[1] Trans. of Edin. Geol. Soc., vol. ii. p. 252.

[2] Phil. Mag., January, 1863.

[3] Athenæum, September 22, 1860.

[4] Trans. Glasgow Geol. Soc., vol. iv., p. 313.

[5] See Mr. Hopkin’s remarks on this theory, Quart. Journ. Geol. Soc., vol. viii.

[6] See Chap. xxv.

[7] See Chap. iv.

[8] “Treatise on Astronomy,” § 315; “Outlines,” § 368.

[9] Annuaire for 1834, p. 199. Edin. New Phil. Journ., April, 1834, p. 224.

[10] “Cosmos,” vol. iv. p. 459 (Bohn’s Edition). “Physical Description of the Heavens,” p. 336.

[11] Phil. Mag. for February, 1867, p. 127.

[12] The Gulf-stream at the narrowest place examined by the Coast Survey, and where also its velocity was greatest, was found to be over 30 statute miles broad and 1,950 feet deep. But we must not suppose that this represents all the warm water which is received by the Atlantic from the equator; a great mass flows into the Atlantic without passing through the Straits of Florida.

[13] It is probable that a large proportion of the water constituting the south-eastern branch of the Gulf-stream is never cooled down to 40°; but, on the other hand, the north-eastern branch, which passes into the arctic regions, will be cooled far below 40°, probably below 30°. Hence I cannot be over-estimating the extent to which the water of the Gulf-stream is cooled down in fixing upon 40° as the average minimum temperature.

[14] “Physical Geography of the Sea,” § 24, 6th edition.

[15] “Physical Geography,” § 54.

[16] Trans. of Roy. Soc. of Edin., vol. xxi., p. 57. Phil. Mag., § 4, vol. ix., p. 36.

[17] “Smithsonian Contributions to Knowledge,” vol. ix.

[18] “Heat as a Mode of Motion,” art. 240.

[19] Trans. Roy. Soc. of Edin., vol. xxv., part 2.

[20] See “Smithsonian Contributions to Knowledge,” vol. ix.

[21] “Meteorology,” section 36.

[22] Comptes-Rendus, July 9, 1838. Taylor’s “Scientific Memoirs,” vol. iv., p. 44 (1846).

[23] The mean temperature of the Atlantic between the tropics and the arctic circle, according to Admiral Fitzroy’s chart, is about 60°. But he assigns far too high a temperature for latitudes above 50°. It is probable that 56° is not far from the truth.

[24] The probable physical cause of this will be considered in the Appendix.

[25] The mean temperature of the equator, according to Dove, is 79°·7, and that of the north pole 2°·3. But as there is, of course, some uncertainty regarding the actual mean temperature of the poles, we may take the difference in round numbers at 80°.

[26] Trans. of Roy. Soc. Edin., vol. xxii., p. 75.

[27] Connaissance des Temps for 1863 (Additions). Lagrange’s determination makes the superior limit 0·07641 (Memoirs of the Berlin Academy for 1782, p. 273). Recently the laborious task of re-investigating the whole subject of the secular variations of the elements of the planetary orbits was undertaken by Mr. Stockwell, of the United States. He has taken into account the disturbing influence of the planet Neptune, the existence of which was not known when Leverrier’s computations were made; and he finds that the eccentricity of the earth’s orbit will always be included within the limits of 0 and 0·0693888. Mr. Stockwell’s elaborate Memoir, extending over no fewer than two hundred pages, will be found in the eighteenth volume of the “Smithsonian Contributions to Knowledge.”

[28] When the eccentricity is at its superior limit, the absolute quantity of heat received by the earth during the year is, however, about one three-hundredth part greater than at present. But this does not affect the question at issue.

[29] Scoresby’s “Arctic Regions,” vol. ii., p. 379. Daniell’s “Meteorology,” vol. ii., p. 123.

[30] Tyndall, “On Heat,” article 364.

[31] Tyndall, “On Heat,” article 364.

[32] See Phil. Mag., March, 1870, p.

[33] Captain Cook’s “Second Voyage,” vol. ii., pp. 232, 235.

[34] “Antarctic Regions,” vol. ii., pp. 345−349.

[35] Ibid., vol. i., p. 167.

[36] Ibid., vol. ii., p. 362.

[37] Edinburgh Philosophical Journal, vol. iv., p. 266.

[38] Scoresby’s “Arctic Regions,” vol. i., p. 378.

[39] Ibid., p. 425.

[40] See Meech’s memoir “On the Intensity of the Sun’s Heat and Light,” “Smithsonian Contributions,” vol. ix.

[41] “Antarctic Regions,” vol. i., p. 240.

[42] Challenger Reports, No. 2, p. 10.

[43] See “Smithsonian Contributions,” vol. ix.

[44] Quart. Journ. Geol. Soc., vol. xxv., p. 350.

[45] Trans. of Glasgow Geol. Soc. for 1866.

[46] Revue des Deux Mondes for 1867.

[47] Letter to the author, February, 1870.

[48] “Révolutions de la Mer,” p. 37 (second edition).

