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The error of making an even number, which was a violation of the Pythagorean principle of odd numbers as the symbol of perfection, was corrected in the Hemming lectures, adopted at the union of the two Grand Lodges of England, by striking out the eleven, which was also objectionable as receiving a sectarian explanation.

In that, he is simply following the tradition of the Pythagorean society to which he belonged, as is shown by his identification of matter with space, or rather with 'room'. So far as can be seen at present, we are not entitled to ascribe this view to Plato without more ado, but that is a point on which the last word has not yet been said.

For the physical science of the ancients was traditional, descending through many generations of Ionian and Pythagorean philosophers.

The Pythagorean philosophy, as Zeller has shown, is the systematic form of this mathematical mysticism, for which numbers are not symbols of quantitative relations, but the very essence of things.

The Neo-Platonists inherited from Pythagoras and Plato, and their works should be studied by those who would realise something of the grandeur and the beauty preserved for the world in the Mysteries. The Pythagorean School itself may serve as a type of the discipline enforced.

"'Good! cried the professor, beaming all over. 'I knew you were a fellow-scientist. Possibly you are a brother-member of the Boston Dodo Society of Pythagorean Research. Are you a dodo? "I shook my head. 'No, I am not a dodo. "'Only a jay? "'A what? I said, angrily. "'A jay. We call the members of the Junior Ornithological Jay Society of New York, jays, just as we refer to ourselves as dodos.

Actually, Kepler's great work, Harmonices Mundi, in the last part of which he announces his third law, is entirely devoted to proving the truth of the Pythagorean doctrine that the universe is ordered according to the laws of music. This doctrine sprang from the gift of spiritual hearing still possessed by Pythagoras, by which he could perceive the harmonies of the spheres.

There is no reason whatever to doubt the statement, which Plato makes more than once, that he had met Parmenides and Zeno at a still earlier date. At any rate, the influence of Zeno on the dialectic of Socrates is unmistakable. We may also take it that he was familiar with all sorts of Orphic and Pythagorean sectaries.

The idea of such an explanation did not originate with Hipparchus. The germs of the thought were as old as the Pythagorean doctrine that the earth revolves about a centre that we cannot see. Eudoxus gave the conception greater tangibility, and may be considered as the father of this doctrine of wheels epicycles, as they came to be called.

Si recte probandi facultate destitui nos sentimus, ab eodem spiritu qui per prophetas suos loquitur portenda est, saith Calvin. We will not then call any man rabbi, nor jurare in verba magistri, nor yet be Pythagorean disciples to the church herself, but we will believe her and obey her in so far only as she is the pillar and ground of truth. Sect. 1.