It has been fuppofed that the number of equations that have equal roots is but fmall, and confequently, that the chief ufe of the rules for finding their roots, is to obtain limits and approximations to the roots of equations in general. That ufe, it must be allowed, were it the only one, is fufficient to repay the labour of inveftigating them; but if the equations that have equal roots fhould hereafter be found not fo few as has been generally fuppofed, the ufe of Mr. Hellins's theorems will become more extenfive.

The concluding paragraph, as it fuggefts that Mr. Hellins has other improvements by him in this branch of fcience, we will give in his own words. "I beg leave to add, that this fhort effay is but a fmall part of a work, in which, if I ever fhould have leifure to put a finishing hand to it, fomething more on this fubject may very poffibly appear. In the mean while, I hope, this little piece will be candidly viewed by thofe who have more leifure and better abilities for ftudies of this kind." We heartily with Mr. Hellins leifure to finish his work; and fhall difinifs this article with obferving, that by the title of his paper, it appears that Mr. Hellins's proviñon is a curacy; we cannot but lament that fcience and ingenuity has found no better encouragement.

IN. Some further Confiderations on the Influence of the vegetable King

dom on the Animal Creation. By John Ingenhousz, Counfellor to the Court, and Body Phyfician to the Emperor, F. R. S. &c.

Read June 13, 1782.

The ingenious author of this paper has publishedthefe Further Confiderations, in order to defend the item which he laid down in a former memoir, which feveral of his friends had afferted was quite overturned by the fifth volume of Dr. Priestley, and by an experiment quoted in Mr. Cavallo's book upon air.

The experiments which are here defcribed, were made by Dr. Ingenhousz, in the prefence of feveral friends, in a hot-houfe of the botanical garden, in the winter 1782.

This paper from its nature will not admit of extract; and an abridged view of it would probably rather hurt than forward his caufe. We muft, therefore, refer thofe who have been ftaggered by the authorities of Priestley and Cavallo to the memoir, as it ftands in the Tranfactions.

X. A Microfcopic Defcription of the Eyes of the Monoculus Polyphemus Linzi. By Mr. William André, Sur geon.

This paper, with which the volume concludes, has already been inferted in this mifcellany. The reader will find it, in the department allotted to Natural History, in the London Magazine for August 1783.

MY DEAR FRIEND,

WHEN I wrote to you laft, I little thought it would fo foon have fallen to my lot, to have an-. nounced to you the melancholy news of the death of our great and incomparable EULER. On the 16th of September he found himself much indifpofed, and was taken with a giddinefs in his head. On the 18th, at four

o'clock in the afternoon, he was ftruck with an apoplectic stroke, which on a fudden deprived him of his fenfes. He lay until eleven o'clock the fame evening, when he died. He retained all that prefence of mind, and folidity of-judgement, fo natural to him, until the fatal moment that he was feifed, as you will fee by the converfation I

had with him on the day of his death; and which I have the honour to fend you in this letter.

The life of our incomparable Euler had been one continual scene of the moft fublime refearches into every part of the mathematics: even during the laft days of his life, when the dizzinefs of his head prevented him from making calculations, his mind did not ceafe from being occupied in meditating on different fubjects, and even the most delicate parts of the mathematics, as I myself have been witness, in the converfation I had with this excellent mathematician a few hours before he was feifed with the fatal ftroke that put an end to a life fo ufeful and fo glorious to humanity. And as the laft moments of the exiftence of great men do not fail to excite curiofity, I am perfuaded that the recital of what paffed in our converfation will give pleafure to thofe who knew the great merits of the deceased.

After fpeaking concerning the ftate of his health, he began a converfation, by asking me if I had read the pieces which have been given in, relating to the aftronomical queftion concerning the diurnal motion of the earth: and when I told him fome things concerning thefe memoirs, he affured me he was perfuaded that the only circumftance capable of producing any change in the rotation of the earth was the refiftance of the ether, and as the effect of this refitance would lengthen the tine of the diurnal revolution, it would confequently fhorten the length of the year; and in comparing the ancient obfervation concerning the length of the year with the modern ones, he believed it might be nearly difcovered if there was really any change in the duration of the diurnal revolution: for, if the duration of the diurnal rotation had fuffered any alteration, it muft appear in making thefe comparifons. When I obferved to him, that much dependence could not be placed on the obfervations of the ancients, he replied, that from fome ancient obfervations MAYER had found a fecular

equation of the moon's motion with fufficient certainty.

Saying afterwards that he had underflood that the trials I had made with MR. DE MAGELLAN's inftrument, invented to measure the distance of the moon from the fixed ftars, &c. had been fufficiently correct, he defired a defcription of the conftruction of that inftrument (the circular inftrument) and asked what were the principal advantages to be derived from it, which gave him. occafion to make fome reflections on. the ufe of inftruments employed at fea.

