A short account of some observations made with chronometers, in two expeditions sent out by the admiralty, at the recommendation of the board of longitude, for ascertaining the longitude of Madeira and of Falmouth. In a letter to Thomas Young, M. D. For. Sec. R. S. and Secretary to the Board of Longitude. By Dr. John Lewis Tiarks

Dr. Tiarks was sent to Madeira in the year 1822 with 15 chronometers, of which the rates had principally been ascertained in the Royal Observatory of Greenwich; he touched at Falmouth both in going out and returning; and having again ascertained the rates of his time-keepers, he was thus enabled to obtain two distinct determinations of the longitude of Falmouth, which differed about four seconds of time from that which had been inferred from the Trigonometrical Survey of Great Britain. It became therefore desirable that some further operations should be undertaken for the removal or elucidation of this discordance; and the following year a similar method was adopted with 25 chronometers, for determining the difference of longitude between Falmouth and Dover; this latter station having been chosen as easy of access, and as being perfectly determined; and the computations were made by interpolation, without employing any other rates for the chronometers than those which were observed in the different trips while they were actually on board the ship; and latterly, when Dover Roads became unsafe, the operations were limited to the distance from Portsmouth to Falmouth: thus, between the months of July and September, the observations were made three times at Dover, four times at Falmouth, and three times at Portsmouth; and the comparison of their results affords a correction of five seconds of time for the difference of longitude of Dover and Falmouth, and of three for the difference of Falmouth and Portsmouth, agreeing completely with the error of four seconds, attributed from the observations of the preceding year to the difference of longitude of Falmouth and Greenwich. Hence Dr. Tiarks thinks it fair to conclude that the diameter of the parallel circle, in which the longitude is measured, has in the survey been taken somewhat too great, and consequently the earth’s ellipticity greater than the truth. He remarks that the measurement of the spheroidal triangle concerned, determines only the actual flatness of the part of the earth’s surface on which it is situated, and not the actual magnitude of the whole parallel, unless its curvature be supposed perfectly uniform, which we cannot assume with confidence; while on the other hand, if we compute the ellipticity from the result of the chronometrical determination, it becomes one 314th instead of one 150th, and agrees with the most accurate measurements obtained from different principles. The longitude of Falmouth is finally determined to be 20 m 11 s. 1 of time, and that of the British Consul’s garden at Funchal, 1 h 7 m 39 s W. of Greenwich.