M. Paucton, Mr. Taylor, and those who have adopted and followed their pyramid metrological ideas, seem to imagine that if, by multiplying one of their measures or objects, they can run the calculation out into a long tail of terminal 0's, then something very exact and marvellous is proved. "When" (upholds Mr. Taylor), "we find in so complicated a series of figures as that which the measures of the Great Pyramid and of the Earth require for their expression, _round numbers_ present themselves, or such as leave no remainder, we may be sure we have arrived at _primitive_ measures." But many small and unimportant objects, when thus multiplied sufficiently, give equally startling strings of 0's. Thus, if the polar axis of the earth be held as 500,000,000 inches, and Sir Isaac Newton's "Sacred Cubit" be held, as Professor Smyth calculated it to be, viz. 24.82 British inches--then the long diameter of the brim of the lecturer's hat, measuring 12.4 inches, is 1-40,000,000th of the earth's polar axis; a page of the print of the Society's Transactions is 1-60,000,000th of the same; a print page of Professor Smyth's book, 6.2 inches in length, is 1-80,000,000th of this "great standard;" etc. etc. etc. Professor Smyth seems further to think that the figure or number "five" plays also a most important symbolical and inner part in the configuration, structure, and enumeration of the Great Pyramid. "The pyramid" (says he) "embodies in a variety of ways the importance of five." It is itself "five-angled, and with its plane a five-sided solid, in which everything went by fives, or numbers of fives and powers of five." "With five, then, as a number, times of five, and powers of five, the Great Pyramid contains a mighty system of consistently subdividing large quantities to suit human happiness." To express this, Mr. Smyth suggests the new noun "fiveness." But it applies to many other matters as strongly, or more strongly than to the Great Pyramid. For instance, the range of rooms belonging to the Royal Society is "five" in number; the hall in which it meets has five windows; the roof of that hall is divided into five transverse ornamental sections; and each of these five transverse sections is subdivided into five longitudinal ones; the books at each end of the hall are arranged in ten rows and six sections--making sixty, a multiple of five; the official chairs in the hall are ten in number, or twice five; the number of benches on one side for ordinary fellows is generally five; the office-bearers of the Society are twenty-five in number, or five times five; and so on. These arrangements were doubtless, in the first instance, made by the Royal Society without any special relation to "fiveness," or the "symbolisation" of five; and there is not the slightest ground for any belief that the apparent "fiveness" of anything in the Great Pyramid had a different origin. GREAT MINUTENESS OF MODERN PRACTICAL STANDARDS OF GAUGES.