POLAR ICE-CAPS

INFLUENCE IN

AND THEIR

CHANGING

SEA LEVELS.

[Being Paper read before the Geological Society of Glasgow, February 16, 1888.]

THE subject I have to speak about this evening is not exactly geological. I may say that the immediate proposal to lecture on such a subject is to be found in an extract which I shall read to you from Dr. Croll's book on Climate and Time. In chaps. xxiii., xxiv., of this volume Mr. Croll deals with the physical causes of the submergence and emergence of land during the glacial epoch, and he has given some very curious, while at the same time mathematically correct, explanations of the effects due to a certain assumed displacement of ice from one hemisphere to the other. After

loyally calling attention, in his opening words, to the fact of his having been anticipated by M. Adhémar, (in a work Révolutions de la Mer,) in the suggestion of heaped-up ice being a probable cause of the submergence and emergence of land, Mr. Croll proceeds to investigate the probable effect of an ice-cap of a given description. In this connection Mr. Croll refers to an article on the subject published by him in the Reader for January 13, 1866, and the extract which I will now read to you from this volume, Climate and Time (pp. 372-374), consists of a note written by myself, at Mr. Croll's request, in regard to the objection brought forward in that article:

"Mr. Croll's estimate of the influence of a cap of ❝ice on the sea level is very remarkable in its rela"tion to Laplace's celebrated analysis, as being "founded on that law of thickness which leads to "expressions involving only the first term of the "series of 'Laplace's functions,' or 'spherical har"monics.' The equation of the level surface, as "altered by any given transference of solid matter, "is expressed by equating the altered potential

"function to a constant. This function, when ex"panded in series of spherical harmonics, has for "its first term the potential due to the whole mass supposed collected at its altered centre of gravity. "Hence a spherical surface round the altered centre "of gravity is the first approximation in Laplace's "method of solution for the altered level surface. "Mr. Croll has with admirable tact chosen, of all "the arbitrary suppositions that may be made "foundations for rough estimates of the change of

'sea level due to variations in the polar ice-caps, "the one which reduces to zero all terms after the "first in the harmonic series, and renders that first "approximation (which expresses the essence of the result) undisturbed by terms irrelevant to the "great physical question.

"Mr. Croll, in the preceding paper, has alluded "with remarkable clearness to the effect of the

change in the distribution of the water in increasing, by its own attraction, the deviation of "the level surface above that which is due to the

"given change in the distribution of solid matter.

The remark he makes, that it is round the centre

VOL. II.

Y

of gravity of the altered solid and altered liquid

“that the altering liquid surface adjusts itself

expresses the essence of Laplace's celebrated "demonstration of the stability of the ocean, and suggests the proper elementary solution of the "problem to find the true alteration of sea-level "produced by a given alteration of the solid. As 'an assumption leading to a simple calculation, "let us suppose the solid earth to rise out of the "water in a vast number of small flat-topped "islands, each bounded by a perpendicular cliff, "and let the proportion of water area to the whole "be equal in all quarters. Let all of these islands "in one hemisphere be covered with ice, of thick"ness according to the law assumed by Mr. Croll

—that is varying in simple proportion to the sine

of the latitude. Let this ice be removed from the "first hemisphere and similarly distributed over the "islands of the second. By working out according "to Mr. Croll's directions, it is easily found that "the change of sea-level which this will produce "will consist in a sinking in the first hemisphere “and rising in the second, through heights varying

66

according to the same law (that is, simple propor"tionality to sines of latitudes), and amounting at

"each pole to

(I-w)it

I- ωτο

"when t denotes the thickness of the ice-cap at the “pole, i the ratio of the density of ice, and w that "of sea-water to the earth's mean density; and w "the ratio of the area of ocean to the whole

"t

surface.

2/3, and

Thus, for instance, if we suppose ∞ = 2,

=

6,000 feet, and take 1/6 and 1/5 as the "densities of ice and water respectively, we find "for the rise of sea-level at one pole, and depression “at the other,

"or approximately 320 feet.

“I shall now proceed to consider roughly what "is the probable extent of submergence which, "during the glacial epoch, may have resulted from "the displacement of the earth's centre of gravity

Y