Mr. Mill enjoins four methods of experimental inquiry, which he calls _the Method of Agreement_, _the Method of Difference_, _the Method of Residues_, and _the Method of Concomitant Variations_[271]. They are all described by formulæ of this kind:--Let there be, in the observed facts, combinations of antecedents, _ABC_, _BC_, _ADE_, &c. and combinations of corresponding consequents, _abc_, _bc_, _ade_, &c.; and let the object of inquiry be, the consequence of some cause _A_, or the cause of some consequence _a_. The Method of Agreement teaches us, that when we find by experiment such facts as _abc_ the consequent of _ABC_, and _ade_ the consequent of _ADE_, then _a_ is the consequent of _A_. The Method of Difference teaches us that when we find such facts as _abc_ the consequent of _ABC_, and _bc_ the consequent of _BC_, then _a_ is the consequent of _A_. The Method of Residues teaches us, that if _abc_ be the consequent of _ABC_, and if we have already ascertained that the effect of _A_ is _a_, and the effect of _B_ is _b_, then we may infer that the effect of _C_ is _c_. The Method of Concomitant Variations teaches us, that if a phenomenon _a_ varies according as another phenomenon _A_ varies, there is some connexion of causation direct or indirect, between _A_ and _a_. 39. Upon these methods, the obvious thing to remark is, that they take for granted the very thing which is most difficult to discover, the reduction of the phenomena to formulæ such as are here presented to us. When we have any set of complex facts offered to us; for instance, those which were offered in the cases of discovery which I have mentioned,--the facts of the planetary paths, of falling bodies, of refracted rays, of cosmical motions, of chemical analysis; and when, in any of these cases, we would discover the law of nature which governs them, or, if any one chooses so to term it, the feature in which all the cases agree, where are we to look for our _A_, _B_, _C_ and _a_, _b_, _c_? Nature does not present to us the cases in this form; and how are we to reduce them to this form? You say, _when_ we find the combination of _ABC_ with _abc_ and _ABD_ with _abd_, then we may draw our inference. Granted: but when and where are we to find such combinations? Even now that the discoveries are made, who will point out to us what are the _A_, _B_, _C_ and _a_, _b_, _c_ elements of the cases which have just been enumerated? Who will tell us which of the methods of inquiry those historically real and successful inquiries exemplify? Who will carry these formulæ through the history of the sciences, as they have really grown up; and show us that these four methods have been operative in their formation; or that any light is thrown upon the steps of their progress by reference to these formulæ?