with these, and must often return to them to examine his progress by them.  Here is his secure hold:  and as he sets out from thence, so if he likewise trace not often his steps backwards with caution, he will be in hazard of losing his way in the labyrinths of Nature.’—­(Maclaurin:  An Account of Sir I. Newton’s Philosophical Discoveries.  Written 1728; second edition, 1750; pp. 18, 19.)

]

[Footnote 10:  I do not wish to encumber the conception here with the details of the 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.]