trace backwards, step by step, the series of intermediate movements by which it is connected with the vis motrix. In doing so, there is undoubtedly a sort of mental decomposition of the machine, inasmuch as all its parts are successively considered in detail; but it is not this decomposition which constitutes the analysis. It is the methodical retrogradation from the mechanical effect to the mechanical power.*

The passages in Condillac to which these criticisms refer, are all selected from his treatise on Logic, written purposely to establish his favourite doctrine with respect to the influence of language upon thought. The paradoxical conclusions into which he himself has been led by an unwarrantable use of the words Analysis and Synthesis, is one of the most remarkable instances which the history of modern literature furnishes of the truth of his general principle.

That this circumstance of retrogradation or inversion, figured more than any other in the imagination of Pappus, as the characteristical feature of geometrical analysis, appears indisputably from a clause already quoted from the preface to bis 7th Book ;--Την τοιαύτην έφοδον ανάλυσιν καλέμεν δον αναπαλον λυσιν. To say, therefore, as many writers have done, that the analysis of a geometrical problem consists in decomposing or resolving it in such a manner as may lead to the discovery of the composition or synthesis, --is at once to speak vaguely, and to keep out of view the cardinal principle on which the utility of the method hinges. There is indeed one species of decomposition exemplified in the Greek geometry;-that which has for its object to distinguish all the various cases of a general problem; but this part of the investigation was so far from being included by the ancients in their idea of analysis, that they bestowed upon it an appropriate name of its own; the three requisites to a complete solution being (according to Pappus) αναλύσαι, και συνθεῖναι, και διορίζεσθαι κατα πτωσιν.

Nor does this observation apply merely to the productions of his more advanced years. In early life, he distinguished himself by an ingenious work, in which he professed to trace analytically the history of our sensations and perceptions; and yet, it has been very justly remarked of late, that all the reasonings contained in it are purely synthetical. A very eminent mathematician of the present times has even gone so far as to mention it "as a model of geometrical synthesis."* He would, I apprehend, have expressed his idea more correctly, if, instead of the epithet geometrical, he had employed, on this occasion, logical or metaphysical; in both of which sciences, as was formerly observed, the analytical and synthetical methods bear a much closer analogy to the experimental inductions of chemistry and of physics, than to the abstract and hypothetical investigations of the geometer.

The abuses of language which have been now under our review, will appear the less wonderful, when it is considered that mathematicians themselves do not always speak of analysis and synthesis with their characteristical precision of expression; the former word being frequently employed to denote the modern calculus, and the latter, the pure geometry of the ancients. This phraseology, although it has been more than once censured by foreign writers, whose opinions might have been expected to have some weight, still continues to prevail very generally upon the Continent. The learned and judicious author of the History of Mathematics complained of it more than fifty years ago; remarking the impropriety "of calling by

* M. Lacroix. See the Introduction to his Elements of Geometry.

the name of the synthetic method, that which employs no algebraical calculus, and which addresses itself to the mind and to the eyes, by means of diagrams, and of reasonings expressed at full length in ordinary language. It would be more exact (he observes farther) to call it the method of the ancients, which, (as is now universally known,) virtually supposes, in all its synthetical demonstrations, the previous use of analysis. As to the algebraical calculus, it is only an abridged manner of expressing a process of mathematical reasoning;-which process may according to circumstances, be either analytical or synthetical. Of the latter, an elementary example occurs in the algebraical demonstrations given by some editors of Euclid, of the propositions in his second Book."*

This misapplication of the words analysis and synthesis, is not, indeed, attended with any serious inconveniences, similar to the errors occasioned by the loose phraseology of Condillac. It were surely better, however, that mathematicians should cease to give it the sanction of their authority, as it has an obvious tendency,-beside the injustice which it involves to the inestimable remains of Greek geometry,-to suggest a totally erroneous theory, with respect to the real grounds of the unrivalled and transcendent powers possessed by the modern calculus, when applied to the more complicated researches of physies.†

*Histoire des Mathématiques, par Montucla, Tome Premier, pp. 175, 176. † In the ingenious and profound work of M. De Gerando, entitled, Des Signes et de l'Art de Penser, considérés dans leur rapports mutuels, there is a very valuable chapter on the Analysis and Synthesis of metaphysicians and of geometers. (See Vol. IV. p. 172.) The view of the subject which I have taken in the foregoing section, has but little in common with that

SECTION IV.

The Consideration of the Inductive Logic resumed.

1.

Additional Remarks on the distinction between Expe rience and Analogy.—Of the grounds afforded by the latter for Scientific Inference and Conjecture.

In the same manner in which our external senses are struck with that resemblance between different individuals which gives rise to a common appellation, our superior faculties of observation and reasoning, enable us to trace those more distant and refined similitudes which lead us to comprehend different species under one common genus. Here, too, the principles of our nature, already pointed out, dispose us to extend our conclusions from what is familiar to what is comparatively unknown: and to reason from species to species, as from individual to individual. In both instances, the logical process of thought is nearly, if not exactly, the same; but the common use of language has established a verbal distinction between them; our most correct writers being accustomed

given by this excellent philosopher; but in one or two instances, where we have both touched upon the same points, (particularly in the strictures upon the logic of Condillac) there is a general coincidence between our criticisms, which adds much to my confidence in my own conclusions.

Y y

(as far as I have been able to observe) to refer the evidence of our conclusions, in the one case, to experience, and in the other to analogy. The truth is, that the difference between these two denominations of evidence, when they are accurately analyzed, appears manifestly to be a difference, not in kind, but merely in degree; the discriminative peculiarities of individuals invalidating the inference, as far as it rests on experience solely, as much as the characteristical circumstances which draw the line between different species and different genera.*

In these observations on the import of the word analogy, as employed in philosophical discussions, it gives me great pleasure to find, that I have struck nearly into the same train of thinking with M. Prévost. I allude inore particularly to the following passage in his Essais de Philosophie.

"Le mot Analogie, dans l'origine, n'exprime que la ressemblance. Mais l'usage l'applique à une ressemblance éloignée: d'ou vient que les conclusions analogiques sont souvent hasardées, et ont besoin d'être déduites avec art. Toutes les fois donc que, dans nos raisonnemens, nous portons des jugemens semblables sur des objets qui n'ont qu'une ressemblance éloignée, nous raisonnons analogiquement. La ressemblance prochaine est celle qui fonde la première généralisation, celle qu'on nomme l'espèce. On nomme éloignée la ressemblance qui fonde les généralisations superieures, c'est-àdire, le genre et ses divers degrès. Mais cette definition n'est pas rigoureusement suivie.

"Quoiqu'il en soit, on conçoit des cas, entre lesquels la ressemblance est si parfaite, qu'il ne s'y trouve aucune différence sensible, si ce n'est celle du tems et du lieu. Et il est des cas dans lesquels on apperçoit beaucoup de ressemblance, mais où l'on decouvre aussi quelques différences indépen dantes de la diversité du temps et du lieu. Lorsque nous ferons un jugement general, fondé sur la première espèce de ressemblance, nous dirons que nous usons de la méthode d'induction. Lorsque la seconde espèce de ressemblance autorisera nos raisonnemens, nous dirons que c'est de la méthode d'analogie que nous faisons usage. On dit ordinairement que la méthode d'induction conclut du particulier au général, et que la methode d'analogie conclut du semblable au senblable. Si l'on analyse ces defini