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netic, and has a specific gravity of 2.3636 at 25° C. The lava-bed, although its course was a very short one, nevertheless had a surface-temperature of 70°, whilst at the depth of half a metre it had a temperature of 90°; and the temperature increases at the points where the secondary phenomena are found. The outward manifestations of the eruption at the date of which I write may be said. to be over, since the mouth of the new crater and the thirty-five eruptive openings of the chasm, though they are still open, only emit a small quantity of vapour, now in an increasing, now in a decreasing quantity, similar to that observed in the great central crater. The activity observed in the central crater from the end of May to the latter days of August, when the eruption broke out, has now quite ceased. This sudden paroxysm of Etna, which in such a short time (in less than a day) has left the mark of a formidable eruption, has furnished us with a curious fact in the special history of our volcano. It was known that from the chief crater, in consequence of its elevation of 3314 metres above the sea, there could only be eruptions of short duration; but it was also known that if the volcanic force reached such a degree of intensity as to produce a lateral outbreak, the eruptions that followed would probably be of long duration, as they had been formerly in this and in preceding centuries, similar to those which usually happen in Etna at intervals of ten or twelve years. How can we then explain the cessation of the recent phenomenon? If upon such a subject an opinion may be given which likewise goes to explain the occurrence of earthquakes permanently which agitated the ground after the eruptive activity had ceased, I would suggest that the violent shock felt on the N.N.E. side of the mountain may have created an outlet extensive and deep enough for the lava breaking forth from the axis of eruption at Mongibello to find a more easy channel into subterranean caves and channels than to be forced more slowly out to the surface.

This idea would be confirmed by seeing all the preparation for an eruption with the thirty-five mouths remaining inactive, though open and smoking, and by hearing in their immediate neighbourhood a deep noise as of a flowing subterranean mass. It would also tend to support the theory which maintains that the cause of earthquakes is the completion of some subterranean eruption, if we may so designate a movement of fluid and gaseous matter in the interior of the earth.

Such a conjecture would perfectly agree with the phenomenon of the shocks which occurred when the outward flow of the eruption continued nearly in full force; for it is generally the case

This theory is also maintained by Sig. Rudolph Falb, of Vienna, who after my prophecy of July came to stay near Etna to observe the new eruption.

in eruptions elsewhere that the outward flow of the lava ceases when the shocks are felt.

It suffices to mention the earthquakes which agitated the eastern side of Etna when the external manifestations of the eruption of 1865 had just ceased, specially that terrible one in the neighbourhood of Giarre, which destroyed the village called Fondo Macchia. These earthquakes gradually decreased in number and intensity in the direct ratio which is observed in the movement of the lava in an eruption, which by gradually checking itself soon ceases altogether. The eruptive apparatus, still hot and smoking and placed thus along an abyss of lava, we must believe will now remain inactive, and that a great eruption is not to be expected as imminent; since it seems strange to admit that when the intensity of the volcanic force has reached the point of creating this imposing apparatus, it should then have chosen to interrupt its course after a few hours' eruption, in order to resume it again afterwards. The truth is more probably, as I have said, that in the dislocation and breaking up of the consolidated strata of the mountain the mass of lava has found a way of penetrating more quietly into the caverns of the earth, deviating from the axis of eruption, and deriving its mechanical force from the gases and vapours, from which in time it may acquire such dynamic energy as to cause explosions capable of driving it out to the surface with the ordinary phenomena of eruption.

It is very probable that a future eruption of Etna, when it takes place, will happen on the side of the mountain already opened, where certainly the lava will find less difficulty in coming to the surface.

This last eruption of Etna has enriched the history of volcanoes with a new and important page, and the appearance of this preparation for a great eruption which remains inactive is of interest in the annals of volcanic science. It remains quite unchanged by any emission of volcanic matter, but, remaining fully open, seems to give material testimony to the fact of nature having been surprised and disturbed in one of her great operations. Indeed any one who may wish to form a clear idea of how an explosion in a great volcano, outside of the central crater, begins, and by means of what mechanism it is completed, can now visit and observe with attention the interesting localities of the eruption of August 1874.

This disturbance of Etna which we have described is not an isolated one in the Italian volcanic system.

In the nearest island of Vulcano, after a century's inactivity, a new abyss opened in the large crater nine months before the eruption of Etna (from the 20th of September to the 20th of October, 1873). This was accompanied by an eruption of

netic, and has a specific gravity of 2.3636 at 25° C. The lava-bed, although its course was a very short one, nevertheless had a surface-temperature of 70°, whilst at the depth of half a metre it had a temperature of 90°; and the temperature increases at the points where the secondary phenomena are found. The outward manifestations of the eruption at the date of which I write may be said to be over, since the mouth of the new crater and the thirty-five eruptive openings of the chasm, though they are still open, only emit a small quantity of vapour, now in an increasing, now in a decreasing quantity, similar to that observed in the great central crater. The activity observed in the central crater from the end of May to the latter days of August, when the eruption broke out, has now quite ceased. This sudden paroxysm of Etna, which in such a short time (in less than a day) has left the mark of a formidable eruption, has furnished us with a curious fact in the special history of our volcano. It was known that from the chief crater, in consequence of its elevation of 3314 metres above the sea, there could only be eruptions of short duration; but it was also known that if the volcanic force reached such a degree of intensity as to produce a lateral outbreak, the eruptions that followed would probably be of long duration, as they had been formerly in this and in preceding centuries, similar to those which usually happen in Etna at intervals of ten or twelve years. How can we then explain the cessation of the recent phenomenon? If upon such a subject an opinion may be given which likewise goes to explain the occurrence of earthquakes permanently which agitated the ground after the eruptive activity had ceased, I would suggest that the violent shock felt on the N.N.E. side of the mountain may have created an outlet extensive and deep enough for the lava breaking forth from the axis of eruption at Mongibello to find a more easy channel into subterranean caves and channels than to be forced more slowly out to the surface.

