themselves, but yet all agreeing within certain limits, and only a comparatively small number of them deviating considerably from the mean of all; and from these he is called upon to say, definitively, what he shall consider to have been the most probable place of his star at the moment. Just so in the calculation of physical _data_; where no two results agree exactly, and where all come within limits, some wide, some close, what have we to guide us when we would make up our minds what to conclude respecting them? It is evident that any system of calculation that can be shown to lead of necessity to the most probable conclusion where certainty is not to be had must be valuable. However, as this doctrine is one of the most difficult and delicate among the applications of mathematics to natural philosophy, this slight mention of it must suffice at present. (231.) In the foregoing pages we have endeavoured to explain the spirit of the methods to which, since the revival of philosophy, natural science has been indebted for the great and splendid advances it has made. What we have all along most earnestly desired to impress on the student is, that natural philosophy is essentially united in all its departments, through all which one spirit reigns and one method of enquiry applies. It cannot, however, be studied as a whole, without subdivision into parts; and, in the remainder of this discourse, we shall therefore take a summary view of the progress which has been made in the different branches into which it may be most advantageously so subdivided, and endeavour to give a general idea of the nature of each, and of its relations to the rest. In the course of this, we shall have frequent opportunity to point out the influence of those general principles we have above endeavoured to explain, on the progress of discovery. But this we shall only do as cases arise, without entering into any regular analysis of the history of each department with that view. Such an analysis would, indeed, be a most useful and valuable work, but would far exceed our present limits. We are not, however, without a hope that this great desideratum in science will, ere long, be supplied from a quarter every way calculated to do it justice. PART III. OF THE SUBDIVISION OF PHYSICS INTO DISTINCT BRANCHES, AND THEIR MUTUAL RELATIONS. CHAPTER I. OF THE PHENOMENA OF FORCE, AND OF THE CONSTITUTION OF NATURAL BODIES.