as the mere reading of the limb of the instrument is concerned, is very beautiful, as it reduces the separate readings of a number of observations to two, namely, one at the commencement and the other at the end of a repeated angle, equivalent, in magnitude, to the sum of the total number of separate or individual readings, so that the error is reduced to an inappreciable quantity by being divided amongst so many parts of the multiple, or repeated angle; and it was therefore supposed possible to attain the utmost precision with very small repeating circles. But it must be manifest that whilst correcting the errors in reading of the divisions of the instrument, nothing has been done towards correcting the errors of observation or of bisection of the object observed, consequent on the use of small instruments; and further, that the difficulty of guarding against any slight movements of the concentric circles during observation by any system of clamping hitherto devised has not been remedied. Schumacher, whilst admitting that the repeating circles of Reichenbach far surpass those of the French artists, still asserts, "that it is impossible to rely upon any permanency in the constant error when the limb of the instrument is placed in a vertical direction," and adds, that he "should not consider his work well finished, if the amplitude of the arc were to depend only on observations made with an instrument, the peculiarities of which were as yet insufficiently known, and not on those made with an excellent sector." It will be readily, there

fore, supposed that any opportunity of bringing these two instruments into direct comparison with each other would be hailed with satisfaction by astronomers, and something in that respect was anticipated from the co-operation of the French and English geodesists, during the year 1817.

In October, 1816, M. Arago, on the part of La Place, communicated to Colonel Mudge the wish of that illustrious philosopher that the latitude of Yarmouth should be determined by the sector, in order to terminate at that point the French arc. "He sees," says Arago, "in the arc extending from Formentara to Yarmouth the means of determining with great precision the value of a degree of latitude at the 45th degree. The situation of the two extreme stations almost on the same meridian would render the result entirely independent of any flattening of the parallel, if such really exist. This operation, indeed equally remarkable for its extent, for its object, and for its precision-would further have the more precious advantage of belonging equally to England as to France, and would become one day perhaps the basis of a uniform system of weights and measures." On the 4th of July, 1817, La Place himself writes: "Thanking you for your very kind reception of my proposition to terminate the French arc at Yarmouth, I must, at the same time, express my assent to your opinion that as it is now intended to extend the British arc to the Shetland Islands, Yarmouth may be replaced by the terminal station in these

islands, even though Formentara is about 1 degree in longitude to the eastward of it. The difference in latitude between the extreme points will then be about 22 degrees, and as their difference in longitude is so very small, the geodesical operations of France and England may be referred to this are without fear of any sensible error. It is therefore most important to determine the latitude of the sta tion selected in Shetland with the utmost precision, and for that purpose to determine the zenith distances of as many as possible of the stars, which may be observed for altitude at Greenwich and Paris. My friend M. Biot will not fail, I am sure, to use every care in determining the length of the pendulum at that station. We are about to measure a great arc of the parallel between Strasbourg and Brest, and we shall then have all the data required for a correct knowledge of the portion of the earth on which we live—and surely, thus to study the earth is far better than to devastate it by conquests, however brilliant and glorious they may appear. I am de lighted to hear that you propose to send the great sector to Brest, and I think that M. Arago will join you there, and assist in the determination of the latitude, either by observing with the sector, or by simultaneously observing with a good repeating circle; and as the singularity of an increase in the degrees from the pole to the equator, as shown by your observations, has excited so much discussion, I would suggest that it might be advisable that you should afterwards repeat with Messrs. Arago and

Biot, the zenith observations for latitude at Dunnose." With a view, then, to this co-operation between the French and English geodesists, so strongly advocated by La Place, and supported by the French Institute and Bureau de Longitude, M. Biot came over alone as a commissioner, on the part of the French, his colleague M. Arago being unfortunately retained in France by other business. The special object of this visit was stated by M. Biot himself, who, after having expressed his opinion that the French arc, when compared with the independent measurements of Svanberg and Lambton, was specially entitled to become the fundamental type of a system of measures, observes, "Since the rebellion of 1745, the English Government has felt the advantage of a detailed map of the three kingdoms to serve as the basis of works of improvement peace and works of defence in war. The English triangulation, commenced by General Roy, and continued by Colonel Mudge, has already been carried from the south of England to the north of Scotland, so as to embrace several degrees of a terrestrial meridian, measured with excellent instruments. It was natural to wish that this arc should be joined to that of France, but the geographical position of England being a little to the west of our arc, it was feared that if all the terrestrial meridians were not similar the difference of longitude might affect the results deduced from such a junction. The Bureau de Longitude, therefore, wished that the pendulum apparatus which had been used in Spain

in

and France should be also applied to similar trials at the principal stations of the English arc, as measures deduced from the pendulum are much less affected by small irregularities in the figure of the earth than are measured degrees." M. Biot subsequently adds: "When we had finished our experiments [at Leith] we were to have gone to the Orkneys to repeat them there, as the terminal station of the English arc, but Colonel Mudge, always anxious to render his operations as complete as possible, considered that it would be possible to connect the Shetland Islands with the Orkneys, by a triangulation embracing the intermediate islets or rocks of Faira and Foula-a plan which, whilst it extended the are about two degrees to the north, also had the great advantage of bringing the English meridional arc two degrees more to the east, or almost in the prolongation of the meridian of Formentara." From what has been said, however, in a preceding page, it is manifest that M. Biot was in error in supposing that the design of terminating the English arc in the Shetland Islands was a sudden and after thought partly adopted, as it were, in reference to the French arc; as it has been shown, that Captain Colby had long before considered it a matter of course that the arc should be co-extensive with the triangulation, and therefore be terminated at the Shetland Islands; and that Colonel Mudge had finally adopted the same opinion there is not the slightest reason for doubting. The proposition of the French Board of Longitude was warmly re