motion, but I may draw attention to the beautiful model
of Prof. Lyman, wherein waves are shown to be produced by the
_circular_ motion of the particles. This, as proved by the brothers
Weber, is the real motion in the case of water-waves.]

[Footnote 11: Copied from Weber's _Wellenlehre_.]

[Footnote 12: See _Lectures on Sound_, 1st and 2nd ed., Lecture VII.;
and 3rd ed., Chap. VIII. Longmans.]

[Footnote 13: _Boyle's Works_, Birch's edition, p. 675.]

[Footnote 14: Page 743.]

[Footnote 15: The beautiful plumes produced by water-crystallization
have been successfully photographed by Professor Lockett.]

[Footnote 16: In a little volume entitled 'Forms of Water,' I have
mentioned that cold iron floats upon molten iron. In company with my
friend Sir William Armstrong, I had repeated opportunities of
witnessing this fact in his works at Elswick, 1863. Faraday, I
remember, spoke to me subsequently of the perfection of iron castings
as probably due to the swelling of the metal on solidification. Beyond
this, I have given the subject no special attention; and I know that
many intelligent iron-founders doubt the fact of expansion. It is
quite possible that the solid floats because it is not _wetted_ by the
molten iron, its volume being virtually augmented by capillary
repulsion. Certain flies walk freely upon water in virtue of an action
of this kind. With bismuth, however, it is easy to burst iron bottles
by the force of solidification.]

[Footnote 17: This beautiful law is usually thus expressed: _The index
of refraction of any substance is the tangent of its polarizing
angle_. With the aid of this law and an apparatus similar to that
figured at page 15, we can readily determine the index of refraction
of any liquid. The refracted and reflected beams being visible, they
can readily be caused to inclose a right angle. The polarizing angle
of the liquid may be thus found with the sharpest precision. It is
then only necessary to seek out its natural tangent to obtain the
index of refraction.]

[Footnote 18: Whewell.]

[Footnote 19: Removed from us since these words were written.]

[Footnote 20: The only essay known to me on the Undulatory Theory,
from the pen of an American writer, is an excellent one by President
Barnard, published in the Smithsonian Report for 1862.]

[Footnote 21: _Boyle's Works_, Birch's edition, vol. i. pp, 729 and
730.]

[Footnote 22: _Werke_, B. xxix. p. 24.]

[Footnote 23: Defined in