simple harmonic motion: see harmonic motion.

law of simple multiple proportions, in chemistry, the statement that when two or more elements form more than one compound, the ratio of the weights of one element that combine with a given weight of another element in the different compounds is a ratio of small whole numbers. For example, carbon and oxygen combine in carbon dioxide (CO₂) and carbon monoxide (CO). A sample of carbon dioxide containing 1 gram of carbon contains 2.66 grams of oxygen; a sample of carbon monoxide containing 1 gram of carbon contains 1.33 grams of oxygen. The ratio of the two weights of oxygen (2.66:1.33) is exactly 2:1. The law of simple multiple proportions can be regarded as an extension of the early law of definite composition, which states that the proportions by weight of the elements present in any pure compound are always the same. An even broader generalization is the law of combining (or equivalent) weights (also known as the law of reciprocal proportions), which states that the ratio in which two substances react with each other is the ratio, or some multiple of the ratio, of the weight of the same two substances reacting with a third substance. All three laws are elementary consequences of the atomic theory, as proposed by John Dalton (see atom; chemistry).

Any of the simple sugars that serve as building blocks for carbohydrates. They are classified based on their backbone of carbon (C) atoms: Trioses have three carbon atoms, tetroses four, pentoses five, hexoses six, and heptoses seven. The carbon atoms are bonded to hydrogen atoms (singlehorzbondH), hydroxyl groups (singlehorzbondOH; see functional group), and carbonyl groups (singlehorzbondCdoublehorzbondO), whose combinations, order, and configurations allow a large number of stereoisomers (see isomer) to exist. Pentoses include xylose, found in woody materials; arabinose, found in gums from conifers; ribose, a component of RNA and several vitamins; and deoxyribose, a component of DNA. Important hexoses include glucose, galactose, and fructose. Monosaccharides combine with each other and other groups to form a variety of disaccharides, polysaccharides, and other carbohydrates.

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Repetitive back-and-forth movement through a central, or equilibrium, position in which the maximum displacement on one side is equal to the maximum displacement on the other. Each complete vibration takes the same time, the period; the reciprocal of the period is the frequency of vibration. The force that causes the motion is always directed toward the equilibrium position and is directly proportional to the distance from it. A pendulum displays simple harmonic motion; other examples include the electrons in a wire carrying alternating current and the vibrating particles of a medium carrying sound waves.

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In law, an inheritable freehold estate in real property (see real and personal property). The word derives from fief, as used in feudal law. Modern property law includes several varieties of fee, including fee simple (alienable and of indefinite duration), fee tail (granted to an individual and his or her descendants but subject to reversion if a tenant dies with no descendants), and life fee or life estate (held only during the lifetime of the grantee).

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