13. _Fluids press Equally in all Directions._--The doctrines which concern the equilibrium of fluids depend on principles no less certain and simple than those which refer to the equilibrium of solid bodies; and the Greeks, who, as we have seen, obtained a clear view of some of the principles of Statics, also made a beginning in the kindred subject of Hydrostatics. We still possess a treatise of Archimedes _On Floating Bodies_, which contains correct solutions of several problems belonging to this subject, and of some which are by no means easy. In this treatise, the fundamental assumption is of this kind: 'Let it be assumed that the nature of a fluid is such, that the parts which are less pressed yield to those which are more pressed.' In this assumption or axiom it is implied that a pressure exerted upon a fluid in one direction produces a pressure in another direction; thus, the weight of the fluid which arises from a downward force produces a lateral pressure against the sides of the containing vessel. Not only does the pressure thus diverge from its original direction into all other directions, but the pressure is in all directions exactly equal, an equal extent of the fluid being taken. This principle, which was involved in the reasoning of Archimedes, is still to the present day the basis of all hydrostatical treatises, and is expressed, as above, by saying that _fluids press equally in all directions_. Concerning this, as concerning previously-noticed principles, we have to ask whether it can rightly be said to be derived from experience. And to this the answer must still be, as in the former cases, that the proposition is not one borrowed from experience in any usual or exact sense of the phrase. I will endeavour to illustrate this. There are many elementary propositions in physics, our knowledge of which {231} indisputably depends upon experience; and in these cases there is no difficulty in seeing the evidence of this dependence. In such cases, the _experiments_ which prove the law are prominently stated in treatises upon the subject: they are given with exact measures, and with an account of the means by which errours were avoided: the experiments of more recent times have either rendered more certain the law originally asserted, or have pointed out some correction of it as requisite: and the names, both of the discoverers of the law and of its subsequent reformers, are well known. For instance, the proposition that 'The elastic force of air varies as the density,' was first proved by Boyle, by means of operations of which the detail is given in his _Defence_ of his _Pneumatical Experiments_[18\3]; and by **Mariotte in his _Traité de l'Équilibre des Liquides_, from whom it has generally been termed Mariotte's law. After being confirmed by many other experimenters, this law was suspected to be slightly inaccurate, and a commission of the French Academy of Sciences was appointed, consisting of several distinguished