By comparing reaction cells sealed from the same manifold temperature dependency corresponding to activation energies ranging from 11 to 18 Af was observed while dependence on the first power of the light intensity seemed to be indicated in most cases.

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 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 1866, he had developed three classes of stellar spectra:

By scattering photons off electrons in the crystal, one can sample the energy spectra of the electrons.

By examining the spectra of nebulae, astronomers deduce their chemical content.

By contrast, high-excitation objects ( narrow-line radio galaxies ) have emission-line spectra similar to those of Seyfert 2s.

By analyzing the spectra of electrical signals, dominant frequency, power, distortion, harmonics, bandwidth, and other spectral components of a signal can be observed that are not easily detectable in time domain waveforms.

By the time Deep Space 1 reached Braille, its ultraviolet spectrometer had failed, but it did return two CCD images of medium resolution and three infrared spectra during the encounter.

By using this method, spatially resolved photoemission spectra can be acquired with spatial resolutions on the 100 nm scale and with sub-eV resolution.

By 1905 he had acquired hundreds of spectra by tedious point-by-point measurements with a prism instrument of his own construction.

By studying the spectra of various stars, one can find their temperature and from that, using Saha's equation, determine the ionisation state of the various elements making up the star. Besides continuing on his works in astrophysics, Saha was also keen to pursue experiments to verify his theory of thermal ionisation, which however called for advanced laboratories equipped with high-temperature facilities.

By DFT and TDDFT methods one can obtain IR, Raman and UV spectra.

By a theorem of Devinatz – Hopkins – Smith, every thick subcategory of the category of finite p-local spectra is the subcategory of type-n spectra for some n.

By fitting the observed spectrum to model spectra, it is estimated that Gliese 876 has a slightly lower abundance of heavy elements compared to the Sun ( around 75 % the solar abundance of iron ).

By comparing the attenuation of the transmitted light with the incident, an Absorption spectroscopy | absorption spectra can be obtained.

By experiment, he discovered that this was because the excitation and emission lines of the spectra barely overlapped, and that by mixing suitable powders he could increase the afterglow.

By distinguishing superlunary ( celestial ) and sublunary ( terrestrial ) existence, and reinforcing this with the four-element physics of Empedocles, Aristotle came to speak of the stars as perfect bodies, which moved in only a perfect way, viz. in a perfect circle.

By studying these images, they can detect solar system objects by their movements relative to the background stars, which remain fixed.

By the third millennium BCE, widespread civilizations had developed sophisticated awareness of celestial cycles, and are believed to have consciously oriented their temples to create alignment with the heliacal risings of the stars.

By absorbing other stars and merging with other black holes, supermassive black holes of millions of solar masses may form.

By the time the Marxes made their first movie, they were major stars with sharply honed skills, and when Groucho was relaunched to stardom on You Bet Your Life, he had already been performing successfully for half a century.

By 2006, astronomers had resolved dust disks believed to be Kuiper belt-like structures around nine stars other than the Sun.

By 1861, it was modified to show 34 stars ( the number of states then in the Union ).

By studying their abundances in open cluster stars, variables such as age and chemical composition are fixed.

By convention, astronomers grouped stars into constellations and used them to track the motions of the planets and the inferred position of the Sun.

By the following century, the idea of the stars being the same as the Sun was reaching a consensus among astronomers.

By 1936, contracts of musical and silent stars were not renewed and new talent, tough-talking, working-class types, were hired who more suitably fit in with these sort of pictures.

By the 1940s, Tracy was one of the studio's top stars.

By contrast, nuclear reactions within stars destroy deuterium and isotopes of other light elements, beryllium, lithium, and boron, which were contained in the initial compositions of the stars.

By 1958, he was one of the hottest new stars in Hollywood.

By the modern definition, the term binary star is generally restricted to pairs of stars which revolve around a common centre of mass.

By 1803, he had observed changes in the relative positions in a number of double stars over the course of 25 years, and concluded that they must be binary systems ; the first orbit of a binary star, however, was not computed until 1827, when Félix Savary computed the orbit of Xi Ursae Majoris.

By 1786 ten variable stars were known.

By the late 1970s she was one of Australia's top singing stars, winning several Queen of Pop awards and hosting her own national TV variety series.

By comparing astronomical observations with laboratory measurements, astrochemists can infer the elemental abundances, chemical composition, and temperatures of stars and interstellar clouds.

By late 1967 the Airplane were national and international stars and had become one of the hottest groups in America.

By January 1996 the flag was replaced with a new one which was not based on the British flag, but the eight stars were retained.