[49] Edin. Phil. Journ., vol. iv., p. 262 (1821).

[50] Phil. Mag., § 4, vol. xxviii., p. 131. Reader, December 2nd, 1865.

[51] This point will be found discussed at considerable length in the Phil. Mag. for September, 1869.

[52] See Phil. Mag. for October, 1870, p. 259.

[53] Proceedings of the Royal Society, No. 138, p. 596, foot-note.

[54] The edition from which I quote, unless the contrary is stated, is the one published by Messrs. T. Nelson and Sons, 1870, which is a reprint of the new edition published in 1859 by Messrs. Sampson Low and Co.

[55] “Physical Geography,” article 57.

[56] Philosophical Magazine, vol. xii. p. 1 (1838).

[57] “Mémoires par divers Savans,” tom. i., p. 318, St. Petersburgh, 1831. See also twelfth number of Meteorological Papers, published by the Board of Trade, 1865, p. 16.

[58] Dubuat’s “Hydraulique,” tom. i., p. 64 (1816). See also British Association Report for 1834, pp. 422, 451.

[59] See Proceedings of the Royal Society for December, 1868, November, 1869. Lecture delivered at the Royal Institute, Nature, vol. i., p. 490. Proceedings of the Royal Geographical Society, vol. xv.

[60] Trans. of Glasgow Geol. Soc. for April, 1867. Phil. Mag. for February, 1867, and June, 1867 (Supplement).

[61] Phil. Mag. for February, 1870.

[62] “The Depths of the Sea,” pp. 376 and 377.

[63] “The Threshold of the Unknown Region,” p. 95.

[64] See “Physical Geography of the Sea,” chap. ix., new edition, and Dr. A. Mühry “On Ocean-currents in the Circumpolar Basin of the North Hemisphere.”

[65] “Depths of the Sea,” Nature for July 28, 1870.

[66] “Memoir on the Gulf-stream,” Geographische Mittheilungen, vol. xvi. (1870).

[67] Dr. Carpenter “On the Gulf-stream,” Proceedings of Royal Geographical Society for January 9, 1871, § 29.

[68] Dr. Petermann’s Mittheilungen for 1872, p. 315.

[69] Proceedings of the Royal Society, vol. xvii., p. 187, xviii., p. 463.

[70] The average depth of the Pacific Ocean, as found by the soundings of Captain Belknap, of the U.S. steamer Tuscarora, made during January and February, 1874, is about 2,400 fathoms. The depth of the Atlantic is somewhat less.

[71] Proceedings of Royal Geographical Society, vol. xv., § 22.

[72] It is a well-established fact that in polar regions the temperature of the sea decreases from the surface downwards; and the German Polar Expedition found that the water in very high latitudes is actually less dense at the surface than at considerable depths, thus proving that the surface-water could not sink in consequence of its greater density.

[73] Proceedings of the Royal Society, vol. xix., p. 215.

[74] Nature for July 6, 1871.

[75] Since the above objection to the Gravitation Theory of the Gibraltar Current was advanced three years ago, Dr. Carpenter appears to have abandoned the theory to a great extent. He now admits (Proceedings of Royal Geographical Society, vol. xviii., pp. 319−334, 1874) that the current is almost wholly due not to difference of specific gravity, but to an excess of evaporation in the Mediterranean over the return by rain and rivers.

[76] Proceedings of Royal Society, No. 138, § 26.

[77] Proceedings of Royal Geographical Society, January 9, 1871.

[78] Ibid.

[79] See §§ 20, 34; also Brit. Assoc. Report for 1872, p. 49, and other places.

[80] See also to the same effect Brit. Assoc. Report, 1872, p. 50.

[81] Phil. Mag. for Oct. 1871.

[82] The actual slope, however, does not amount to more than 1 in 7,000,000.

[83] Proc. of Roy. Geog. Soc., January 9, 1871, § 29.

[84] Trans. of Geol. Soc. of Glasgow for April, 1867; Phil. Mag. for June, 1867.

[85] Nature, vol. i., p. 541. Proc. Roy. Soc., vol. xviii., p. 473.

[86] Chapter II.

[87] Chapter II.

[88] Chapter II.

[89] Mr. Findlay considers that the daily discharge does not exceed 333 cubic miles (Brit. Assoc. Rep., 1869, p. 160). My estimate makes it 378 cubic miles. Mr. Laughton’s estimate is 630 cubic miles (Paper “On Ocean-currents,” Journal of Royal United-Service Institution, vol. xv.).

[90] Proceedings of the Royal Geographical Society, vol. xviii., p. 393.

[91] Phil. Mag. for October, 1871, p. 274.

[92] Proceedings of the Royal Geographical Society, vol. xv.

[93] Phil. Mag., February, 1870.

[94] Brit. Assoc. Report, 1869, Sections, p. 160.

[95] Journal of Royal United-Service Institute, vol. xv.

