First, let us suppose that the ice is obtained at the expense of the sea; in other words, suppose that the quantity of ice at the south pole, when the north is under glacial conditions, is the same as at present. The cap extends to lat. 35°, where, by Archdeacon Pratt's law, it will be 3290 feet thick. Calling the earth's surface 1, this area will be 0.2132; and if three-fourths of the remainder, or 59, be sea, & the depression of the sea, h' the mean thickness of the ice-cap, then

=

The total quantity of ice forming the cap is Tax h× cos2 lat., which, taken from lat. 35° to the pole, Ta2 xhx 0.671, whence I deduce the mean thickness h'=h× 0.787.

If we take h=7000 feet, the assumption of Mr. Croll and of Archdeacon Pratt, h=5500 feet, and 81833 feet. Archdeacon Pratt has shown that a thickness of 7000 feet at the pole would produce an elevation of the sea equal to 1000 feet at lat. 60°; and as it appears that the drain on the sea would lower it 1833 feet, the result is a depression of 833 feet.

Let us now suppose that all the ice is supplied by the melting of that at present in south latitudes. The quantity required to produce a submergence of 2300 feet is

7000
1000

× 2300, or 16,100 feet of ice at the pole, which, by Archdeacon Pratt's law, will be thinned out to 5300 feet at lat. 35°.

Sir James Ross sailed for hundreds of miles east and west in latitudes higher than 70°. The ice-barrier in lat. 76° and 78° was under 200 feet. The valleys near Mount Herschel are said to be filled with snow several hundred feet thick. If we allow all the Antarctic regions down to lat. 70° to be covered by a uniform cap of ice 2000 feet thick, I think it will be admitted that this is an exaggerated estimate of the existing ice. A simple calculation will show that such a cap, covering, as it does, only 0-06 of the surface of the globe, would not supply the twentieth part of the ice required.

It appears to me, therefore, that this theory, however tempting, must be abandoned.

As the quantity of ice to be supplied by the melting of that at the south pole is so greatly disproportionate to its object, it is unnecessary to discuss what appears to me to have been too lightly assumed―viz. that when one pole is under glacial conditions, the opposite will be entirely free from ice.

Phil. Mag. S. 4. Vol. 31. No. 210. May 1866.

2 C

LV. On the Change of Eccentricity of the Earth's Orbit regarded as a Cause of Change of Climate. HAUGHTON, F.R.S.

By the Rev. SAMUEL

To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN,

IN

N the January Number of the Philosophical Magazine an interesting paper is published by Mr. James Croll on the Connexion of the "Glacial Epoch" with the Eccentricity of the Earth's Orbit, founded on Leverrier's Mémoire sur les variations séculaires des éléments des orbites pour les sept planètes principales, Mercure, Vénus, la Terre, Mars, Jupiter, Saturne et Uranus (Paris 1843), 8vo.

In this memoir M. Leverrier calculates and gives a graphical representation of the eccentricity of the earth's orbit for 100,000 years before the epoch January 1, 1800; from which it appears that the unit of 10,000 years is sufficiently large to develope the law of change, as the eccentricity in 100,000 years attains two maxima and two minima ranging from 0-0473 to 0.0040, or nearly in the proportion of 12 to 1. Under these circumstances it seems to me that Mr. Croll's assumption of the unit of 50,000 is not only unnecessary, but that it tends to mask the real law of change of eccentricity.

With regard to another and more important point, Mr. Croll's paper appears open to objection. He fixes the times of greatest cold at the times of maximum eccentricity, and infers the existence of two glacial epochs; one 200,000 years before A.D. 1800, when the eccentricity was 0.0569, and the other ranging from 950,000 to 750,000 years before the present epoch, with three maxima of eccentricity, viz. 0.0517, 0·0747, and 0.0575. The following are Mr. Croll's words :

"We have already stated it as our opinion that the glacial epoch of the geologist was the period beginning about 240,000 years ago and extending down till about 80,000 years ago ('Reader,' October 14, December 2 and 9). The time of the greatest cold would be about 200,000 or 210,000 years ago.

"It will be seen from an inspection of the Table that the next glacial epoch prior to this occurred about 750,000 years ago. At that time the eccentricity was exactly equal to what it was 210,000 years ago. Going back 50,000 years further, we find the eccentricity to be only 0.0132. But 50,000 years still further back, viz. 850,000 years ago, the eccentricity almost reached its superior limit. It is quite possible that this, and not 200,000 years ago, may have been the period of the boulder-clay. Pro

but at the period 950,000 years ago it reached the high value of 0.0517. Here we have three glacial epochs following each other in close succession or rather, we should say, one long glacial epoch of about 250,000 years broken up by two mild periods 100,000 years apart."

