The integration can be effected without much difficulty.
18), the nearest point on the wave-front, is wholly intercepted, and on the left the integration is to be taken from s = CA to s = co.
Laplace owned that he had despaired of effecting the integration of the differential equations relative to secular inequalities until Lagrange showed him the way.
Cauchy, without the use of Gilbert's integrals, by direct integration by parts.
He finds that throughout the universe there is an unceasing redistribution of matter and motion, and that this redistribution constitutes evolution when there is a predominant integration of matter and dissipation of motion, and constitutes dissolution where there is a predominant absorption of motion and disintegration of matter.
Next, he supposes that mind obeys the same law of evolution, and exemplifies integration by generalization, differentiation by the development of the five senses, and determination by the development of the order of consciousness.
A; and similarly the optical distance between AoBo and B is represented by f (,t+So.)ds, the integration being along Bo.
The processes which have to be performed in the mensuration of figures of this kind are in effect processes of integration; the distinction between mensuration and integration lies in the different natures of the data.
He supposes that evolution is primarily integration, from the incoherent to the coherent, exemplified in the solar nebula evolving into the solar system; secondly differentiation, from the more homogeneous to the more heterogeneous, exemplified by the solar system evolving into different bodies; thirdly determination, from the indefinite to the definite, exemplified by the solar system with different bodies evolving into an order.
Proceeding on this suggestion, and misled by the mathematical expression which he had given to Weber's law, Fechner held that a conscious sensation, like its stimulus, consists of units, or elements, by summation and increments of which conscious sensations and their differences are produced; so that consciousness, according to this unnecessary assumption, emerges from an integration of unconscious shocks or tremors.
Of his philosophical doctrine proper, the most striking characteristic is Integration, as opposed to Disintegration, both in thought and in reality.
Journ., 18 43, 3, p. 46), determine the law of the secondary wave, by comparing the result of the integration with that obtained by supposing the primary wave to pass on to P without resolution.
The limits of integration for x may thus be taken to be -2a and -Fla, and for y to be -2b, +2b.
The European inhabitants live principally in the new town, which was gradually formed by the integration of Weltevreden (Wellcontent), Molenvliet (Mill-stream), Rijswijk (Rice-town), Noordwijk (North-town), Koningsplein (King's square), and other suburban villages or stations.