In the same way that a musical composition implies the division of time into equal and regular beats, so a work of architecture should have for its basis some unit of space. This unit should be nowhere too obvious and may be varied within certain limits, just as musical time is retarded or accelerated. The underlying rhythm and symmetry will thus give value and distinction to such variation. Vasari tells how Brunelleschi. Bramante and Leonardo da Vinci used to work on paper ruled in squares, describing it as a "truly ingenious thing, and of great utility in the work of design." By this means they developed proportions according to a definite scheme. They set to work with a division of space analogous to the musician's division of time. The examples given herewith indicate how close a parallel may exist between music and architecture in this matter of rhythm (Illustrations 91-93). [Illustration 93] It is a demonstrable fact that musical sounds weave invisible patterns in the air. Architecture, correspondingly, in one of its aspects, is geometric pattern made fixed and enduring. What could be more essentially musical for example than the sea arcade of the Venetian Ducal Palace? The sand forms traced by sound-waves on a musically vibrating steel plate might easily suggest architectural ornament did not the differences of scale and of material tend to confuse the mind. The architect should occupy himself with identities, not differences. If he will but bear in mind that architecture is pattern in space, just as music is pattern in time, he will come to perceive the essential identity between, say, a Greek rosette and a Gothic rose-window; an arcade and an egg and dart moulding (Illustration 94). All architectural forms and arrangements which give enduring pleasure are in their essence musical. Every well composed façade makes harmony in three dimensions; every good roof-line sings a melody against the sky. [Illustration 94: ARCHITECTURE AS PATTERN] CONCLUSION In taking leave of the reader at the end of this excursion together among the by-ways of a beautiful art, the author must needs add a final word or two touching upon the purpose and scope of these essays. Architecture (like everything else) has two aspects: it may be viewed from the standpoint of utility, that is, as construction; or from the standpoint of expressiveness, that is, as decoration. No attempt has been made here to deal with its first aspect, and of the second (which is again twofold), only the universal, not the particular expressiveness has been sought. The literature of architecture is rich in works dealing with the utilitarian and constructive side of the art: indeed, it may be said that to this side that literature is almost exclusively devoted. This being so, it has seemed worth while to attempt to show the reverse of the medal, even though it be "tails" instead of "heads."