Young's theorem, and as obtained from his own very accurate experimental determination, both by the horizontal and the dipping needle.

The greatest variation of the experiment from the computation is less than a seventeenth of the whole; an agreement perfectly unexpected in an approximation exposed to so great irregularity. Dr.

Young, in 1807, had made the magnetic pole 15° more northerly, and 8° more easterly; Biot 19° more northerly, and 500 more easterly!

In the experiments on the diurnal variation both at Hammerfest and at Spitzbergen, the needle seems to have passed its mean position about half an hour before noon and midnight.

The dip sector, employed for observing the depression of the horizon in the neighbourhood of the gulf stream, was found to afford very correct results, but less irregular than might have been expected from the actual diversities of temperature of the sea and air concerned in the refraction; the error of the tabular dip never amounting to two minutes. It was ascertained in Jamaica, by some delicate thermométrical experiments, that the heat communicated by the sun's rays is very sensibly greater in the upper regions of the atmosphere, than on the level of the sea. A number of important geographical and hydrographical notices, especially relating to the currents in the Atlantic, are contained in this volume, together with appropriate charts.

It is impossible to quit the subject of Captain Sabine's experimental labours without giving the strongest testimony of applause to his zeal and diligence and accuracy, and expressing a hope that he may find both private and public motives for continuing his exertions with equal ardour in the prosecution of further investigations connected with the advancement of physical science.

vi. Extract from a Letter addressed by Professor BESSEL to Professor SCHUMACHER, relating to the GREENWICH Observations. When I had the pleasure of being your guest at Altona, you showed me the numbers of the Philosophical Magazine, which contain a very severe censure of the Greenwich Observations for 1821. I saw this censure with some surprise, because I had always considered the collection of observations at Greenwich as singularly valuable, and as a rich source of astronomical truths; nor were you, I believe, of a different opinion; and we were perfectly agreed respecting the unimportance of the inaccuracies that were imputed to this work in the two papers published in the 64th volume of the Philosophical Magazine.

For those who are acquainted with the Greenwich observations, and who compare them with the critic's remarks, every further explanation would be superfluous; but since it may be supposed that these remarks will fall into the hands of many persons not deeply versed in astronomy, I readily comply with the request which you made, that I would commit to writing our common view of the subject. I feel, as well as yourself, the propriety of doing my best on the occasion, in order that too great importance may not be attached to this censure of an establishment, to which astronomy is indebted for a great proportion of its advancement; and that its importance cannot be very great, is sufficiently shown by the facility with which Mr. Olufsen has computed the declina-tions of the fundamental stars, as published in the Nachrichten, No. 73, from the Greenwich observations for 1822.

The greater number of the errors which have been pointed out by the censor, are merely accidental errors of the pen. Errors of this kind are certainly disagreeable, and it would be better if they could be entirely avoided; but since all collections of observations in existence do contain such errors, they clearly appear to be unavoidable.

The first class of errors mentioned in the Philosophical Magazine contains the cases in which the mean deduced from the readings of the two microscopes A and B differs from the column in which that mean is assigned. Since there must be some manifest oversight in all these cases, it may sometimes be difficult to determine whether it is in the readings or in the mean assigned; but it will, in general, be easy to distinguish, from the preceding or following observations of the same star, where the error lies.

The second class contains the differences between different records of the same observation. These must be errors in the copies sent to the press, and not in the readings of the microscopes; and they may generally be corrected by a comparison of the two passages they sometimes extend to whole degrees, or to the tens of the minutes, and are then of no importance; for example, in the observations of Procyon the 23d Feb. 1821, and of 6 Cephei the 8th Dec. where there are errors of 30° and 5° respectively.

The sixth class of errors contains the intervals between the micrometer wires, as they are deduced from different observations of the same star. These are often dependent on errors of the pen, as in the observation of Capella on the 7th February, and in that of Sirius on the 8th, where there are errors of 5′′ and of 40′′ respectively in the fourth wire; frequently also they arise from inaccuracies of observation. In the former case they are of no consequence whatever, being easily detected at first sight; in the latter they are fundamental imperfections; but such imperfections are inseparable from the nature of observations, and it would be ridiculous to expect from an astronomer that he should perform impossibilities. All registers of observations exhibit inaccuracies of this kind, and if any should be produced without them, it might with confidence be asserted to be a forgery. The diligence of the astronomer is proved, not by the perfect agreement in his tenths of seconds, but by the magnitude of his mean or his probable error; and it would probably be difficult for the critic to prove that this error is much greater in the Greenwich observations, than the' nature of the instruments renders unavoidable.

The errors of the fifth class, which comprehends the differences between the polar distances observed with two and with six microscopes, seem to me to have been introduced without the least propriety: they are either insignificant errors of the pen, as in the case of Draconis, 28th March, or slight accidental errors of observation, mixed with the changes of place of the stars and of the refraction, or, lastly, changes of the place of the pole on the instrument. For this last the observer can by no means be responsible. Had the critic pointed out any new method of fixing the instrument so that it should be subject to no alterations, he would have deserved the thanks of all practical astronomers; but the constant result of past experience shows that the greatest possible care, in procuring a firm foundation for the pillars, affords us only a comparative and not an absolute stability. The fixing of the instruments at Greenwich has been such as to keep them for a long time admirably firm; but at other times it has not been so successful, as may be seen in the table of the place of the pole, printed in the

Nachrichten, No. 73; the differences between the latter days of July and the beginning of August, 1821, depending on a change of this kind, so that they cannot be considered as accidental errors of observation, nor are they of material importance, as they may be readily determined by a series of observations of the pole star,' so complete as those which are made at Greenwich. The accidental irregularities of the polar distances, which remain after the correction of the place of the pole, can be as little considered as an imputation on the accuracy of the observer, as those of the intervals of the micrometer wires. The truth of this remark is illustrated in the Nachrichten, No. 73.

The fourth class contains the differences between the times of transits observed with the transit telescope, and the mural circle. The latter instrument, however, not being intended for the observation of transits, nor being ever actually so employed, it would have been of no manner of use to seek for greater accuracy in the memorandums which are made merely with a view of determining its place with respect to the meridian. We ought to acknowledge the occasional insertion of these memorandums with gratitude, as they assure us that the instrument never deviates so much from the meridian as to affect the polar distances; but they are not intended for any other purpose. Neither Bradley nor Maskelyne have ever noted the times of the transits by their mural quadrant, although it was more liable to variation than the mural circle. But to correct the place of the axis of this circle continually, so as to bring it perfectly into the plane of the meridian, would certainly be of no advantage to the Greenwich observations.

Other errors which are criticized, for example, those of the names of the stars, of the hour or minute of their transits, and so forth, are of no material importance whatever; and how difficult it is to avoid errors of this kind, may be inferred from the circumstance of my having found about 1400 such errors in Bradley's observations. [The catalogue of these errors is already printed at the expense of the Board of Longitude, and is to be annexed to the publication of Mayer's original observations, which is nearly completed.]