In the former part of this paper, Dr. Herschel mentioned the changes he had noticed in the situation of six double stars; and in investigating the causes of those changes, he declared that he had recourse to the most authentic observations he could find of their motions in right ascensions and polar distance, especially in the instance of the double star Castor: but finding in the tables which have been lately published in the last volume of the Greenwich Observations, which give the proper motions of thirty-six stars, that (especially in the instance of the above-named star,) the motions are somewhat different from those he assigned to them in his former communication, he now undertakes to review the arguments he there used, in order to ascertain what will be the result of these new motions. As this investigation, which forms the first part of the present paper, has a continual reference to the contents of the preceding one, it will be in vain to attempt an abridgement, which could not be rendered intelligible within our usual limits. Nor can we enter here into a detail of the sequel of Dr. Herschel’s observations on the changes in the situation of a great number of additional double stars; this second part of the paper, in which they are fully detailed, being itself a minute of his proceedings, in which he is at particular pains to point out that these changes of situation are not the effect of parallax.