series of elliptical vibrations (including in this term plane and circular vibrations), all the vibrations of each series being similar to each other, but the vibrations of one series having no relation to those of another. The number of vibrations in each series must amount to at least several hundreds; but the series must be so short that several hundred series enter the eye in every second of time. It must be observed that a gradual change in the nature of the vibrations is inadmissible. If, for instance, we supposed the vibrations elliptical, and supposed the ellipse to revolve uniformly about its center, it would be found that the vibrations in each plane could be resolved into two whose lengths of wave were different; and compounding the corresponding vibrations in perpendicular planes, we should have two rays of elliptically polarized light of different colours. As a simple instance of our general supposition, suppose 1000 similar vibrations in one plane to be followed by 1000 vibrations, of magnitudes equal to the former, in the plane at right angles to the former plane; then 1000 in the same plane as at first, &c. The succession of similar waves would be sufficient to give all the phænomena of interferences in perfection. At the same time, no colours would be exhibited with a crystal and an analyzing plate. For the first series alone would give rings and colours, but the second would give rings, &c. with intensities exactly complementary* to the former: and as these would enter the eye in such rapid succession that we could not distinguish them, we should only perceive the combined effect, which would be a uniform white. 184. We have always spoken of the colour of a ray as if it alone were sufficient to identify the nature of the ray. Perhaps, however, it would have been better to consider a ray as defined by its refrangibility. The remarkable experiment of Fraunhofer (84), from which it appears that the interruptions in the spectrum formed by interference corre This is seen in our expressions (155) by putting +90° instead of 4, and a-90° instead of a. spond exactly to those in the spectrum formed by refraction, seems decisive as to this point, that rays of the same refrangibility are produced by waves of the same length. It has, however, long been the opinion of some philosophers that there are rays of different colours which have the same degree of refrangibility, and that there are rays of the same colour with different degrees of refrangibility. Taking this as established, the conclusion seems to be, that colour does not depend on the length of a wave, but probably on some other circumstance, as perhaps the nature of the vibration. The law of vibration may be, not that of a cycloidal pendulum (as we have all along supposed), but something slightly different. It may be that the effect of an absorbing medium is to suppress all that part of the vibration which follows that law, and to allow only the other to pass. These, however, are very vague conjectures, which can scarcely be examined till our knowledge of the subject in question is much more extensive than it is at present. Hor M 159 TABLE of the NUMERICAL VALUES of the DEFINITE INTEGRAL φ 4 $ (n) = = √„ √/ (1 − π |