The foregoing conclusions are irreconcileable with the opinion commonly held by astronomers, that the quantity of heat received from the sun annually increases with the increase of the eccentricity; so that the periods selected as glacial epochs by Mr. Croll are probably nearer the times of maximum heat, so far as this is dependent on the eccentricity of the orbit.

The following demonstration of the law, "That the quantity of heat received per annum from the sun varies inversely as the minor axis of the orbit," may be of use to some of your junior readers :

:

1

(2)

If we expand in terms of e, we shall have

From this expression, neglecting powers of e higher than its square, we find that the minimum amount of heat is received when the orbit is a circle, and that the excess above this minimum varies as the square of the eccentricity.

If the eccentricity of the earth's orbit have a real influence in producing glacial epochs, it would appear from M. Leverrier's calculations that it should be sought for in the future, and not in the past; for at about 24,000 years after A.D. 1800, the eccentricity of the earth's orbit will attain a smaller minimum than usual, and the heat receivable from the sun will be less than at any period within 100,000 years before the epoch. It may be useful here to reproduce M. Leverrier's Table.

In round numbers, during these 130,000 years, the eccentricity varied from 0.05 to 0.005; therefore its square varied from 1 0.0025 to 0.000025, or from to 400 40,000

1

In equation (3) unity represents the total annual heat received from the sun when the earth's orbit is circular, and e2 represents on the same scale the increment due to eccentricity; hence the total heats per annum received at the epoch 100,000 before A.D. 1800, and receivable at 25,000 after A.D. 1800, are to each other as

or as 80,100 to 80,001, showing an amount of change of between the epochs.

This change of quantity of heat is very considerable, and capable of producing important results; but whether it is capable of producing a so-called "glacial epoch" would be difficult to say. I am, yours respectfully,

Trinity College, Dublin,
April 16, 1866.

SAMUEL HAUGHTON.

LVI. Note on Dr. Siemens's Paper "On the Question of the Unit of Electrical Resistance." By A. MATTHIESSEN, F.R.S.*

IT

T is not my intention to open a discussion on this subject, as it has already been fully entered upon in the Reports of the British Association for 1862-64. I will, however, point out

*On applying to the Editor of the Philosophical Magazine to insert this Note in answer to the paper which appeared in Poggendorff's Annalen, No. 2, 1866, he informed me that he had received from the author a translation of it for insertion in the present Number, and that therefore the

some of the mistakes which Dr. Siemens has made in his paper, probably owing to his not having carefully read the Reports and papers he criticises.

Page 327, Dr. Siemens states, "I am rather surprised that Dr. Matthiessen should have observed in German silver marked changes within short periods of time, as I have always found this alloy remarkably constant." In the Report of 1863 (p. 126) I point out that although the conducting-power of the German silver experimented with altered, yet this is no proof that all German silver will do so. Again, in Report for 1864 (p. 347), it is remarked, "A somewhat capricious change has been observed in certain annealed German-silver wires, while others have been proved constant [referring to my experiments in Report of the same year, p. 352]. This result has been independently observed by other members of the Committee."

Page 327, Dr. Siemens states, "It is true Dr. Matthiessen brings forward an argument in favour of the electrical permanency of an alloy of silver and gold-in which I can scarcely suppose him to be serious: it is, that we have never found a gold chain to become brittle." In the Report for 1862 (p. 149), the passage referring to this will be found in that part of the Report where we discuss the effects of homogeneity and molecular condition on the gold-silver alloy as a means of reproducing standards, and is as follows:-"It has been argued that the molecular condition of all alloys is liable to undergo a change by age, and that therefore alloys are not fit to be used as standards. Thus it is well known that brass and German silver become brittle and crystalline by age, and that the same may occur with the gold-silver alloy; but on looking at the composition of the alloy, it will be found to have nearly the same as that of the gold chains of commerce. Now we do not know of a single instance where such a chain, even after years of use, becomes brittle or crystalline by age; so that we think it more than possible that the alloy will not change its molecular condition by age."

Page 328, Dr. Siemens states, "On this ground it is certainly significant that the Committee should have made ten normal measures instead of one single one, even supposing them to agree with each other to within 003 per cent., as asserted." Dr. Siemens should have added after the words within 0.03 per cent., at 15°.5, and are equal to one another at some temperature stated on each coil, lying between 140.5 and 16°5 C.*

With regard to my assertion †, that no true mercury unit has Proceedings of the Royal Society, No. 74, p. 160. The translation of paper (Poggendorff's Annalen, vol. cxxvi. p. 369) is afterwards quoted by Dr. Siemens.

this

Phil. Mag. May 1865, p. 364. Poggendorff's Annalen, vol. cxxv. p. 91.