which meets those requirements fairly well, and although the British system declares the weight of one cubic inch of distilled water at 62° F. to be 252.458 grains, and the metric system (q.v.) fixes the kilogram as the weight of one cubic decimeter of water at maximum density, the Anglo-Saxon still uses the troy pound and the avoirdupois pound (see below).
Although a fortunate selection be made, the determination and construction of a standard are difficult matters. The French engineers spent seven years in determining a kilometer, and even then failed to obtain 0.0001 of the earth's quadrant. The difficulties of establishing a standard pendulum and of computing the lengths of others vibrating in given times are many and great. In the first place, the experiments are made in air, and the buoyancy of the air lessens the actual weight of the pendulum. Then, since the earth has a diurnal motion on its axis, every object placed on it has a centrifugal tendency which modifies what otherwise would be its gravitation. This centrifugal tendency produces the earth's oblateness and causes a variation in the intensity of gravitation from one latitude to another. Thus a stone is actually heavier in Boston than in New York. This change in gravitation cannot be measured by a balance because the weights at each end of the balance are changed alike, but it is apparent in the motion of a clock; for a pendulum regulated to beat seconds in Washington is found to go too fast when taken to a higher latitude, and to lose time when carried nearer to the equator; and again the attraction which the earth exerts upon bodies placed near it diminishes with their distances from its centre, being inversely proportional to the squares of the distances, so that a clock carried from the bottom to the top of a hill loses time perceptibly. In addition to these niceties, there are others connected with the manipulation, such as the parallelism of the knife-edges, their bluntness, the amplitude of the oscillation, and the stability of the support, so that altogether the exact measurement of the length of the seconds pendulum is a matter of very great difficulty. (See Pendulum.) But granted that a length be chosen and be expressed as a distance between two lines on a metal bar, the tendency to oxidize in air, to change with temperature, and to wear with handling, all combat the preservation of the standard and interfere with the process of copying.
The principles of metrology summarized above, however, are modern compared to weights and measures themselves. Before man had developed beyond the savage state he felt the need of some methods of measurement. So old is the idea that there is found in Josephus the statement that Cain invented weights and measures. Upon the idea of numbers followed closely those of time, distance, and quantity. Measurement of time has been simplified by nature, which furnished the aboriginal, as well as the modern, standard, the diurnal rotation of the earth upon its axis. A measure of distance was easily furnished in the day's journey, as the Indian of the West indicates distance by the number of repetitions of the sign meaning from sunrise to sunset. As a smaller unit became necessary, the stride, or pace, came into use, and finally, as a still smaller unit, the dimensions of parts of the body appear. Although reference is made in Deuteronomy (ii. 3) to the ‘foot breadth’ and the foot came into very general use in Greek, Roman, and subsequent times, nevertheless the common unit in Asia Minor and Egypt was the cubit, derived from the length of the forearm, from the point of the elbow to the end of the middle finger. In the inscriptions and records of these countries continual reference is made to this unit and its subdivisions. Among the Greeks and Romans the pace and foot came into almost universal use, and by them were handed down to subsequent Western nations. The passus became the ‘pace,’ the mille (passuum) the ‘mile,’ and the pondus the ‘pound,’ which appear in most European nations until the present day. Under the Roman Empire the standards wore preserved in a Roman temple, and were the standards for the civilized world. With the fall of the Empire and the rise of small principalities, a chaotic condition as to standards developed which extended through the Middle Ages and thereafter, until in Italy alone, as late as the end of the eighteenth century, there were over two hundred lengths called the foot. Every little dukedom and principality had its own standards of weight and measure, and the insignificant intercourse between these small towns did not suffer from these conditions, but the maritime leagues felt the need of common standards.
An example of the method of deriving the standards in the sixteenth century in Germany is given by the following quotation from Koebel's work on surveying:
“To find the length of a rood in the right and lawful way, and according to scientific usage, you shall do as follows: Stand at the door of a church on a Sunday, and bid sixteen men to stop, tall ones and small ones, as they happen to pass out when the service is finished; then make them put their left feet one behind the other, and the length thus obtained shall be a right and lawful rood to measure and survey the land with, and the sixteenth part of it shall be a right and lawful foot.”
In England, we find Henry I. establishing the yard as the distance from the point of his nose to the end of his thumb, and Parliament seriously establishing standards of length and weight according to grains of wheat or barley. Doubtless, few people realize that shoes are still numbered according to the length of a grain of barley, in a system of numeration by thirteens. We have, as example of other units from the dimensions of the body, the ‘fathom’ (faethm, the embrace), the length of the two arms from tip to tip; the ‘hand,’ 4 inches; the ‘span,’ 9 inches; the ‘finger,’ ⅛ of a yard; the ‘nail,’ 2¼ inches, from the tip of the thumb nail to the base joint. Yard is derived from the word gyrdan, meaning the girth of the body.
It might appear surprising that the length of the cubit should have remained rather constant so long in Egypt, but where such important buildings were constructed and such continuity of dynasties was maintained, it should not be surprising that the unit or standard of length should have remained constant, inasmuch as the standards would naturally be handed down from dynasty to dynasty, and indeed, if destroyed, could easily be recovered from the dimensions of existing buildings, just as to-day it would be possible to restore the foot from the dimensions and descriptions of existing struc-
