He considered the position of the window, and of the prism; repeated the experiment over and over; and in virtue of the eminently distinct conceptions of space which he possessed, resolved the phenomena into its geometrical conditions. A believer in accident would not have sought them; a person of less clear ideas would not have found them. A person must have a strange confidence in the virtue of chance, and the worthlessness of intellect, who can say that {49} 'in all these fundamental discoveries appropriate ideas had no share,' and that the discoveries 'might have been made by the most ordinary observers.' 21. I have now, I trust, shown in various ways, how the _Explication of Conceptions_, including in this term their clear development from Fundamental Ideas in the discoverer's mind, as well as their precise expression in the form of Definitions or Axioms, when that can be done, is an essential part in the establishment of all exact and general physical truths. In doing this, I have endeavoured to explain in what sense the possession of clear and appropriate ideas is a main requisite for every step in scientific discovery. That it is far from being the only step, I shall soon have to show; and if any obscurity remain on the subject treated of in the present chapter, it will, I hope, be removed when we have examined the other elements which enter into the constitution of our knowledge. {{50}} CHAPTER III. OF FACTS AS THE MATERIALS OF SCIENCE. APHORISM IV. _Facts are the materials of science, but all Facts involve Ideas. Since in observing Facts, we cannot exclude Ideas, we must, for the purposes of science, take care that the Ideas are clear and rigorously applied._ APHORISM V. _The last Aphorism leads to such Rules as the following:--That Facts, for the purposes of material science, must involve Conceptions of the Intellect only, and not Emotions:--That Facts must be observed with reference to our most exact conceptions, Number, Place, Figure, Motion:--That they must also be observed with reference to any other exact conceptions which the phenomena suggest, as Force, in mechanical phenomena, Concord, in musical._ APHORISM VI. _The resolution of complex Facts into precise and measured partial Facts, we call the_ Decomposition of Facts. _This process is requisite for the progress of science, but does not necessarily lead to progress._ 1. WE have now to examine how Science is built up by the combination of Facts. In doing this, we suppose that we have already attained a supply of definite and certain Facts, free from obscurity and doubt. We must, therefore, first consider under what conditions Facts can assume this character.