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Other crystals of more complicated structure affect transmitted light in a more complex way, developing a double polarity very similar to that induced in the iron filings when brought under the influence of the two poles of the magnet. With this polarised light the most beautiful coloured rings can be produced from the waves of the different colours into which the white light has been analysed in passing through the crystal, which alternately flash out and disappear as the crystal is turned round its axis, and which present a remarkable analogy to the curves into which the iron filings form themselves under the single or double poles of the magnet.

The importance of this will appear afterwards, but for the present it is sufficient to show that the waves of ether which cause light really penetrate through the molecules of crystals, but in doing so may be affected by them.

Rings of Polarised Light, Uniaxial Crystals. Rings of Polarised Light, Biaxial Crystals.

In dealing with these excessively small magnitudes it may assist the reader who has some acquaintance with mathematics in forming some conception of them, to refer to that refinement of calculation, the differential and integral calculus. And even the non-mathematical reader may find it worth while to give a little attention in order to gain some idea of this celebrated calculus which was the key by which Newton and his successors unlocked the mysteries of the heavens. The first rough idea of it is gained by considering what would happen if, in a calculation involving hundreds of miles, we neglected inches. Suppose we had a block of land to measure, 300 miles long and 200 wide; as there are, say, 5,000 feet in a mile, and the error from omitting inches could not exceed a foot, the utmost error in the measurement of length could not exceed 1/1500000th, and in width 1/1000000th part of the correct amount. In the area of 300 × 200 = 60,000 square miles, the limit of error would, by adding or omitting the rectangle formed by multiplying together these two small errors, not exceed 1/1500000 × 1/1000000 = 1/1500000000000th part. It is evident that the first error is an excessively small part of the true figure, and the second error a still more excessively small part of the first error. But, as we are dealing with abstract numbers, we can just as readily conceive our initial error to be the 1/100th or 1/1000th of an inch, as one inch; and, in fact, diminish it until it becomes an infinitesimally small or evanescent quantity. In doing so, however, it is evident that we shall make the second error such a still more infinitesimally small fraction of the first that it may be considered as altogether disappearing.