evident that colonel Frederick had drawn up a manuscript account of the island, for the inspection of his Royal Highness.

After an absence of a few months on the continent, Frederick returned to London with a ribband in his hat. He also occasionally appeared in a green uniform, richly laced with silver, and long German epaulets; and, as he was said to have obtained the brevet rank of colonel from the late duke of Wurtemburgh, and also the croix de merite, he was ever after recognised by that appellation. Al though not formally acknowledged as his serene highness's agent in this country, it is well known, however, that he transacted business of a diplomatic nature in his name; and helped him to dispose of a regiment of his subjects to the English East India Company. To, wards the latter end of the American war, the colonel also tendered the service of a body of Wurtemburgers, ready disciplined and accoutred; and he was accustomed to assert, that the premier having cheerfully acceded to the proposition, the troops were actually put in motion, and considerable expences incurred. On being countermanded, soon after this, by an order from Great Britain, the colonel preferred a claim for bat and forage money, pay and subsistence, amounting to many thousand florins; and his pretensions were backed by repeated memorials, addressed to all the different administrations that have succeeded each other since that period until 1797:

In the year 1791 an affair which promised to be of some service to his finances occurred. The prince of Wales, and some of the younger branches of the 10yal family, had conceived the idea of obtaining a considerable loan on the continent, by means of their joint security; and colonel Frederick was actually sent to Antwerp to negociate the business. His majesty, however, disliking the scheme, openly interposed by means of his agents; and prevailed not only on a respectable banking-house abroad to withdraw its countenance, but also prevented the subscribers from advancing the money according to agreement. On the failure of this unprosperous affair he returned to England, much chagrined and disappointed; and never mentioned the subject without a considerable degree of emotion. Soon after this he drew up a statement of the case, which death alone prevented him from publishing.

His finances, during many years, were in a deranged state; and for some time before his demise, he had been occasionally supplied with little sums from various friends. Being a great economist, his expences were small; but, notwithstanding this, he had contracted several trifling debts, and one in particular to an amount which subjects a man's body to the rigours of a jail. In short, he was in daily danger of being arrested; and thus became prevented from frequenting those places and persons rendered dear to him by custom.

Another object, of no small concern to a feeling mind, occupied and agitated his thoughts. This was the situation of his daughter, Mrs. Clarke, a lady who had also her full share of misfortunes. His amiable grand-daughters too were grown up, but remained whelly unprovided for. It had been the colonel's custom to visit them fre

quently,

quently, and on all occasions, when it suited his convenience, he was sure to make little presents to the family. Unable to administer to their relief, he had not repaired to their residence, in St. Mary-leBone, for a considerable time previously to the melancholy catas trophe that soon after ensued; and he sent word, "that he would never see them again, until he could do it in a satisfactory manner."

As it now became dangerous to remain any longer at his lodgings in Northumberland-street, in the Strand, where he had resided during many years, he repaired to Waghorn's coffee-house, under the house of lords, and communicated his fears to Mrs. Seagoe, who permitted him, during that night, to sleep in another house belonging to her in the neighhourhood. In the morning he repaired to the attorney of the plaintiff, who had sued out, a writ against him, to solicit a little delay, but he was refused this in a brutal manner. He then asked a friend for the loan of twenty pounds; but receiving an equi vocal answer, became distracted at his situation. His misfortunes now multiplied every hour, and his calamities became, at length, so great, that he determined to put an immediate period to his existence. It was at this critical period that he is supposed to have written the following melancholy note, on a slip of paper:

"All the curses in the tragedies are fallen upon me; without a house, without a country, without a friend; having for enemies even those men whom I have obliged. Incumbered with debts, and so poorthat I live only from day to day, and sometimes I have nothing to live. "To these I have opposed inagnanimity to distress, nature to law, and reason to the troubles of the soul."

On this awful occasion (his purpose being at length fixed) his conduct afforded a singular specimen of calm intrepidity; and there is perhaps no instance on record, in which suicide has ever been committed with more cool determination. Indeed he seems, on this occasion, to have resolved the long agitated problem, whether selfdestruction be not always produced by insanity?

Having procured and loaded a pistol, and being no longer apprehensive of the myrmidons of the law, whose power he could now set at defiance, he arose at the usual hour in the morning of Wednesday February 1, 1796, and walked out in his customary manner, without exhibiting any signs of agitation, or betraying any symptons of his dreadful purpose, to those whom he accosted.

Towards the afternoon he proceded to Storey's-gate coffee-house, Westminster, a place often frequented by him, where he dined. He then called for his half pint of port, a quantity he rarely exceeded; looked over the morning papers; asked for and perused an evening one; and departed at eight o'clock, with his accustomed screnity.

Having then repaired straight to the gate of Westminster-abbey, which is in the immediate vicinage, he pulled out the instrument of destruction from his pocket, and applying it to his temple, drew the fatal trigger, and in a moment ceased to exist.'

This work, we are told by the editor, is to be continued annually. It will certainly be no common industry that will enable him to furnish yearly such a volume as the present.

ART.

ART. V. Philosophical Transactions of the Royal Society of London, for the Year 1800. Part I. 4to. sewed. Elmsly and Bremner.

ACCORDING to our former practice, we shall divide the papers in this volume into classes; and we shall now begin with those which range under the head of

MATHEMATICS.

On the Method of determining, from the real Probabilities of Life, the Values of Contingent Reversions in which three Lives are involved in the Survivorship. By William Morgan, Esq. F.R.S.

