## Indices Sentence Examples

- This suggests that we should write; la as a l l3; and we find that the use of fractional
**indices**in this way satisfies the laws of integral**indices**. - 54) also measured the refractive
**indices**of various gases, using a prism containing the gas to be experimented on, and he found that the deviation by the prism agreed very closely with the theoretical values of sound in the gas and in air. - The refractive
**indices**for different wave lengths must be known for each kind of glass made use of. - This combination of circumstances has given the Graptoloidea a paramount stratigraphical importance as palaeontological
**indices**of the detailed sequence and correlation of the Lower Palaeozoic rocks in general. - The explanation of this change in the direction of
**indices**of steadiness cannot be proved to consist in any peculiarity in the supplies of recent years. - Do not involve x, and the
**indices**of the powers of x are all positive integers, is called a rational integral function of x of degree n. - The files and
**indices**of the English Historical Review, Historische Zeitschrift, Revue historique, or American Historical Review will alone reveal the strength and character of historical research in the later 19th century. - Among De Morgan's miscellaneous writings may be mentioned his Explanation of the Gnomonic Projection of the Sphere, 1836, including a description of the maps of the stars, published by the Useful Know ledge Society; his Treatise on the Globes, Celestial and Terrestrial,1845, and his remarkable [[Book]] of Almanacks (2nd edition, 1871), which contains a series of thirty-five almanacs, so arranged with
**indices**of reference, that the almanac for any year, whether in old style or new, from any epoch, ancient or modern, up to A. - The only completed lexicon (apart from the
**Indices**of Naudet, 1832, and Weise, 1838) is that of Pareus (2nd ed., 1634). - (iv.) When the terms of a multinoniial contain various powers of x, and we are specially concerned with x, the terms are usually arranged in descending (or ascending) order of the
**indices**; terms which contain the same power being grouped so as to give a single coefficient. - Then a+a = as = a; hence numerical coefficients and
**indices**are not required. - He possessed clear ideas of
**indices**and the generation of powers, of the negative roots of equations and their geometrical interpretation, and was the first to use the term imaginary roots. - Hence, in order that a double line may be resolved whose components have
**indices**and A ct--S i ., it is necessary that t should exceed the value given by the following equation: - t= X/S / 8. - Moreover, his association with glass manufacture led him to study the refractive
**indices**of different kinds of glass; he further undertook abstruse researches on electrostatic capacity, the phenomena of the residual charge, and other problems arising out of Clerk Maxwell's electro-magnetic theory. - This quantity may readily be expressed in terms of the refractive
**indices**for the three colours, for if A is the angle of the prism (supposed small) bc=(/1c - I)A, bD =(/ AD - OA, F - I)A, where µc, A n, µ F are the respective**indices**of refraction. - It is more useful than (1), as the refractive
**indices**may be measured with a prism of any convenient angle. - 68, hanc ei gloriam concessere Antigonus et Xenocrates, qui de pictura scripsere), while Antigonus is named in the
**Indices**of xxxiii.-xxxiv. - His
**indices**auctorum are, in some cases, the authorities which he has actually consulted (though in this respect they are not exhaustive); in other cases, they represent the principal writers on the subject, whose names are borrowed second-hand for his immediate authorities. - Bain's Calendars (Edinburgh, 1881-1888), are useful
**indices**, but not infrequently need to be checked by the manuscripts. - The only refractive
**indices**which had been measured were the optical refractive**indices**of a number of transparent substances. - A detailed analysis of these scriptures has been published by the celebrated Hungarian scholar Csoma de Korbs, whose authoritative work has been republished in French with complete
**indices**and very useful notes by M. - ., the series of
**indices**being the standard series; and we have also seen (§ 44) that multiplication of any two of these numbers corresponds to addition of their**indices**. - Hence we may insert in the power-series numbers with fractional
**indices**, provided that the multiplication of these numbers follows the same law. - 2, as base, and take as
**indices**the successive decimal numbers to any particular number of places of decimals, we get a series of antilogarithms of the**indices**to this base. - Fleischer (2 vols., Leipzig, 