[96] Dr. Carpenter (Proc. of Roy. Geog. Soc., vol. xviii., p. 334) misapprehends me in supposing that I attribute the Gibraltar current wholly to the Gulf-stream. In the very page from which he derives or could derive his opinion as to my views on the subject (Phil. Mag. for March, 1874, p. 182), I distinctly state that “the excess of evaporation over that of precipitation within the Mediterranean area would of itself produce a considerable current through the Strait.” That the Gibraltar current is due to two causes, (1) the pressure of the Gulf-stream, and (2) excess of evaporation over precipitation in the Mediterranean, has always appeared to me so perfectly obvious, that I never held nor could have held any other opinion on the subject.

[97] Paper read to the Edinburgh Botanical Society on January 8, 1874.

[98] Proc. Roy. Geog. Soc., vol. xviii., p. 362. A more advantageous section might have been chosen, but this will suffice. The section referred to is shown in Plate III. The peculiarity of this section, as will be observed, is the thinness of the warm strata at the equator, as compared with that of the heated water in the North Atlantic.

[99] The temperature of column C in Dr. Carpenter’s section is somewhat less than that given in the foregoing table; so that, according to that section, the difference of level between column C and columns A and B would be greater than my estimate.

[100] Captain Nares’s Report, July 30, 1874.

[101] See Chapter IV.

[102] Phil. Mag. for August, 1864, February, 1867, March, 1870; see Chap. IV.

[103] Quarterly Journal of Science for October, 1874.

[104] See a paper by M. Morlot, on “The Post-Tertiary and Quaternary Formations of Switzerland.” Edin. New Phil. Journal, New Series, vol. ii., 1855.

[105] Edin. New Phil. Journ., New Series, vol. ii., p. 28.

[106] Vogt’s “Lectures on Man,” pp. 318−321.

[107] See Mr. Prestwich on Flint Implements, Phil. Trans. for 1860 and 1864. Lyell’s “Antiquity of Man,” Second Edition, p. 168.

[108] Edin. New Phil. Journ., New Series, vol. ii., p. 28. Silliman’s Journ., vol. xlvii., p. 259 (1844).

[109] Quart. Journ. Geol. Soc., vol. xxvii., p. 534.

[110] Ibid., vol. xxviii., p. 17.

[111] “Glacial Drift of Scotland,” p. 54.

[112] “Glacial Drift of Scotland,” p. 58.

[113] Quart. Journ. Geol. Soc., vol. v., p. 22.

[114] “Glacial Drift of Scotland,” p. 64.

[115] Trans. Edin. Geol. Soc., vol. ii., p. 391.

[116] Trans. of Geol. Soc. of Glasgow, vol. iv., p. 146.

[117] Geol. Mag., vi., p. 391.

[118] See “Memoirs of Geological Survey of Scotland,” Explanation of sheet 22, p. 29. See also Trans. Glasgow Geol. Soc., iv., p. 150.

[119] “Great Ice Age,” p. 374.

[120] “Great Ice Age,” p. 384.

[121] “Geological Survey of Ohio, 1869,” p. 165. See also “Great Ice Age,” chap. xxviii.

[122] Quart. Journ. Geol. Soc., xxviii., p. 435.

[123] Brit. Assoc. Report, 1863.

[124] Trans. Glasgow Nat. Hist. Soc., vol. i., p. 115.

[125] Trans. of the Geol. Soc. of Glasgow, vol. iii., p. 133. See also “Great Ice Age,” chaps. xii. and xiii.

[126] Chap. XXIX.

[127] Edin. New Phil. Journ., vol. liv., p. 272.

[128] “Newer Pliocene Geology,” p. 129. John Gray & Co., Glasgow.

[129] “Glacial Drift of Scotland,” p. 67.

[130] “Glacial Drift of Scotland,” p. 12.

[131] See Chapter IV.

[132] “Discovery of the North-West Passage,” p. 213.

[133] “Voyage of the Resolute,” p. 294.

[134] Quart. Journ. Geol. Soc., vol. xi., p. 540.

[135] “McClure’s North-West Passage,” p. 214. Second Edition.

[136] “British Association Report for 1855,” p. 381. “The Last of the Arctic Voyages,” vol. i., p. 381.

[137] Mr. James Geikie informs me that the great accumulations of gravel which occur so abundantly in the low grounds of Switzerland, and which are, undoubtedly, merely the re-arranged materials originally brought down from the Alps as till and as moraines by the glaciers during the glacial epoch, rarely or never yield a single scratched or glaciated stone. The action of the rivers escaping from the melting ice has succeeded in obliterating all trace of striæ. It is the same, he says, with the heaps of gravel and sand in the lower grounds of Sweden and Norway, Scotland and Ireland. These deposits are evidently in the first place merely the materials carried down by the swollen rivers that issued from the gradually melting ice-fields and glaciers. The stones of the gravel derived from the demolition of moraines and till, have lost all their striæ and become in most cases well water-worn and rounded.

[138] Report on Icebergs, read before the Association of American Geologists, Silliman’s Journal, vol. xliii., p. 163 (1842).

[139] “Manual of Geology,” p. 677.

[140] Quart. Journ. Geol. Soc., vol. ix., p. 306.

[141] Dana’s “Manual of Geology,” p. 677.

[142] Quart. Journ. Geol. Soc., vol. ix., p. 306.