This idea would be confirmed by seeing all the preparation for an eruption with the thirty-five mouths remaining inactive, though open and smoking, and by hearing in their immediate neighbourhood a deep noise as of a flowing subterranean mass. It would also tend to support the theory which maintains that the cause of earthquakes is the completion of some subterranean eruption*, if we may so designate a movement of fluid and gaseous matter in the interior of the earth.

Such a conjecture would perfectly agree with the phenomenon of the shocks which occurred when the outward flow of the eruption continued nearly in full force; for it is generally the case

*This theory is also maintained by Sig. Rudolph Falb, of Vienna, who after my prophecy of July came to stay near Etna to observe the new eruption.

in eruptions elsewhere that the outward flow of the lava ceases when the shocks are felt.

It suffices to mention the earthquakes which agitated the eastern side of Etna when the external manifestations of the eruption of 1865 had just ceased, specially that terrible one in the neighbourhood of Giarre, which destroyed the village called Fondo Macchia. These earthquakes gradually decreased in number and intensity in the direct ratio which is observed in the movement of the lava in an eruption, which by gradually checking itself soon ceases altogether. The eruptive apparatus, still hot and smoking and placed thus along an abyss of lava, we must believe will now remain inactive, and that a great eruption is not to be expected as imminent; since it seems strange to admit that when the intensity of the volcanic force has reached the point of creating this imposing apparatus, it should then have chosen to interrupt its course after a few hours' eruption, in order to resume it again afterwards. The truth is more probably, as I have said, that in the dislocation and breaking up of the consolidated strata of the mountain the mass of lava has found a way of penetrating more quietly into the caverns of the earth, deviating from the axis of eruption, and deriving its mechanical force from the gases and vapours, from which in time it may acquire such dynamic energy as to cause explosions capable of driving it out to the surface with the ordinary phenomena of eruption.

It is very probable that a future eruption of Etna, when it takes place, will happen on the side of the mountain already opened, where certainly the lava will find less difficulty in coming to the surface.

This last eruption of Etna has enriched the history of volcanoes with a new and important page, and the appearance of this preparation for a great eruption which remains inactive is of interest in the annals of volcanic science. It remains quite unchanged by any emission of volcanic matter, but, remaining fully open, seems to give material testimony to the fact of nature having been surprised and disturbed in one of her great operations. Indeed any one who may wish to form a clear idea of how an explosion in a great volcano, outside of the central crater, begins, and by means of what mechanism it is completed, can now visit and observe with attention the interesting localities of the eruption of August 1874.

This disturbance of Etna which we have described is not an isolated one in the Italian volcanic system.

In the nearest island of Vulcano, after a century's inactivity, a new abyss opened in the large crater nine months before the eruption of Etna (from the 20th of September to the 20th of October, 1873). This was accompanied by an eruption of

cinders and burning matter, together with flames, rumbling, and earthquakes. These phenomena, which had a gradually decreasing course, lasted through all the month of July 1874; and traces of them still remain.

Stromboli also in June last had an unusual eruption, being violently agitated, and throwing out stones as far as the inhabited district which lies underneath it, showing much greater activity than in the little explosions every two or three minutes which characterize its usual action. It seems that Vesuvius also has not remained indifferent to all this; and I saw myself from its crater, as well as from that of Stromboli, a remarkable and unusual amount of thick smoke coming out at the same time that the eruption of Etna took place.

XVII. On Primary Forms.

1.

By Sir JAMES COCKLE, F.R.S., Corresponding Member of the Literary and Philosophical Society of Manchester, President of the Queensland Philosophical Society, &c.*

COMPARING P.

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p. 428 of Boole's 'Differential Equations' (1865), and pp. 184 and 190 of the Supplement, with a citation in Mr. Harley's recent paper "On the Theory of Differential Resolvents" (which purports to be reprinted from the Report of the British Association for 1873), it seems to me that Boole did not always use the term primary in the same sense. By primary I mean integrable, but not through Boole's reductions. By a factorial substitution I mean a change of y into Xy, where X is a function of x. By taking the criticoid of a biordinal I mean reducing its middle term to zero and dividing the equation so transformed by the coefficient of its first term. This criticoidal transformation is effected by factorial substitution, not by change of the independent variable. By the equation of the casura, or briefly the caesura, I mean an equation derived from a given equation by expunging its last term and diminishing by unity the indices of the differential coefficients.

2. The regular forms, as we may term those solved through Boole's reductions, are of two descriptions. In one factors are preserved which in the other are lost. The first description of binomial biordinal may be written

where

-

{(A—2m) (A-1) — (▼ +2n) (▼ − 1)x2 }y=0, . (1)

A=D+B and y=D+a.

* Communicated by the Rev. Robert Harley, F.R.S.

† As to this user of the term criticoidal, see my paper "On Hyperdistributives" (Phil. Mag. for April 1872) and the papers connected therewith.

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