A cathedral embodies such miracles of audacity and aspiration, that one scarcely looks in it for that complete harmony of proportion which distinguishes a Classic temple. The latter was the product of men who had ceased to believe in the deities they professed to honour and had made a religion, according as they were Hellenes or Romans, of abstract perfection or of systematised order. Gothic cathedrals, on the other hand, were the material and spiritual expression of intense religious devotion and of civic pride and freedom. They were the memorials, not of old nations in the decline of their political and social ideals, but of young races, struggling toward nationalism and fired with the splendour of dawning aspirations. No level line of entablature, resting upon columns ever so stately, could embody such elevated enthusiasm. It must mount into the sky, with soaring lines and vaulting arches, spires and pinnacles, ever straining upward; giving voice to the grandeur of concerted uplift. Some of the cathedrals grew up from ground to ridge roof and towers under the guiding mind of one architect; more represent the continuous growth of the community; but in either case embody in their variety and organised complexity the Soul of the Crowd. For one must not think of them only as temples of worship. They embraced also the functions now distributed in schools and libraries. They were the shrines of the culture of their day, in which the truths of religion, legends of saints, and the mysteries of belief were unfolded in sculpture, paintings, and stained glass. =Asymmetries or Refinements.=--In order to ensure their monopoly the gilds of masons of the Middle Ages jealously preserved the secrets of their art. Accordingly, there are no written treatises of the period. Moreover, with the advent of the Renaissance the Gothic was held in contempt and the indifference to it continued until about the middle of the nineteenth century. Then, in the renewed enthusiasm for Mediæval architecture, buildings were studied, measurements taken, and plans of the old churches and cathedrals were drafted. But the surveyors, having measured the distance between one pair of piers on opposite sides of the nave and between two piers on one side, plotted the plan as if these measurements were uniform throughout the whole nave. In this and in other matters they assumed that the design was symmetrical. The contrary, however, in the case of many churches and cathedrals, has been proved by the recent researches of Professor William H. Goodyear, whose work in connection with Hellenic, Byzantine, and Romanesque refinements or asymmetries has been noted already. His researches, which have covered most of the Gothic edifices of Italy, many of the most important churches and cathedrals in France, and some in England, prove that the “mysteries” of the Mediæval gilds included asymmetrical refinements. The most important deviations from mechanical formality are as follows: