The configurations of the pentaand tetra-aldoses have been determined by similar arguments; and those of the ketoses can be deduced from the aldoses.
The determination of the series of configurations developing out of given initial conditions is not, however, the problem of the kinetic theory: the object of this theory is to explain the general properties of all gases in terms only of their molecular structure.
The problem of determining the possible configurations of equilibrium of a system of particles subject to extraneous forces which are known functions of the positions of the particles, and to internal forces which are known functions of the distances of the pairs of particles between which they act, is in general determinate For if n be the number of particles, the 3n conditions of equilibrium (three for each particle) are equal in number to the 351 Cartesian (or other) co-ordinates of the particles, which are to be found.
If we imagine a rigid body to be acted on at given points by forces of given magnitudes in directions (not all parallel) which are fixed in space, then as the body is turned about the resultant wrench will assume different configurations in the body, and will in certain positions reduce to a single force.
F,, represent two configurations of the series of particles, then Z(m.
Of ii, if we imagine the two configurations of the system then referred to to be those corresponding to the instants 1, l+t Thus ~(m.~) =~(m).~.
Thus the form of heat or the form of light is the same thing as the law of heat or the law of light."' " Matter rather than forms should be the object of our attention, its configurations and changes of configuration, and simple action, and law of action or motion; for forms are figments of the human mind, unless you will call those laws of action forms."
It handles the configurations and the appetites or motions of matter.
The configurations, or inner structure of bodies, include dense, rare, heavy, light, hot, cold, &c., - in fact, what are elsewhere called simple natures.
11 " To inquire into the form of a lion, of an oak, or gold, nay, even of water or air, is a vain pursuit; but to inquire the form of dense, rare, hot, cold, &c., as well configurations as motions, which in treating of physic I have in 6 Valerius Terminus, iii.
If we now suppose the crevasse produced by direct separation of its walls, the work necessary must be the same as before, the initial and final configurations being identical; and we recognize that the tension may be measured by half the work that must be done per unit of area against the mutual attraction in order to separate the two portions which lie upon opposite sides of an ideal plane to a distance from one another which is outside the range of the forces.
But while the atoms thus differ in quantity, their differences of quality are only apparent, due to the impressions caused on our senses by different configurations and combinations of atoms. A thing is only hot or cold, sweet or bitter, hard or soft by convention (v6,4; the only things that exist in reality (TEfj) are the atoms and the void.
Let us now consider the effect of this relation upon the configurations and relations of the two planets.
Neison (now Neville), The Moon and the Conditions and Configurations of its Surface (London, 1876); M.
- On the theory that crystal form and structure are the result of the equilibrium between the atoms and molecules composing the crystals, it is probable, a priori, that the same substance may possess different equilibrium configurations of sufficient stability, under favourable conditions, to form different crystal structures.
Under the general heading "Geometry" occur the subheadings "Foundations," with the topics principles of geometry, non-Euclidean geometries, hyperspace, methods of analytical geometry; "Elementary Geometry," with the topics planimetry, stereometry, trigonometry, descriptive geometry; "Geometry of Conics and Quadrics," with the implied topics; "Algebraic Curves and Surfaces of Degree higher than the Second," with the implied topics; "Transformations and General Methods for Algebraic Configurations," with the topics collineation, duality, transformations, correspondence, groups of points on algebraic curves and surfaces, genus of curves and surfaces, enumerative geometry, connexes, complexes, congruences, higher elements in space, algebraic configurations in hyperspace; "Infinitesimal Geometry: applications of Differential and Integral Calculus to Geometry," with the topics kinematic geometry, curvature, rectification and quadrature, special transcendental curves and surfaces; "Differential Geometry: applications of Differential Equations to Geometry," with the topics curves on surfaces, minimal surfaces, surfaces determined by differential properties, conformal and other representation of surfaces on others, deformation of surfaces, orthogonal and isothermic surfaces.
The motion of the outwardscreeping inland ice will naturally be more independent of the configurations of the underlying land in the interior, where its thickness is so enormous, than near the margin where it is thinner.
In this way, any of the possible configurations may be easily produced.
The taxonomic importance of the configurations of the palate was first pointed out by J.
He demonstrated the rotation of the satellites of Jupiter round the planet, and gave rough predictions of their configurations, proved the rotation of the sun on its axis, established the general truth of the Copernican system as compared with that of Ptolemy, and fairly routed the fanciful dogmas of the philosophers.
A number of molecules moving in obedience to dynamical laws will pass through a series of configurations which can be theoretically determined as soon as the structure of each molecule and the initial position and velocity of every part of it are known.
We are therefore called upon, not to trace the series of configurations of any single gas, starting from definite initial conditions, but to search for features and properties common to all series of configurations, independently of the particular initial conditions from which the gas may have started.
Employing the notation in which the molecule is represented vertically with the aldehyde group at the bottom, and calling a carbon atom+or - according as the hydrogen atom is to the left or right, the possible configurations are shown in the diagram.