by comparing them with the numbers which have been published from the highest authority (that of the Astronomer Royal) in the Philosophical Magazine. The longitudes of the comet, deter mined at Greenwich and Glasgow Observatories, coincide to the fraction of a minute. The time of the perihelion passage may be considered as pretty accurately fixed, either for Sept. 12 or 9, or, as is more probable, at some intermediate period. From this we can fully explain some of the phænomena generally remarked. From the 9th, as stated in the Glasgow papers by a correspondent, the comet was observed to increase considerably both in brilliancy and in the apparent magnitude of the coma, but particularly of the tail, in the course of eight days. This verifies very happily the observation of Sir Isaac Newton, that it is not till immediately after the perihelion passage, that comets acquire their maximum of lustre and of size. The enlarge-. ment therefore uniformly takes place at that time, whether the comet is coming nearer us or moving in the opposite direction. The quantity of increase due to its approximation alone, in six or eight days, can be calculated, and we know that there is no instrument in Scotland capable of measuring the change of apparent magnitude produced by this cause. Whether the exquisite micrometer of Troughton, applied to our great Herschelian telescope, may show any difference, I shall be able to ascertain in a few days, as that instrument is lately dispatched from London for us. I must acknowledge, however, that I entertain very slender hopes of success in this kind of observation on a minute body surrounded with such a nebulosity, and at a distance from us much greater than that of the sun. It has been said, that this comet was ascertained to be the same with that of 1661. The two are as different as can be imagined in every respect. Hence we may see how much safer in the event, scientific investigation is than vague conjectures. I subjoin the elements of the comet of 1661, and those now given by Burckhardt: COMET 1661. BURCKHARDt. Long. of node .... 82 deg. 30 min.... 140 deg. 13 min. Inclination ...... 32 deg. 35 min.... 58 min.... 72 deg. 42 min. 74 deg. 12 min. Place of perihelion, 115 deg. I am, Sir, your obedient servant, Alterations in the Angle of the Direction of the Envelope. Nov. 4. 10 feet reflector. Large double eye-glass. The streams departed from their source in a greater angle of divergence. This probably arose from a contraction of the envelope towards the sun, but not about the root of the streams, where it remained extended as before. Nov. 13. 10-feet. The angle of the bending of the envelope at its vertex was considerably enlarged. In the night-glass the divergence of the streams themselves was certainly not increased. Nov. 24. 10-feet. The divergence of the light, which may still be called the envelope, although no longer to be distinguished from the head, was from 60 to 65 degrees; but in the night-glass, the branches which were hardly to be seen were closer together than formerly. The additional faint duplicates of the envelope, Nov. 4, 5, 13, and 14, always departed from the vertex in an angle considerably greater than the permanent interior streams. The Shortening of the Tail. The 5th of November, the air being very clear, I found, when attending to the tail of the comet, that its length was much reduced; its utmost extent not exceeding 124 degrees. The 9th, it was 10 degrees long. The 15th. In the night-glass the tail was much shortened. The 16th. With the naked eye the tail was nearly 7 degrees long. The 19th. Its length was about 6° 10. Dec. 2. The tail was hardly 5 degrees long, and of a very feeble light. The 9th, the length of the tail was not materially altered. The 14th, it still remained as before, but the end of it was much fainter. Increasing Darkness between the Streams that inclose the Tail. The 4th of November, the darkness near the head on the side from the sun was grown more conspicuous, and much less filled up with scattered light. The 5th, the darkness of the atmosphere on the side opposite the sun was stronger than on the sun side. The 10th. A considerable darkness prevailed between the two branches of the tail. The 14th. In the tail, close to the head, there was a large space almost free from scattered light; where the small stars of the milky-way are as bright as if nothing had intercepted their light. The 16th. The space between the streams was of a considerable darkness. The 19th. 10-feet reflector. The darkness between the streams was increased. Dec. 9. The space close to the head on the side from the sun was quite dark, or rather transparent. The 14th. Many small stars of the milky-way were in the dark interval of the tail close to the head of the comet. Of the real Construction of the Comet, and its various parts. Hitherto I have only related the appearances of the several parts of the comet, in order to determine their linear extent; but the observations which are now before us, contain facts that will allow me also to ascertain the construction of the comet and its various parts in their solid dimensions. From the laws of gravitation we might be allowed