In this paper, the ingenious author pursues his investigation of the doctrine of contingent reversions, as they are applicable to those cases in which three lives are concerned in the survivorship; and the problems now presented to the public, added to those contained in his former papers, afford a complete view of the subject to persons who are conversant in this department of science. As Mr. Morgan's eminence in disquisitions of this nature is universally acknowleged, it may be suffi cient to observe, on the present occasion, that we are indebted to him for the first solutions that have ever been deduced, in the case of two and three lives, from just principles, and the real probabilities of life; and that, with respect to many of the problems, none have ever attempted so much as to approximate to the value of the reversion. Being possessed (says Mr. M.) of correct solutions of all the cases in which two or three lives are involved in the survivorship, we are possessed of all that is really useful, and therefore I feel the greater satisfaction in closing my inquiries on this subject. For, in regard to contingencies depending on four or more lives, the cases are not only much too humerous and intricate to admit of a solution, but they occur so seldom in practice, as to render the entire investigation of them, were it even possible, a matter of little or no importance.'

Of Mr. Hellins's second Appendix to the improved Solution of a Problem in Physical Astronomy, inserted in the Philosophical Transactions for the Year 1798, we shall only say that it is a valuable addition to his former communications on the same subject; as it furnishes improved formula for facilitating and abridging the calculations that are necessary in the solution. of the problem to which they relate. Sir Godfrey Copley's medal has been adjudged to Mr. H. for this solution, and his other mathematical papers.

PHILOSOPHY.

On the Power of penetrating into Space by Telescopes; with a comparative Determination of the Extent of that Power in Natural

Vision,

Vision, and in Telescopes of various Sizes and Constructions; illustrated by select Observations. By William Herschel, LL.D. F.R.S.

In order to proceed with clearness and facility in the discussion of the subjects of this paper, the author begins with defining the terms which most frequently occur, and explaining some algebraic symbols which he has adopted for expressing them. He ascribes brightness to bodies that throw out light, and those which throw out most light are the brightest. The whole quantity of light thrown out by a luminous surface is called L; and the luminous physical points which compose this surface are denoted by N. If the copiousness of the emission of light from each of these points were precisely the same, it might be expressed by C: but, as that is most probably never the case, C is made to signify the mean quantity. Hence it appears that CN is equal to L; and brightness will consequently be truly defined by CN. In estimating the appearance of luminous objects at any assigned distance, it will be proper to leave out of the account every part of CN, which is not applied to the purpose of vision; and, therefore, as L represents the whole quantity of light thrown out by CN, that part of it which is used in vision, either by the eye or by a telescope, is denoted by 7. Accordingly, the equation of light, in this sense of it, is CN=1. As the density of light, however, decreases in the ratio of the squares of the distances of the luminous objects, the quantity of it at the distance D will be expressed by D2

1

In natural vision, the quantity undergoes a considerable change by the opening and contracting of the pupil of the eye. If we call the aperture of the iris a, it is known to vary consi derably in different persons. The variation of a in different circumstances is not easily ascertained: but, in determining the quantity of light admitted through a telescope, no such difficulty occurs. This must depend on the diameter of the object-glass, or mirror; and its aperture A may at all times be duly measured. Hence it follows that the expression. will always be accurate for the quantity of light ad

a'l

D2

Al
D

mitted by the eye, and sufficiently so for the telescope.

After having answered some objections to the theory of brightness here proposed, the author proceeds to investigate the general extent of natural vision.

Among the reflecting luminous objects, our penetrating powers are sufficiently ascertained. From the Moon we may step to Venus, to Mercury, to Mars, to Jupiter, to Saturn, and last of all to the Georgian planet. An object seen by reflected light at a greater distance than this, it has never been allowed us to perceive: and indeed it is much to be admired, that we should see borrowed illumination to the distance of more than 18 hundred millions of miles; especially when that light, in coming from the Sun to the planet, has to pass through an equal space before it can be reflected, where by it must be so enfeebled as to be above 368 times less intense on that planet than it is with us, and when probably not more than one-third part of that light can be thrown back from its disk. For, according to Mr. Bouguer, the surface of the Moon absorbs about two-thirds of the light it receives from the Sun.

The range of natural vision with self-luminous objects, is incomparably more extended, but less accurately to be ascertained. From our brightest luminary, the Sun, we pass immediately to very distant objects; for Sirius, Arcturus, and the rest of the stars of the first magnitude, are probably those that come next; and what their distance may be, it is well known, can only be calculated imperfectly from the doctrine of parallaxes, which places the nearest of them at least 412,530 times farther from us than the Sun.'

Next to these stars of the first magnitude, a second set will occur; of which the situation, one with another, may be taken at about double the distance of the former from us. If we suppose a Cygni, ẞ Tauri, &c. to belong to this class of the second magnitude, it is known that, whether we look at these or at the former, the aperture of the iris will probably undergo no change; and therefore a becomes a given quantity, and may be left out in the above expression for the bright

a21

D2

ness of these objects. D', according to the preceding statement of distance, will be in one case four times that of the other; and consequently the two expressions for the brightness of the stars will be for those of the first magnitude, and / for those of the second.

The quantities being thus prepared, what I mean to suggest (say the author) by an experimet is, that since sensations, by their nature, will not admit of being halved or quartered, we come thus to know by inspection, what phenomenon will be produced by the fourth part of the light of a star of the first magnitude. In this sense, I think we must take it for granted, that a certain idea of brightness, attached to the stars which are generally denominated to be of the second magnitude, may be added to our experimental knowledge; for, by this means, we are informed what we are to a2l al understand by the expressions

29

Sirius

al

Tauri

The names of the objects, Sirius, & Tauri, are here used to

express their distance from us.'

We