IX. An account of trigonometrical operations in the years 1821, 1822 and 1823, for determining the difference of longitude between the Royal Observatories of Paris and Greenwich. By Captain HENRY KATER, V.P.R.S.

`Read January 31, and February 7, 1828.

SECTION 1.

IN the year 1790, a series of trigonometrical operations was carried on by General Roy, in co-operation with Messrs. DE CASSINI, MECHAIN, and LEGENDRE, for the purpose of connecting the meridians of Paris and Greenwich. In England, the work commenced with a base measured on Hounslow Heath, whence triangles were carried through Hanger Hill Tower and Severndroog Castle on Shooter's Hill, to Fairlight Down, Folkstone Turnpike, and Dover Castle on the English coast; which last stations were connected with the church of Nôtre Dame at Calais, and with Blancnez and Montlambert upon the coast of France. An account of these operations will be found in the Philosophical Transactions for 1790.

In the year 1821, the Royal Academy of Sciences and the Board of Longitude at Paris communicated to the Royal Society of London their desire, that the operations for connecting the meridians of Paris and Greenwich should be repeated jointly by both countries, and that commissioners should be nominated by the Royal Academy of Sciences and by the Royal Society of London for that purpose. This proposal having been readily acceded to, Messrs. ARAGO and MATTHIEU were chosen on the part of the Royal Academy of Sciences, and Lieut.-Colonel (then Captain) COLBY and myself were appointed by the Royal Society to co-operate with them.

The instrument employed on this occasion was RAMSDEN'S great theodolite, the property of the Royal Society, the same which had been used by General ROY. A party of the Royal Artillery and a sufficient number of tents were supplied by his Grace the DUKE OF WELLINGTON, then Master General of the

Ordnance, and every means were afforded which could tend to facilitate the work.

It was at first proposed to adopt some one of the distances given by the Trigonometrical Survey of Great Britain, as a base, and to connect this with General Roy's stations upon Fairlight Down and near Folkstone Turnpike. But the attempt to discover General Roy's stations upon Fairlight and at Folkstone proved, in the first instance, fruitless; and unfortunately, the gun which had marked the important station of the trigonometrical survey on Beachey Head, was not to be found. It is to be feared that, in consequence of some misapprehension, it had been removed along with some old guns which were formerly near that place, and thus one of the most valuable points of the survey of Great Britain was irrecoverably lost.

Colonel COLBY was so good as to allow Mr. GARDNER (then one of the assistants on the trigonometrical survey, and now agent for the sale of the Ordnance maps,) to accompany us; and to the talents, zeal, and exertion of that gentleman, on various occasions of difficulty, we were much indebted.

The signals used for connecting the stations upon the coasts of England and France were lamps with compound lenses, constructed under the direction of M. FRESNEL, and of which he has published an account. It will be sufficient here to mention, that the lens, composed of numerous pieces, was three feet in diameter, and that the light far exceeded that of any of our light-houses, appearing at the distance of forty-eight miles like a star of the first magnitude. Staffs were also erected near the lamps, but these were only occasionally visible. Having selected convenient stations upon Fairlight Down and near Folkstone Turnpike, and placed the lamps there with steady men to attend them, the party crossed the Channel on the 24th of September 1821, and proceeded to Cape Blancnez, a station to the south-west of Calais. Here we found an old guard-house, the roof of which was partially destroyed, but of which we nevertheless took possession, as it promised a less comfortless abode than our tents at that season would have afforded. At Blancnez we experienced very tempestuous weather; and on the night of the 4th of October it blew so violently that the men's tents were carried away, and we were obliged to take down the theodolite to preserve it from injury.

The observations at Blancnez having been concluded on the 7th of October,

we proceeded to Montlambert (or as it is commonly called Boulambert), a small fort situated on a height near Boulogne; and by the 9th of October the instru ment was ready for observing. In the course of our work at this station some delay was experienced in consequence of the lamp at Fairlight not being lighted, and M. MATTHIEU and Mr. GARDNER were dispatched to know the cause of this omission. On their arrival at Calais, finding no packet ready to depart, their anxiety led them to cross in an open boat, at night, in weather so tempestuous that they were nearly lost. They found that the glass chimneys of the lamp at Fairlight were all broken; but their ingenuity remedied this by joining the remaining pieces together; and on the evening of the 13th the light was seen, and satisfactory angles obtained between it and the other stations.

On the 14th of October, the observations at Montlambert being completed, we left that station for Calais. On the 17th we re-crossed the Channel, and on the 19th proceeded to Fairlight. Here I endeavoured to find General Roy's station, and discovered the cause of the failure of the former attempt. In the account of General Roy's operations, his station is stated to be 347 feet southward from the Mill; and the angle at his station between the Mill and Fairlight Church is given. Now it happens that the mill which stood in General Roy's time has been destroyed, and another built upon the Down in a different situation. A circular trace however of the old mill was at length discovered; and the distance from its centre to the station having been carefully measured nearly in the proper direction, a small theodolite placed at the end of this radius was shifted until the centre of Roy's Mill and Fairlight Church subtended the given angle. On digging under the theodolite, the wooden pipe by which General Roy had marked his station was found at the depth of four feet. In order to preserve this point, a millstone having the words "Roy'S STATION" cut upon it, was placed level with the surface of the ground, its centre being precisely over the centre of the pipe.

The observations at Fairlight were completed by the 22nd of October, and the party proceeded on the 24th to a station chosen near Folkstone Turnpike. In order to carry on the series towards London, stations had been selected on Stede Hill and Wrotham Hill; but as these were not visible from Folkstone, it became necessary to employ an intermediate point on Tolsford Hill.

A staff had been erected on General Roy's station upon Dover Castle, in

order to connect this with the Church of Nôtre Dame at Calais. But as it would have been peculiarly inconvenient, and would have been attended with some risk to have got the great theodolite upon the Castle, the angle there was not taken; but the distance between Dover station and Nôtre Dame has been determined by means of two sides and the included angle, in a manner which will probably appear to be sufficiently satisfactory, as no other station is dependent upon this distance.

The observations at Folkstone were completed on the 27th of October; and with great regret we now bade adieu to our much-esteemed companion M. ARAGO, who left us for Paris; and as the season was too far advanced to admit of any further proceedings, the party returned to London.

It was now our intention to connect our triangles with the base measured by General Roy upon Hounslow Heath; but though upon examination it was found that the guns marking the termination of this base still existed, it was not thought advisable to attempt to avail ourselves of it, from the many buildings which intervened, and which prevented one end of the base being seen from the other. We were therefore under the necessity of employing the distance from Severndroog Castle to Hanger Hill Tower, as these were the nearest stations to General Roy's base that could be identified with sufficient precision.

During the operations of 1821, I was strongly impressed with the inconvenience of changing the zero point of the theodolite, in order to obtain the angle upon different arcs, so as to do away errors of division; and on my return to London I caused four additional microscopes to be adapted to the instrument, by Mr. CAREY. On this important alteration I shall have further to remark in the Appendix.

The summer of 1822 was employed in the choice of stations, one of which was the temporary meridian mark erected near Chingford for the Royal Observatory. This station was chosen, in order that a side of one of our triangles might coincide with the meridian of Greenwich, and that the azimuths of the different stations, with respect to that meridian, might thence be deduced with greater accuracy than might have resulted from observations of the pole star. Stations were also selected upon Leith Hill, Wrotham Hill, Stede Hill, and Crowborough. We anxiously sought a station to the south of Chingford, for