simplification of which the calculations are susceptible is effected by supposing that the product u, u,,.. u, has been reduced to its canonical form, viz. +y3+(az+μy)3. Then the differential equation which V must satisfy takes the form

Developing the differential equation and equating the coefficients of the powers and products of x, y in the two sides, we have a series of linear equations for determining the ratios of a: B: y...; from the solution of which it turns out that each of the coefficients of the covariant V is equal to the product of XP μ9, multiplied by a rational integral function of X, μ3, independent of all intermediate powers of λ, p.

On the Involution of Axes of Rotation.

By Professor SYLVESTER, M.A., F.R.S.

After a brief statement as to the most general mode of representing the displace ment of a rigid body in space by means of angular rotations about six distinct axes fixed in position, it was shown that under peculiar conditions the six axes would become insufficient, being, in fact, equivalent to a smaller number, in which case they would be said to form a system in involution. Various constructions for representing such and similar systems were stated, and the remarkable conclusion presented, that the necessary and sufficient condition for three, four, five, or six lines being thus mutually, as it were, implicated and involved consists in their lying in ruled surfaces of the first, second, third, and fourth orders respectively. The theory of involution originated with Prof. Mobius, by whom, however, it had been left in an imperfect condition. The author referred for further information on the subject to some recent notes by himself in the Comptes Rendus' of the Academy of Sciences of Paris, and to certain masterly geometrical investigations of M. Chasles and Mr. Cayley, to which these had given rise.

ASTRONOMY.

On the Almanac. By M. N. ADLER.

In this paper the author gave easy methods for finding, by a direct mental process, the fundamental points requisite in forming the almanac for any year.

Remarks on Dr. Hincks's Paper on the Acceleration of the Moon's Mean Motion as indicated by the Records of Ancient Eclipses. By the ASTRONOMER ROYAL.

The author stated his unaltered conviction that the Tables of Hansen gave the date of the great solar eclipse which terminated the Lydian war, as all the most reliable records of antiquity fixed it, in the year 585 B.C. He said he must first recall to their remembrance some geographical facts, and he sketched on the board a rough plan of Asia Minor, Upper Asia, the Black Sea, and the Mediterranean. An impassable mountain barrier, which the ancients called Mount Taurus, stretches across between Asia Minor and Upper Asia, leaving only two passes at all practicable for an army: one to the north, along the shore of the Black Sea, celebrated for the well-known retreat of the Ten Thousand Greeks, as chronicled by Xenophon, but so extremely difficult that only one army besides had ever traversed it; the other to the south-east of Asia Minor, through which, all the circumstances rendered it highly probable, the invading Assyrian army entered Asia Minor, as it was certain the army of Alexander the Great passed through it in the opposite direction when he invaded Syria, Egypt, and Upper Asia; and every other recorded march between Asia Minor and Upper Asia had been made through the same pass. Now, in the line between this pass and the capital of Lydia it was nearly certain the decisive battle was fought, and calculation from the Tables showed that at the date assigned to the eclipse, commonly called the Eclipse of Thales, because pre

dicted by him, the centre of a total eclipse of the sun actually swept over this district. The Astronomer Royal then explained how Thales was able, by the aid of the Saros, or period of 18 years 15 days and 8 hours, to predict the eclipse; and then, if the previously-observed eclipse at the beginning of this cycle occurred in the morning (which agrees with calculation), the odd 8 hours would ensure that this one would occur in the afternoon (which also agrees with calculation), and the eclipse might really be predicted, as was recorded. He then pointed out how calculation from the same Tables led us to the time and circumstances of the eclipse of Agathocles, when the Grecian fleet escaped out of the harbour of Syracuse; also to the darkness, which, no doubt, was an eclipse, which was stated to have taken place when the Persian army entered Larissa or Nimrud.

On the Resistance of the Ether to the Comets and Planets, and on the Rotation of the latter. By J. S. STUART GLENNIE, M.A.

This paper was an application to the motions of the comets and planets of the following theorem, on the hypothesis, favoured or adopted by Encke and Pontécoulant, of a medium whose resistance is inversely as the square of the distance from the sun. According as the resultant of the resistance to a revolving and rotating body passes or not through the centre of gravity, will it affect the revolution or the rotation of the body.

Some Considerations on M. Haidinger's Communication on the Origin and Fall of Aerolites. By R. P. GREG, F.G.S.

M. Haidinger and Dr. Laurence Smith differ in their opinion as to the cause and origin of the blackish-coloured crust observed in almost all meteoric stones; the latter conceives that they were thus coated previous to their entering the confines of the earth's atmosphere; the former much more reasonably alleges that it has been caused by simple superficial fusion after the meteorite has entered the atmosphere, either by resistance to the air causing heat, or by the superheated air surrounding the stony matter of the fireball itself. Dr. Smith seems to have been misled by circumstances presented on the fall of some very large stones in Ohio, May 1, 1860, which evidently at the time of their fall could not have been very hot. But he seems to have overlooked the fact stated by Haidinger, that in large stones (especially) the internal parts must affect the temperature of interplanetary space, and tend almost instantaneously to efface the very superficial heat caused by the sudden fusing of their exterior.

M. Haidinger and Dr. Smith both agree in thinking that meteorites enter our atmosphere more commonly in groups or "flocks" of small fragments, than as a single and larger mass. This seems to me opposed both to fact and probability. In the case of the celebrated fall of meteoric stones at L'Aigle in Normandy, in 1803, April 26, though it is quite true that nearly 3000 stones fell (the major number not larger than walnuts, and the largest only seventeen pounds), yet we must bear in mind that but one single fireball was seen previously to the bursting and fall of the meteorite. The stones presented irregular shapes, chiefly angular, with the edges slightly rounded, and all similarly covered with a crust. Surely it is more natural to conceive that one large fragment was by explosion and unequal heating broken up into many smaller ones. Moreover, were individual fireballs to contain within themselves numerous small stones, would it not rather militate against M. Haidinger's theory, since the opposing air would then pass between them like a sieve, and the whole notion of the head of the meteorite forcing up before it the film of air that is to curl up behind (to contain the vacuum which on the collapse of the fireball is to cause the noise), would have to be abandoned as untenable.

M. Haidinger's idea that the noise or report is caused by the collapse of the vacuum carried forward in the rear of the fireball deserves attentive consideration, and much might be said in favour of it as well as against it. Besides the possibility of the noise being due to the discharge of electricity, Dr. Smith likewise considers the noise is not caused by the bursting of a solid, but rather by concussion in the atmosphere arising from the rapid motion of the body through it. Mr. Benjamin * But, then, why should we not hear the noise produced by the simple passage of any

Marsh, in his able notice of the great daylight meteor in the United States, November 15, 1859, affirms, however, that the sound following the bursting of that meteor "was explosive, and not caused by the falling in of the air after the meteor, as in the latter case it must have been continuous and interrupted; but the testimony of Dr. Beesley and others shows that it ceased entirely and then began again. Suppose the meteor to have been a stony mass, we may perhaps consider the explosion to have consisted of a series of decrepitations caused by the sudden expansion and heating of the surface. At the forward end these explosions would take place under great pressure, which may account for the loudness of the sound." Again, "the explosions were very numerous, the whole occupying only half a second of time; but the individual sounds were distinguishable because of the different distances they had to travel to reach the ear; the whole duration of the sound extending in reality over a minute."

Though I am inclined to agree to a great extent with Mr. Marsh respecting the cause and effects of the sound being caused by a series of decrepitations taking place, under pressure of the resisting atmosphere, yet that would hardly explain the sadden disruption and disappearance of fireballs, actually occurring in the majority of cases; it would be too gradual a breaking up to accord altogether with facts.

One obstacle in the way of a satisfactory solution arises from the difficulty of ascertaining the real size of an aerolitic fireball, which at the distance of 40 miles or more may appear as large as the moon; for it has been proved that a very small body, such as a small stone, when in a state of powerful incandescence, appears much larger than it really is; e. g., Dr. Smith has himself shown that a piece of lime less than half an inch in diameter, in the flame of the oxyhydrogen blowpipe, has, in a clear evening, appeared at the distance of half a mile to present an apparent diameter equal to twice that of the moon! On the other hand, while this fact seems to afford us facilities for a simple solution, it may still be quite possible that the stony matter is but a nucleus inside a larger envelope of highly compressed and heated air, containing likewise, as Haidinger supposes and explains, the vacuum, which subsequently collapses with a loud report.

It may be here mentioned, that occasionally large meteors (evidently aerolitic) have been seen to divide into two nearly equal portions (a loud detonation following some minutes afterwards), and that both have then passed off again into space without other apparent change*.

