over 1798-9 included a considerable number of observations made for topographical purposes, and were therefore chiefly conducted by the chief draughtsman and surveyors of the Tower, under whom the actual survey was carried on; and also the measurement, in 1798, of a base on King's Sedgemoor, Somersetshire, in which a chain of 50 feet, made by Ramsden, was combined with the longer chains, and found very useful in facilitating a measurement ground intersected by numerous ditches. The length of this base was 27,680 feet: but from the soft and shaky character of the ground, Captain Mudge considered it subject to an error of not less than six or more than nine inches, and it was found that the length of the base, as determined by triangulation from that of Salisbury Plain, differed from the measured length by nearly one foot. account of all these operations was accompanied by a great number of latitudes and longitudes of stations, deduced geodesically from the calculated distances and meridional bearings. Hitherto the survey had done little towards the great astronomical question of the figure of the earth, although this object had always been present to the minds of its successive directors, and a new instrument, a zenith sector, had been several years before ordered from Mr. Ramsden by the Duke of Richmond, for the express purpose of being used in the celestial observations required in such an inquiry. This instrument was at length completed about the end of 1801, by Mr. The Berge, Mr. Ramsden dying just before he had put the last touch to it. It was the intention of Major Mudge to apply the extension of the survey triangulation northwards to the determination of an arc of the meridian, extending from Dunnose to the mouth of the Tees; and in 1802 the triangulation had been carried so far as to enable him to comprise within his celestial observations an arc of 2° 50′ 23′′ 38, extending from Dunnose in the Isle of Wight, to Clifton in Yorkshire; the sector having been observed at both these stations, and at Arbury Hill between them. This remarkable instrument was provided with a telescope 8 feet long, supported at its summit by means of a conical axis, on the Y's of a strong frame, and with a graduated arch 15° in extent, struck by the telescope as a radius. It admitted, therefore, of observing stars 7° 30' on either side of the zenith. The instrument admitted of reversal in the plane of the meridian, and great ingenuity was displayed in all the arrangements for adjusting the plumb-line, for relieving the axis from pressure, for securing stability, and for facilitating the operations of observing, reading, &c.; and it was therefore naturally expected that with an instrument provided with an arch of so large a circle, the results of observation would be very superior, and most important data be obtained for comparison with the measurements of other countries; but it is remarkable that the results proved at variance with the deductions from other measurements, as the length of a degree increased in approaching the equator in the following manner :— Middle point between Arbury and Clifton. Middle point between Arbury 51 35 18 60,864 51 2 54 60,884 Hill and Dunnose . Middle point between Dunnose and Greenwich General Mudge did not conclude from these unexpected results that the earth was an irregular solid of revolution, and still less did he deduce from them an argument against the Newtonian theory of its figure; on the contrary, he explained them as the effects of deflections of the plumb-line of the sector, consequent on an unequal attraction due to the irregular distribution of the matter in the vicinity of the sector stations. It cannot indeed be doubted that all instruments of which the vertical adjustment depends on a plumb-line or any other contrivance, subject to be influenced by the force of gravitation, must, more or less, be exposed to this source of error, though at the same time it appears possible by a judicious combination of observations-as, for example, by observing at subsidiary stations to the north or south of the suspected station, and at short accurately measured distances from it-to detect if not to avoid the error, and to determine its amount and direction. All geodesists did not, however, concur in opinion with General Mudge, and in 1812 a paper was published in the "Philosophical Transactions," by Don J. Rodriguez, in which that writer endeavours to show that the possible errors of the sector, as exhibited in the various readings of the same zenith distances, are sufficient to explain the observed anomalies; and the mode in which he conducts his investigation is curious. He first assumes an ellipsoid for the earth's figure, depending on the compression or ellipticity deduced from the. various measurements of degrees in northern and southern latitudes, independent of the English, and then, with the calculated distances and observed azimuths, published in the account of the English survey, determines by calculation the length of the meridional arc in feet or fathoms, and deduces from that length and the elliptic elements the length in degrees, minutes, and seconds. Comparing this length as deduced from calculation with that obtained by the sector observations, he maintains that the difference is not beyond the limits of error of the instrument. Don Rodriguez, in conducting this comparison, adopts successively three different compressions, so as to get rid of any probable error in their determination, namely,; and to prove the applicability of his method, makes a similar comparison between the observed and the calculated lengths of Svanberg's Arc in Lapland, and Lambton's Arc in the East Indies, in both of which calculation and observation were found to be in perfect accordance. The last publication of the proceedings of the Survey, with which General Mudge was connected, was dated one year before the paper of Don Rodriguez; and it does not, therefore, appear that his remarks were ever replied to by General Mudge, though it must be admitted that they merited consideration, and seemed to render necessary fresh observations of zenith distances at the great sector stations, in order to confirm their accuracy and to support their testimony. When it is remembered that Don Rodriguez adopts an ellipsoid which had been determined from a comparison of the northern and southern degrees, it cannot be considered remarkable that, with that ellipsoid, he should again arrive, by calculation backwards, as it were, at those degrees; and though the difference between the observed English arc and the arc as obtained by calculation on Don Rodriguez's system does not much exceed the difference between some of the individual observations, it would be quite unreasonable to consider the whole of the extreme differences between the observations as due to error. In most cases the mean of a set of angles is more likely to be correct when by their variations they embrace every cause of error, than when they are all apparently identical in reading, though probably only so because they have been affected by the same errors acting in the same direction; still, however, when the demonstration of a remarkable physical fact seems to depend on the right interpretation. of ob |