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.