A', fig. 47) are seen surrounded, not by
circles, but by curves of another order and of a perfectly definite
mathematical character. Each band, as proved experimentally by
Herschel, forms a _lemniscata_; but the experimental proof was here,
as in numberless other cases, preceded by the deduction which showed
that, according to the undulatory theory, the bands must possess this
special character.

Sec. 10. _Power of the Wave Theory_.

I have taken this somewhat wide range over polarization itself, and
over the phenomena exhibited by crystals in polarized light, in order
to give you some notion of the firmness and completeness of the theory
which grasps them all. Starting from the single assumption of
transverse undulations, we first of all determine the wave-lengths,
and find that on them all the phenomena of colour are dependent. The
wavelengths may be determined in many independent ways. Newton
virtually determined them when he measured the periods of his Fits:
the length of a fit, in fact, is that of a quarter of an undulation.
The wave-lengths may be determined by diffraction at the edges of a
slit (as in the Appendix to these Lectures); they may be deduced from
the interference fringes produced by reflection; from the fringes
produced by refraction; also by lines drawn with a diamond upon glass
at measured distances asunder. And when the length determined by these
independent methods are compared together, the strictest agreement is
found to exist between them.

With the wave-lengths once at our disposal, we follow the ether into
the most complicated cases of interaction between it and ordinary
matter, 'the theory is equal to them all. It makes not a single new
physical hypothesis; but out of its original stock of principles it
educes the counterparts of all that observation shows. It accounts
for, explains, simplifies the most entangled cases; corrects known
laws and facts; predicts and discloses unknown ones; becomes the guide
of its former teacher Observation; and, enlightened by mechanical
conceptions, acquires an insight which pierces through shape and
colour to force and cause.'[18]

But, while I have thus endeavoured to illustrate before you the power
of the undulatory theory as a solver of all the difficulties of
optics, do I therefore wish you to close your eyes to any evidence
that may arise against it? By no means. You may urge, and justly urge,
that a hundred years ago another theory was held by