar spectra due to the absorption of specific frequencies by the atmosphere.

By comparing the spectrum to computed models of stellar evolution, the age, mass, radius and luminosity of Tau Ceti can be estimated.

By monitoring vegetation changes over time, droughts can be monitored by comparing the current vegetation state to its long term average.

By instead comparing the radiated power in a given direction to the actual power that the antenna receives from the transmitter, the power gain takes into account that poorer efficiency, making it a more useful figure of merit for the ability of a transmitter in sending a radio wave toward a receiver.

By expanding the left hand side and then comparing the real and imaginary parts under the assumption that x is real, it is possible to derive useful expressions for cos ( nx ) and sin ( nx ) in terms of cos x and sin x.

By comparing the arrival times of gamma showers with the separations of the spacecraft, a location can be determined, for follow-up with other telescopes.

By comparing this with the account of stupteria given by Dioscorides in the 123rd chapter of his 5th book, it is obvious that the two are identical.

* 1862 – By analysing the spectroscopic signature of the Sun and comparing it to those of other stars, Father Angelo Secchi determines that the Sun is itself a star.

By counting numbers of live and dead mites that developed every 15 days and comparing this with his initial count on the infant, he was able to estimate how long that infant was dead.

By writing as a Laurent series and explicitly comparing terms, one may verify that it satisfies the relation

By contrast, the energetic reaction of the leader to the full demands his decision imposes upon him strengthens the moral intuition and gives us the measure of the man.

By lowering the activation energy, the enzyme speeds up that reaction by a rate of 10 < sup > 11 </ sup > or more: a reaction that would normally take over 3, 000 years to complete spontaneously might take less than a second with an enzyme.

By studying how quickly the reagent species disappears in the presence of differing concentrations of a ( usually stable ) co-reagent species the reaction rate constant at the low temperature of the CRESU flow can be determined.

By mid-century, however, a synthesis of the ideas of Romanticism with more stable political ideas had emerged, partly in reaction to the failed Romantic and democratic Revolutions of 1848.

A reaction consisting of the histone octamers and a naked DNA template can be incubated together at a salt concentration of 2 M. By steadily decreasing the salt concentration, the DNA will equilibrate to a position where it is wrapped around the histone octamers, forming nucleosomes.

By 1975 both Number 96 and The Box, perhaps as a reaction to declining ratings for both shows, de-emphasised the sex and nudity moving more in the direction of comedy.

By Legendre-transforming this expression, he defined the concepts of enthalpy and " free energy " ( now universally known as the " Gibbs free energy "), a thermodynamic potential which is especially useful to chemists since it determines whether a reaction will proceed spontaneously at a fixed temperature and pressure.

By leaving the vehicle's power source on the ground and by using ambient atmosphere as reaction mass for much of its ascent, a lightcraft would be capable of delivering a very large percentage of its launch mass to orbit.

By the time of the first performance, which was well received, Donizetti reported to his publisher the audience's reaction to most of the numbers, specifically that " in the duet for Vial and Salvatore, many shouts of bravi, but at the end ( so they say ) the situation is so moving that they were weeping ".

By using stainless steel for the bomb, the reaction will occur with no volume change observed.

By using a chemical reaction rather than a connection to an oxygen tank, these devices supply breathing oxygen for long enough for the airliner to descend to thicker, more breathable air.

Although the Eradicator's effects ( altering the DNA of all Kryptonian life-forms so that they would instantly die upon leaving the planet ) were felt immediately, the Destroyer's effects were possibly more significant: By the time the Kryptonian government admitted defeat and abolished the clone banks, a pro-clone rights terrorist faction known as Black Zero had started the Destroyer, a device which functioned as a giant nuclear gun, projecting massive streams of nuclear energy into the core of Krypton, intended to trigger an explosive chain reaction within Krypton's core almost immediately.

By restoring 10 minutes to the film, the complex story now fits together in a seamless way, filling in those gaps found in the previous theatrical release, and proving that Peckinpah was firing on all cylinders for this, his grandest achievement .... And the one overwhelming feature that the director's cut makes unforgettable are the many faces of the children, whether playing, singing, or cowering, much of the reaction to what happens on-screen is through the eyes, both innocent and imitative, of all the children.

By such means Bahrdt succeeded in maintaining himself until, on the death of Frederick the Great, the religious reaction set in at the Berlin court.

By mounting an offensive with considerable ( but not decisive ) force, the commander hopes to elicit a strong reaction by the enemy that reveals its own strength, deployment, and other tactical data.

By contrast, Generative Art, which may be interactive, but not responsive per se, tends to be a monologue-the artwork may change or evolve in the presence of the viewer, but the viewer may not be invited to engage in the reaction but merely enjoy it.

By definition, fissile materials can sustain a chain reaction with neutrons of any energy.

Middle: By increasing the mass of the sphere to a critical mass, the reaction can become self-sustaining.

By late 1920, Stresemann gradually moved to cooperation with the parties of the left and centre — possibly in reaction to political murders like that of Walther Rathenau.

By the early spring of 1975 North Vietnam realized the time was right to achieve its goal of re-uniting Vietnam under communist rule, launched a series of small ground attacks to test U. S. reaction.

Neuronal activity related to the act of seeing lasts for more than 100 ms. A fast reaction, such as swerving to avoid a car crash, takes around 200 ms. By about half-a-second, awareness and reflection of the incident sets in.

By contrast the S < sub > N </ sub > 1 reaction involves two steps.

By combining the rate law with a mass balance for the system in which the reaction occurs, an expression for the rate of change in concentration can be derived.