by Saint Paul; and it was at the ninth hour that Christ died.  Ten is the number of laws given by Jehovah, the law of fear; but Saint Augustine explains it otherwise, saying that it includes the knowledge of God, since it may be decomposed into three, the symbol of a triune God, and seven, figuring the day of rest after the Creation.  Eleven, the same saint explains as an image of transgressing the law and an emblem of sin; and Twelve is the great mystic number, the tale of the patriarchs and the Apostles, of the tribes, the minor prophets, the virtues, the fruits of the Holy Ghost, and the articles of faith embodied in the Credo.  And this might be repeated to infinity.  Hence it is quite evident that the artists of the Middle Ages added to the meaning they assigned to certain creatures and certain things, that of quantity, supporting one by the other, emphasizing or moderating a suggestion by this added-means, working back sometimes on a former idea, and expressing this duplication in a different form or concentrating it in the energetic conciseness of a cipher.  They thus produced a whole at once speaking to the eye and, at the same time, giving synthetical expression to the complete text of a dogma in a compact allegory.”

“But what hermetic concentration!” exclaimed Durtal.

“Very true; these various meanings of persons and objects, resulting from numerical differences, are at first very puzzling.”

“And do you suppose that, on the whole, the height, breadth, and length of a cathedral reveal a specialized idea, a particular purpose on the part of the architect?”

“Yes; but I must at once confess that the key to these religious calculations is lost.  Those archaeologists who have racked their brains to find it have vainly added together the measurements of naves and clerestories; they have not yet succeeded in formulating the idea they expected to see emerge from the sums total.

“In this matter we must confess ourselves ignorant.  Besides, have not the standards of measurement been different at different times?  As with the value of coins in the Middle Ages, we know nothing about them.  So, in spite of some very interesting investigations carried out from this point of view by the Abbe Crosnier at the Priory of Saint Gilles, and the Abbe Devoucoux at the Cathedral of Autun, I remain sceptical as to their conclusions, which I regard as very ingenious, but far from trustworthy.

“The method of numbers is to be seen in perfection only in the details, such as the pillars of which I spoke just now; it is no less evident when we find the same number prevailing throughout the edifice, as for instance at Paray-le-Monial, where all things are in threes.  There the designer has not been content to reproduce the sacred number in the general scheme of the structure; he has applied it in every part.  The church has, in fact, three aisles; each aisle has three compartments; each compartment is formed by three arches surmounted by three windows.  In short, it is the principle of the Trinity, the primary Three, applied to every part.”