[143] “Journal,” vol. i., p. 38.

[144] “Short American Tramp,” pp. 168, 174.

[145] “Short American Tramp,” pp. 239−241.

[146] “Travels in North America,” vol. ii., p. 137.

[147] Ibid., vol. ii., p. 174.

[148] Proceedings of the Royal Society of Edinburgh, Session 1865−66, p. 537.

[149] “Short American Tramp,” pp. 77, 81, 111.

[150] “Second Visit,” vol. ii., p. 367.

[151] “Memoirs of Boston Society of Natural History,” vol. i. (1867), p. 228.

[152] “Antiquity of Man,” p. 268. Third Edition.

[153] “Great Ice Age,” p. 512.

[154] Brit. Assoc., 1870, p. 88.

[155] Quart. Journ. Geol. Soc., vol. v., p. 10. Phil. Mag. for April, 1865, p. 289.

[156] “Great Ice Age,” p. 512.

[157] Jukes’ “Manual of Geology,” p. 421.

[158] See also Quarterly Journal Geological Society, vol. xi., p. 510.

[159] The Reader for August 12, 1865.

[160] “History of the Isle of Man,” p. 86. My colleague, Mr. John Horne, in his “Sketch of the Geology of the Isle of Man,” Trans. of Edin. Geol. Soc., vol. ii., part iii., considers this conglomerate to be of Lower Carboniferous age.

[161] See Selwyn, “Phys. Geography and Geology of Victoria.” 1866. pp. 15−16; Taylor and Etheridge, Geol. Survey Vict., Quarter Sheet 13, N.E.

[162] Report on the Geology of the District of Ballan, Victoria. 1866. p. 11.

[163] Atrypa reticularis.

[164] Quart. Journ. Geol. Soc., vol. xii., p. 58.

[165] “Great Ice Age,” p. 513.

[166] “Great Ice Age,” p. 513.

[167] Brit. Assoc. Report for 1873.

[168] Quart. Journ. Geol. Soc., vol. xi., p. 519.

[169] Orthis resupinata.

[170] Prod. semireticulatus var. Martini. Sow.

[171] “Belcher’s Voyage,” vol. ii., p. 377.

[172] “Journal of a Boat Voyage through Rupert-Land,” vol. ii., p. 208.

[173] Quart. Journ. Geol. Soc., vol. xi., p. 197.

[174] Explanation Memoir to Sheet 47, “Geological Survey of Ireland.”

[175] Phil. Mag., vol. xxix., p. 290.

[176] “Memoirs of the Geological Survey of India,” vol. i., part i.

[177] Quart. Journ. Geol. Soc., vol. xxvi., p. 514.

[178] Ibid., vol. xxvii., p. 544.

[179] Phil. Mag., vol. xxix., p. 290.

[180] Journal of the Royal Dublin Society for February, 1857.

[181] Quart. Journ. Geol. Soc., vol. xi., p. 519.

[182] “The Last of the Arctic Voyages,” by Captain Sir E. Belcher, vol. ii., p. 389. Appendix Brit. Assoc. Report for 1855, p. 79.

[183] Ibid., vol. ii., p. 379. Appendix.

[184] “Manual of Geology,” pp. 395, 493.

[185] Appendix to McClintock’s “Arctic Discoveries.”

[186] Quart. Journ. Geol. Soc., vol. xiv., p. 262. Brit. Assoc. Report for 1857, p. 62.

[187] Quart. Journ. Geol. Soc., vol. xvi., p. 327. Geologist, 1860, p. 38.

[188] Phil. Mag., vol. xxix., p. 290.

[189] Trans. Geol. Soc. of Glasgow, vol. v., p. 64.

[190] “Principles,” vol. i., p. 209. Eleventh Edition.

[191] “Memoirs of the Royal Academy of Science of Turin,” Second Series, vol. xx. I am indebted for the above particulars to Professor Ramsay, who visited the spot along with M. Gastaldi.

[192] “Antiquity of Man,” Second Edition, p. 237.

[193] Dr. Robert Brown, in a recent Memoir on the Miocene Beds of the Disco District (Trans. Geol. Soc. Glasg., vol. v., p. 55), has added considerably to our knowledge of these deposits. He describes the strata in detail, and gives lists of the plant and animal remains discovered by himself and others, and described by Professor Heer. Professor Nordenskjöld has likewise increased the data at our command (Transactions of the Swedish Academy, 1873); and still further evidence in favour of a warm climate having prevailed in Greenland during Miocene times has been obtained by the recent second German polar expedition.

