242.  It should be no cause for astonishment that I endeavour to elucidate these things by comparisons taken from pure mathematics, where everything proceeds in order, and where it is possible to fathom them by a close contemplation which grants us an enjoyment, so to speak, of the vision of the ideas of God.  One may propose a succession or series of numbers perfectly irregular to all appearance, where the numbers increase and diminish variably without the emergence of any order; and yet he who knows the key to the formula, and who understands the origin and the structure of this succession of numbers, will be able to give a rule which, being properly understood, will show that the series is perfectly regular, and that it even has excellent properties.  One may make this still more evident in lines.  A line may have twists and turns, ups and downs, points of reflexion and points of inflexion, interruptions and other variations, so that one sees neither rhyme nor reason therein, especially when taking into account only a portion of the line; and yet it may be that one can give its equation and construction, wherein a geometrician would find the reason and the fittingness of all these so-called irregularities.  That is how we must look upon the irregularities constituted by monstrosities and other so-called defects in the universe.

243.  In this sense one may apply that fine adage of St. Bernard (Ep. 276, Ad Eugen., III):  ’Ordinatissimum est, minus interdum ordinate fieri aliquid.’  It belongs to the great order that there should be some small disorder.  One may even say that this small disorder is apparent only in the whole, and it is not even apparent when one considers the happiness of those who walk in the ways of order.

244.  When I mention monstrosities I include numerous other apparent defects besides.  We are acquainted with hardly anything but the surface of our globe; we scarce penetrate into its interior beyond a few hundred fathoms.  That which we find in this crust of the globe appears to be the effect of some great upheavals.  It seems that this globe was once on fire, and that the rocks forming the base of this crust of the earth are scoria remaining from a great fusion.  In their entrails are found metal and mineral [278] products, which closely resemble those emanating from our furnaces:  and the entire sea may be a kind of oleum per deliquium, just as tartaric oil forms in a damp place.  For when the earth’s surface cooled after the great conflagration the moisture that the fire had driven into the air fell back upon the earth, washed its surface and dissolved and absorbed the solid salt that was left in the cinders, finally filling up this great cavity in the surface of our globe, to form the ocean filled with salt water.