Page:Popular Science Monthly Volume 78.djvu/575

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sible because it is infinitely large or infinitely small; no time must seem impossible on account of its infinite length or of its infinite shortness; the grains of sand of the ocean bed and the bubble capacity of a million tons of soap are crude and inadequate figures of comparison. e must remember that in extra-mathematical investigation we judge everything by human standards, but that in reality anything which can be expressed as a mathematical formula is as simple in nature and in operation as the facts of every-day life. If we do not get away from the habit of setting limits to every conception—limits based upon our own surroundings—we shall find our speculations conflicting with science at every turn.

The knowledge of principles clears the fog in which the speculative mind wanders in search of resting spaces, and the secret of clear conception lies in the ability of ridding oneself of pre-conceptions. If in attempting to conceive the speed of propagation of light we bring to mind the speed of a railway train or of a rifle bullet, we set a limit to our mental grasp, just as a student who can not assimilate an algebraical formula without an arithmetical parallel shuts himself out of the higher mathematics.

The greatest limitation from which our forefathers suffered was the rushing to conclusions from analogies, and the shallowness of the results can not be better illustrated than by quoting from a book called "The Art of Metals," published in the year 1640, and at one time considered an authority in matters metallurgical. Referring to blue copperas, or sulphate of copper, the learned author writes:

It is admirable to see its effect in Aqua-Fortis, (in which all Mettals like Salt dissolve and are turned into water) and an occular demonstration of th« possibility of the transmutations of Mettals one into another, for with Copperas dissolved in Aqua-Fortis, (without any other artifice) Iron, Lead and Tin become fine Copper, and Silver will lose of its value, and be turned into Copper also.

When discussing the principles of physical science we are confronted by a condition which continually vitiates clearness of exposition. Conceptions of energy and of matter are now becoming more and more convergent and we find ourselves in the dilemma of having at times to think of matter as energy and at the same time to describe energy in material terms. The world of science is becoming daily more accustomed to the convertibility of the terms energy and matter; but there is a natural tendency to incredulity, for, as some one recently stated:

In the estimation of material beings matter must necessarily assume a position of special importance; but nature may not perhaps regard it otherwise than as one of numerous forms of force, between which (as Newton wrote) it "delights in effecting transmutations."

We shall return to this subject later.

There exists a public impression that the dreams of the old alche-