in reference to the latitudes obtained by these stars admits of no hesitation; the results below the pole should be rejected, and those above the pole preserved.

6

To deduce, in the most advantageous manner, from the results thus preserved, and from the results of all the series with the other stars in which no remarkable difference from the mean is observed, we must adopt a mode of combination essentially different from that employed in the Base du Systême Métrique,' and of which experience subsequent to that period has established the preference. It is now known, that however skilful the artist by whom a repeating circle has been made, and notwithstanding the utmost attention which an observer can bestow on the adjustments, the zenith distances observed with it are still liable to be affected by certain errors which have obtained the name of "constant errors," but which are nevertheless constant only in a certain sense; since the transportation of the instrument from one station to another, or the mere laying it by, and putting it together again at the same station, may cause an alteration in the bearing of the parts relatively to each other, and thus a change in the amount of error. It is now therefore admitted, that, whatever may be the nature and sources of such errors, the best mode of obtaining latitudes free from their influence is, to observe several series of wellknown stars both north and south of the zenith, and, as far as may be possible, at equal distances from it; then if the mean result of those observed to the north gives the latitude in excess or in defect, the mean result of those observed to the south will give it erroneous to an equal amount but in an opposite direction, and the mean of the two will be the correct latitude.

In applying this method to the observations of M. Méchain, we shall at once perceive that it affords an explanation of the supposed difference between the latitudes of Montjouy and Barcelona: hardly, indeed, had the method been established, before this was inferred by those who were engaged in similar operations: at a meeting of the Bureau des Longitudes in November, 1818, M. Arago, whilst reading an account of the mode in which M. Biot and, himself had proceeded in determining the latitude of Dunkirk, remarked, that the latitude of Barcelona, deduced in a similar manner from the

northern and southern stars, accords with the geodesical mea

surements.

Happily M. Méchain observed & Tauri and Pollux to the south of the zenith. He has himself expressed regret at his choice of these stars, and still more in having employed Ursa Majoris. With regard, indeed, to the last named star, it was matter of just regret; but if he still lived, he would, without doubt, on the contrary, rejoice, to find that those two stars south of the zenith are the means of preserving the whole work. The several series of Pollux and B Tauri, compared with those of the northern stars, show the existence of unsuspected errors in the circle of M. Méchain of the nature of those to which we have alluded. The latitudes observed to the south of the zenith are less than those to the north, and the difference is greater at Barcelona than at Montjouy. But all are in accord by the application of the new method of combination; the anomalies disappear; the latitudes of Barcelona and Montjouy agree, or at least present only the small difference of 0",21, which is well within the limits of probable error of observation, and which it would be an unnecessary refinement to endeavour to remove by further research.

The following table contains the conclusions in regard to the several stars, and to both the latitudes :

MONTJOUY.

Ursa Minoris, pass. sup. et inf. 326 obs. 41 21 44,91 B Ursa Minoris, pass. sup. et inf. 288 do.

Stars observed

g Ursa Majoris, pass. sup.

a Draconis, pass. sup.

north of the zenith.

The four stars

45,21

82 do.

44,98

Stars observed

north of the zenith.

BARCELONA.

Ursa Minoris, pass. sup. et inf. 208 obs. 41 22 47,43 6 Ursa Minoris, pass. sup. et inf. 228 do. Ursa Majoris, pass. sup.

48,37

80 do.

46,73

Capella

106 do.

44,51

Latitude of Montjouy

41 21 44,535

Latitude adopted in the Base du Systême Métrique 41 21 44,960

Correction of the latitude of the extreme station

of the Arc of the Meridian

0,425

The final latitude deduced for the southern extremity of the arc of the meridian between the parallels of Dunkirk and Montjouy is 45° 21' 44",535; being less by 0",42 than that adopted by the commission of weights and measures. But the great mass of observations combined in this determination, and the verification of the calculations which I have now made, appear to me to entitle it to great confidence. It is founded on 134 series, comprising 1722 observations, whilst the former rested on 44 series, comprising only 756 observations.

