PHYSICAL AND MATHEMATICAL SCIENCES. 207

quently, who have never studied systems of rhetoric ;hut all this does not in the least disparage the abstractphilosophic excellence of such systems respectively.These systems present a view of the theory of thoseprinciples into which the real results may be analysed,and from which they might synthetically be traced.The value of such systems is of a higher and more phi-losophical kind ; and though it may be true that manyhave succeeded in arriving at their conclusions withoutsuch aid, yet it by no means follows that all can dis-pense with it, nor that even these persons might nothave succeeded more completely and more easily if theyhad been in possession of some settled principles onwhich to proceed.

Again, it must be borne in mind that all the sys-tematic enumeration of Bacon was made purely fromtheory and by anticipation. He was bound to considerand examine every possible avenue to philosophic truth,to scrutinise every conceivable channel through whichinvestigation might be conducted; and it might wellhappen that some of these should afterwards be foundpractically of far more importance, and far more fre-quent use than others: that, in point of fact, induc-tive science should mainly proceed by means of somefew of the principles here developed, whilst the occur-rence of others should hardly be recognised.

We have a remarkable instance of this in the “ in-stantise radii.” Bacon appears to attach no moreimportance to this class of facts than to any others;but yet in modern research it has come to pass thatnearly every subject of enquiry, which can claim tobelong to the exact sciences, has been brought underthe dominion of measurement, and subjected to thetest of numerical agreement with mathematical laws.Something to the same purpose we have already re-marked of the “ instantiee crucis.” This is, in fact, inreal practice, the sort of experiment most frequentlyappealed to, and that from which the most satisfactoryconviction is derived. Again, it not unfrequently hap-