It is also equally certain that no noise is heard unless a large fireball actually bursts into two or more considerable portions; and that the principal noise is cer tainly the direct result of this rupture. How such violent noises and atmospheric concussions as take place are produced and also heard and felt on the surface of the earth is strange, and as yet not fully understood: the height at which fireballs thus burst varies from 15 to 40 miles. The cases where stones have fallen from fireballs without noise are very rare indeed.

Dr. Laurence Smith considers the light emitted by fireballs does not arise from mere incandescence, but is caused by electricity and other causes. M. Haidinger speaks of air heated to whiteness. There must, however, be a certain amount of light arising from the incandescence of solid matter, judging from the fused crusts of all aerolites, and from the fact of some meteorites, especially iron ones, being known to fall red-hot; but that at heights of from 20 to 40 or even 100 miles, where the supply of oxygen must be inconceivably small, part of the light may be owing to a development of electricity, seems highly probable.

large meteor? No noise is ever heard unless the entire fireball is ruptured or flies to pieces. Besides, at elevations of 30 or 40 miles the air would be too rarefied to produce much noise from simply rushing into the space left in the wake of the meteorite.

* As was the case with the celebrated meteors of August 18, 1783, in England, and that of July 20, 1860, in North America; which being the fact, goes against M. Haidinger's theory of incandescent air enclosing a vacuum in the rear of the main fireball; for the bursting would, in the cases just cited, probably have destroyed, at least temporarily, their subsequent visible existence. In these two cases it seems most reasonable to suppose that a large stone (several feet in diameter), while in a state of high superficial incandescence, "broke" into two parts with a loud crack or report, the sound of which, under the very great pressure caused by resistance to the atmosphere, would be greatly magnified or in

creased.

In briefly alluding to the origin of meteorites, I consider it now almost universally admitted by the highest authorities, that, mineralogically speaking, aerolites falling to the earth are merely fragments of larger rocks, some of which may be considered to be strictly volcanic: whether stone or iron, they enter our atmosphere as irregular-shaped fragments, which may again become broken into smaller fragments before reaching the surface of the earth. In explaining the original or "nascent" state of meteoric matter as he does, M. Haidinger is simply proposing a new theory to account for the original condition of planetary matter and its consolidation; and whether that was fluid or gaseous, or pulverulent, may perhaps be a step too remote for the present state of aerolitic investigation; though whether their present condition will throw additional light on the physical history of our own earth, or the reverse, I am not prepared at present to say. The idea that meteoric stones are fragments of a larger and broken-up mass of planetary matter, itself originally formed, as I understand it, by the external consolidation, by gravitation, of fine impalpable dust, in the form of an external crust (or series of concentric crusts), internally contracting somewhat after the manner of septaria, and afterwards, from heat, chemical action, unequal expansion, bursting like a projectile filled with explosive material, is certainly a bold idea, and I only regret that M. Haidinger's abstract of his original paper does not more fully give all his facts, comparisons, and arguments. To my own mind, however, the idea of an original state of fine planetary dust is not satisfactory; for dust rather implies the notion of waste, or wear and tear of matter already previously consolidated.

However originally formed, our meteoric planet may in the course of time be supposed from some cause or other to become broken up into fragments more or less dispersed, and occasionally, in the form of aerolites, to come into contact with our own earth. This may be all the more probable, when I add that I hear that M. Leverrier has quite recently come to the conclusion that there exists "a mass of matter equal to about th of the mass of the earth revolving round the sun at very nearly the same mean distance as the earth, and which is probably split up into an immense number of small asteroids." (See Monthly Register of Facts for August 1861.)

The structure, composition, and specific gravity of meteorites agree very closely with that of similar rocks on our own globe; and it may not be unreasonable to suppose that the former are representatives of that mysterious planetary matter, of whose aggregate mass M. Leverrier has just informed us, and which in the course of ages, at the rate of several thousand tons annually, may eventually be all absorbed, as Reichenbach has suggested, by our own earth.

An attempt to account for the Physical Condition and the Fall of Meteorites upon our Planet. By W. HAIDINGER, Hon. Mem. R.S. L. & E., H.F.R.G.S., F.F.G.S., H.M. SS. of Cambridge, Manchester, Edinburgh, Truro, &c.

I beg leave to lay before the British Association for the Promotion of Science, the outline of some considerations which have been impressed on my mind during late studies in this most interesting department of physical science, and one which is still involved in many difficulties and contradictions.

