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So the development of man's religious ideas from early, crude beginnings until now is not a process which one would wish to stop at any point in order to achieve infallible security. The movement is not haphazard and discontinuous change, like disparate particles in a kaleidoscope falling together in new but vitally unrelated ways.
As compared with the normal Flat-fish they arise by a discontinuous variation, they are mutations, whereas the normal Flat-fish as compared with its symmetrical ancestor arises by a continuous change. In order to make my meaning clear I must point out that I have been using the word continuous in a different sense from that in which it is used by other biologists, Bateson for example.
Yet I fear that to speak so is rationalism, and would be found to involve, to the horror of our philosopher, that life is cognitive and spiritual, but dependent, discontinuous, and unsubstantial.
It seemed as though the tragic calamities of the eruption of A.D. 79 were about to be repeated. But gradually the force of the explosions decreased, and the noise from the crater became discontinuous, so that on the 30th the detonations were very few, and by the 1st May the eruption was completely over. Such is a condensed account of one of the most formidable eruptions of our era.
Because a jump-spark sets up periodic oscillations, that is, the oscillations are discontinuous, it cannot be used for wireless telephony. An electric arc or a vacuum tube sets up sustained oscillations, that is, oscillations which are continuous.
No one will question that mathematicians have a way of thinking all their own; but even this is too general. The arithmetician, the algebraist, and more generally the analyst, in whom invention obtains in the most abstract form of discontinuous functions symbols and their relations cannot imagine like the geometrician.
Sir Norman Lockyer promptly perceived the applicability of the surprising discovery of line-shiftings through end-on motion to the study of prominences, the discontinuous light of which affords precisely the same means of detecting movement without seeming change of place, as do lines of absorption in a continuous spectrum.
Helmholtz’s theory of musical harmony depends on the experimental fact that a continued impression gives a pleasant, a discontinuous an unpleasant sensation. The mechanics of muscular structure prove that what are called graceful motions are those which are the mechanical resultant of the force of the muscle, those which it can perform at least waste.
Such a fruitful source of disturbance, generated by so slight an accident as the upward movement of the saturated air, expanded by its own agency to so great an extent, so sudden and discontinuous in its action, so obscure in its origin, and so distinct in its effects, such a phenomenon defies the powers of mathematical prediction, and rouses all the winds to sedition.
While the animal evolved, not without accidents along the way, toward a freer and freer expenditure of discontinuous energy, the plant perfected rather its system of accumulation without moving. We shall not dwell on this second point. Suffice it to say that the plant must have been greatly benefited, in its turn, by a new division, analogous to that between plants and animals.
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