I strolled a discrete distance from her side as we entered the gardens.
Kinetics of a system of discrete particles.
When we pass from the consideration of discrete particles to that of continuous distributions of matter, we require some physical postulate over and above what is contained in the Laws of Motion, in their original formulation.
It would seem that "the general theory of discrete and continuous quantity" is the exact description of the topics of these sciences.
The doctrine that matter can be divided into, or regarded as composed of, discrete particles (termed " atoms " by early writers, and " molecules " by modern ones) has at all times played an important part in metaphysics and natural science.
This manner of conceiving is absolutely general and distinct, and accordingly affords the possibility of an all-comprehensive and perfect science, the science of discrete quantity.
In mathematics and music, the adjective has been used as synonymous with "continuous" as opposed to "discrete," i.e.
If we have a continuous distribution of matter, instead of a system of discrete particles, the summations in (6) are to be replaced by integrations.
Kinetics of a System of Discrete Particles.The momenta of the several particles constitute a system of localized vectors which, for purposes of resolving and taking moments, may be reduced like a system of forces in statics (~ 8).
The identical relation between the ideas of space and time and the impressions corresponding to them apparently leads him to regard judgments of continuous and discrete quantity as standing on the same footing, while the ideal character of the data gives a certain colour to his inexact statements regarding the extent and truth of the judgments founded on them.
In many questions relating to systems of discrete particles the internal force R55 (which we will reckon positive when attractive) between any two particles m,, m5 is a function only of the distance r55 between them.
This antithesis is no doubt influenced by the idea that the two words derive from a common origin, whereas "discrete" is derived from the Latin discernere.
It has now become apparent that the traditional field of mathematics in the province of discrete and continuous number can only be separated from the general abstract theory of classes and relations by a wavering and indeterminate line.
For most purposes the solid media are to be preferred, since bacterial growth appears as a discrete mass and accidental contamination can be readily recognized.
Each neuron or nerve cell is a morphologically distinct and discrete unit connected functionally but not structurally with its neighbours, and leading its own life independently of the destiny of its neighbours.
It has been usual to define mathematics as "the science of discrete and continuous magnitude."
If material systems are constituted of discrete atoms, separated from each other by many times the diameter of any of them, this simple plan of exhibiting their interactions in terms of direct forces between them would indeed be exact enough to apply to a wide range of questions, provided we could be certain that the laws of the forces depended only on the positions and not also on the motions of the atoms. The most important example of its successful application has been the theory of capillary action elaborated by P. S.
THE Molecular Structure Of Matter An enormous mass of experimental evidence now shows quite conclusively that matter cannot be regarded as having a continuous structure, but that it is ultimately composed of discrete parts.
If the aether were itself constituted of discrete molecules, on the model of material bodies, such transparency would not be conceivable.