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pens, and more especially when any branch of science has been long cultivated, and research is limited to a narrow track, that, in fact, a large portion of the work is already done to our hands, and the trouble of referring to a number of different considerations to guide our experimental labours, superfluous.

These, and other considerations of a similar kind, may tend to show the real value and efficacy of such a system as that which Bacon has developed; and to convince any one, that, although the study of it may not be of absolute necessity to every prosecutor of experiments, yet it will in all cases be accompanied with inestimable advantages: and we cannot doubt, if it were more generally and attentively dwelt upon, we should see the records of science much less frequently blotted with unphilosophical arguments, and should much less frequently witness the labours of ingenious experimenters thrown away in the pursuit of unskilfully devised theories.

It is undoubtedly true, that we find the principles of inductive philosophy not only acted upon, but distinctly professed, by writers prior to Bacon. We have already seen this exemplified in the productions of Kepler and Galileo and Tycho Brahe, in a letter to Kepler, gives him this advice: "first to lay a solid foundation for his views by actual observation; and then, ascending from these, to strive to reach the causes of things." Gilbert, in his treatise " De Magnete," has laid down very explicitly the inductive principles by which he was guided in his experiments. We have also in some passages of the writings of Leonardo da Vinci equally strong expressions to the same purport.

"In treating any particular subject," he observes, "I would first of all make some experiments, because my design is first to refer to experiment, and then to demonstrate why bodies are constrained to act in such a manner. This is the method we ought to follow in investigating the phenomena of nature. It is very true that nature begins by reasoning, and ends with experiment; but it matters not; we must take the opposite

course; as I have said, we must begin by experiment, and endeavour by its means to discover general principles."

Again,-"Theory is the general: experiments are the soldiers. The interpreter of the works of nature is experiment that is never wrong. It is our judgment which is sometimes deceived, because we are expecting results which experiment refuses to give. We must consult experiment, and vary the circumstances, till we have deduced general rules, for it alone can furnish us with them. But you will ask, What is the use of these general rules? I answer, that they direct us in our enquiries into nature and the operations of art. They keep us from deceiving ourselves and others by promising ourselves results which we can never obtain.” *

We have been led to refer to these views more particularly, because some modern writers of considerable eminence have been rather disposed to undervalue the character of Bacon's writings, and to deny their extensive or beneficial influence on the researches of subsequent philosophers. It has been alleged that Galileo, Copernicus, and even Kepler, had exhibited perfect examples of the inductive method of philosophising, and that Leonardo da Vinci, in the passages just quoted, as well as Galileo and some other authors of that period, have, in fact, in such expressions delivered a brief but complete summary of all the essentials of the inductive method. Even the alchemists of that day, absurd and visionary as were the objects of their pursuit, yet, it is urged, in the indefatigable toils of their laboratories, at least showed that they considered the whole value of their science to rest upon experiments. Kepler, in the wildest of his reveries, submitted them most scrupulously to the test of accordance with observation, and unhesitatingly sacrificed the labours of years if the results did not stand the test. Thus, it is said, those philo.. sophers had all thrown off the yoke of the schools, and

* Venturi, Essai sur les Ouvrages de L. da Vinci, p. 32.

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not only fully understood the value of the inductive method, but resolutely acted in accordance with it. Thus, Bacon cannot be said to have invented or constructed the method to which modern science owes its existence. And later philosophers have not disclosed in their methods any closer adherence to Bacon's rules than his predecessors did. Newton, Boyle, Huygens, and their followers, have never alluded to the guidance of the "prerogativæ instantiarum," nor mentioned to which class their arguments were to be referred.

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The remarks we before made will almost supply an answer to these animadversions. We may, however, more completely reply by putting a parallel cașe. possessed many eloquent writers in the English language before an English Grammar was composed; and since that, we boast many more who have neither written better English, nor, in every sentence, quoted the grammatical rule by virtue of which that sentence was constructed. Will it, therefore, be argued that grammar is useless, or the man who first formed one entitled to no praise?

The "Novum Organon" is the grammar of inductive philosophy. Its principal merit lies, not in supplying practical rules, without a technical knowledge of which no man could conduct a philosophical enquiry; nor in teaching men the value or utility of the unfettered appeal to experiment: but its main excellence consists in bringing into the form of a philosophical system those principles which, though already practically recognised, had not yet been viewed in their mutual connection and dependence; and in reducing to a scientific arrangement those scattered truths which were already approved by the practice of the most cautious and judicious enquirers into nature.

If, then, a philosopher of a subsequent age, conducting his discoveries on inductive principles, should make no especial mention of Bacon, and should state his experiments and describe his results, without explicitly telling us whether they belong to the class of "instantiæ

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curriculi," or experimenta crucis;" should refute errors, without formally classifying them as "idola specus," or "idola fori;" would this be any argument either that those systematic distinctions were unknown to him, or that the philosophical arrangement of them, according to their characteristic differences, was an idle, useless, or chimerical speculation ?

We conceive, upon the whole, we hardly need urge more to vindicate the exalted rank to which Bacon is entitled among the philosophres, not only of his own, but of any age. He was, doubtless, deficient in mathematical knowledge, and he did not, himself, push his principles to the discovery of any actual physical laws. He did not, perhaps, shine with so much lustre among his contemporaries, as he does to posterity. We walk familiarly on the surface of the earth without perceiving the light it reflects, but to the distant lunarians it is a brilliant luminary. The immediate value of the discoveries of Galileo was more striking. Bacon wrote for ages to come. And it may be safely affirmed, that, though we could name several philosophers who, placed in the same circumstances as Galileo, might have made the same discoveries, yet we cannot say this of Bacon; we might find substitutes for the one, but not for the other. Galileo was the immediate minister of science, whose services enlightened his own times: Bacon was its prophet, whose credit was not established till his predictions were verified. Galileo entered and took possession of the vast regions which science was henceforth to call her own. Bacon, from his lofty elevation, took a complete survey of the rich territory of the promised land; but expired, like Moses on Mount Nebo, without himself entering it. In a word, we must entirely agree with D'Alembert, that, "when one considers the sound and enlarged views of this great man, the multitude of the objects to which his mind was turned, and the boldness of his style, which unites the most sublime images with the most rigorous precision, one is disposed to regard

him as the greatest, the most universal, and the most eloquent of philosophers."

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The succession of discoveries to which we have re ferred, during the latter part of the sixteenth and beginning of the seventeenth centuries, brought algebraic analysis to a state of very considerable perfection. The way was thus prepared for the brilliant discoveries in reference to the application of this analysis to geometry, which constitute the peculiar characteristic of the "modern geometry," and confer upon it those extended powers and capacities to which the ancient system could not attain. Such applications had been made in a few instances (as we have noticed) by Vieta and others. But the grand advance, to which we now refer, was that effected by Des Cartes, and which forms one of the most important epochs in the history of mathematical science.

This philosopher, celebrated in so many departments of science, was born at La Haye, in Touraine, in 1596, and at an early age displayed great proficiency in various branches both of literature and science. After going

through the usual course in the Jesuits' college at La Flêche, he entered upon the military profession, and, soon after, visited various parts of Europe. The versatility of his genius showed itself in the variety of different studies he pursued, embracing almost every department of science, metaphysical as well as mathematical. He died in 1650. It was in Holland, in 1637, that he first published his Geometry, in which the great inventions above referred to are contained. This work is a tract of no more than 106 quarto pages: but there is, probably, no production of the same size which ever conferred so much and so just celebrity on its author.

In the first book, he treats of such geometrical problems as can be resolved by the help of circles and * Disc. Préliminaire de l'Encyclop.

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