1815. Wind. Max. Min. Med. Max. Min. Med. Hygr. at The observations in each line of the table apply to a period of twenty-four hours, beginning at 9 A. M. on the day indicated in the first column. A dash denotes, that the result is included in the next following observation. REMARKS. Eleventh Month.-23. Serene, with hoar frost. 24. Hoar frost: light rain for a few minutes, p. m. 25. Hoar frost, with Cirrostratus in the horizon: steady breeze. 26. Hoar frost: the clouds coloured at sun-rise: clear, p. m. 27. a. m. Overcast: some light rain, a. m.: Cumulus capped, and inosculating with Cirrostratus, p. m. 28. Fine: the ground lightly covered with granular snow. 29. Hoar frost: about one, p. m. a slight snow, granular, and in stars : in the evening a mist over the marshes; and at about 8h 30′ p. m. a brilliant meteor. It resembled a sky-rocket, and fell almost directly down with an uniform motion, blazing out larger before it became extinct. This meteor, with two others which I lately saw in the same quarter (S. W.) passing in the same track at about a minute's interval, had very much the appearance of a simple electrical discharge between two horizontal beds of cloud at different elevations. 30, a. m. Wet: p. m. cloudy, the wind rising at S. and S. E. Twelfth Month.-1. Much wind and early, with rain. 2. Fine, a. m. with Cirrostratus: then Cumulus, with Cirrus. 3. a. m. Very dark, with clouds: wind S. E.: p. m. Cumulostratus, after which Nimbus in the horizon: the new moon. conspicuous in an opaque twilight. 4. A wet morning windy at S. W.: in the fore part of the night much wind. 5. Notwithstanding the dryness of the air, which was also clear below, there was this forenoon a continuous cloud above at a great height, with a hollow sound in the wind. We had a steady rain after this, and a gale of wind in the night. 6. Much wind: Cumulus, with Cirrostratus : wet, p. m. : a gale through the night, shifting to N. and N. E. 7. a. m. Cloudy: the barometer, which the N, W. wind failed to bring up, now rises, with a continued hard gale from N. E,: the hygrometer receded to 51°: in the evening the moon's disk appeared small, and its light scanty, though no visible cloud intervened. 8. Clear, dry, windy morning. 9. Steady breeze, clear: hygr. receded to 489. 10. a. m. Sleet: lunar halo, evening. 12. For these three days past we have had a pleasant clear air, with a fragrant smell, like that which exhales from the dry turf after showers. 13. a. m. Cloudy: drizzling: the windows of a room without a fire, for the first time this season, collect moisture on the outside, remaining dry within: sounds come louder than usual from the N. E. 14. Hoar frost: a fine day: after dark, a lunar corona, occasioned by bars of Cirrus pointing N. and S., and appearing to converge in the horizon. These soon passed to Cirrostratus, and were followed by wind and rain from the southward. 15. Much wind: cloudy: some rain. A very stormy night, with showers. 16. Cumulus, mixed with Cirrostratus: early in the afternoon the lofty summits of the former, rising from a fore ground of the latter on the E. horizon, presented the resemblance of an Alpine landscape. In the evening, and on 17, a. m. the wind N. W., with Nimbi, bringing some snow, followed by much cloud, and a gale at evening. 18. Fine day. 19. Hoar frost, clear: then overcast from the south, and some snow in large loose grains. In the evening more snow, followed by rain from S. 20. a. m. Cloudy: much wind at S., with a hollow sound: rain p.m. and a gale through the night. 21. Fine morning: the ground slightly frozen. 22. Very white frost: Cirrus above, and Cirrostratus to the S. E.: a little granular snow on the ice. Snow in the night. Winds variable, but with a larger proportion of Northerly than usual at this ANNALS OF PHILOSOPHY. FEBRUARY, 1816. ARTICLE I. Observations on the present State of the Mathematical Sciences in Great Britain. I HAVE read with considerable interest in the 34th number of the Annals of Philosophy your liberal and judicious remarks on the present depressed state of the mathematical sciences in this country; a country which, with regard to the analytical branches of them, may be considered as their native soil; a country which boasts of having produced a Newton, a Barrow, a Cotes, and many other mathematicians of the first order, whose names will ever be immortalized in the annals of those sciences. You have endeavoured to point out the cause of this humiliating reflection; and I perfectly agree with you to the extent to which you have carried your observations; but I think more might be said, and ought to be said, on the subject; and I hope, therefore, you may be induced to give publicity, through the medium of your Journal, to the following remarks, which, whatever may be their defects and inaccuracies, are certainly dictated by no other motive than an anxious and honourable feeling for the scientific character of England. It is to me, and doubtless to every Englishman, a painful consideration when he reflects that this country, once the favourite seat of the mathematical sciences, and the character of whose natives is so well calculated for penetrating to the depths of those speculative truths, should have fallen from the first rank of scientific nations VOL. VII. No II. G to so humiliating a distance even below mediocrity; yet truth and candour require the acknowledgment. For the last 30 years the mathematics have been pursued on the Continent, and particularly in France, with an ardour and perseverance that ensured the success with which that pursuit has been attended; while in this country, if they have not retrograded, they have at