[194] The following are M. Leverrier’s formulæ for computing the eccentricity of the earth’s orbit, given in his “Memoir” in the Connaissance des Temps for 1843:—

Eccentricity in (t) years after January 1, 1800 = √h² + l² where

h = 0·000526 Sin (gt + ß) + 0·016611 Sin (g₁t + ß₁) + 0·002366 Sin (g₂t + ß₂)
+ 0·010622 Sin (g₃t + ß₃) − 0·018925 Sin (g₄t + ß₄)
+ 0·011782 Sin (g₅t + ß₅) − 0·016913 Sin (g₆t + ß₆)

and

l = 0·000526 Cos (gt + ß) + 0·016611 Cos (g₁t + ß₁) + 0·002366 Cos (g₂t + ß₂)
+ 0·010622 Cos (g₃t + ß₃) − 0·018925 Cos (g₄t + ß₄)
+ 0·011782 Cos (g₅t + ß₅) − 0·016913 Cos (g₆t + ß₆)

g  =  2″·25842	ß   = 126° 43′ 15″
g1 =  3″·71364	ß1 =   27   21  26
g2 = 22″·4273	ß2 = 126   44    8
g3 =  5″·2989	ß3 =   85   47  45
g4 =  7″·5747	ß4 =   35   38  43
g5 = 17″·1527	ß5 = −25   11   33
g6 = 17″·8633	ß6 = −45   28   59

[195] See Professor C. V. Zenger’s paper “On the Periodic Change cf Climate caused by the Moon,” Phil. Mag. for June, 1868.

[196] Phil. Mag. for February, 1867.

[197] Phil. Mag. for May, 1868.

[198] Student’s “Elements of Geology,” p. 91. Second Edition.

[199] In an interesting memoir, published in the Phil. Mag. for 1850, Mr. Alfred Tylor estimated that the basin of the Mississippi is being lowered at the rate of one foot in 10,000 years by the removal of the sediment; and he proceeds further, and reasons that one foot removed off the general surface of the land during that period would raise the sea-level three inches. Had it not been that Mr. Tylor’s attention was directed to the effects produced by the removal of sediment in raising the level of the ocean rather than in lowering the level of the land, he could not have failed to perceive that he was in possession of a key to unfold the mystery of geological time.

[200] Proc. Roy. Soc., No. 152, 1874.

[201] I have taken for the volume and mass of the sun the values given in Professor Sir William Thomson’s memoir, Phil. Mag., vol. viii. (1854).

[202] Phil. Mag., § 4, vol. xi., p. 516 (1856).

[203] Phil. Mag. for July, 1872, p. 1.

[204] “Principles,” p. 210. Eleventh Edition.

[205] “Principles,” vol. i., p. 107. Tenth Edition.

[206] The conception of submergence resulting from displacement of the earth’s centre of gravity, caused by a heaping up of ice at one of the poles, was first advanced by M. Adhémar, in his work “Révolutions de la Mer,” 1842. When the views stated in this chapter appeared in the Reader, I was not aware that M. Adhémar had written on the subject. An account of his mode of viewing the question is given in the Appendix.

[207] Petermann’s Geog. Mittheilungen, 1871, Heft. x., p. 377.

[208] Geol. Mag., 1872, vol. ix., p. 360.

[209] “Open Polar Sea,” p. 134.

[210] Journal of the Royal Geographical Society, 1853, vol. xxiii.

[211] “Physics of Arctic Ice,” Quart. Journ. Geol. Soc. for February, 1871.

[212] Some writers have objected to the conclusion that the antarctic ice-cap is thickest at the pole, on the ground that the snowfall there is probably less than at lower latitudes. The fact is, however, overlooked, that the greater thickness of an ice-cap at its centre is a physical necessity not depending on the rate of snowfall. Supposing the snowfall to be greater at, say, lat. 70° than at 80°, and greater at 80° than at the pole; nevertheless, the ice will continue to accumulate till it is thicker at 80° than at 70°, and at the pole than it is at 80°.

[213] It is a pity that at present no record is kept, either by the Board of Trade or by the Admiralty, of remarkable icebergs which may from time to time be met with. Such a record might be of little importance to navigation, but it would certainly be of great service to science.

[214] See Chapter XXVII., and also Geol. Mag. for May and June, 1870, and January, 1871.

[215] Phil. Mag. for April, 1866, p. 323.

[216] Ibid., for March, 1866, p. 172.

[217] Reader, February 10, 1866.

[218] In a former paper I considered the effects of another cause, viz., the melting of polar ice resulting from an increase of the Obliquity of the Earth’s Orbit.—Trans. Glasgow Geol. Soc., vol. ii., p. 177. Phil. Mag., June, 1867. See also Chapter XXV.

[219] Phil. Mag. for November, 1868, p. 376.

[220] Phil. Mag., November, 1868.

[221] “Origin of Species,” chap. xi. Fifth Edition.

[222] Lieutenant-Colonel Drayson (“Last Glacial Epoch of Geology”) and also Mr. Belt (Quart. Journ. of Science, October, 1874) state that Leverrier has lately investigated the question as to the extent of the variation of the plane of the ecliptic, and has arrived at results differing considerably from those of Laplace; viz., that the variation may amount to 4° 52′, whereas, according to Laplace, it amounts to only 1° 21′. I fear they are comparing things that are totally different; viz., the variation of the plane of the ecliptic in relation to its mean position with its variation in relation to the equator. Laplace estimated that the plane of the ecliptic would oscillate to the extent of 4° 53′ 33″ on each side of its mean position, a result almost identical with that of Leverrier, who makes it 4° 51′ 42″. But neither of these geometricians ever imagined that the ecliptic could change in relation to the equator to even one-third of that amount.

