ERROMAN’GA

or ERROMAN’GO, one of the more important of the New He brides Islands, with an area of about 400 sq. miles, hilly and not very fertile, but with spots well cultivated. Several mi ionaries have been murdered by the natives—including the mi ionary John Williams—but perhaps half of the 2,500 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 @ 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 215 ERSCH 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 sueh 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 fe as evenly as po ible among the plotted points. Where great accuracy is wanted, analytical methods are also available. See SQUARES, METHOD OF LEAST; PROBABILITY.