1846-1848;
**indices**ed. - Since the two circular streams have different speeds, Fresnel argued that it would be possible to separate them by oblique refraction, and though the divergence is small, since the difference of their refractive
**indices**in the case of quartz is only about o 00007, he succeeded by a suitable arrangement of alternately rightand left-handed prisms of quartz in resolving a plane-polarized stream into two distinct circularly polarized streams. A similar arrangement was used by Ernst v. - Lord Rayleigh has pointed out that all theories are defective in that they disregard the fact that one at least of the media is dispersive, and that it is probable that finite reflection would result at the interface of media of different dispersive powers, even in the case of waves for which the refractive
**indices**are absolutely the same. - 504), who has found the remarkable result that copper, gold, magnesium and silver have refractive
**indices**less than unity, and this has been completely confirmed by observations with metallic prisms of small refracting angle. - Theoretically the best construction for prisms of this class is the following: a rectangular block of Iceland spar, of length about four times the width and having its end and two of its side faces parallel to the optic axis, is cut in half by a plane parallel to the optic axis and making an angle of about 14° with the sides; the two halves are then reunited with a cement whose refractive index is between the ordinary and extraordinary
**indices**of the spar and as nearly as possible equal to the latter. - It is clear that direct transmission through the plate at a point where the thicknesses of the prisms are d 1 and d 2 will introduce a relative retardation of (µ,; -, u o) (d l - d2) between streams polarized in planes parallel and perpendicular to the edges of the prisms,, u o, and being the ordinary and the extraordinary refractive
**indices**; and it is hence possible by an adjustment of the thickness to reduce elliptically polarized to plane polarization at an assigned point marked off by two parallel lines. - The immersion liquids in common use are water, glycerine, cedar-wood oil, monobromnaphthalene, &c. Immersion systems in which the embedding liquid, coverslip, immersion-liquid and front lens have equal refractive
**indices**are called " homogeneous immersion systems." - This concept is extended to algebra: since a line, surface and solid are represented by linear, quadratic and cubic equations, and are of one, two and three dimensions; a biquadratic equation has its highest terms of four dimensions, and, in general, an equation in any number of variables which has the greatest sum of the
**indices**of any term equal to n is said to have n dimensions. - It appears that Newton made the mistake of supposing that all prisms would give a spectrum of exactly the same length; the objections of his opponents led him to measure carefully the lengths of spectra formed by prisms of different angles and of different refractive
**indices**; and it seems strange that he was not led thereby to the discovery of the different dispersive powers of different refractive substances. - The radii, thicknesses, refractive
**indices**and distances between the lenses, was solved by L. - (4) After eliminating the aberration on the axis, coma and astigmatism, the relation for the flatness of the field in the third order is expressed by the " Petzval equation," I 1 = o, where is the radius of a refracting surface, n and n' the refractive
**indices**of the neighbouring media, and / the sign of summation for all refracting surfaces. - Experimental methods were devised for the further exact measurements of the electromagnetic velocity and numerous determinations of the dielectric constants of various solids, liquids and gases, and comparisons of these with the corresponding optical refractive
**indices**were conducted. - Irmisch (1789-1805), with elaborate
**indices**, but the notes are very diffuse; critical editions by I. - The figures given are the partial dispersions for ordinary crown and ordinary extra dense flint glasses, styled in Messrs Schott's catalogue of optical glasses as o 60 and 0.102 respectively, having refractive
**indices**of 1 5179 and 1.6489 for the D ray respectively, and (µ D -I)/(l F -µc) =60 2 and 33.8 respectively to indicate their dispersive powers (inverted), = v. - Negative
**Indices**and Logarithms. - (i.) Applying the general principles of ï¿½ï¿½ 47-49 to**indices**, we find that we can interpret Xm as being such that X m .Xm =X 0 =I; i.e. - A doubly linked pair of atoms is denoted by the sign A with the index corresponding to the side; if there are two pairs of double links, then
**indices**corresponding to both sides are employed.