Laplace demonstrated that the change in the plane of the ecliptic affected the position of the equator, causing it to vary along with it, so that the equator could never possibly recede further than 1° 22′ 34″ from its mean position in relation to the ecliptic (“Mécanique Céleste,” vol. ii., p. 856, Bowditch’s Translation; see also Laplace’s memoir, “Sur les Variations de l’Obliquité de l’Écliptique,” Connaissance des Temps for 1827, p. 234), and I am not aware that Leverrier has arrived at a different conclusion.

[223] Memoir on the Secular Variations of the Elements of the Orbits of the Planets, “Smithsonian Contributions to Knowledge,” vol. xvii.

[224] “Smithsonian Contributions to Knowledge,” vol. ix.

[225] “Distribution of Heat on the Surface of the Globe,” p. 14.

[226] Chapter IV.

[227] Quart. Journ. Geol. Soc., June, 1866, p. 564.

[228] Quart. Journ. Geol. Soc., vol. xxi., p. 186.

[229] “Geological Observer,” p. 446. See also Mr. James Geikie’s valuable Memoir, “On the Buried Forests and Peat Mosses of Scotland.” Trans. of the Royal Society of Edinburgh, vol. xxiv., and Chambers’ “Ancient Sea-Margins.”

[230] See Lyell’s “Antiquity of Man,” Second Edition, p. 282; “Elements,” Sixth Edition, p. 162.

[231] In order to determine the position of the solstice-point in relation to the aphelion, it will not do to assume, as is commonly done, that the point makes a revolution from aphelion to aphelion in any regular given period, such as 21,000 years; for it is perfectly evident that owing to the great irregularity in the motion of the aphelion, no two revolutions will probably be performed in the same length of period. For example, the winter solstice was in the aphelion about the following dates: 11,700, 33,300, and 61,300 years ago. Here are two consecutive revolutions, the one performed in 21,600 years and the other in 28,000 years; the difference in the length of the two periods amounting to no fewer than 6,400 years.

[232] Quart. Journ. Geol. Soc., vol. xxvii., p. 232. See also “The Last Glacial Epoch of Geology,” by the same author.

[233] Quart. Journ. of Science, October, 1874.

[234] The longer diameter passes from long. 14° 23′ E. to long. 165° 37′ W.

[235] “Principles,” vol. i., p. 294. Eleventh Edition.

[236] Phil. Mag. for August, 1864.

[237] “Elementary Geology,” p. 399.

[238] “The Past and Present Life of the Globe,” p. 102.

[239] “Memoirs of the Geological Survey,” vol. ii., Part 2, p. 404.

[240] “Coal Fields of Great Britain,” p. 45. Third Edition.

[241] “Journal of Researches,” chap. xiii.

[242] “Coal Fields of Great Britain,” p. 67.

[243] See “Smithsonian Report for 1857,” p. 138.

[244] Quart. Journ. Geol. Soc., May, 1865, p. civ.

[245] “Geology of Fife and the Lothians,” p. 116.

[246] “Life on the Earth,” p. 133.

[247] Quart. Journ. Geol. Soc., vol. xi., p. 535.

[248] Ibid., vol. xii., p. 39.

[249] Miller’s “Sketch Book of Practical Geology,” p. 192.

[250] From Geological Magazine, May and June, 1870; with a few verbal corrections, and a slight re-arrangement of the paragraphs.

[251] See Phil. Mag. for November, 1868, p. 374.

[252] See Phil. Mag. for November, 1868, pp. 366−374.

[253] Journ. Geol. Soc., vol. xxi., p. 165.

[254] Specimens of the striated summit and boulder clay stones are to be seen in the Edinburgh Museum of Science and Art.

[255] Phil. Mag. for April, 1866.

[256] “Tracings of the North of Europe,” 1850, pp. 48−51.

[257] Quart. Journ. Geol. Soc., vol. ii., p. 364.

[258] “Tracings of the North of Europe,” by Robert Chambers, pp. 259, 285. “Observations sur les Phénomènes d’Erosion en Norvège,” by M. Hörbye, 1857. See also Professor Erdmann’s “Formations Quaternaires de la Suède.”

[259] “Glacial Drift of Scotland,” p. 29.

[260] Geological Magazine, vol. ii., p. 343. Brit. Assoc. Rep., 1864 (sections), p. 59.

[261] Trans. Roy. Soc. Edin., vol. vii., p. 265.

[262] “Tracings of Iceland and the Faroe Islands,” p. 49.

[263] See Chap. XXIII.

[264] Mr. Thomas Belt has subsequently advanced (Quart. Jour. Geol. Soc., vol. xxx., p. 490), a similar explanation of the steppes of Siberia. He supposes that an overflow of ice from the polar basin dammed back all the rivers flowing northward, and formed an immense lake which extended over the lowlands of Siberia, and deposited the great beds of sand and silt with occasional freshwater shells and elephant remains, of which the steppes consist.

[265] Proc. Roy. Phys. Soc., Edin., vols. ii. and iii.

