Erroman´go, or Erroman´ga, one of the more important of the New Hebrides Islands, with an area of about 400 sq. miles, hilly and not very fertile, but with spots well cultivated. Several missionaries have been murdered by the natives—including the missionary John Williams—but perhaps half of the 2500 natives are now Christians.
Errors of Observation. In scientific measurements, objects and instruments alike are so constituted that numerical results can only be approximate. We have to find the value of some quantity, not exactly, but to so many significant figures. Even so, when a number of measurements are made of the same quantity, it regularly happens that different values are obtained, the difference between a value as obtained and the true value being called an error of observation. It remains to combine the various measurements in such a way as to obtain the best result which they are capable of yielding.
The usual method is to take the arithmetic mean of the values obtained as the correct value. It is also customary in careful work to state the average deviation of the observed values from the mean. For example, various experimenters found the following numbers for the charge on an electron: 4.67, 4.77, 4.65, 4.79, 4.69. Here the mean is 4.71, and the average deviation from the mean, taken without regard to algebraic sign, is .05. The final result is stated as 4.71 ± .05. The ambiguous term ± .05 is sometimes called the probable error. The smaller the probable error, the more reliable is the mean result.
A case of much practical importance occurs when the results obtained by two distinct methods differ by greater amounts than can be accounted for by the uncertainty of either result. In this case there must be a constant error present in at least one of the sets of measurements. Recognition of a constant error has occasionally led to an important discovery; for instance, the hint which led to the detection of argon in the atmosphere came from the observed discrepancy in the densities of atmospheric nitrogen and nitrogen from ammonia.
In many measurements what is sought is not the value of a single quantity, but the relation between the values of two variable quantities. In such cases graphical methods are of great service. Corresponding values of the two variables are found and plotted; and a smooth curve, or it may be a straight line, is drawn to lie as evenly as possible among the plotted points. Where great accuracy is wanted, analytical methods are also available. See Squares, Method of Least; Probability.
Ersch (ersh), John Samuel, German bibliographer, born 1766, died 1828. He was principal librarian and professor of geography and statistics at Halle. Among his publications are: a Dictionary of French Writers; a Manual of German Literature; and, in connection with Gruber, the Universal Encyclopædia of Arts and Sciences.
Ers´kine, Ebenezer, the founder of the Secession Church in Scotland, born 1680, died 1754. He studied at Edinburgh, and was ordained minister of Portmoak, in Fife, in 1703, in which situation he continued for twenty-eight years, when he removed to Stirling. His attitude towards patronage and other abuses in the Church led to his being deposed, when, in conjunction with his brother and others, he founded the Secession Church. Erskine was the leader of the Burghers (q.v.). He is the author of several volumes of sermons.
Erskine, The Hon. Henry, Scottish barrister, was the third son of Henry David, tenth Earl of Buchan: born at Edinburgh 1746, died 1817. After studying at the Universities of St. Andrews,
Edinburgh, and Glasgow, he adopted the legal profession, and in 1768 was called to the Bar. He twice held the office of Lord-Advocate, was for long the leader of the Scottish Bar, and held a high reputation as a wit.
Erskine, John, of Carnock, afterwards of Cardross, Scottish jurist, born 1695, died 1768. He was called to the Scottish Bar in 1719, and was author of Principles of the Law of Scotland, and the Institutes of the Law of Scotland, both works of authority.