not be satisfactorily explained without the annexed figures. The practical rule deduced from these principles is as follows:

When the sun comes within fifteen degrees of the meridian, in the morning, let his altitude be taken, and the time of the observation be accurately marked; and let another altitude be taken after he has passed the meridian, whilst his distance from it is less than fifteen degrees; and let the time of this observation likewise be noted. Then, with the supposed latitude of the place, compute the times corresponding to each of the altitudes in terms of the log. cosine of the hour-angle, and take the difference of the intervals, as shewn by the clock, and determined by calculation, and divide it betwixt the observations*. Compute the log. cosine of the hour-angle a second time, with the greatest altitude and the latitude increased or dimi nished by a minute, according as it appears, from a comparison of the intervals, to have been too little or too great; and take the difference betwixt this log. cosine and that which resulted from the first operation, when the same altitude was employed. Having thus obtained the two areas as exhibited in the annexed figure†, we must subtract their logarithms from each other, and with their difference entering the second table we shall find the degrees, minutes and seconds, by which the assumed latitude is to be increased or diminished.'

The latitude determined in this manner, will be nearly equiwalent, in point of accuracy, to the mean result of two meridian altitudes. I am satisfied, from experience, that I can take an altitude of the sun with greater exactness, when he is in any other situation, than when he is upon the meridian.' It is one of the principal advantages of this method, that we can avail ourselves of any number of altitudes, and, of course, approximate as near as we please to a true conclusion, with so little additional labour. The practical astronomer will also think it a circumstance of some moment, that the principal part of the work consists in finding the time, an operation which he is obliged so frequently to perform.'

The author recommends a rule for the above purpose, different from any of the three methods usually adopted, which he conceives to be better than any of the others; and he specifies the advantages which attend it. In the sequel of the paper, he recites the errors to which his method is liable, and states the mode of correcting them. From a review of the inaccuracies that may occur in particular cases, he concludes that

None of them can ever be of sufficient importance to affect the mariner. If he only computes the time with each of the altitudes and the latitude by account, and an incremental area with the greatest altitude and the former latitude varied ten minutes, the correction will generally be deduced within much less than a second; and, in the most unfavourable circumstances, within a minute, of the truth.

* The author has previously explained the manner of doing this. See the Transactions.

L3

But

But the astronomer, in every instance, even when the latitude and declination are nearly equal and of the same kind, by adopting the precautions which have been recommended, may be assured of a result perfectly exact.'

In the application of this method, the author has directed the altitudes to be taken on different sides of the meridian; and he has stated the reason why this process is, in most instances, to be preferred: but it is by no means necessary that we should invariably adhere to it. Several examples are subjoined, in order to illustrate and evince the utility of the rule here given; together with five tables, which serve to facilitate the appli

cation of it.

A Fourth Catalogue of the comparative Brightness of the Stars. By W. Herschel, LL.D. F. R.S.

The principles upon which these catalogues are formed, and the useful purposes to which they may be applied, have been explained in the Phil. Trans. for 1796, Part I. p. 166, &c. The stars now enumerated are those of the following constellations Auriga, Draco, Lynx, Lyra, Monoceros, Perseus, Sextans, Taurus, and Triangulum. By the notes subjoined, we learn which of these stars have been observed by Flamsteed and others; which of them are periodical and changeable; and what other circumstances attend any of them, that deserve to be recorded. In looking over these notes, we find that Flamsteed, on the 13th of December 1690, had seen the Georgian planet, though he took it for a fixed star, and registered it as such in his catalogue. The magnitude, 6m,' says Dr. Herschel, which he assigned to it, agrees perfectly well with the lustre of the planet, compared with other stars which the same author has marked 6m; and with his telescope, he could not have the most distant suspicion of its being any other object than a fixed star of about the 6th magnitude.'

PHILOSOPHICAL AND CHEMICAL PAPERS.

The Bakerian Lecture. Observations upon an unusual Horizontal. Refraction of the Air; with Remarks on the Variations to which the lower Parts of the Atmosphere are sometimes subject. By the Rev. S. Vince, A. M. F.R.S. and Plumian Professor of Astronomy, &c. Cambridge.

The uncertainty of the horizontal refraction is a phænomenon that has been long known, and the general causes of it are sufficiently understood:- but those objects, that are seen through the atmosphere which lies over the sea, sometimes exhibit appearances in consequence of an unusual refraction, that

* See Monthly Rev. N. S. vol. xxiii. p. 37-42.

are

are of a more extraordinary kind, and require particular explanation. In the Phil. Trans. for 1797, Mr. Huddart recited some appearances of this kind; and he satisfactorily accounted for them by supposing that, by the evaporation of the water, the refractive power of the air is not greater at the surface of the sea, but at some distance above it:-but the phenomena observed by Professor Vince at Ramsgate, 1st August 1798, from about half an hour after four o'clock till between seven and eight, were very different from those which Mr. H. has described. The day had been extremely hot, and the evening was very sultry. The sky was clear, with the exception of a few flying clouds. The phænomena were observed with a terrestrial telescope, which magnified between 30 and 40 times, but they were visible to the naked eye. None of them were altered by varying the height of the eye. Most of them were seen by the eye at about 25 feet above the surface of the water, but some of them at 80 feet. These very extraordinary appearances are exhibited by apposite figures; from the want of which, our account must be somewhat imperfect.

