Being at present chiefly taken up with the computation of his predecessor's observations, the author takes this opportunity of examining into what is going on in other Observatories; and then endeavours, from the results of such a survey, to select some unpursued branch of Astronomy, as the proper subject to which the Edinburgh Observatory should be devoted; and he dwells much on the great caution to be used, in the present multiplication of astronomical observatories, that several of them be not working against each other on the same subject; and urges the extreme importance of first selecting an appropriate object of research, and then following it up with a constancy enduring through ages, after the manner of the Greenwich Observatory, which has consequently produced results of such inestimable service to the promotion of the science.