[266] From Geol. Mag. for January, 1871.

[267] Quart. Journ. Geol. Soc., xxvi., p. 517.

[268] British Assoc. Report for 1864 (sections), p. 65.

[269] Quart. Journ. Geol. Soc., xxvi., p. 90.

[270] Geol. Mag., vii., p. 349.

[271] Trans. Edin. Geol. Soc., vol. i., p. 136.

[272] Geol. Mag. for June, 1870. See Chap. XXVII.

[273] This was done by Mr. R. H. Tiddeman of the Geological Survey of England (Quart. Journ. Geol. Soc. for November, 1872), and the result established the correctness of the above opinion as to the existence of a North of England ice-sheet. Additional confirmation has been derived from the important observations of Mr. D. Mackintosh, and also of Mr. Goodchild, of the Geological Survey of England.

[274] Trans. Geol. Soc., vol. v., p. 516 (first series).

[275] Quart. Journ. Geol. Soc., vol. xi., p. 492. “Memoir of the Country around Cheltenham,” 1857. “Geology of the Country around Woodstock,” 1859.

[276] Geol. Mag., vol. vii., p. 497.

[277] Quart. Journ. Geol. Soc., vol. xxvi., p. 90.

[278] My colleague, Mr. R. L. Jack.

[279] The greater portion of this chapter is from the Trans. of Geol. Soc. of Edinburgh, for 1869.

[280] Chapter XV., p. 253.

[281] Trans. of the Geol. Soc. of Glasgow, vol. iii., part i., page 133.

[282] Mr. Milne Home has advanced, in his “Estuary of the Firth of Forth,” p. 91, the theory that this trough had been scooped out during the glacial epoch by icebergs floating through the Midland valley from west to east when it was submerged. The bottom of the trough, be it observed, at the watershed at Kilsyth, is 300 feet above the level of its bottom at Grangemouth; and this Mr. Milne Home freely admits. But he has not explained how an iceberg, which could float across the shallow water at Kilsyth, say, 100 feet deep, could manage to grind the rocky bottom at Grangemouth, where it was not less than 400 feet deep. “The impetus acquired in the Kyle at Kilsyth,” says Mr. Milne Home, “would keep them moving on, and the prevailing westerly winds would also aid, so that when grating on the subjacent carboniferous rocks they would not have much difficulty in scooping out a channel both wider and deeper than at Kilsyth.” But how could they “grate on the subjacent carboniferous rocks” at Grangemouth, if they managed to float at Kilsyth? Surely an iceberg that could “grate” at Grangemouth would “ground” at Kilsyth.

[283] Trans. of the Geol. Soc. of Glasgow, vol. iii., p. 141.

[284] Mr. John Young and Mr. Milne Home advanced the objection, that several trap dykes cross the valley of the Clyde near Bowling, and come to so near the present surface of the land, that the Clyde at present flows across them with a depth not exceeding 20 feet. I fear that Mr. Young and Mr. Milne Home have been misinformed in regard to the existence of these dykes. About a mile above Bowling there are one or two dykes which approach to the river-bank, and may probably cross, but these could not possibly cut off a channel entering the Clyde at Bowling. In none of the borings or excavations which have been made by the Clyde Trustees has the rock been reached from Bowling downwards. I may also state that the whole Midland valley, from the Forth of Clyde to the Firth of Forth, has been surveyed by the officers of the Geological Survey, and only a single dyke has been found to cross the buried channels, viz., one (Basalt rock) running eastward from Kilsyth to the canal bridge near Dullatur. But as this is not far from the watershed between the two channels it cannot affect the question at issue. See sheet 31 of Geological Survey Map of Scotland.

[285] Trans. Geol. Soc. Glasgow, vol. iv., p. 166.

[286] “Great Ice Age,” chap. xiii.

[287] See further particulars in Mr. Bennie’s paper on the Surface Geology of the district around Glasgow, Trans. Geol. Soc. of Glasgow, vol. iii.

[288] See also Smith’s “Newer Pliocene Geology,” p. 139.

[289] British Association Report for 1863, p. 89. Geologist for 1863, p. 384.

[290] See Geological Magazine, vol. ii., p. 38.

[291] Proc. Geol. Soc., vol. iii., 1840, p. 342.

[292] “Antiquity of Man” (Third Edition), p. 249.

[293] “Glacial Drift of Scotland,” p. 65. Trans. Geol. Soc. Glas., vol. i., part 2.

[294] “Memoir, Geological Survey of Scotland,” Sheet 23, p. 42.

[295] Mr. Robert Dick had previously described, in the Trans. Geol. Soc. Edinburgh, vol. i., p. 345, portions of these buried channels. He seems, however, to have thought that they formed part of one and the same channel.

[296] A description of this channel was read to the Natural History Society of Glasgow by Mr. James Coutts, the particulars of which will appear in the Transactions of the Society.

[297] “Occasional Papers,” pp. 166, 223.

[298] Memoir read before the Royal Society, January 7, 1869.

[299] “Alpine Journal,” February, 1870.