One reflection naturally suggests itself from this Memoir; the anomalies which have caused so much trouble and uneasiness can no longer be attributed to faults in the observer, or to the effects of local attraction; they were caused solely, as we have seen, by the imperfect state of our knowledge; an imperfection of which we are now ourselves aware. In perusing the notice of M. Méchain's life, and the fragments of his correspondence, published by M. Delambre, his friend and biographer, it is impossible to avoid a lively sensation of regret, in witnessing the deplorable influence that a matter, which now appears to us so trivial, exercised on the whole course of his

latter years. From the moment that his mind dwelt on these supposed errors, from the day when he adopted the fatal resolution of concealing the principal one, in the hope of returning to verify his observations, the happiness which he had hitherto enjoyed entirely forsook him. The weight of his secret, the accident which endangered his life, his wearisome captivity, the fatigues which he endured with so much perseverance, the separation from his family at that unsettled period, without obtaining tidings of them for many months, all combined to change his character, and to produce a state of melancholy, reserve, irresolution, and sometimes of apparent indifference and inactivity, which his friends in vain sought to comprehend or to overcome. Ten years were passed in crosses and disappointments which embittered and shortened his life. Méchain died at a distance from his country, his family, and his friends, a victim to the zeal and devotion with which he pursuedthe objects of his employment; and deprived of that period of life when he might have enjoyed the consideration and celebrity to which his services so justly entitled him. His name, inseparable from that of Delambre, remains, however, honourably attached to operations which will preserve the high station assigned to them amidst the achievements which distinguish the progress of science in the eighteenth century.

J. N. NICOLLET.

On the Annealing of the Specula of Reflecting Telescopes. By J. MAC CULLOCH, M.D., F.R.S., &c. &c.

(Communicated by the Author.)

Ir is much more than twenty years since I spent some time in constructing specula for reflecting telescopes; nor, till very recently, had I any reason to conjecture that in any part of the process, which it was my lot, like that of others, to labour through for myself, I was possessed of knowledge which was not equally known to every one who had attended to this subject-much more to the makers of such telescopes. Having lately, however, had an opportunity of conversing with Mr. Ramage about his processes, I believe that there is one point. at least which has been misunderstood, and, consequently,

often mismanaged: the result being the production, by accident, of good metals, perhaps one good metal only, among many failures, when, if I am right, those may be produced with comparative certainty, and possibly, in such hands as those of Mr. Ramage himself, with absolute precision. It may perhaps, indeed, be considered that it is wrong here to suppose that because this excellent constructor has overlooked a necessary portion of his process, others should be supposed to have done the same: but as I have no means of ascertaining what is the knowledge and practice of the different makers, I must even hazard the chance of here attempting to teach any one what he knew before; while I must still trust that some may hereafter derive, from my experience, precautions by which they will be saved considerable disappointment and some expense. Such is the apology for this paper, should it prove superfluous to any one: while I cannot help considering the subject as of some importance, as, not merely the colour of the metal, but, as I think, its durability, and its power of giving a clear image, depend much on the nature of the management in that part of the process to which I allude.

I am not aware that it is necessary to say anything respecting the proportions of the two metals in the alloy; though I would caution makers of specula respecting the purity of the tin and copper, being convinced by some trials that the presence of arsenic is apt to lead, in time, to the tarnishing of the surface. I must equally presume that every one is acquainted with the temperature required for the separate metals before mixing, with the necessary flux, the method of pouring in the alloy, the position of the mould, and so forth; though with respect to the best form of the metal itself, that is, as to relative thickness in its several parts, I must confess that I have never yet been able to satisfy myself: such are the complicated difficulties, entangled between the cooling and annealing first, and the optical consequences afterwards depending on changes of temperature, and on weight or flexure, that beset any calculations on this subject; while it is probable that they are really irreconcileable, or that there is no one form which will be the best, as concerns the original nature of the metal and its action when completed.