I then spoke to him of the method of combining eye glaffes in a telescope, practifed by MA. HERSCHEL; of which MR. DE MAGELLAN had fent me an account: he was very defirous to learn what effect thefe eye glaffes had; and if, by magnifying three of fix thousand times, it would not be impoflible to difcern any thing diftinét-. ly for want of light.

Talking afterwards upon the priaci ples on which the acroftatic globes are conftructed, he remarked that it was a curious mathematical problem to determine the motion of fuch a globe, from knowing the proportion between the denfity of the air contained in the globe and of the common air. He obferved alfo, that fuppofing this propor tion to be as one to trvo, the greatest velocity of the globe would be 41 feet in a second*.

During the time we were at table, he difcourfed of the new planet difcovered by Mr. Herfchel, and enquired. if any body had yet conftructed tables.

of its motion.

I Take up the pen to announce to you, my dear friend and brother academician, an event extremely afflicting to me. My father, after a moft virtuous and glorious life of feventy-fix years, has paid the debt of nature. He finished his days on the 7th of Sept. old file, by a fit of the apoplexy, which furprifed him at a time when he was employed in making new difcoveries; and he was, at that moment, entertaining himfelf with his friends. His end was as peaceable as his life: he had but just time to fay je me meurs [I die] from which time till the moment of his diffolution, which was a few hours afterwards, he was deprived of fenfe and motion.

I beg of you, my dear Sir, to notify this melancholy event to the Royal Society of London; and principally to the Commiffioners for determining the longitude at fea. Aflure all thofe gentlemen of the perfect gratitude that my deceafed father bore, towards them, to the moment of his death, for the friendship and benevolence with which they recompenfed his labours.

I had forgotten, my dear friend, to acquaint you, in my laft letter, that the Marquis D'Arconati had fent me your letter, upon his arrival in this city; and to thank you for the obligation conferred on me by his acquaint

ance, which has given me much plea fure. This worthy gentleman is much afflicted at the fudden death of my father. He had afked permiffion to affift in the evening at a lecture, which my deceafed father gave regularly to his pupils. My father, who took a pleasure in converfing with the Marquis, answered him that he did him honour. The Marquis called three days after, and judge of his confternation, when one of my nephews met him on the ftair-cafe, and told him of the death of my father. He turned back in great hafte, and I have not feen him fince*.

Immediately upon the death of my father, the members of the Imperial Academy of Sciences, in a meeting in which I was not permitted to affift, refolved unanimously to erect a monument to their deceased Senior. Mr. De Stehlin, the most antient academician next to my father, read a difcourfe in memory of the deceased; and fix of the principal academicians, difciples of my father, agreed to carry the corpfe to the grave. The interment took place the day before yesterday in the evening, at the Proteftant church of St. Paul; and the affembly was the most crouded and brilliant imaginable.

My dear Sir! I trust you will take a fenfible part in my affliction, which is extreme; and I flatter myself that you will continue to me your friendhip, and hope you will not doubt of my reciprocal fentiments. I am, with the most perfect esteem,

Your very humble,

And very obliged fervant,
JEAN ALBERT EULER.,

As every philofopher and mathematician muft feel themfelves affected at the death of this truly great man, we think that we are much indebted to Mr. Magellan for his communication of these two letters.

"PAUL D'ARCONATL

PHILOSOPHY.

OUR UR knowledge of meteors is fo fcanty, and they make their appearance under fuch a variety of forms, have fuch different motions, and are attended with fo many and fuch various circumftances, that a collection of all the circumftances that have been obferved concerning them must be very defireable. It will moreover appear from fome of the following relations that they are not merely the innocent and harmless fports of nature, which most people have hitherto taken them to be, but that they may, and, indeed, fometimes have been attended with danger, and, in one inftance, have done mifchief; nor are we by any means certain that other fhips have not perifhed at fea by their means, although that from which we have this well authenticated relation, happily escaped. On all these accounts, they must be allowed objects not only of curious and philofophical, but of ufeful enquiry likewife: I fhall, therefore, endeavour to collect the best and most authentic accounts that I can meet with of the feveral remarkable meteors, or fire-balls, which have hitherto been obferved in different parts of the world. I fhall next relate fuch facts concerning the late meteors, and fuch obfervations of them as have come to my knowledge; I fhall afterwards deduce fuch inferences as thefe obfervations feem to point out; and, laftly, give the opinions which learned men have entertained concerning them, fo far as I have been able to collect from the Philofophical Tranfactions, and other publications of the times when meteors fimilar to these have appeared.

The first meteor of this kind that I can meet with any account of, is one deferibed by Kepler, that happened on LOND. MAG. Nov. 1783.

the 17th of Nov. N. S. 1623. On this day (fays he) a fiery meteor was feen, or a burning ball, flying over all Germany from west to eaft. In Auftria they fay it gave a found like a clap of thunder, which I cannot think is true; for the defcriptions that are extant do not confirm it.