[300] Phil. Mag., January, 1872.

[301] Phil. Mag., July, 1870; February, 1871.

[302] Philosophical Magazine for January, 1870, p. 8; Proceedings of the Royal Society for January, 1869.

[303] Philosophical Magazine for March, 1869.

[304] Proceedings of Bristol Naturalists’ Society, p. 37 (1869).

[305] Ibid., vol. iv., p. 37 (new series).

[306] Phil. Mag., S. 4, vol. x., p. 303.

[307] Proceedings of the Bristol Naturalists’ Society, vol. iv., p. 39 (new series).

[308] See Philosophical Transactions, December, 1857.

[309] There is one circumstance tending slightly to prevent the rupture of the glacier, when under tension, which I do not remember to have seen noticed; that is, the cooling effect which is produced in solids, such as ice, when subjected to tension. Tension would tend to lower the temperature of the ice-molecules, and this lowering of temperature would have the tendency of freezing them more firmly together. The cause of this cooling effect will be explained in the Appendix.

[310] Phil. Mag., March, 1869; September, 1870.

[311] “Forms of Water,” p. 127.

[312] See text, p. 10.

[313] Mathematical and Physical Series, vol. xxxvi. (1765).

[314] “Memoirs of St. Petersburg Academy,” 1761.

[315] The calculations here referred to were made by Lagrange nearly half a century previous to the appearance of this paper, and published in the “Mémoires de l’Académie de Berlin,” for 1782, p. 273. Lagrange’s results differ but slightly from those afterwards obtained by Leverrier, as will be seen from the following table; but as he had assigned erroneous values to the masses of the smaller planets, particularly that of Venus, the mass of which he estimated at one-half more than its true value, full confidence could not be placed in his results.

Superior limits of eccentricity as determined by Lagrange, Leverrier,and Mr. Stockwell:—

	By Lagrange.	By Leverrier.	By Mr. Stockwell.
Mercury	0·22208	0·225646	0·2317185
Venus	0·08271	0·086716	0·0706329
Earth	0·07641	0·077747	0·0693888
Mars	0·14726	0·142243	0·139655
Jupiter	0·06036	0·061548	0·0608274
Saturn	0·08408	0·084919	0·0843289
Uranus	—	0·064666	0·0779652
Neptune	—	—	0·0145066

[316] “Mém. de l’Acad. royale des Sciences.” 1827. Tom. vii., p. 598.

[317] Absolute zero is now considered to be only 493° Fah. below the freezing-point, and Herschel himself has lately determined 271° below the freezing-point to be the temperature of space. Consequently, a decrease, or an increase of one per cent. in the mean annual amount of radiation would not produce anything like the effect which is here supposed. But the mean annual amount of heat received cannot vary much more than one-tenth part of one per cent. In short, the effect of eccentricity on the mean annual supply of heat received from the sun, in so far as geological climate is concerned, may be practically disregarded.—[J. C.]

[318] “Principles of Geology,” p. 110. “Mr. Lyell, however, in stating the actual excess of eight days in the duration of the sun’s presence in the northern hemisphere over that in the southern as productive of an excess of light and heat annually received by the one over the other hemisphere, appears to have misconceived the effect of elliptic motion in the passage here cited, since it is demonstrable that whatever be the ellipticity of the earth’s orbit the two hemispheres must receive equal absolute quantities of light and heat per annum, the proximity of the sun in perigee exactly compensating the effect of its swifter motion. This follows from a very simple theorem, which may be thus stated: ‘The amount of heat received by the earth from the sun while describing any part of its orbit is proportional to the angle described round the sun’s centre,’ so that if the orbit be divided into two portions by a line drawn in any direction through the sun’s centre, the heats received in describing the two unequal segments of the ellipse so produced will be equal.”

[319] When the eccentricity of the earth’s orbit is at its superior limit, the absolute quantity of heat received by the globe during one year will be increased by only 1/300th part; an amount which could produce no sensible influence on climate.—[J. C.]

[320] Sir Charles has recently, to a certain extent, adopted the views advocated in the present volume, viz., that the cold of the glacial epoch was brought about not by a decrease, but by an increase of eccentricity. (See vol. i. of “Principles,” tenth and eleventh editions.) The decrease in the mean annual quantity of heat received from the sun, resulting from the decrease in the eccentricity of the earth’s orbit—the astronomical cause to which he here refers—could have produced no sensible effect on climate.—[J. C.]

[321] It is singular that both Arago and Humboldt should appear to have been unaware of the researches of Lagrange on this subject.

[322] “Révolutions de la Mer,” p. 37. Second Edition.

[323] See text, p. 37.

[324] See Philosophical Magazine for December, 1867, p. 457.

[325] Silliman’s American Journal for July, 1864. Philosophical Magazine for September, 1864, pp. 193, 196.

[326] Philosophical Magazine for August, 1865, p. 95.

[327] See text, p. 80.

[328] See text, p. 222.

[329] Proc. Roy. Soc., No. 157, 1875.

[330] See text, p. 522.

[331] Phil. Trans. for 1859, p. 91.

[332] See text, p. 527.