The substance of _M. Le Monier_’s argument is this. In 1739, when _M. Bouvet_’s discovery is supposed to have been made, the methods for determining the longitude of a ship at sea were very defective; and, of course, the longitude of any land which happened accidentally to be seen by one, was equally uncertain. On a presumption that this was the case with respect to Cape Circumcision, _M. Le Monier_ enquires into the quantity of the variation of the magnetic needle, observed by M. Bouvet at that place, and also into observations of the same kind, made at other places in the neighbourhood of it, about the same time, as well as both before and since. And by comparing these observations together, he concludes, that at the time when Captain Cook was in these seas, the variation of the needle at Cape Circumcision must have been 10° westerly: whereas, in the most westerly point of Captain Cook’s track, where he was sufficiently near the parallel of 54° south, to have seen land situated in it, the variation was 13-1/2° westerly. This difference of 3-1/2°, in the variation, answers to about 7° of longitude, in this part of the parallel of 54° south: and by so much did Captain Cook fall in with this parallel to the eastward of what he ought to have done to see the land in question. “Hence (M. Le Monier infers), that it is not surprising the British navigator should not find Cape Circumcision under a meridian which is 28-1/2° to the eastward of Ferro, when it is really situated under a meridian which is but 21-1/2° to the eastward of it.” In replying to these allegations, I shall first show, that, granting the dependence which _M. Le Monier_ supposes may be placed on observations of the variation made at sea, he has stated the quantity of the variation observed on board the Resolution, very erroneously. Secondly, I shall prove, beyond contradiction, that observations of the variation, made at sea, cannot be depended on for the purposes to which _M. Le Monier_ has applied them. And, lastly, that no material error had crept into _M. Bouvet_’s reckoning; but that if any error did exist, it must have been of a contrary nature to that which _M. Le Monier_ supposes.