a piece of music we can continue to make equal beats when the first beat has been given, but cannot ensure commencing with the same length of beat on a future occasion; and hence, lastly, the fact, that of all magnitudes, those of linear extension are those of which the equality is most accurately ascertainable, and those to which by consequence all others have to be reduced.  For it is the peculiarity of linear extension that it alone allows its magnitudes to be placed in absolute juxtaposition, or, rather, in coincident position; it alone can test the equality of two magnitudes by observing whether they will coalesce, as two equal mathematical lines do, when placed between the same points; it alone can test equality by trying whether it will become identity.  Hence, then, the fact, that all exact science is reducible, by an ultimate analysis, to results measured in equal units of linear extension.

Still it remains to be noticed in what manner this determination of equality by comparison of linear magnitudes originated.  Once more may we perceive that surrounding natural objects supplied the needful lessons.  From the beginning there must have been a constant experience of like things placed side by side—­men standing and walking together; animals from the same herd; fish from the same shoal.  And the ceaseless repetition of these experiences could not fail to suggest the observation, that the nearer together any objects were, the more visible became any inequality between them.  Hence the obvious device of putting in apposition things of which it was desired to ascertain the relative magnitudes.  Hence the idea of measure.  And here we suddenly come upon a group of facts which afford a solid basis to the remainder of our argument; while they also furnish strong evidence in support of the foregoing speculations.  Those who look sceptically on this attempted rehabilitation of the earliest epochs of mental development, and who more especially think that the derivation of so many primary notions from organic forms is somewhat strained, will perhaps see more probability in the several hypotheses that have been ventured, on discovering that all measures of extension and force originated from the lengths and weights of organic bodies; and all measures of time from the periodic phenomena of either organic or inorganic bodies.

Thus, among linear measures, the cubit of the Hebrews was the length of the forearm from the elbow to the end of the middle finger; and the smaller scriptural dimensions are expressed in hand-breadths and spans.  The Egyptian cubit, which was similarly derived, was divided into digits, which were finger-breadths; and each finger-breadth was more definitely expressed as being equal to four grains of barley placed breadthwise.  Other ancient measures were the orgyia or stretch of the arms, the pace, and the palm.  So persistent has been the use