A day or two afterward I was stringing beads of different sizes in symmetrical groups--two large beads, three small ones, and so on.
The partition method of treating symmetrical algebra is one which has been singularly successful in indicating new paths of advance in the theory of invariants; the important theorem of expressibility is, directly we exclude unity from the partitions, a theorem concerning the expressibility of covariants, and involves the theory of the reducible forms and of the syzygies.
Probably a sphere would prove most useful for a pressure anemometer, since owing to its symmetrical shape it would not require a weathercock.
It is rare to find in the polyp a regular, symmetrical disposition of the tentacles as in the medusa.
In all other Siphonophores, the ancestral form was a Siphonula, a bilaterally symmetrical Anthomedusa After Haeckel, from Lankester's Treatise on Zoology.
It is impossible here to give even a list of the names of the many observers who in recent times have made empirical study of the effects of growth-forces and of the symmetrical limitations and definitions of growth.
Before full adjustment has been attained the river bed may be broken in places by waterfalls or interrupted by lakes; after adjustment the bed assumes a permanent outline, the slope diminishing more and more gradually, without a break in its symmetrical descent.
Of the tri-substitution derivatives, 1.2.3.-compounds are known as " adjacent " or " vicinal " (v), the 1.2.4 as " asymmetrical " (as), the 1.3.5 as " symmetrical " (s), of the tetrasubstitution derivatives, 184.108.40.206-compounds are known as " adjacent," 220.127.116.11 as " asymmetrical," and 18.104.22.168 as " symmetrical."
The proof is divided into two parts: (1) that four hydrogen atoms are equal, and (2) that two pairs of hydrogen atoms are symmetrical with reference to a specified hydrogen atom.
Therefore there must be another pair of hydrogen atoms, other than 2 and 6, which are symmetrical with respect to 1.
Formula (4) is symmetrical and based on Kekule's formula: it is in full accord with the syntheses and decompositions of the naphthalene nucleus and the number of isomers found.
Pyridine gives origin to: pyridazine or ortho-diazine, pyrimidine or metadiazine, pyrazine or para-diazine, osotriazine, unsymmetrical triazine, symmetrical triazine, osotetrazone and tetrazine.
Of the tri-derivatives the symmetrical compounds boil at the lowest temperature, the asymmetric next, and the vicinal at the highest.
Soc.), regards the property as occasioned by internal vibrations within the molecule conditioned by a symmetrical double tautomerism, light of one wave-length being absorbed by one form, and emitted with a different wave-length by the other.
Although the theories of Meyer and Hewitt do not explain (in their present form) the behaviour of anthranilic acid, yet Hewitt has shown that his theory goes far to explain the fluorescence of substances in which a double symmetrical tautomerism is possible.
It is remarkable that a great many polymorphous substances assume more symmetrical forms at higher temperatures, and a possible explanation of the increase in density of such compounds as silver iodide, &c., may be sought for in the theory that the formation of a more symmetrical configuration would involve a drawing together of the molecules, and consequently an increase in density.
The insufficiency of this argument, however, is shown by the data for arsenious and antimonious oxides, and also for the polymorphs of calcium carbonate, the more symmetrical polymorphs having a lower density.
Owen for that division of ungulate mammals in which the toe corresponding to the middle (third) digit of the human hand and foot is symmetrical in itself, and larger than those on either side (when such are present).
In the tapirs and many extinct forms the fifth toe also remains on the fore-limb, but its presence does not interfere with the symmetrical arrangement of the remainder of the foot on each side of the median line of the third or middle digit.
The valves are, consequently, essentially symmetrical, which is not the case with the Lamellibranchiata, - so much so, that certain Brachiopod shells were named Lampades, or lamp shells, by some early naturalists; but while such may bear a kind of resemblance to an antique Etruscan lamp, by far the larger number in no way resemble one.
" The symmetric function (m ï¿½8 m' 2s m ï¿½3s ...) whose is 2s 3s partition is a specification of a separation of the function symbolized by (li'l2 2 l3 3 ...) is expressible as a linear function of symmetric functions symbolized by separations of (li 1 12 2 13 3 ...) and a symmetrical table may be thus formed."
(iv.) We can write n (;) in the more symmetrical form n(r)- (n - r) !
From time to time efforts were made by those who believed that the Creator must have followed a symmetrical system in his production of animals to force one or other artificial, neatly balanced scheme of classification upon the zoological world.
