2. And religion, the religion of a few, as if in acknowledged sympathy with these sceptics, surrendered everything but God--God being more a longing than an actual fact; a spirit than a positive thing or person. Even within the Catholic Church the Oratory of Jesus, a society energetically opposed for good and sufficient reasons by the Jesuits, was organized in the interests of a purified, truly spiritual Christianity; and among those who had broken with the Catholics appeared new sects of many names, such as the "Friends of God," "Collegiants," and the "Brotherhood of the Christian Life," but with one ideal, the direct untrammelled worship of God. "God is," they proclaimed in so many words; "and God, just God, is all. Church and creeds and rites and priests are hindrances, not helps, to true religion." This attitude, commentary as of course it was on the conditions of the day, had almost more satire in it and more doubt than any of the words [p.177] of the most active scoffers; it was so unconscious; so quietly and so piously it picked up the crumbs that the scoffers left. Indeed, the sceptics and their devout, pure-minded contemporaries, Pierre Charron (1541-1603) and Jakob Boehme (1595-1624), both advocates of religious purity against theology and sensuous ritual, must be said not to have engaged in separate activities, but to have shared the labour of a single activity. Scepticism and such mysticism are but two sides of the same shield. 3. But with the scoffing scepticism and its complementary counterpart, the dogmatic mysticism of religion, there was associated also a most visionary gnosticism. Thus the science of mathematics was heralded as a key to all the secrets of the universe. A few simple applications of mathematics to physical phenomena had been successfully made by the scientists--for example, by Galilei--and ere long certain men in the world of the intellectual life went wild over the possibilities of mathematics. Obliged, as soon they were, to abandon every other field of knowledge--theology, politics, material science, tradition, and convention--they needed but little encouragement to give themselves heart and soul to this last resort. Their enthusiasm for mathematics doubtless had a deeper source than this simple account of its rise would suggest, for an intellectual atmosphere in which just such a purely logical, abstract science would develop was the natural product of medievalism; but Galilei's successes may be said to have precipitated the movement, and in any case for many mathematics became, both in its principles and in its method, an intellectual [p.178] cure-all, and in consequence not only were remarkable advances made in the science itself, but men went to the extreme of applying the methods and the formulæ of mathematics in every conceivable direction. Religion, morality, and politics, as well as natural science, were all subjected to mathematical treatment. Among the surviving monuments to this