Extracts from the letter of my friend, Sira Sigurður Gunnarsson, the priest of Hallormstað, addressed to the "Norðanfari" of April 24, appeared in the "Times" of July 1, 1875. It is dated March 29, 1875, and headed "Fall of Pumice and Ashes in Múlasýla.” The author, I may remark, has more than once visited the Vatnajökull. The following interesting details may be added to the abstract :-" During the Yule of 1873, and in early 1874, an earthquake shook the eastern regions, after which the people of the Fjöll country saw two tall pillars of thick smoke apparently proceeding from the Askja or Dyngjufjöll; and viewed from Hallormstaðarháls they rose at a considerable distance from each other. Early in the year there was no fire in the Mý-vatnsöræfi, and the earthquake became less violent towards the end of the winter." After noticing the thunderings and the ash and pumice rain of March 29 (Easter Monday) reported in the "Times," my reverend friend continues:-"The movement appears to have taken place in the southern part of the Dyngjufjöll, westward of Herðubreið, and a short way north of the winter Gjá. The direction of the ashes was on both sides of a line to Mödrudal and Fossvellir, as far as the Unáos in Hjaltarstaðarthingá and the Vatnsdalsfjall. Another shower, travelling from west to east, and extending four (Danish) miles, fell at Brú, and a mile and a half east of Aðalbol (Rrafnkelsdal), Kleif (Fljótsdal), Skriðdal, and as far as Fáskruosfjörð to the south-east. The amount which fell east of that line in Breiðdal and Stöðvarfjörð was trifling. If we draw one straight line from the focus of the eruption eastward between Fáskrúðs and Stöðvarfjörð, and a second from Vatnsdalsfjall near Njarðvik, also to the east, the area upon which the ashes and pumice rained would hardly be less than 100 square miles. Also assuming the average depth of the layer at 3 inches, we must assign to the discharge of March 19 a weight of 3840 tons."

"It is reported that the ash showers have ruined twenty farms in the Jökulsdal (between the Lagarfljót and the eastern Jökulsá) and in the northern Múla Sýsla, where the owners are preparing to abandon their property. The position of the Fljótsdalshèrad, where the scoriaceous rains fell thickest, are the Jökulsdal, Fell, Fljóstdal, Skogar, Skriðdal, Vellir, and Eyðathinghá. Heavy and terrible showers also desolated Norefjörð, Reyðarfjörð, Mývafjörð, and

Loðmundarfjörð. Where the land has abundance of water, as in parts of Skriðdal, Vellir, and Eyðathinghá, the farmers hope that the ashes will disappear during the spring, and that they will be dissolved by the rains." This interesting letter concludes with an exhortation "not to abandon the holdings for good," and with excellent advice about the measures to be taken. Yet it owns that "from this fearful visitation all husbandry in the east country must come to utter ruin," and the less Icelanders are advised not to emigrate the better for the island.

The writer of "An Appeal for Iceland" ("Times," July 1, 1875), compares this mild and harmless eruption, which has not destroyed a single life, with the terrible convulsions of 1783, which killed some 14,000 human beings. He also calculates the destruction of pastures to the extent of 2500 to 3000 square miles, while popular computations make 4000 square miles the habitable area of Iceland.

According to Páll Pálsson only four farms on the west of the Jökulsá have suffered severely. These are, going from south to north, Brú, Eyrikstaðir, Hákonarstaðir, and Arnórstaðir. Herra Thórður Gudjónsson, factor at Húsavík, never even heard of the eruption till I showed him the nepawspers. Finally, the brown shadings in my chart, marking the eastern and north-eastern limits of the ash showers, and copied from an Iceland map obligingly lent to me by my friend, Mr Robert Mackay Smith, may be allowed to prove that the damage extends over a small area.

Mr Jón A. Hjaltalín, of the Advocate's Library, Edinburgh, received (June 26) trustworthy accounts of the ash and pumice rain. "It extended over several parts of Norður Múlasýsla and Suður Múlasýsla, depositing a layer about 1 inches thick. In some places the winds have carried it off, but sundry parishes will be unable to keep their live stock at home this summer. Next hot season, however, it is expected that the pastures will be all right."

Mr W. L. Watt, who has just ridden over the ground, found the pumice and ashes beginning about the middle course of the Svartá (N. lat. 64° 50′), and extending northwards to Herðubreið (65° 10′), or a total depth of 20 to 25 miles, bounded eastward by the Jökulsâ, where the country is not, and never has been, habited by man.

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The limits of this paper do not permit me to enter into all the details of the last eruption in Iceland; but the reader may be assured that the outline and the main features of the subject are correctly drawn.

The following Gentlemen were elected Fellows of the Society:

BRUCE AILAN BREMNER, M.D.

Rev. FRANCIS EDWARD BELCOMBE.

SIR WILLIAM THOMSON, President, in the Chair.

The following Communications were read:

1. Vortex Statics. By Sir William Thomson.

(Abstract.)

The subject of this paper is steady motion of vortices.

1. Extended definition of " steady motion." The motion of any system of solid or fluid or solid and fluid matter is said to be steady when its configuration remains equal and similar, and the velocities of homologous particles equal, however the configuration may move in space, and however distant individual material particles may at one time be from the points homologous to their positions at another time.

2. Examples of steady and not steady motion :

(1.) A rigid body symmetrical round an axis, set to rotate round any axis through its centre of gravity, and left free, performs steady motion. Not so a body having three unequal principal moments of inertia.

(2.) A rigid body of any shape, in an infinite homogeneous liquid, rotating uniformly round any, always the same, fixed line, and moving uniformly parallel to this line, is a case of steady motion. (3.) A perforated rigid body in an infinite liquid moving in the

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manner of example (2.), and having cyclic irrotational motion of the liquid through its perforations, is a case of steady motion. To this case belongs the irrotational motion of liquid in the neighbourhood of any rotationally moving portion of fluid of the same shape as the solid, provided the distribution of the rotational motion is such that the shape of the portion endowed with it remains unchanged. The object of the present paper is to investigate general conditions for the fulfilment of this proviso; and to investigate, farther, the conditions of stability of distribution of vortex motion satisfying the condition of steadiness.

3. General synthetical condition for steadiness of vortex motion. The change of the fluid's molecular rotation at any point fixed in space must be the same as if for the rotationally moving portion of the fluid were substituted a solid, with the amount and direction of axis of the fluid's actual molecular rotation inscribed or marked at every point of it, and the whole solid, carrying these inscriptions with it, were compelled to move in some manner answering to the description of example (2). If at any instant the distribution of molecular rotation* through the fluid, and corresponding distribution of fluid velocity, are such as to fulfil this condition, it will be fulfilled through all time.

4. General analytical condition for steadiness of vortex motion. If, with (§ 24, below) vorticity and "impulse," given, the kinetic energy is a maximum or a minimum, it is obvious that the motion is not only steady, but stable. If, with same conditions, the energy is a maximum-minimum, the motion is clearly steady, but it may be either unstable or stable.

5. The simple circular Helmholtz ring is a case of stable steady motion, with energy maximum-minimum for given vorticity and given impulse. A circular vortex ring, with an inner irrotational annular core, surrounded by a rotationally moving annular shell (or endless tube), with irrotational circulation outside all, is a case of motion which is steady, if the outer and inner contours of the

* One of the Helmholtz's now well-known fundamental theorems shows that, from the molecular rotation at every point of an infinite fluid the velocity at every point is determinate, being expressed synthetically by the same formulæ as those for finding the "magnetic resultant force" of a pure electro-magnet. ―Thomson's Reprint of Papers on Electrostatics and Magnetism.