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Moreover, a truly liberal education implies enough knowledge of mathematics to use it as a key for getting at those more elementary and fundamental principles upon which external nature is built. A knowledge of these principles is itself an indispensable part of an education. The extreme advocates of a scientific, as distinguished from a literary and philosophical culture, are accustomed to consider themselves as the only representatives of a really modern education. And it is undoubtedly true that natural science has only comparatively recently begun to come to the front as a claimant of rights—of something more than mere bits of tardily granted concessions. These advocates too often forget, however, that this is because natural science is itself so new, and is still so comparatively crude and ill instructed as to the most effective methods of liberal culture; is even so doubtful as to the actual results which it could show if the higher education of the country were more fully committed to its hands. For here again it is simple matter of fact that literature and philosophy were brought to a very high pitch of cultivation centuries before the first crude beginnings of real natural science were made. It is true also that the equipment and accredited method of these two-thirds of a liberalizing education are still superior to that of natural science. And now I wish I might be pardoned (though I am sure I shall not be) for