to conclude that the planetary body containing the solid matter of the comet must be spherical; but actual observation will furnish a more substantial argument; for in no part of the long, geocentric path described by the comet, did I see its little disk otherwise than round; whereas it would not have preserved this appearance, if its con struction were not spherical. If what has been said in my last paper, when treating of round nebulæ, be remembered, the head of the present comet, which by observation appeared round like a nebula, cannot be supposed to be of any other than a spherical construction. With my collection of round nebulæ the arguments, however, which proved their globular form, rested only, though very soundly, upon the doctrine of chances, and the known effects of gravitation; but here, on the contrary, while nebulæ remain in their places, the geocentric position of the head of the comet has undergone a change amounting to a whole quadrant; in all which time I have observed it to retain its roundness without any visible alteration; from which it neces sarily follows that its form is globular. Glasgow Observatory, Oct. 16. SIR-In the Glasgow Courier of October 5, I had the honour of submitting to the public the results of the joint labours of Mr. Cross and myself, for the preceding month, on the comet, at the Glasgow Observatory. In The Star newspaper of October 11, appeared for the first time the elements of the orbit, as determined by the celebrated Burckhardt, Member of the National Institute. It is a duty which I owe to the skill and the unwearied exertions of my associate Mr. Cross, to this patriotic establishment, and also to this country, hitherto considered by the French mathematicians and astronomers unequal to the primary solution of this difficult problem, to state the following facts:-On October 8, at eight hours fifteen minutes, by observations made here, with every precaution to insure the utmost accuracy, the comet had deviated 42 degrees 18 minutes from the longitude which Burckhardt's elements assign for that instant. On October 14, at two o'clock in the morning, the longitude, as deduced from a most satisfactory transit, was 206 degrees 42 minutes. By the French computation it ought to have been 248 degrees 1 minute, differing from nature by 41 degrees 19 minutes. By our elements, which have received a partial correction from my observations since the 5th, the coincidence on the 8th, at the same time, was within 15 minutes, and on the 14th, within 13 minutes. Our computed latitudes on the 13th agree to a minute with observation, while those of Burckhardt differ by 3 degrees or 180 times that quantity. The examination of both has been made by the excellent tables of the parabola, constructed by Delambre, imperial observer at Paris. It is in the longitude of the perihelion that the chief discordance exists between the French elements and ours, and this amounts to about 31 degrees; the former being, in our judgment, too small by this quantity. The comet has been continually approaching the earth for many weeks. From September 15th till October 14th, its decrease of distance amounted to 25 millions of miles, yet its brilliancy and the magnitude of its tail have gone on diminishing, as Burckhardt properly remarked. Persons ignorant of astronomy would naturally infer from this diminution the recedure of the comet from us, as, from its increase they conjectured its approach. Astronomers laugh at such idle dreams when applied to a demonstrative science, in which conjecture has found no place since the days of Newton. Its first principles teach, that these phænomena arise from the comet's varying distance from the sun. At the period of the perihelion passage these bodies are known uniformly to attain their maximum of size and brightness. [Tilloch's Phil. Mag.] ANDREW URE. CHAP. XIII OF SOLAR AGENCY IN THE PRODUCTION OF COMETIC PHENOMENA. As we are now in a great measure acquainted with the physical construction of the different parts of the present comet, and have seen many successive alterations that have happened in their ar rangement, it may possibly be within our reach to assign the probable manner in which the action of such agents as we are acquainted with has produced the phænomena we have observed. In its approach to a perihelion, a comet becomess exposed to the action of the solar rays, which, we know are capable of producing light, heat, and chemical effects. That their influence on the present comet has caused an expansion, and decomposition of the cometic matter, we have experienced in the growing condition of the tail and shining quality of its light, which seems to be of a phos phoric nature. The way by which these effects have been produced may be supposed to be as follows. The matter contained in the head of the comet would be dilated by the action of the sun, but chiefly in that hemisphere of it which is immediately exposed to the solar influence; and being more increased in this direction than on the opposite side, it would become eccentric, when referred to the situation of the body of the comet; but as the head is what draws our greatest attention, on account of |