any

for determining the form of the sun's orbit; thus Archimedes, possessing a steady notion of mechanical pressure, was able, not only to deduce the properties of the lever and of the centre of gravity, but also to see the truth of those principles respecting the distribution of pressure in fluids, on which the science of hydrostatics depends.

With such distinct ideas, the inductive sciences rise and flourish; with the decay and loss of such distinct ideas, these sciences become stationary, languid, and retrograde. When men merely repeat the terms of science, without attaching to them any clear conceptions; when their apprehensions become vague and dim;—when they assent to scientific doctrines as a matter of tradition, rather than of conviction, on trust rather than on sight;-when science is considered as a collection of opinions, rather than a record of laws by which the universe is really governed; it must inevitably happen, that men will lose their hold on the truths which the great discoverers who preceded them have brought to light. They are not able to push forwards the truths on which they lay so feeble and irresolute a hand; probably they cannot even prevent their sliding back towards the obscurity from which they had been drawn, or from being lost altogether. Such indistinctness and vacillation of thought appear to have prevailed in the stationary period, and to be, in fact, intimately connected with its stationary character. I shall point out some indica

tions of the intellectual peculiarity of which I speak.

1. Collections of Opinions.-The fact, that mere Collections of the opinions of physical philosophers came to hold a prominent place in literature, already indicated a tendency to an indistinct and wandering apprehension of such opinions. I speak of such works as Plutarch's five Books "on the Opinions of Philosophers," or the physical opinions which Diogenes Laërtius gives in his "Lives of the Philosophers." At an earlier period still, books of this kind appear; as for instance, a large portion of Pliny's Natural History, a work which has very appropriately been called the Encyclopædia of Antiquity; even Aristotle himself is much in the habit of enumerating the opinions of those who had preceded him. To present such statements as an important part of physical philosophy, shows an erroneous and loose apprehension of the nature of such philosophy; for the only proof of which its doctrines admit, is the possibility of applying the general theory to each particular case. The authority of great men, which in moral and practical matters may or must have its weight, is here of no force; and the technical precision of ideas which the terms of a sound physical theory usually demand, renders a mere statement of the doctrines very imperfectly intelligible to readers familiar with common notions only. To dwell upon such collections of opinions, therefore, implies, and pro

duces, in writers and readers, an obscure and inadequate apprehension of the full meaning of the doctrines thus collected; if there be among them any which really possess that clearness, solidity, and reality, which make them important in the history of science. Such diversities of opinion convey no truth; such a multiplicity of statements of what has been said, in no degree teaches us what is; such accumulations of indistinct notions, however vast and varied, do not make up one distinct idea. On the contrary, the habit of dwelling upon the verbal expressions of the views of other persons, and of being content with such an apprehension of doctrines as a transient notice can give us, is fatal to firm and clear thought: it indicates wavering and feeble conceptions, which are inconsistent with sound physical speculation.

We may, therefore, consider the prevalence of Collections of the kind just referred to, as indicating a deficiency of philosophical talent in the ages now under review. As evidence of the same character, we may add the long train of publishers of Abstracts, Epitomes, Bibliographical Notices, and similar writers. All such writers are worthless for all purposes of science, and their labours may be considered as dead works; they have in them no principle of philosophical vitality; they draw their origin and nutriment from the death of true physical knowledge; and resemble the swarms of insects that are born from the perishing carcass of some nobler animal.

2. Indistinctness of Ideas in Mechanics.-But the indistinctness of thought which is so fatal a feature in the intellect of the stationary period, may be traced more directly in the works, even of the best authors, of those times. We find that they did not retain steadily the ideas on which the scientific success of the previous period had depended. For instance, it is a remarkable circumstance in the history of the science of mechanics, that it did not make any advance from the time of Archimedes to that of Stevinus and Galileo. Archimedes had established the doctrine of the lever; several persons tried, in the intermediate time, to prove the property of the inclined plane, and none of them succeeded. But let us look to the attempts; for example, that of Pappus, in the eighth book of his Mathematical Collections, and we may see the reason of the failure. His problem shows, in the very terms in which it is propounded, the want of a clear apprehension of the subject. "Having given the power which will draw a given weight along a horizontal plane, to find the additional power which will draw the same weight along a given inclined plane." This is proposed without previously defining how powers, producing such effects, are to be measured; and as if the rate at which the body were drawn, and the nature of the surface of the plane, were of no consequence. The proper elementary problem is, to find the force which will support a body on an inclined plane; and no doubt the solution of Pappus has more reference

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to this problem than to his own. His reasoning is, however, totally at variance with mechanical ideas on any view of the problem. He supposes the weight to be formed into a sphere; and this sphere being placed in contact with the inclined plane, he assumes that the effect will be the same as if the weight were supported on a horizontal lever, the fulcrum being the point of contact of the sphere with the plane, and the power acting at the circumference of the sphere. Such an assumption implies an entire absence of those distinct ideas of mechanical pressure, on which our perception of the identity or difference of different modes of action must depend;—of those ideas by the help of which Archimedes had been able to demonstrate the properties of the lever, and Stevinus afterwards discovered the true solution of the problem of the inclined plane. The motive to Pappus's assumption was probably his perceiving that the additional power, which he thus obtained, vanished when the plane became horizontal, and increased as the inclination became greater. Thus his conceptions were vague; he had no grounds of rational conviction, and he tried a conjecture. This is not the way to real knowledge.

Pappus (who lived about A. D. 400) was one of the best mathematicians of the Alexandrian school; and, on subjects where his ideas were so indistinct, it is not likely that any much clearer were to be found in the minds of his contemporaries. Accordingly, on all subjects of speculative mechanics, there