Various attempts have been made in modern times to discover these rules, and in some instances with apparent success. It unfortunately happens that we have not often an intact ground plan, and if the original plan was simple, the additions render it complex. In many cases these additions were made without any regard to the proportion of the original. It appears probable that these proportions were geometric rather than arithmetical—that is to say, made by simple operations of the compasses and rulers, rather than by any proportions of numbers. The small churches of the North are valuable from not having been altered by additions.
Though in the foregoing notes the proportions on which the churches were built may not have been ascertained in all cases, yet in some the coincidences are too remarkable to be chance. Although, no doubt, a system of proportions was extended to the elevations and certain details, yet as to most of these in the churches here enumerated we are in ignorance, because most of the superstructure is gone. It appears that there were, in fact, only two figures on which the proportions were founded—a circle, a square, and an equilateral triangle. For most purposes of proportion the circle and square are identical. The vesica piscis is two equilateral triangles on opposite sides of a common base, and hence equal in proportion to the half of one such triangle.
There is, however, one proportion in which a square is not equivalent to a circle—the diagonal of the square the proportion of which to the side is nearly as 10 to 7. The height or length of an equilateral triangle is to half its base nearly as 7 to 4.
All these proportions are somewhat flexible, inasmuch as they may include the side walls and exclude the end walls, or the reverse; or they may include both, or they may exclude both; or they may be applied in one way to the nave, and in another to the chancel, and in another to the tower. But the proportion must not be deemed as ascertained unless the figure really fits within 2 or 3 inches.
DATES.
As to the dates of these buildings we have but little to guide us. Only fragments of the buildings are left, and those of the plainest description.
Scotch architecture has some mystifying peculiarities. Dates have been suggested from architectural and historical evidence for Orphir, Birsay, and Egilsey. Orphir, 1090-1160; Birsay, 1100; Egilsey, 1000. Wyre has been assigned to the twelfth or thirteenth, the Ness to the fourteenth, and St. Ola to the sixteenth century.
It may be fairly observed that there must have been churches erected in the fourteenth and fifteenth centuries. Where are the remains of them? Possibly some of the ruins described are of those centuries.
It does not appear impossible that from evidence yet to be collected, a nearer approximation to the dates of these buildings may be got.