Tonalamatl

“ The 4th sign on all the four pages seems to refer to a period like the one hitherto discussed. On page 26 the sign resembles that for the 13th Uinal (Mac) and hence appears to refer to the Tonalamatl, as in the first column on page 24. Above it is the sign for the south. The corresponding hieroglyphs of the other pages are obliterated, but strange to say the vestiges suggest that they too had below them the sign for the south. Now the south and the Bacab of the south preside over the fourth quarter of the year from which ensues the transition to the new year in question here. ”

“ In the racemic form, if one should be deposited from the mixed solutions of the two optical antipodes as a molecular compound of the latter, we have an occurrence akin to polymerism, that is, the combination into a single whole entity of a number of molecules, essentially two in the case of racemism. Just as polymeric varieties of organic substances are always found to have quite different crystalline forms, so an optically inactive racemic form of a substance is generally quite different crystallographically to the dextro and lævo varieties. ”

“ The only exception is contra-Uranium, the opposite number of the last element in the normal periodic table, which will not explode as long as it is isolated from the heavy elements near its opposite number on the table. Thus in a fluorine atmosphere, with a bromide soil and—"
"Look, Doc," Donelli said wearily. "I learned all that in School years ago. Next you'll be telling me that it's thousands of times more powerful than ordinary atomic fuels because of its explosive contra-terrene nature. ”

“ All but the tantalum lamp operates equally well on alternating or direct current. The tantalum cannot be recommended for alternating-current circuits. No incandescent lamps will operate well on frequencies lower than forty cycles. The natural distribution of light is mostly [270] in the horizontal plane and for good illumination reflectors should be provided.
The color value is in the following order: Tungsten, tantalum, graphitized filament, carbon filament. None are equal for color-matching purposes to the intensified arc or the Moore tube. ”

“ A 60°-prism, for instance, cut from a cube of rock-salt, for the purpose of obtaining the refractive index of the mineral by the ordinary method of producing a spectrum and arranging it for minimum deviation of the refracted rays, affords but a single spectrum, or a single sharp image of the spectrometer slit when the latter is fed by pure monochromatic light instead of ordinary white light. This is true however the prism may have been cut, as regards its orientation with respect to the natural crystal faces. ”

“ The tonic is the final in which everything ultimately resolves: the dominant stands on one side of it as a chord based on the note harmonically most closely related to the tonic, and the subdominant stands on the other side as the converse and opposite of the dominant, weaker than the dominant because not directly derived from the tonic. The other triads obtainable from the notes of the scale are all minor, and of less importance ”

“ This is, indeed, the very simple principle of the reflecting goniometer, invented by Wollaston in the year 1809, and which in its modern improved form is the all-important principal instrument of 64the crystallographer’s laboratory. The work with it consists largely in the measurement of the angles between the faces in all the principal zones developed on the crystal. The very fact, however, that crystal faces occur so absolutely accurately in zones immeasurably lightens the labours of the crystallographer, and is one of prime importance. ”

“ M. Berthelot remarked that the exhibition of the lines of hydrocyanic acid would furnish an argument for the hypothesis of the electric origin of the light, as the spectra of acetylene and hydrocyanic acid are characteristic of the electrical illumination of a gas containing carbon, hydrogen, and nitrogen, whether free or in combination. M. Thollon described the nucleus as giving a brilliant continuous spectrum, and the nebulosity around the nucleus as showing three bands, one quite distinct, the others dim, separated upon a ground forming a continuous spectrum. ”

“ When monochromatic light is employed, yellow sodium light for instance, it is found that if the plate be not too thick, say a millimetre in thickness, the dark field is restored when the analyser is rotated in a particular direction, either to the right or to the left, for a specific angle, which is 21° 42′ for a plate of quartz one millimetre thick. Moreover, if the plate has been cut from a crystal showing the distinctive trapezohedral-class faces s and x on the right (Fig. 69) the analysing Nicol requires to be rotated to the right ”

“ EFFECT OF THE SYMMETRY OF CRYSTALS ON THE PASSAGE OF LIGHT THROUGH THEM. QUARTZ, CALCITE, AND GYPSUM AS EXAMPLES. The action of transparent crystals on the rays of light which they transmit is a subject not only of the deepest interest, but also of the utmost importance. For it is immediately possible to detect a cubic crystal, and to discriminate between two groups, optically uniaxial and biaxial respectively, of the other six systems of symmetry, three systems going to each group, by this means alone. For a cubic crystal is singly refractive in all directions. ”

“ Again, the antithesis of tonic and dominant is accompanied in Diabelli’s theme by a part of the melodic figure being repeated a step higher at the change of harmony; and this naturally produces such devices as the answering of the tonic by the super tonic in variation 8, and, still more surprisingly, by the flat super tonic in variation 30. In so enormous and resourceful a work, occupying fifty minutes in performance, it is natural that some variations should drift rather farther from the anatomy of the theme than can be explained by any strict principle ”

“ II. A real answer is possible for any subject which begins and ends in the key of the tonic without modulating to the dominant; but if the subject begins with a leap between tonic and dominant or commences on the dominant, a tonal answer is mostly preferable.
III. If the subject modulate between the keys of the tonic and dominant, the answer should make the converse modulations between dominant and tonic.
IV. A modulation should always be made as early as possible. ”

“ The diagram is thus designed to show the variation of the inclination of these latter dome faces to the two rectangular axial plane faces b and c. The outer crystal outline represents a similar section of a crystal of the corresponding cæsium salt, and the middle outline that of a crystal of the rubidium salt.
The progressive alteration of the angle of the q-face will be obvious, the direction of the change being correct, but the amount of change, as already stated, being much exaggerated; in reality it never reaches a degree between the two extreme (potassium and cæsium) salts. ”

