Let A B, fig. 57, be the plate in which the slit is cut, and C D the grossly exaggerated width of the slit, with the beam of red light proceeding from it at the obliquity corresponding to the first dark band. Let fall a perpendicular from one edge, D, of the slit on the marginal ray of the other edge at _d_. The distance, C _d_, between the foot of this perpendicular and the other edge is the length of a wave of the light. The angle C D _d_, moreover, being equal to R C R', is, in the case now under consideration, 1'38". From the centre D, with the width D C as radius, describe a semicircle; its radius D C being 1.35 millimeter, the length of this semicircle is found by an easy calculation to be 4.248 millimeters. The length C _d_ is so small that it sensibly coincides with the arc of the circle. Hence the length of the semicircle is to the length C _d_ of the wave as 180° to 1'38", or, reducing all to seconds, as 648,000" to 98". Thus, we have the proportion-- 648,000 : 98 :: 4.248 to the wave-length C _d_. Making the calculation, we find the wave-length for this particular kind of light to be 0.000643 of a millimeter, or 0.000026 of an inch. FOOTNOTES: [Footnote 1: Among whom may be especially mentioned the late Sir Edmund Head, Bart., with whom I had many conversations on this subject.] [Footnote 2: At whose hands it gives me pleasure to state I have always experienced honourable and liberal treatment.] [Footnote 3: One of the earliest of these came from Mr. John Amory Lowell of Boston.] [Footnote 4: It will be subsequently shown how this simple apparatus may be employed to determine the 'polarizing angle' of a liquid.] [Footnote 5: From this principle Sir John Herschel deduces in a simple and elegant manner the fundamental law of reflection.--See _Familiar Lectures_, p. 236.] [Footnote 6: The low dispersive power of water masks, as Helmholtz has remarked, the imperfect achromatism of the eye. With the naked eye I can see a distant blue disk sharply defined, but not a red one. I can also see the lines which mark the upper and lower boundaries of a horizontally refracted spectrum sharp at the blue end, but ill-defined at the red end. Projecting a luminous disk upon a screen, and covering one semicircle of the aperture with a red and the other with a blue or green glass, the difference between the apparent sizes of the two semicircles is in my case, and in numerous other cases, extraordinary. Many persons, however, see the apparent sizes of the two semicircles reversed. If with a spectacle glass I correct the dispersion of the red light over the retina, then the blue ceases to give a sharply defined image. Thus examined, the departure of the eye from achromatism appears very gross indeed.]