normal equations

Normal \Nor"mal\ (n[^o]r"mal), a. [L. normalis, fr. norma rule,
   pattern, carpenter's square; prob. akin to noscere to know;
   cf. Gr. gnw`rimos well known, gnw`mwn gnomon, also,
   carpenter's square: cf. F. normal. See {Known}, and cf.
   {Abnormal}, {Enormous}.]
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   1. According to an established norm, rule, or principle;
      conformed to a type, standard, or regular form; performing
      the proper functions; not abnormal; regular; natural;
      analogical.
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            Deviations from the normal type.      --Hallam.
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   2. (Geom.) According to a square or rule; perpendicular;
      forming a right angle; as, a line normal to the base.
      Specifically: Of or pertaining to a normal.
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   3. (Chem.) Standard; original; exact; typical. Specifically:
      (a) (Quantitative Analysis) Denoting a solution of such
          strength that every cubic centimeter contains the same
          number of milligrams of the element in question as the
          number of its molecular weight.
      (b) (Chem.) Denoting certain hypothetical compounds, as
          acids from which the real acids are obtained by
          dehydration; thus, normal sulphuric acid and normal
          nitric acid are respectively {S(OH)6}, and {N(OH)5}.
      (c) (Organ. Chem.) Denoting that series of hydrocarbons in
          which no carbon atom is bound to more than two other
          carbon atoms; as, normal pentane, hexane, etc. Cf.
          {Iso-}.
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   {Normal equations} (Method of Least Squares), a set of
      equations of the first degree equal in number to the
      number of unknown quantities, and derived from the
      observations by a specified process. The solution of the
      normal equations gives the most probable values of the
      unknown quantities.

   {Normal group} (Geol.), a group of rocks taken as a standard.
      --Lyell.

   {Normal place} (of a planet or comet) (Astron.), the apparent
      place in the heavens of a planet or comet at a specified
      time, the place having been determined by a considerable
      number of observations, extending perhaps over many days,
      and so combined that the accidental errors of observation
      have largely balanced each other.

   {Normal school}, a school whose methods of instruction are to
      serve as a model for imitation; an institution for the
      training of teachers.
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   Syn: {Normal}, {Regular}, {Ordinary}.

   Usage: Regular and ordinary are popular terms of well-known
          signification; normal has now a more specific sense,
          arising out of its use in science. A thing is normal,
          or in its normal state, when strictly conformed to
          those principles of its constitution which mark its
          species or to the standard of a healthy and natural
          condition. It is {abnormal} when it departs from those
          principles.
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