least remained nearly stationary. I do not mean to assert that we have no mathematicians who have kept pace with the general improvements; I mean only that the greater part have not; and that we have none, or very few works, that we can refer to as a favourable specimen of English science; while in France how many distinguished mathematicians has not the above short period produced? and how many brilliant discoveries do we not owe to their persevering industry and genius? The names of Laplace, Lagrange, and Delambre, without enumerating many others of nearly equal eminence, will add more real splendour, and more durable monuments, to the glory of France, than all the victories that have been achieved by her arms; the one is transient, and may be eclipsed by reverses; the other is immutable, like the truths from which it emanates. If we even turn to Russia, a country but just emerging from barbarism, we shall find that it can boast of its mathematicians that would put Englishmen to the blush. Examine the Petersburg Memoires, and compare them, in point of mathematical discussion, with the Transactions of the Royal Society, and I am afraid that England would be a loser by the comparison. The Memoirs or Berlin, before the late fatal degradation of Prussia, were equally honourable to the scientific character of the Government and people. Even the little state of Brunswick has to boast of a mathematician of the first order; and Gauss, in his turn, has the proud satisfaction of acknowledging the patronage and protection of the head of the state. Olbers, Arbogast, and Burckhart have each also done much for the honour of Germany. Sweden is another country rapidly rising in its scientific character, and even already holds a distinguished situation in this respect amongst the nations of Europe. Denmark, again, has its academy and prize essays; while England alone-England, the first nation in Europe in every other respect, remains stationary, and feels herself inferior in the cultivation of those sciences which have ever been cherished by all civilized states, both ancient and modern. There may be some persons, who have thought little on this subject, that may be led to think this representation too strong, that the picture is overcharged, and that the writer is one of those anti-patriotic souls who would wish to elevate all that is foreign at the expense of every thing that is English. There is, perhaps, unfortunately, such a class of men in this country; but if I know my own heart, I am as directly opposed to such principles as the antipodes of the opposite hemispheres. My view is not to depre ciate English talents, but to prove that talents of the first order are kept here in a dormant state, for want of due encouragement, and the means of bringing them into proper activity. It may not be amiss, however, in order to clear myself entirely of such suspicion, to draw a slight comparison between the productions of the French and English press, as far as relates to the mathematical sciences, within the last 20 or 30 years; and in order to do this the more effectually, I shall divide those productions into three classes, viz.: 1. Real inventions and discoveries; 2. Extensions and improvements to principles previously established; and, 3. The new editions and translations of the most celebrated ancient authors. To the first class belong the Theorie des Fonctions Analytiques, by Lagrange; the Mecaniques Analytiques of the same author; to which we may also add his Resolution des Equations Numeriques: the Descriptive Geometry, by Monge, and the new Calculus of Probabilities, by Laplace, are also works of the same kind, each having added many important discoveries to our previous stock of knowledge, and furnished us with the means of still increasing them by further researches: and if we only allow ourselves to step across the Rhine, we may add to these the Calcul des Derivations, by Arbogast, and the Disquisitiones Arithmeticæ, by Gauss. Now what has the English press produced, in the same period, of a nature that can be compared with any of those original productions? I am afraid not even one solitary volume! I say nothing of our Philosophical Transactions; because whatever may have appeared there will doubtless find an equivalent in the Memoirs of the National Institute. Thus far, then, I hope I have acquitted myself of an exaggeration in my former statement. Let us now examine the second class of works, in which extension has been given to principles previously established. The most distinguished work of this kind is the Mecaniques Celestes, by Laplace; for which we can boast of no equivalent in English. The Calcul Differential et Calcul Integral, by Lacroix, may also, without much violation of our classification, be introduced under this head, which work, without naming many other respectable performances of the same kind, will not only not find its equal, but no work with which it can be in any way compared in our language. The same may be said of the Geodesie, by Puissant; the Geometrie de Position, by Carnet; the Hydrodynamiques of Bossut; the Astronomical Tables, by Burckhart; the Trigonometrical Tables answering to the new division of the circle by Borda; the Mecaniques Hydrauliques, by Prony; the Theory of the Planets, by Gauss; and the Histoire des Mathematiques, by Montucla. With respect to the Base du Systeme Metrique Decimal, we have a work worthy of comparison in the Trigonometrical Survey of England; but this, it will be observed, is a national undertaking, and protected by the Government, and therefore adds strength to the argument I shall endeavour to establish; that protection is all |