I meet with no more of this fort of meteor, until the year 1676, which, like the prefent year, was fruitful in productions of this kind. The famous Montanari, profeffor of Mathematics at Bononia in Italy, defcribes very particularly, an exceeding remarkable one that appeared there about an hour and three quarters after fun-fet, on the 31ft of March, N. S. He informs us that at Bononia its greateft altitude was 38°, and it happened when the meteor bore S. S. E.At Sienna its greatest altitude was 58°, and happened when the meteor bore N. N. W. That its courfe, by the concurrence of all the obfervers, was from E. N. E. to W. S. W. That it came over the Adriatic fea, as if from Dalmatia, croffed over all Italy, and was nearly vertical at Rimini, on one fide, and at Leghorn on the other. That in all places near its courfe, it was heard to make a noife like afky-rocket, or to hifs through the air like a train of gunpowder when fired. That at Leghorn it was heard to give a great report, louder than that of a large cannon, and laftly, that from this place it went off to fea, towards Corfica.

The next of which we meet any account, happened September 20th, 1676, and is recorded in the 135th number of the Philofophical Tranfactions, by that eminent mathematician Dr. Wallis; who relates that about feren o'clock in the evening, or foon after, 3 M

ther

there appeared a fudden light equal to that of noon day; and above, in the air, at no great diftance as was fuppofed, a long appearance of fire, with a great knob at the end of it, fhooting along very swiftly." Atits difappearing, it feemed to break into fmall fparks, like thofe of a rocket, or other artificial fire-works, when they burft. It was fo furprizing, and of fuch fhort continuance, that it was fcarcely feen by any but those who happened then to be abroad. "I am told (fays he) by fome, that it fcarcely continued longer that while one may tell 15, or 20 at moft." This meteor was feen nearly at the fame inftant of time in moft parts of England; namely, at Oxford, and many parts of Oxfordshire; in Northamptonshire, Gloucefterfhire, Worcestershire, Somerfetfhire, Devonfhire, Hampshire, Suffex, Surry, Kent, Eflex, and particularly by the watermen on the Thames, between London and Gravefend. Dr. Wallis further recites, that he was not able to conclude which way the motion of this ftrange meteor was; as the furprize it caufed in the beholders, and the fhortnefs of its appearance, prevented them from remarking this circumftance diftinctly. One who faw it between Brackley and Banbury in Northamptonshire thought it moved towards the S. W. On the contrary, an observer between Winchefter and Southampton faid its motion was S. E. and therefore nothing can be concluded with certainty on this head.

On the 22d of May, 1680, O. S. about three o'clock in the morning, a meteor of this kind was feen at Leipfic in Germany. It was feen there defcending with a confiderable degree of rapidity towards the north, and left a long white treak behind it, where it paffed. The fame meteor was feen, and about the fame time, at Hamburg, Lubeck, and Stralfund; every one of which are about forty German miles from Leipfic. But, on account of the time of the night when this meteor made its appearance, it was not feen by any perfon capable of defcribing its path, and the circumftances which attended it. It muft, however, have been exceeding high.

In the year 1686, and on the 9th day of July, O. S. at half an hour paft one in the morning, another meteor was feen at Leipfic. This meteor, as it is defcribed by Mr. Kirch, in his German Ephemerides for the year 1688, was very remarkable: for he relates that it appeared like a ball of fire, with a long tail, in 80 of Aquarius, and 4° to the north; where it continued immoveable for the space of half a quarter of an hour. Its diameter was nearly equal to the femi-diameter of the moon. At first, its light was fo great that one might fee to read by it without a candle, but it diminished by degrees, and at last entirely vanished, without removing out of the place where it was firft feen. The fame thing was feen by others, about the fame time, in different places, particularly at Schlaize, a town about eleven German miles from Leipfic, almoft due fouth, and at an altitude of about 60° above the horizon. As the fun was, at the time when this meteor appeared, in about 261° of Cancer, the meteor muft have been feen about S. by W. and, by its declination, it could not have been more than 24 high at Leipfic, when it is faid to be about 60 high at Schlaize, from which data it may eafily be inferred that it was about feven fuch miles high. Though Mr. Kirch fays it remained ftationary for half a quarter of an hour, yet it appears, by a figure of it, which he has given, that it moved obliquely downwards, towards the S. W. and, when it ended, left behind it two very faint globules or nodes of light.

Mr. H. Barham thus defcribes a meteor which he happened to fee in Jamaica about the year 1700:-" As I was riding one morning from my habitation, which is fituated about three miles N. W. of St. Jago de la Vega, I faw a ball of fire, that appeared to me to be about the fize of a bomb, falling down fwiftly with a great blaze. Î thought it fell into the town; but when I came within a quarter of a mile of it, a little to the fouthward, in the Savannah, I faw a number of people gathered together, and admiring the frange manner in which the ground

was