medes's "Treatise on Floating Bodies." And from this principle are deduced the solutions, not only of the simple problems of the science, but of some of considerable complexity.

The difficulty of holding fast this idea of fluidity, so as to trace its consequences with infallible strictness of demonstration, may be judged of from the circumstance that, even at the present day, men of great talents, not unfamiliar with the subject, sometimes admit into their reasonings an oversight or fallacy with regard to this very point. The importance of the idea when clearly apprehended and securely held, may be judged of from this, that the whole science of hydrostatics in its most modern form is only the developement of the idea. And what kind of attempts at science would be made by persons destitute of this idea, we may see in the speculations of Aristotle concerning light and heavy bodies, which we have already quoted; where, by considering light and heavy as opposite qualities, residing in things themselves, and by an inability to apprehend the effect of surrounding fluids in supporting bodies, the subject was made a mass of false or frivolous assertions, which the utmost ingenuity could not reconcile with facts, and still less deduce from them any additional truths.

In the case of statics and hydrostatics, the most important condition of their advance was undoubtedly the distinct apprehension of these two appropriate ideas, statical pressure, and hydrostatical pressure. For

the ideas being once clearly possessed, the experimental laws which they served to express (that the whole pressure of a body downwards was always the same; and that water, and the like, were fluids according to the idea of fluidity) were so obvious, that there was no doubt nor difficulty about them. These two ideas lie at the root of all mechanical science; and the firm possession of them is, to this day, the first requisite for a student of the subject. After being clearly awakened in the mind of Archimedes, these ideas slept for many centuries, till they were again called up in Galileo, and more remarkably in Stevinus. This time, they were not destined again to slumber; and the results of their activity have been the formation of two sciences, which are as certain and severe in their demonstrations as geometry itself, and as copious and interesting in their conclusions; but which, besides this recommendation, possess one of a different order;that they exhibit the exact impress of the laws of the physical world; and unfold a portion of the rules according to which the phenomena of nature take place, and must take place, till nature herself shall alter.

VOL. I.

II

CHAPTER II.

EARLIEST STAGES OF OPTICS.

THE progress made by the ancients in Optics was nearly proportional to that which they made in statics. As they discovered the true grounds of the doctrine of equilibrium, without obtaining any sound principles concerning motion, so they discovered the law of the reflection of light, but had none but the most indistinct notions concerning refraction.

The extent of the principles which they really possessed is easily stated. They knew that vision is performed by rays which proceed in straight lines, and that these rays are reflected by certain surfaces (mirrors) in such manner that the angles which they make with the surface on each side are equal. They drew various conclusions from these premises by the aid of geometry; as, for instance, the convergence of rays which fall on a concave speculum.

It may be observed that the idea which is here introduced, is that of visual rays, or lines along which vision is produced and light carried. This idea once clearly apprehended, it was not difficult to show that these lines are straight lines, both in the case of light and of sight. In the beginning of Euclid's "Treatise on Optics," some of the arguments are mentioned by which this was established.

We are

told in the Proem, " In explaining what concerns the sight, he adduced certain arguments from which he inferred that all light is carried in straight lines. The greatest proof of this is shadows, and the bright spots which are produced by light coming through windows and cracks, and which could not be, except the rays of the sun were carried in straight lines. So in fires, the shadows are greater than the bodies if the fire be small, but less than the bodies if the fire be greater." A clear comprehension of the principle would lead to the perception of innumerable proofs of its truth on every side.

The law of equality of angles of incidence and reflection was not quite so easy to verify; but the exact resemblance of the object and its image in a plane mirror, (as the surface of still water, for instance,) which is a consequence of this law, would afford convincing evidence of its truth in that case, and would be confirmed by the examination of other

cases.

With these true principles was mixed much error and indistinctness, even in the best writers. Euclid, and the Platonists, maintained that vision is exercised by rays proceeding from the eye, not to it; so that when we see objects, we learn their form as a blind man would do, by feeling it out with his staff. This mistake, however, though Montucla speaks severely of it, was neither very discreditable nor very injurious; for the mathematical conclusions on each supposition are necessarily the same. Another curious

assumption is, that these visual rays are not close together, but separated by intervals, like the fingers when the hand is spread. The motive for this invention was the wish to account for the fact, that in looking for a small object, as a needle, we often cannot see it when it is under our nose; which it was conceived would be impossible if the visual rays reached to all points of the surface before us.

These errors would not have prevented the progress of the science. But the Aristotelian physics, as usual, contained speculations more essentially faulty. Aristotle's views led him to try to describe the kind of causation by which vision is produced, instead of the laws by which it is exercised; and the attempt consisted, as in other subjects, of indistinct principles, and ill-combined facts. According to him, vision must be produced by a medium,-by something between the object and the eye,-for if we press the object on the eye, we do not see it; this medium is light, or "the transparent in action;" darkness occurs when the transparency is potential not actual; colour is not the absolute visible, but something which is on the absolute visible; colour has the power of setting the transparent in action; it is not, however, all colours that are seen by means of light, but only the proper colour of each object; for some things, as the heads, and scales, and eyes of fish, are seen in the dark; but then they are not seen with their proper colour1.

1 De Anim. ii. 6.