་

XVI. An Account of the Measurement of an Arc of the Meridian, extending from Dunnose, in the Isle of Wight, Latitude 50° 37' 8", to Clifton, in Yorkshire, Latitude 53° 27′ 31′′, in course of the Operations carried on for the Trigonometrical Survey of England, in the Years 1800, 1801, and 1802. By Major William Mudge, of the Royal Artillery, F. R. S.

In the last account presented to the Royal Society, I expressed my intentions of making the operations which were to follow that period, subservient to the purpose of measuring a portion of the meridional arc, running from Dunnose, in the Isle of Wight, into the northern part of Yorkshire. In the account referred to, (See Phil. Trans. for 1800, page 565,) I stated my reasons for adopting that resolution, and my hopes that Mr. Ramsden would shortly finish the zenith sector which his Grace the Duke of RICHMOND had bespoken of him, when Master General of the Ordnance. As that celebrated artist, from the beginning of the year 1800 till the middle of the following summer, had proceeded with little interruption, except from illness, towards its completion, the whole was brought so near to a conclusion before he died, that Mr. BERGE found no difficulty in rendering it sufficiently perfect.

It is proper I should state, more fully than I have formerly

done, my reasons for selecting Dunnose as one of the extremities of my meridional line, and also those for preferring its meridian to any other; which I shall do as briefly as possible.

In a country whose surface, throughout its whole extent, is equally diversified with hilly ground, that particular part of it should be chosen, for carrying on a meridional measurement, which comprehends the most extensive arc. This arises from the necessary consequence which attends an operation in a country so circumstanced; as, possibly, no spot fixed on for a place of observation, could be supposed free from the effects of the unequal attraction in the adjoining matter. In such a country, therefore, a measurement upon the most extensive arc, must give the most accurate conclusion; for the errors arising from the cause here mentioned, like those of observation, lessen in their effects, on their application to arcs of increasing magnitude.

If Great Britain were a country thus diversified, the most eligible part would be that where the meridian from Lyme, in Dorsetshire, passes northward into Scotland. The difference of latitude between that place and Aberdeen, near to which that line cuts its parallel, is 4° 47', nearly. But, however great the advantages attending such a length of arc might be, under the general circumstances of accurate terrestrial measurement, and accurate observations at its extremities, no beneficial consequences could be expected to attend the placing of the sector at intermediate stations; as the arc would be found running, almost every where, through a country abounding with hills, considerable both in magnitude and number.

Under this consideration, I determined to measure a portion of the meridian which proceeds from Dunnose to the mouth of the Tees; because, from inquiry, I had reason to suppose it the