sical tone of the author's speculations probably tended to its favourable reception in other schools, as it at least furnished interminable subjects for scholastic disputation.

In the English universities it obtained almost undisputed sway in proportion as the Aristotelian physics were rejected, and it was necessary to have some determinate system to substitute in their place. The " Physics" of Rohault, conceived entirely on the Cartesian principles, continued, till a much later period, the favourite and established text-book in Cambridge. That and other systems of the same kind were also read in Oxford and the Scottish universities. We shall not be surprised at the popularity which the Cartesian system acquired throughout Europe, if we remark that it appealed strongly to the imagination, and very little to the reason, of mankind. In explaining all the movements of the heavenly bodies by a system of vortices in a fluid medium diffused through the universe, Des Cartes had seized upon an analogy of the most alluring kind. Those who had seen heavy bodies revolving in the eddies of a whirlpool, or in the gyrations of a vessel of water to which a rotatory motion had been given, had no difficulty in conceiving how the planets might revolve round the sun by analogous movements. The mind instantly grasped at an explanation of so palpable a character, and which required for its developement neither the exercise of patient thought nor the aid of mathematical skill. Above all, the immediate chain of connection by which the author affected to deduce it from the attributes of the Deity stamped it with that religious sanction which, once obtained, gives currency to any absurdities, however glaring; and even stigmatises with impiety the most rational and demonstrable truths opposed to the notions it has once countenanced.

Thus much, however, we may safely say in praise of the Cartesian theory, that its popularity certainly helped materially to explode the more gross errors of the Ptolemaic system; and, from seeing one system give way to

another, men's minds were so far opened as to begin to lose their excessive devotion to authority, and to acknowledge that every system should be fairly open to examination.

We have before noticed the successive attempts made by Alhazen, Vitello, and Kepler, to investigate the law of refraction. The enquiry appears to have been first prosecuted with complete success by Willebrord Snell, a Dutch mathematician, who flourished about 1600.

His mode of conceiving the problem by a geometrical construction is certainly more complex than necessary; but this construction, when put into the more convenient and perspicuous language of trigonometry, unquestionably amounts to the simple announcement of the law which had been so long sought, and which connects together the deviation of the refracted ray towards the perpendicular, and the angle of incidence, for all values of that angle. The relation is that of a constant ratio between the sines of the angles which the incident and refracted rays form with the perpendicular. This remains invariable for all incidences, while the media are the same, but varies for different media. If we suppose the ray to pass out of vacuum into the given medium, the ratio for the partiticular, medium in this case is called the refractive index of that medium.

Snell, however, certainly did not announce his discovery in this precise language. Des Cartes, in his Dioptrics, published in 1637, gives it in this form of enunciation, without making the smallest mention of Snell; and the discovery, in consequence, went forth as that of Des Cartes. It has been said that Snell's works containing this discovery were not published at the time Des Cartes wrote; other accounts, however, give as the date of their publication 1619, or even earlier. At any rate, Snell had communicated his researches to his

friends, and they had been made public by his countryman, Professor Hortensius, in his lectures. It may also be true that Des Cartes made an independent discovery of the same truth. His character, however, is well known to have been marked with an envious desire to disparage the merits of those who might be his rivals; and this circumstance throws considerable doubt on his claim to originality.

Des Cartes, in this as well as other parts of his speculations, affected to reason from those abstract principles, which were, in fact, nothing more than arbitrary assumptions. He deduced the law of refraction, not from a comparison of observations, but from the hypothesis that light proceeds more rapidly in denser media.

The hypothetical character of this reasoning was exposed and censured by Fermat, who, nevertheless, himself attempted to deduce the law upon a principle which, in the existing state of the science, was scarcely less hypothetical, though it has been fully confirmed by later researches. This was termed "the principle of least action;" that is, he assumed that light must always move so as to pass from one given point to another in the least possible time, and that the course it takes under the influence of the different density of the media will be determined in accordance with this principle and contrary to the theory of Des Cartes, assuming that light is retarded in proportion to the density of the medium, he deduced, on this principle, the same result, a refraction regulated by the law of the sines.

Des Cartes also directed his attention to the forms of lenses, and the means of collecting incident rays accurately to one point as the focus. No spherical lens does this accurately, even if limited to a very small arc of a sphere; and if at all of considerable curvature, the aberration is very great. Des Cartes, therefore, investigated generally the nature of the curve which should give this accurate convergence; and by a very complete

and elegant analysis showed that a certain class of curves of the fourth degree will fulfil the conditions: these, in certain cases, become of the second degree. But the mechanical difficulties in working any glasses except those of a spherical form, are so great as to forbid all hopes of improving optical instruments from the introduction of other curves.

The explanation of the rainbow was advanced an additional step by the researches of Des Cartes. He explained the secondary bow; and accurately traced the paths of the rays, and the angles under which the effect is produced; but the extension of the same principles to the distinct colours was yet wanting. He is, as usual, entirely silent as to the claims of previous writers, and never mentions De Dominis.

The Disciples of Galileo. Physical Science.

Galileo had opened the way to a vast field of research, and also succeeded in inspiring with the desire to explore it, a number of zealous and able disciples, who soon proceeded to the task with equal diligence and success: among these, none were more pre-eminently distinguished than Torricelli, who flourished about 1640.

Torricelli made some additions to the mechanical discoveries of Galileo, in his treatise "De Motu Gravium naturaliter Descendentium et Projectorum." He investigated general theorems relative to the centre of gravity and the equilibrium of bodies.

In hydraulics he seems also to have taken the first step, by showing that the water issues from a hole in the side or bottom of a vessel with the same velocity as that which a body would acquire by falling from the level of the surface to that of the orifice. It is needless to remark the importance of this principle to nearly the whole science of the motion of fluids.

But this is not the greatest discovery we owe to this distinguished friend and disciple of Galileo: he prosecuted with success another enquiry, in which even his

illustrious teacher had failed. Galileo had observed the fact, that water will not rise in an exhausted tube (as in a pump) to a height greater than about thirty-three feet, but he was unable to give an explanation of the principle: Torricelli, however, perceived it, and proceeded to verify it. The column of water was held in equilibrium with a column of air: in the tube all pressure was removed from it; on the other side, or in the reservoir, it was pressed by the whole weight of the column of air reaching from the surface of the water to the top of the atmosphere. The height at which the water stood, or the quantity of water supported, depended on nothing but its weight compared with the weight of air: the same thing ought then to hold good with all other fluids. Mercury is a fluid about thirteen times more dense than water; a quantity of it, therefore, about one thirteenth of the quantity of the water, would be in like manner supported by the same column of air: that is, the column of mercury would stand at about the height of thirty inches.

This, therefore, Torricelli proceeded to try. A tube, closed at one end, being filled with mercury, carefully stopping the open end with his finger, he inverted it with the open end in a basin of mercury: the mercury in the tube immediately fell, and remained stationary at a height of about thirty inches. Thus it was evident that the principle assumed was correct: the weight and pressure of the atmosphere were established; and the theory of suction, nature's horror of a vacuum, and a host of kindred absurdities, at once and for ever exploded. The whole of this class of phenomena were now reduced to one simple law; and the action of the air referred to the same causes as those which influence the grosser forms of matter, however little its subtile nature might at first sight appear amenable to them. A new and wide extension was thus given to our perception of the simplicity and unity of design which pervades all nature; a fresh train of reflection opened to those who were capable of profiting by it; and an important