Our grandfathers supposed that trade began in barter; we have been able to go one step further back in history to find that barter followed upon the custom of exchanging presents. This custom, among shrewd and self-respecting people, came at length to a degree of fairness, and led to rough and ready modes of weighing, gradually improved. In the British Museum, in a papyrus of Hunnafer, who lived in Egypt thirty-three centuries ago, we have pictured a well-constructed balance of equal arms, in which a feather is outweighing a human soul. In its successive improvements the balance registers the progress of many arts and sciences, and in its turn has promoted them all. It must be built of a metal, or an alloy, hard, durable, and not easily corroded. Its centre of motion should be a little above its centre of gravity; its knife edge should have an angle of about 60 degrees. Appliances must render it easy to lift the weighing apparatus when out of use, so that unnecessary wear of the knife edge may be avoided, as well as needless strain throughout the structure. Air currents should be kept off by a suitable case, or, better still, the instrument should be enclosed in a receiver exhausted of air altogether. The weights, made with scrupulous care of standard metal or alloy, should be guarded from tampering, abrasion, and corrosion, from dirt or other accretions. A weighing should be slowly performed, the weights placed in the center of one pan, the object weighed in the center of the other pan; to eliminate errors due to inequality in the length of arms, the article weighed and the weights are then made to exchange places. The platform should be of the utmost strength and rigidity, so as precisely to maintain its level at all times. [Illustration: A Rueprecht balance.]