In order to give a more general view of the present state of progress, I mention the names of some of the more active promoters of the science in our own days. The Imperial Collection at Vienna, which took the lead under v. Schreibers and Partsch, is still foremost under Dr. Hörnes, but closely followed by Prof. Shepard in New Haven; Baron Reichenbach in Vienna; the British Museum under the enlightened superintendence of Mr. Nevil Story Maskelyne; Prof. Gustavus Rose in Berlin; Prof. Wöhler in Göttingen; Mr. R. P. Greg in Manchester,-each possessing from 100 to 163 meteorites with distinct dates of fall or discovery; to the labours of the above-named, add also those of Rammelsberg, Laurence Smith in Louisville, Kentucky, O. Buchner in Giessen. The recent remarkable falls of aerolites near New Concord, and in Guernsey County, Ohio, on the 1st of May, and near Dharamsala, Kangra, Punjab, on the 14th of July, both in 1860, the

The iron masses that occasionally fall are supposed by M. Haidinger very reasonably to have originally existed as veins in the original meteoric planet.

large iron masses brought to light near Melbourne in Australia, and other facts full of interest, are keeping alive the attention of philosophers.

Having joined my excellent friend Dr. Hörnes in the wish to enlarge our Imperial Collection of aerolites, I have from time to time had to give notice of several newly observed facts, and at each step to endeavour to account for some one or other peculiarity. As a result, it seemed to me that I had arrived at a pretty complete theory both of the circumstances attending the fall of meteorites, and the conditions of their consolidation before they entered our atmosphere.

Explanations relative to the telluric fall of aerolites, though more known than formerly, are still not devoid of many difficulties; but these are far surpassed by the difficulties attending the cosmic question, which in fact amount to nothing less than a complete theory of the original formation of celestial bodies generally, at least of the two which come into contact with each other, the aerolite and our own planet. I beg leave to begin with some considerations on the first of these questions.

1. The Phenomena of the Fall of Aerolites.-There can be no doubt relative to the fact that the crust of aerolites, and their body or mass, are formed in two different ways, the one by superficial melting, the other by long-continued consolidation. The form of aerolites betrays them originally to have been fragments. This is most universally granted. In this direction Sir David Brewster and Humboldt gave their verdicts; this also has been placed forward by Laurence Smith and Mr. Greg. "Viewed from most positions, the largest meteoric stone (that of 103 lbs. weight, in Marietta College, Ohio, from the fall of May 1st, 1860) is angular, and appears to have been recently broken from a larger body." Many other examples might be adduced.

Fig. 1.

N.

N.E.

E.

S.E.

S.

Z.

60°

It is well known that in some cases, as at Strakowitz, on November 28th, 1859, and Pegu, December 27th, 1827, the semblance of enlarging and approaching aerolitic fireballs has been observed and described. In these cases the altitude and geographic orientation should be carefully inscribed in a diagram like Z. fig. 1, in order to be able, by comparison with the exact time of hour, day, and year, to find the region from whence 60° they travelled to meet our earth. AB (fig. 1) would be the track of a meteor arriving from an altitude of 75° in the N.N.E., and exploding or extinguished at an altitude of about 40°, while C D might denote a meteor that seemed to travel horizontally from 45° N.E. to 45° H. S.E., its true course being from N. to S., but visible from the side. Observations from several distinct places, when combined together, will allow the real track to be ascertained with considerable accuracy. This was finely exemplified in the Ohio fall of May 1, and in the grand meteor of July 20th, 1860, of Elmira, Long Island, and other places in the United States.

300

N.

B

N.E.

E.

S.E.

30°

F

H.

S.

Viewed from a distance, there is an impression on the eye of a fireball, sometimes more or less lengthened, or ending in a sharp pointed tail, and moving with amazing velocity. When viewed very near, aerolites have been seen to fall down like any other stone, and with no greater velocity.

The velocity of meteors varies from 20 to upwards of 140 miles (4 to 233 German miles), according to joint observations of Julius Schmidt at Bonn (now at Athens), Heis at Aix la Chapelle, and Houzeau at Mons, as recorded in Humboldt's 'Cosmos.' This wonderful velocity may be compared with that of phenomena familiar to us upon our own planet. Commander M. F. Maury, U.S., quotes from Sir John Herschel's article "Meteorology" in the Encyclopædia Britannica,' 1857, the velocity of 92 English miles in an hour for a "Devastating Hurricane," or only 134.9 feet in one second of time, with a horizontal pressure of 379 lbs. to a square foot. The following data are given in Rouse's Anemometric Tables in the Report of the Tenth Meeting of the British Association, &c., at Southampton, in September 1846. (London, 1847, p. 344) :—