of
the first dark band from the centre of the field to be 1'38"; the
angular distances of the second, third, fourth dark bands being twice,
three times, four times this quantity.

[Illustration: Fig. 57.]

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 deg. 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 cove