to many other subjects, on which we cannot here enter. In his mechanical speculations he was less fortunate: he applies geometry with considerable effect to many questions in this science; but, in the investigation of the inclined plane, betrays an erroneous notion of the resolution of forces, which renders defective his estimate of the force necessary to sustain a body on the plane: this defect in the knowledge of so essential a principle marks a point beyond which the ancient mechanics did not extend, and which must have precluded a further advance.

Theon and Proclus, about the same period, or rather later, were known chiefly as commentators on Euclid. To the former we are little indebted for his attempts to improve upon his author; the latter wrote also a treatise on Motion.

Diocles, who lived before a. D. 500, is known as the inventor of an elegant curve, called the cissoid, to which he was led by a previous construction of Pappus for finding two mean proportionals between given extremes. This curve is the locus traced out by the intersection of a chord from one end of the diameter of a semicircle drawn to the summit of an ordinate, with another ordinate equidistant from the centre. A perpendicular at the other end of the diameter becomes an asymptote to the curve; which was named the cissoid*, from a fancied resemblance to a sprig of ivy mounting up a wall, as the curve does up its asymptote.

On alluding to these abstract topics, these elegant fictions, as it were, of a geometrical imagination in which the ancient mathematicians loved to indulge, the question of utility will doubtless be raised; a question which, of course, can only be answered when the objector states to what class of objects he will extend the character of utility. For any practical results these methods are no longer of use, because we now possess easier and shorter processes. But that matters of abstract contemplation, as such, are not useful, is an assertion which surely betrays the most confined · * λισσος, ivy.

notions on the part of him who urges it, and will hardly be maintained by any one who has acquired just views of the relative importance of the different branches of philosophical speculation, and the intimate connection and dependence which subsists between them. And that, of such abstract speculations, those relating to the singular properties of curve lines arising as logical consequences out of the simplest constructions, are among the most beautiful, is a point of taste, for the justness of which we can only appeal to the convictions of every one who will go through the necessary steps to enable him to judge.

The fifth century of the Christian era witnessed the almost total extinction of the sciences in Alexandria. Some students, indeed, were to be found, who continued to keep alive the memory of the achievements of a former age. But the circumstances of the times were unfavourable to the extension of physical research, and at length the invasion of the Saracens, and the wanton destruction of that great repository in which the treasures of literature had been accumulating at Alexandria for nine centuries (A. D. 640), struck the final blow; and from that period we may date the extinction of Greek philosophy.

In Rome, we have already seen that the little taste ever evinced for the physical sciences had long before declined. The writings of the philosophers were composed exclusively in the Greek language. The great division of the empire under the sons of Theodosius placed so broad a line of separation between the eastern and western portions of it, that Greek literature was now no longer cultivated in Rome. Thus the records of science ceased to be accessible to the nations of the West; while the troubles in which this division of the empire was now involved, the continual wars, and irruptions of the Gothic tribes in its later ages, wholly prevented any attempts to raise an indigenous growth of science, even had the germs of it existed in the genius of the people.

General Remarks on the Progress and Character of ancient Science.

Though, in the course of the preceding pages, we have from time to time made incidental remarks on the causes which have affected the progress of science among the ancients; yet it may not be superfluous, in concluding this division of our, subject, briefly to recapitulate, and add a few general observations on such causes, on the spirit and genius of the ancient methods, and its influence on the true interpretation of nature.

If we consider man as a being gifted with the powers of observation and reason, and especially as receiving knowledge through the medium of the external senses, it might seem that the examination of nature, and the investigation of the laws by which its phenomena are regulated, would naturally and necessarily form both an early object of attention, and one to which a peculiar importance would be generally attached. Nevertheless we have observed that the case has been much otherwise and, in following the course of the gradual advance of moral, as well as physical civilisation, we have been compelled to acknowledge that the progress in this great department of intellectual improvement has taken place so tardily, and to such a very limited extent, even under the most apparently favourable circumstances, that it may not be unimportant briefly to notice some of the causes which have probably tended to produce such a result.

In the earlier stages of society, and with a large portion of mankind in all its stages, there are other and more pressing wants to be satisfied before those of the mind. But, supposing that we are arrived at a point beyond this state of things, and that the requisite freedom from the immediate pressure of necessity is enjoyed, still it is long before the particular contemplation of nature, with a view to tracing its order and harmony,

takes possession of the mind. A few, perhaps, are irresistibly led on by some loftier aspirations to devote their attention to what the rest disregard. But in general, even in the most favourable instances, there are many causes operating to render the advance towards the real principles of science extremely slow. The first and foremost obstacle is the want of perception of the value and importance of making exact enquiries into nature; or even of contemplating the material world at all, in any other light than as at best a topic of passing admiration, or in general as the source of new physical enjoyments. This want of a due recognition of the claims of pure philosophic enquiry, apart from the examination of the natural world with a view to the purposes of art or of gain, has been, and still is, the first great impediment in the way of the more general diffusion of a taste for such pursuits, and the more extended cultivation of them. In fact, so slowly, and so rarely, is the full recognition of the intrinsic excellence of abstract enquiry brought about, that in tracing the growth of human society in its emergence out of the depraved condition of savage life towards its just and fair proportions, whenever we can find anything like a due estimation only avowed of the value of the search after truth for its own sake, we cannot hesitate to associote it with the attainment of an uncommonly high point of real moral civilisation. Even when a gifted individual may have opened the way, yet it has usually required the lapse of centuries, and the occurrence of many such brilliant examples, before any similar taste could be at all diffused among the generality of mankind.

But again with the best disposition, the extent and variety of the objects on all sides soliciting attention will rather distract the contemplation, than favour that concentration of the powers on the several parts, by which the gradual knowledge of the whole can alone be promoted.

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Man," (observes Professor Playfair,)" could not at first perceive from what point he must begin his en

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quiries, in what direction he must carry them on, or by what rules he must be guided. He was like a traveller going forth to explore a vast and unknown wilderness, in which a multitude of great and interesting objects presented themselves on every side, while there was no path for him to follow, no rule to direct his survey."

But, amid all this variety of objects, the selection of those to which the attention should be directed, will hardly be a matter of deliberate choice. The mind will always be more powerfully excited by those phenomena which are rare, sudden, and imposing; and the curiosity will be dead to those which are daily surrounding us. Hence, in the earlier stages of knowledge, awe and wonder are first excited by the blaze of a meteor, the explosion of thunder, or the eruption of a volcano ; but no admiration is called forth by the falling of a stone to the ground, or our vision of the face of nature. Surprise at length gives way to a spirit of curiosity: this in like manner is always at first directed to enquire into the causes of the most marvellous, rather than of the most common events; and it is little considered that it is from these last that we can alone reason to the causes of the first. When, however, in any case curiosity is once excited, there is always some hope that rational enquiry may in time follow; or, as an Italian poet expresses it,

But as awe and wonder are the first powerful emotions called forth by the great phenomena of the natural world, it too commonly happens that from this source a very different spirit from that of rational curiosity takes its rise — the feeling of superstition. And, perhaps, of all causes tending to check the spirit of enquiry into the laws of the material world, and the causes of physical phenomena, none is more powerful or extensive in its operation. The origin of this impression would seem to Dissertation on the Progress of Science, p. 56.