cise of his intellect, than the mere observation of a body on the wire of a telescope. As an instance of the extent to which the reductions are carried there, I may mention that in one Italian observatory where the planets were considered the principal object, not only were the observations freed from instrumental errors and astronomical corrections, but the tabular places were computed by direct use of the Tables, (the ephemeris attached to Schumacher's lunar distances not having reached that country,) and the equations of condition were regularly prepared for the correction of the elements. I suppose such a thing has never been done in England. This system must however contribute powerfully to produce that strong connexion between physical theory and practical observation, which is general on the Continent, but which does not exist in England. I believe that in the actual state of our institutions, reasons 7 might be found which would seem to render it improbable that there ever can be so strong a connexion; and I can only hope that my view may be incorrect. There is one point with regard to the foreign astronomers to which I cannot help alluding, without however intending to draw any distinct inference. It is, that they have first obtained distinction while in the lower departments of the observatories. Encke's reputation was first acquired, not when he became Astronomer at Berlin, but when he was assistant at Seeberg: and Bessel became known in every part of Europe, not as Astronomer at Königsberg, but as assistant at Lilienthal. Walbeck and Argelander, in similar situaz tions, have arrived at considerable eminence. I now proceed, and with great pleasure, to consider the second question. And this leads me to explain my opinion on a point respecting which I am anxious that I may not be misunderstood. I am not one of those who have joined in the cry of "the decline of science in England," nor do I believe that in this science there is any foundation for that cry. On the contrary, I assert without hesitation, that it is now and has been for some years rapidly advancing in that country. That there has been a decline, thirty or forty years ago, or rather that we have not kept up with the advances made by foreigners at that time, I am willing to admit. Perhaps this arose from political separation; perhaps in some degree from our pertinaciously retaining a system of mathematics which was insufficient for the deep investigations of Physical Astronomy, (for it was in this principally that we were behind our neighbours). And I have not disguised my opinion that in all the important branches of science we are still behind them. But in all with which I am acquainted a rapid progress has lately been made. In Physical Astronomy more has been done in England within the last five years than in the preceding century; and this not only with regard to the additions actually made by Englishmen to the stock of results drawn from that science, but also with respect to the number of persons who understand its principles, and who at some future time may be expected to contribute to its progress. In the University with which I am best acquainted, the study of this subject has made great advances. Of the amount and excellence of our geodetic measures and pendulum experiments, and of our discussions of refraction and aberration, I have already spoken. In accuracy of examination and correction of instrumental errors, perhaps something has been gained. In the extension of our star catalogues, much more has been done within a few years than in the whole previous time which followed Bradley's death. In the observation of planets, and the regular comparison of observations with Tables, (the first essential step to the improvement of the latter,) it is hoped that a great advance has been made. The observation of occultations and eclipses has extended; the exhibition of the results also, both for terrestrial and celestial determinations, has increased; and the regular publication of them in the Memoirs of the Astronomical Society, saves from oblivion the past and insures more completely the observation of the future. In the observation of double stars very much has been done. In all this I see grounds for exultation at " the advance of science in England." And when I remark the growing intermixture of physical with observing science, I indulge in the hope that the character as well as the extent of our Astronomy is improving, and that the time is approaching when a person will not in England be considered a great astronomer because he can observe a transit or measure a zenith-distance correctly. XI. In conclusion, I shall suggest a few points to which it seems desirable that some attention should be directed. In this part however, more than in any other, the judgement of an individual must be considered fallible. 1. After all that has been done in respect to refraction, I suppose that there is no subject of such continual application, in the theory of which so many difficulties occur, and in whose application there are so many discrepancies. It seems not improbable that some of the latter may depend upon anomalies in the indications of the thermometer, owing perhaps to the effects of radiation, the nature of which till lately has been little understood, and scarcely recognised among astronomers. In some of Mr. Fallows's pendulum experiments it appeared to account for many discordancies. I think that astronomers would be glad to receive simple directions for placing a thermometer so as to indicate correctly the temperature of the air at the place of observation. I omit all discussion of the difference of the external and internal thermometer, as I think the only way of overcoming the difficulty is, to make the external and the internal temperature as nearly as possible equal. 2. In the theory of refraction, the following questions present themselves as only to be solved by experiment. What is the law of the decrease of temperature, or rather of density, in ascending? How does this vary at different times? Can any means be contrived for indicating practically at different times the modulus of variation? (The last question is suggested by the remarks in Mr. Atkinson's valuable paper, Mem. Ast. Soc. vol. 2.) Does the refractive power of air depend simply on its density, without regard to its temperature? Is it well established that the effects of moisture are almost insensible? From Carlini's Tables, as well as from general reasoning, it seems likely that refraction may be different in different azimuths, according to the form of the ground: can any rough rule be given for estimating its effect? Finally, when the atmospheric dispersion is considerable, what part of the spectrum is it best that astronomers should agree to observe ? 