It is with pleasure that I request the attention of the Royal Society to the present communication, in continuation and completion of my former papers, because I think that the anomalies which the Indian Arc has appeared to present are here traced to the true causes. 1. I will explain what those anomalies were. On completing a laborious and wellexecuted survey of the two northern portions of the Indian Arc of Meridian, between Kaliana (29° 30' 48") and Kalianpur (24° 7' 11"), and Kalianpur and Damargida (18° 3' 15"), Colonel Everest found that their astronomical and geodetical amplitudes differed considerably; in the higher arc the geodetic amplitude he found to be in excess by 5"·236, in the lower of the two ares in defect by 3"·791. The three stations had been selected with great care, and were finally chosen as being apparently free from all disturbing causes. Indeed, a fourth station which had been at one time adopted, Takal Khera in Central India, was rejected by Colonel Everest because a neighbouring hillrange was discovered on calculation to produce a deflection of about 5". Kaliana had been chosen nearly sixty miles from the lower hills at the foot of the Himmalaya Mountains, in the full conviction that it would be free from mountain influence. The surprise was therefore great when, on the completion of the survey of the two arcs in question, these two errors were brought to light. The first was attributed to the influence of the Himmalayas, but without any calculation; but the second, with its negative sign, received no interpretation. At this stage I devised a method of calculating the effect of the Himmalayas by a direct process; and found that the deflections produced are far greater than the errors which had to be explained, and the negative sign was left altogether unaccounted for. Thus the perplexity was increased. It next occurred to me that the vast Ocean to the south of India might have some influence on the plumb-line. On making the necessary calculations the effect of this cause was found, as the mountain attraction had been, to be far greater than had been anticipated; the negative sign was still unexplained, and the difficulties were not cleared up. No other cause of disturbance was apparent at the surface. But I showed by calculation that in the crust below one
might
exist sufficient to reduce the large deflections occasioned by the Mountains and the Ocean, and make them accord with the results deduced by Colonel Everest from the arcs themselves. But, being hidden from our sight, neither the magnitude nor indeed the existence of this cause could be
à priori
ascertained, much less reduced to calculation. Whether, moreover, the errors brought to light by Colonel Everest arose solely from local attraction, or from local attraction combined with some local peculiarity in the curvature of the Indian Arc, was not apparent; so that the subject of local attraction and its influence on geodetic operations in this country, was still involved in obscurity, and the anomalies of the Indian Arc remained unexplained in the papers which I have hitherto forwarded to the Society. In the present communication I think ambiguity is removed. It is demonstrated that no peculiarity in the curvature of the arc can produce any part of the errors brought to light by Colonel Everest; that those errors arise solely from local attraction; that they are in fact the exact measure of the difference of the resultant local attraction at the two extremities of each arc, from what ever causes the attraction may arise—mountains, ocean, or crust; lastly, it is proved that there
are
hidden causes in the crust below the Indian Arc, and the differences of their resultant effect upon the stations of the arc are computed. An inference from these results is, that the relative position of places in a Map, laid down from geodetic operations, is accurate, being altogether unaffected by local attraction; though the position of the Map itself on the terrestrial spheroid will be dependent upon the observed latitude of some one station in it, and that observed latitude will be affected by the local attraction at that place. To determine the absolute latitude in some one station connected with the geodetic operations is still a desideratum.