In astronomy the "mean sun" is a fictitious sun which moves uniformly in the celestial equator and has its right ascension always equal to the sun's mean longitude. The time recorded by the mean sun is termed mean-solar or clock time; it is regular as distinct from the non-uniform solar or sun-dial time. The "mean moon" is a fictitious moon which moves around the earth with a uniform velocity and in the same time as the real moon. The "mean longitude" of a planet is the longitude of the "mean" planet, i.e. a fictitious planet performing uniform revolutions in the same time as the real planet. The arithmetical mean of n quantities is the sum of the quantities divided by their number n. The geometrical mean of n quantities is the nth root of their product. The harmonic mean of n quantities is the arithmetical mean of their reciprocals. The significance of the word "mean," i.e., middle, is seen by considering 3 instead of n quantities; these will be denoted by a, b, c. The arithmetic mean b, is seen to be such that the terms a, b, c are in arithmetical progression, i.e. b = ½(a + c); the geometrical mean b places a, b, c in geometrical progression, i.e. in the proportion a : b :: b : c or b² = ac; and the harmonic mean places the quantities in harmonic proportion, i.e. a : c :: a - b : b - c, or b = 2ac/(a + c). The contraharmonical mean is the quantity b given by the proportion a : c :: b - c : a - b, i.e. b = (a² + c²)/(a + c). The arithmetico-geometrical mean of two quantities is obtained by first forming the geometrical and arithmetical means, then forming the means of these means, and repeating the process until the numbers become equal. They were invented by Gauss to facilitate the computation of elliptic integrals. The quadratic mean of n quantities is the square root of the arithmetical mean of their squares. MEASLES, (_Morbilli_, _Rubeola_; the M. E. word is _maseles_, properly a diminutive of a word meaning "spot," O.H.G. _masa_, cf. "mazer"; the equivalent is Ger. _Masern_; Fr. _Rougeole_), an acute infectious disease occurring mostly in children. It is mentioned in the writings of Rhazes and others of the Arabian physicians in the 10th century. For long, however, it was held to be a variety of small-pox. After the non-identity of these two diseases had been established, measles and scarlet-fever continued to be confounded with each other; and in the account given by Thomas Sydenham of epidemics of measles in London in 1670 and 1674 it is evident that even that accurate observer had not as yet clearly perceived their pathological distinction, although it would seem to have been made a century earlier by Giovanni Filippo Ingrassias (1510-1580), a physician of Palermo. The specific micro-organism responsible for measles has not been definitely isolated.