Having accidentally observed the top of the masts of a ship above the horizon of the sea, Mr, Vince discovered at the same time, in the field of view, two complete vertical images of the ship in the air; one of them was inverted, and the other erect, with both their hulls joined. The ship was receding from the shore; and, as it descended, the images ascended. On di recting the telescope to another ship, whose hull was just in the horizon, Mr. V. observed a complete inverted image, the mainmast of which just touched that of the ship itself: but there was no second image, as in the other case. Of another ship, which was so far on the other side of the horizon as just to prevent its hull from being seen, a part only of the inverted image was perceived, the image of the top-sail, with the mast joining that of the ship, the image of the top of the other mast, and that of the end of the bowsprit. These images appeared and disappeared very suddenly after each other, As the ship descended, more of the vessel gradually appeared, till at last the image of the whole was completed, with their main-masts touching each other; and when the ship descended lower, the image and the ship separated :-but no second image was seen, as in the first case.

Observing just at the horizon the top of the mast of another ship, the writer perceived an inverted image vertical to the mast, and also an erect image, both of which were perfect and well defined; and an image of the sea appeared distinctly be tween them. As this ship approached the horizon, the crect image, which was uppermost, gradually disappeared, and at

last vanished; after that, the image of the sea disappeared; and during this time the inverted image descended: but the ship did not rise so near to the horizon as to bring the mainmasts together. The images were visible when the whole ship was below the horizon. An image of the cliffs at Calais was observed above the cliffs themselves, together with an image of the sea separating them.

Some other circumstances were noticed, of which the Professor has given a particular account. While he was observing these cliffs, he discovered two partial elevations of the sea, occasioned by the unusual refraction; and he informs us that, about this time, a very thick fog came on the horizon from the other side, rolling on it with a prodigious velocity; curling as it went along, like volumes of smoke sometimes out of a chimney. This appeared several times.' Hence he concludes that there was a considerable fog on the other side of the horizon. He adds that there was no fog on our coast; and that the ships on this side of the horizon exhibited none of the appearances above recited. The usual refraction was at this time uncommonly great, the tide was high, and the cliffs of Calais were seen at a very considerable height above the horizon, while he stood at the edge of the water; though they are frequently not visible, in clear weather, from the high lands about the place.

Having minutely described the several phænomena which he had an opporunity of observing; and which, on account of their singularity, we have given thus in detail, Mr. Vince proceeds to inquire into the causes which produced them. These causes he has, in our opinion, very justly assigned; and he has satisfactorily explained the manner in which they produced effect, by means of the figure to which he refers.

It is well known that, if there were no variation of the refractive power of the air, a ray of light passing through it would describe a straight line; and therefore the curvature of a ray, in its passage through the atmosphere, must depend on the variation of its refractive power. On this principle, it evidently appears that those rays, which pass through parts of the atmosphere whose variation of refractive power is the quickest, will have the greatest curvature. Supposing, therefore, an object at the horizon, and perpendicular to it, to be viewed by the eye at a certain distance, the tangents to those curves that are formed by the rays which proceed from its extremities, drawn from the eye to the line of direction of the object produced, would determine the limits of its image; and those tangents would make the greatest angle with a line parallel to

the

the horizon; which touch curves at the eye whose curvature is the greatest.

If we recur to the principle already stated, of a quicker variation of refractive power, in those parts of the atmosphere that are above the course of the rays which are refracted in the usual manner, this will account for the elevated images described in this paper. If the cause, which produces these effects, should not operate in that tract of air through which some rays pass, but should operate in the tract through which others pass, we should have a single image either erect or inverted, as the circumstances require: but if it should affect all the rays in a similar manner, we should have two images, such as the author has described. The figure would exhibit these effects to the eye, and supersede the necessity of a verbal description. The alterations of refractive power, here supposed, may arise partly from the variation of the density of the atmosphere, and partly from the variations of its moisture; and the passage of the rays,' says Mr. Vince, through the boundary of the fog, may there suffer a very considerable refraction; for, from the motion of the fog, and that of the images above mentioned, I have no doubt that the fog was a very considerable agent in producing the phænomena.' The author suggests that, if, when these phænomena appear, a vessel, furnished with a barometer, thermometer, and hygrometer, below, and also at the top of the mast, were sent out to pass below the horizon and return again; and an observer at land, having like instruments, were to note, at certain intervals, the situation and figure of the images; it might throw further light upon this subject, and lead to useful discoveries respecting the state of the atmosphere, from a conjunction of the causes which affect these instruments."

The Croonian Lecture. Experiments and Observations upon the Structure of Nerves. By Everard Home, Esq. F. R.S.

The subject of this lecture, in which the author prosecutes his inquiry into the actions of different parts of the organ of vision, is the internal structure of the optic nerve. The experiments, which led to this inquiry, were instituted with a view of ascertaining the cause of the luminous appearance frequently observed in the eye of the cat. Some have supposed that this illumination arises from the external light collected in the eye, and reflected; while others have ascribed it to a quantity of light generated in the organ itself. Mr. Home's experiments serve to confirm the former opinion, adopted by Professor BOHN of Leipsic; or to shew that

No light is generated in the eye; the illumination being wholly