The lineal unit is also that for breadth and thickness ; in other words, for all the dimensions of space. Applied to land measure, which must have been at an early date in the history of agriculture, it developed the science of geometry—at first on its purely practical side, that of the men suration of superficies ; later came the theoretical proofs of its theorems. For the latter we have to thank the lucid intelligence of the ancient Greeks ; for although they themselves professed to have learned geometry from the Egyptians, modern research has shown that the dwellers in the Nile Valley did not go beyond the merely empiric demonstration of the problems of plane geometry.
Measures of include those relating to a person's position and to his horizon. The norm of the former are the true vertical and horizontal lines, and the usual instruments to determine them are the ph/nib-line and the Without these it is not possible to carry out the finer works of architecture and engineering. Yet there is no evidence that either of them was known to the ancient inhabitants of America, although they erected iloninnents of commanding size and impressive designs. Close study of the remains of these show that their lines were determined by the use of long and straight reeds, by the eye, and other lacking in the correctness of the plumb and level. The archi tects of the Old World had the assistance of such contrivances from an age coeval with that of the older Egyptian dynasties.
Cardinal measures of terrestrial direction have been the same in all ages and countries, though the accuracy with which they have been located varies with the mathematical instruction of the people. They are the four cardinal points, North, South, East, and West. That these four should always have been selected depends on the conformation of the human body and its necessary relations to its terrestrial environ ment. The anterior and posterior planes of the body, the right and left hands, suggest the fourfold relation of space, which is borne out by the celestial points defined by the rising and the setting sun and by the revo lution of the starry heavens around the fixed pole-star. A wanderer in a trackless desert with no guides but these, no wonder that the primitive savage took constant note of their bearings, and as he grew in wisdom was governed by them in his weightiest undertakings. This we see the world over in the religions, the arts, the social life, and the forms of gov ernment of men. Long after man had emerged from the condition of sav agery their influence remained. The ancient monarchies of Egypt, Syria, China, Mesopotamia, and India in the Old World, and in the New those of Peru, Araucania,. the Muyscas, the Tlascalans, and others, were organ ized in the form of tetrarchies, divided in accordance with, and in some instances the divisions named after,. the cardinal points. Their chief cities were frequently quartered by streets running north, south, east, and west. The chief officers of the government being four in number, the whole social organization assumed a quadruplicate form. The official title of the Inca of Peru and of the emperor of China was " lord of the four quarters of the earth," the terrestrial plane being conceived as a vast level with four sides and four corners.
Most of the important monuments of ancient architecture are built with careful reference to the cardinal points, their doors, their angles, and their sides being adjusted by them. Often this was connected with
religious sentiments, as that the temples should face the rising sun or look toward the warm south.
Geodesy and earliest astronomy was directed toward finding accurate measures of direction for these points on which so much else depended. The apparent motions of the sun in the ecliptic cast an uncertainty on the precise location of east and west on the hori zon to rectify which demanded long observation. In later days, when the magnetic needle offered a means constantly at hand to ascertain the north, its local and secular variations led to the study of the magnetic meridians and the phenomena of terrestrial magnetism, which has yet far from unfolded its meanings. Geodesy and cartography have only risen to the position of sciences since the measures of direction invented within the present century have reduced to an unimportant minimum the errors of observation.
illeasures of Gravity.—To " heft " an object is so natural a way to test and compare its quantity that one is surprised to find that even the most cultivated nations of the New World do not appear ever to have had a recognized unit of weight. Their records speak of a " load of maize," as much as a man could conveniently carry, but all goods were sold by bulk or number or measure, never by weight. The balance and the scales were totally unknown. Yet on very ancient paintings of the Egyptians the merchant is seen with his scales carefully weighing his wares, and in China they have been in use from the dawn of history. The unit of weight was frequently taken from a grain of a cereal, as the word "grain," grams/, and the Old English " barleycorn," indicate. The discovery of specific gravity, attributed to the philosopher of Syracuse, Archimedes, led in later times to many applications of measures of gravity of high importance.
Jlfelric need not pursue the recent development of the methods of measuring and weighing ; it has been only by their assiduous cultivation, and by the extraordinary perfection which they have in con sequence attained, that modern science has reached the height at which we see it. At the close of the last century the French devised the met ric system, in which a supposed natural unit, a fraction of the diameter of the earth, was taken as the base. Later researches have shown that the computation was erroneous, and that the base of the metric system is as artificial as any other. But the convenience of its details has led to an effort for its general acceptance by civilized peoples.
Measures of of science are well aware that much still remains to be done in this direction. It is only by reaching some common measure of all the expressions of force that we can hope to master the highest problems of physics. Thus, expansive force can be expressed in lineal measure by " foot-pounds," this being the amount of force required to lift a pound the vertical height of one foot. Heat is measured in many ways, chiefly by its expansive action on the column of mercury in the thermometer. Light is estimated in the photometer by "candle-powers," and electricity by the measure of its resistance to tension, as " ohms." The influence of such studies in bringing the forces of nature under the control of man, and thus shaping the character and destiny of races and nations, cannot be overestimated.