What applies to currency units applies also to units of length, area, volume and weight. A simple rational system of such measures must, as is generally admitted, be a decimal system. In this way large and small units may be related like the dollars, cents and mills of our currency. Such a system could not have been introduced until arithmetical science had reached a sufficiently general development, say, at the opening of the eighteenth century.
Commerce and labor must have demanded systems of weight and measures as far back as we have knowledge of the doings of nations. It is no wonder that these systems should have been crude, labor-absorbing and unscientific. No disparagement can be imputed to the English-speaking nations for inheriting from remote ancestry a crude system of weights and measures. Criticism of such nations can surely only be fairly laid at their doors when, seeing that their neighbors have a better modern system, up to date and practical, they remain supine and make no attempt to join the ranks of international progress.
In British and American measures of length we have the following units, all taught in the schools and all used more or less—league, statute mile, furlong, engineer's chain, surveyor's chain, rod-pole-or-perch, yard, foot, engineer's link, span, surveyor's link, hand, inch and line. These numerous units involve more than a hundred cross-connecting ratios, many of which would, it is true, be very seldom called for. Even, however, if we confine ourselves to mile, yard, foot and inch, we have the following six connecting ratios: 3, 12, 36, 1,760, 5,280, 63,360.
In the metric system there is the meter, about ten per cent, longer than the yard, and its decimal derivatives, all evaluated at a glance by a shift of the decimal point. In English speaking countries, roads are measured in miles and furlongs, short distances in yards, houses or ships in feet, horses in hands and small objects in inches. These expressions are not exchangeable or translatable without more or less mental effort. In the metric system, roads are measured in kilometers and hectometers, short distances in meters or dekameters, small objects in centimeters or millimeters and microscopic objects in micrometers or microns. Taking the length of a good-sized bacterium as one micron, it is immediately evident to the mind that a million such bacteria would fit into a meter, and one thousand million into a kilometer. If, however, we take the size of the bacterium as a certain small fraction of an inch, it takes time and considerable mental effort to find the corresponding relation of dimensions.
The same difficulty exists with units of area in the customary system. We have the square inch, square foot, square yard, square rod, rood, acre, square mile and township. All these units are used, although some are used only by surveyors. These involve 45 connect-