When, as in the application to rectangular or circular apertures, the form is symmetrical with respect to the axes both of x and y, S = o, and C reduces to C = ff cos px cos gy dx dy,.
In the case of the circular aperture the distribution of light is of course symmetrical with respect to the focal point p=o, q=o; and C is a function of p and q only through 11 (p 2 -}-q 2).
In these expressions we are to replace p by ks/f, or rather, since the diffraction pattern is symmetrical, by kr/f, where r is the distance of any point in the focal plane from the centre of the system.
If we suppose that everything is symmetrical on the two sides of the primary plane y=o, the coefficients B, (3, S vanish.
Thus, to refer again to the acoustical analogue in which plane waves are incident upon a perforated rigid screen, the circumstances of the case are best represented by the first method of resolution, leading to symmetrical secondary waves, in which the normal motion is supposed to be zero over the unperforated parts.
Fins without spines; caudal fin, if present, without expanded hypural, perfectly symmetrical, and supported by the neural and haemal spines of the posterior vertebrae, and by basal bones similar to those supporting the dorsal and anal rays.
Now, if CD is pressed by its weight or by a spring on the surface AB, the effect of wear will be to produce a symmetrical grinding away of both surfaces, which may be represented thus, fig.
The symmetrical diaminophenazine is the parent substance of the important dyestuff toluylene red or dimethyldiaminotoluphenazine.
68, k), absent in Chondrophorida and Cystophorida; they are contractile and resemble, both in appearance, structure and function, the umbrella of a medusa, with radial canals, ring-canal and velum; but they are without manubrium, tentacles or sense-organs, and are always bilaterally symmetrical, a peculiarity of form related with the fact that they are attached on one side to the stem.
Symmetrical block mountains.
It is absent in the most primitive and symmetrical forms, such as Haliotis and Pleurotomaria.
Shell conical, symmetrical, without slit or perforation.
Nor is it worth while to attempt a logical or symmetrical arrangement of the material.
Although Kekule founded his famous benzene formula in 1865 on the assumptions that the six hydrogen atoms in benzene are equivalent and that the molecule is symmetrical, i.e.
Hence the positions occupied by the nitro groups in the two different nitrobrombenzoic acids must be symmetrical with respect to the carboxyl group. In 1879, Hubner (Ann., 1 95, p. 4) proved the equivalence of the second pair, viz.
Ladenburg (Ann., 1875, 179, p. 163) to be symmetrical trimethyl benzene; terephthalic acid, the remaining isomer, must therefore be the para-compound.
Referring to the esters C9H1802 previously mentioned, it is seen that the highest boilingpoints belong to methyl octoate and octyl formate, the least symmetrical, while the minimum belongs to amyl butyrate, the most symmetrical.
The series H 2 S = - 61°, CH 3 SH = 21 °, (C 11 3) 2 S=41 ° is an example; in the first case, the molecular weight is increased and the symmetry diminished, the increase of boiling-point being 82°; in the second case the molecular weight is again increased but the molecule assumes a more symmetrical configuration, hence the comparatively slight increase of 20°.
Although the apparent crust-waves are neither equal in size nor symmetrical in form, this complementary relationship between them is always discernible.
The article REFLECTION explains the symmetrical arrangement of images formed by two mirrors inclined at an angle which is a sub-multiple of four right angles.
Shell not coiled, symmetrical; pallial cavity ventral.
If the structure of the molecule is so perfectly symmetrical that, in the absence of any external field, the resultant magnetic moment of the circulating electrons is zero, then the application of a field, by accelerating the right-handed (negative) revolutions, and retarding those which are left-handed, will induce in the substance a resultant magnetization opposite in direction to the field itself; a body composed of such symmetrical molecules is therefore diamagnetic. If however the structure of the molecule is such that the electrons revolving around its atoms do not exactly cancel one another's effects, the molecule constitutes a little magnet, which under the influence of an external field will tend to set itself with its axis parallel to the field.
The following table gives the actual values: - In both cases the image of a mathematical point is thus a symmetrical ring system.
Bamberger opposed Claus' formula on the following grounds: - The molecule of naphthalene is symmetrical, since 2.7 dioxynaphthalene is readily esterified by methyl iodide and sulphuric acid to a dimethyl ether; and no more than two mono-substitution derivatives are known.