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SQUARES, METHOD OF LEAST 42 SQUIER, GEORGE OWEN SQUARES, METHOD OF LEAST, an arithmetical process of great importance for combining observations, or sets of observations, so as to obtain the most probable value of a quantity which de- pends on these observations. It is in fact the scientific method of taking certain averages, and it finds its most constant use in astronomy and other physical sciences. The necessity for applying the method arises from the fact that M^hen the greatest precision of measurement is sought, repeated measurements of the same quantity do not agree. Thus, the altitude of a star at culmination, if care- fully measured night after night by the same observer through the same instru- ment, will in general come out a little different in the different observations. All the measurements will, however, lie within a certain range of variation; and if all are equally trustworthy, the arith- metical mean will give the most proba- ble value of the real altitude. The differences between this mean and the individual measurements on which it is founded are called the residuals. The important matliematical property of these residuals is that the sum of their squares is less than the sum of the squares of the differences between the individual measurements and any other single quan- tity that might be taken. Now, this principle of "least squares" holds not only for the simple case just described, but also for more complicated cases in which one observed quantity (y) is to be expressed as an algebraical function of another or of several independently observed quantities (x) . Here the object is to f nd the most probable values of the assumed constants or parameters which enter into the formula. When these values are calculated we can calculate in terms of them and the observed x's a value of y corresponding to each set of observations. Comparing the calculated y's with the observed y's, we get a set of residuals the sum of whose squares is a minimum if the parameters have been calculated according to a particular process. It is this process which is de- scribed as the method of least squares. Its basis is found in the mathematical principles of probability. SQUASH, in botany and horticulture, a popular name for any species of the genus Cucurbita; specifically, C. me- lopepo. Leaves cordate, obtuse, some- what five-lobed; tendrils denticulated, or converted into small leaves; calyx with the throat much dilated; fruit flattened at both ends with white, dry, spongy fruit which keeps fresh for many months. It is boiled and eaten with meat. SQUASH, a ball game of which tennis is believed to be a development. It is played in a court at one end of which rises a wall and the contest revolves on the ability of the players, who are pro- vided with rackets, to strike the ball and send it against the wall above a certain line, keeping it all the time within certain enclosed spaces indicated by a central line on the floor and cross lines which divide it usually into four spaces. The players wait till the ball bounces on the floor and meet it before it touches the floor a second time. Skill is shown both in measuring the amount of energy expended in striking the ball and so placing it within the enclosed spaces as to make it difficult for the opponent to meet it. Points are recorded against the player who fails to meet the ball on the bounce, or who sends it against the wall below the line indicated or who so places the ball that in re- bounding from the wall it falls outside the indicated space on the floor. The game is exhilarating and players often acquire such skill in hitting that the ball is kept on the bounce for a con- siderable time. The game is more sim- ple than tennis, and the racket and ball are usually of a heavier make, owing to the greater wear and tear. SQUID, a popular name of certain cuttle fishes belonging to the dibran- chiate group of the class Cephalopoda, and included in several genera, of which the most familiar is that of the cala- SQUIER, GEORGE OWEN, an Amer- ican army officer, born at Dryden, Mich., in 1865. He graduated from the United States Military Academy in 1887 and received the degree of Ph.D. from Johns Hopkins University in 1903. In 1887 he was appointed second lieutenant of artillery and gradually rose to the rank of major general, which he received in 1917. Much of his sei-vice in the army was devoted to the Signal Corps, of which branch he was placed in com- mand in 1913. In February, 1917, he was made chief signal officer of the United States Army, and from May 20, 1918, he was in charge of the army air service. His other assignments in- cluded service as United States military attache in London in 1912. He did im- portant research work in electricity, especially in connection with the tele- phone and telegraph. He was a member of the National Academy of Sciences, re- ceived the D.S.M., and was made a Knight Commander of the British Order of St. Michael and St. George. His scientific work was rewarded by the