simple and indivisible in itself, and divided from everything else, or it cannot be an original and primary component. For, however far the analysis of a composite may be carried, it may be carried further, unless it has been analysed to its simple constituent parts which are not themselves composite, and therefore simple. It is of no avail to take refuge in the notion of the infinite divisibility of matter. For, apart from the absurdity of the infinite series contained in this notion, one of these infinitesimal entities could certainly be divided from all others by the power of God and made intelligible to the human understanding. And the very question under discussion is, What is the intelligible essence of this ultimate entity? [Footnote 4: The philosophical works of Leibnitz may be consulted for a thorough exposition of this doctrine. Also the Philosophical Manuals of F. Rothenflue, S.J., and the Abbé Branchereau of the Society of St. Sulpice. The philosophical articles of Dr. Brownson in his Review contain some incidental arguments of great value on the same topic. P. Dalgairns of the London Oratory, also treats, with the ability and clearness which characterize all his writings, of this subject, at considerable length, in his work on the Holy Communion.] [Footnote 5: By "imaginary conceptions" is not meant fanciful, unreal conceptions, but conceptions of the imaginative as and intellectual facility which reflects the real.] Another proof that material substance is something intelligible and not something sensible, is, that it has a relation to spiritual substance, and therefore something cognate to spirit in its essence. The Abbé Branchereau defines relation: "Proprietatem qua duo aut plura entia ita se habeat ad invicem, ut unius conceptus conceptum alterius includat aut supponat." "A property by which two or more entities are so constituted in reference to one another, that the conception of one includes or suppose the conception of the other." [Footnote 6] [Footnote 6: Praelect. Philos. De Relat. Entis. Num. 108, 8.]