“ Lehmann’s theory is that any one definitely stereometrically constituted chemical molecule can only display one particular homogeneous structure and form of crystal, and that when at a particular temperature the system or class of symmetry is altered, this occurs because the stereometric arrangement of the atoms within the molecule is altered, that is, a new form of molecule is produced, which naturally gives rise to a new form of crystal. ”

“ This renders the para compounds the most extended in a straight line of all the benzene derivatives. Now Vorländer finds that a particularly favourable condition for the production of liquid crystals is a linear structure of the molecule. As the para substitution products of benzene derivatives possess this elongated structure, many of them exhibit the development of liquid crystals. The more linearly extended the structure becomes, that is, the longer the straight chain of atoms is, the more favourable become the conditions. ”

“ EXPERIMENTS IN CONVERGENT POLARISED LIGHT WITH QUARTZ, AS AN EXAMPLE OF MIRROR-IMAGE SYMMETRY AND ITS ACCOMPANYING OPTICAL ACTIVITY. It has already been shown that crystals are optically divisible into two classes characterised respectively by single and by double refraction. Singly refractive crystals belong exclusively to the system of highest symmetry, the cubic. They afford obviously only one index of refraction, which is generally symbolised by the Greek letter μ, the value of this constant being the same for all directions throughout the crystal. ”

“ For the so-called liquid crystals are extreme cases of softness, and yet in these cases the molecules must still be arranged in accordance with the internal structure of a crystal, either parallel or enantiomorphously definitely orientated with respect to each other, for otherwise it is not possible to account for the optical properties resembling the orientated ones of a crystal. Yet the condition being that of a liquid, the molecules must be able readily to pass and roll over each other, and hence cannot be at the close quarters where mere “fitting-in” comes into play. ”

“ These substances, and also carbon, sulphur, selenium and tellurium, render the metal very brittle. Tantalum is not affected by alkaline solutions, but is disintegrated when fused with potash. Hydrofluoric acid is the only acid which attacks it. It alloys with iron, molybdenum and tungsten, but not with silver or mercury.
In its chemical relationships tantalum is associated with vanadium, columbium and didymium in a sub-group of the periodic classification. In general it is pentavalent, but divalent compounds are known. ”

“ When pressed between the cover-glass and the micro-slip on which the crystallisation is proceeding, extinction of the light occurs throughout the whole mass when polarised light is being employed and the Nicols are crossed. For throughout the entire substance the particles—whether they are the molecules themselves as Lehmann asserts or aggregations of them in the form of ultramicroscopic crystals—arrange themselves with their optic axes (the crystals being uniaxial) perpendicular to the cover-glass and micro-slip, as in the case of ammonium oleate. ”

“ The figure at f represents what is observed in white light, as far as is possible by a drawing in black and white. It consists of a series of concave coloured curves, falling in between the arms of the cross, and looping round the axes, a figure very much like that afforded by brookite and triple tartrate of ammonium, potassium, and sodium, the substances already mentioned in Chapter VII. as being similarly very sensitive to change of wave-length. The figure in red monochromatic lithium light is shown at a in Fig. ”

“ With these prefatory theoretical remarks, which are necessary in order that the experiments now to 187be described should be understood, we may proceed to consider a graduated series of experimental demonstrations which it is hoped will render clear some of the more important features of crystal structure which have been dealt with in previous chapters. Our principal agent will be polarised light, that is, light which has been reduced to vibration in a single plane by means of the well-known Nicol’s prism. ”

“ As a good instance of the use of the principle of isomorphism, we may recall that when Marignac, in 1864, found himself in great difficulty about the atomic weights of the little known metals tantalum and niobium which he was investigating, he discovered that their compounds are isomorphous; the pentoxides of the two metals occur together in isomorphous mixture in several minerals, and the double fluorides with potassium fluoride, K2TaF7 and K2NbF7 are readily obtained in crystals of the same form. ”

“ It becomes obvious 124that the atoms—in their stereometric positions in the molecule, being thus fixed in the solid crystal when the molecules set themselves rigidly in the regular organisation of the space-lattice—form the points of the regular point-system of the crystal structure, which determines to which of the thirty-two classes of symmetry the crystal shall belong. Any movement of the atoms in the crystal, other than that which accompanies change of temperature, and possibly change of pressure, is thus improbable ”

“ The relation between tonic, dominant and subdominant must necessarily appear at the final close, and in a lesser degree at subordinate points of repose; but, where no harmonies were dwelt on as stable and independent entities except the major and minor triads and their first inversions, a scheme in which these were confined to the illustration of their most elementary relationship would be intolerably monotonous. It is therefore neither surprising nor a sign of archaism that the tonality of modal music is from the modern point of view often very indefinite. ”

“ We have never found any other use for radium—it is so active that it combines with water just as sodium does; it is very soft—a useless metal, and dangerous to handle. Our chemists have never been able to understand it—it is always in some kind of reaction no matter what they do, and still it gives off that very light gas, helium, and a heavy gas, niton, and an unaccountable amount of heat.”
“Your world is vastly different from ours,” Arcot commented. He told Tonlos of the different metals of Earth, the non-metals, and their occurrence. ”

“ Such a perfectly normal plate remains quite obscure in the dark field in parallel light, producing neither colour nor interference figure, even on rotation of the object stage with the crystal, in its own plane. For the light traverses the crystal along the optic axis, the axis of single refraction, and the vibrations occur with equal velocity in all directions perpendicular to it. Hence there is no division into two rays, one retarded behind the other on account of less velocity of vibration, and therefore no interference colour. ”