3. I have already stated that I think Lindenau's constant of nutation has been adopted by the German astronomers on insufficient grounds. The value which I should certainly prefer is that determined by Dr. Brinkley, and which Mr. Baily, with his usual judgement, adopted for the catalogue of the Astronomical Society. The Greenwich circles have now been erected, and in a perfect state, long enough (or nearly so,) to determine this constant; and the mass of excellent observations which they have produced, applicable to this question, vastly exceeds any other that has been used for the same purpose. It is highly desirable that the coefficient of nutation should be investigated from the Greenwich circle-observations. 4. Bradley's observations of stars were nearly useless till Bessel undertook to reduce them. In like manner Bradley's and Maskelyne's observations of the sun and planets are still nearly useless. At different times observations of the sun have been reduced (by Delambre, by Burckhardt, and lately by Bessel or Schumacher), and probably much labour has been wasted. A reduction of these observations on a uniform plan (adopting, for instance, Bessel's Tabula Regiomontana,) would be invaluable in the application of the planetary theories. Many observations of the moon have been reduced and published; but, for the sake of uniformity of system, it would be desirable to re-compute them. 5. I have mentioned that the perturbations of the small planets and of Encke's comet give good reason to believe that the mass of Jupiter adopted by Laplace is too small. Laplace's estimation is founded on Pound's measures of the elongation of Jupiter's satellites; and I am not aware that any measures have been made since that time. It is extremely desirable that they should be measured, at least those of the fourth satellite. It would be sufficient, in observing the transit of Jupiter, to observe also the transit of this satellite, one or two days before and one or two days after the time of its greatest elongation, as the theory of the satellites could be applied without difficulty to this measure. 6. The dimensions of the orbit of Encke's comet, as investigated by Encke, depend upon the assumed law of density of the resisting medium. In fact, by assuming a law, he has established a relation between the diminution of the aphelion distance and the diminution of the perihelion distance which would not hold with any other law. It will be interesting now or at some future time to investigate separately from observations the diminution of these two elements, as a means of proving Encke's law, or of suggesting a new one. 7. The perturbations of Biela's comet have not been calculated, I believe, for the interval between 1772 and 1806, nor those of the node and inclination from 1806 to 1826. It is desirable that this should be done, both for ascertaining the identity of the comet of 1772 (which is not perfectly established), and for examining whether this comet, like Encke's, gives any indication of a resisting medium. 8. The most laborious part of the expansions in physical Astronomy is completely dispensed with by the use of Burckhardt's formulæ in the French Mémoires for 1808. But Burckhardt expressed himself very doubtful as to their accuracy; and they do not comprehend any terms depending on inclination. It is desirable that they should be verified, and extended to the terms depending on the inclination. 9. The theory of the perturbations of Pallas has so often and so vainly been proposed, that it would seem useless to urge it again, and still more so to propose the theory of the perturbations of Encke's comet. Yet I conceive this to be the problem which at present demands the efforts of Physical Astronomy. It is plain that there is no hope of solving it by any of the usual methods, as the series, which in other cases are convergent, here either diverge or converge so slowly as to be useless. But it may be possible to choose functions for these expansions, by the use of which the series may become convergent sin (such perhaps as+b cos instead of sin 6). At all events this may be fixed on as being at present the difficult problem of Physical Astronomy. In the preceding suggestions I have endeavoured to fix on definite points for the attention of astronomers. I need not mention that there are other subjects (the theory of Uranus, for instance,) in which the existence of difficulties is known, but in which we have no clue to their explanation. Observatory, Cambridge, G. B. AIRY. Report on the Tides. By J. W. LUBBOCK, V.P. & Treas. R.S. THE Connexion between the Tides and the motion of the moon was known to the ancients; but we are indebted to Newton for the discovery of the mechanical principles which regulate these phænomena. Newton contented himself with explaining the most obvious results of observation, and left all the details open to future inquiries. The subject was next taken up by Bernoulli, Euler and Maclaurin, about the same time, in their several treatises which participated in the prize awarded by the Academy of Paris in 1740. Laplace afterwards undertook this difficult investigation, and succeeded in forming the differential equations from which the explanation of the phænomena is to be derived. The integration of these equations presents, however, so many difficulties, that he confined his attempts to a very simple case, namely, that in which the depth of the ocean is constant, and the solid nucleus but little different from a sphere. Even in this case, his analysis is far from complete, andcontributes but little to unravel a question which he has characterized, as "la plus epineuse de l'Astronomie Physique." Finally, Laplace had recourse to the following indirect consideration, namely, "that the state of any system in which the primitive conditions have disappeared through the resistances which its motion encounters, is periodical with the forces which upon it." Hence he concludes, that if the system is dis act |