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least motion, principle of | leaving group |

A procedure for replacing the discrete set of results obtained from an experiment by a continuous function. It is defined by the following.
For the set of variables
there are
measured values such as
and it is decided to write a relation:
where
are undetermined constants. If it is assumed that each measurement
of
has associated with it a number
characteristic of the uncertainty, then numerical estimates of the
are found by constructing a variable , defined by
except
.
If the relations between the and
are linear, this is the familiar least-squares technique of fitting an equation to a number of experimental points. If the relations between the
and
are non-linear, there is an increase in the difficulty of finding a solution, but the problem is essentially unchanged.

,

and solving the equations obtained by writing Source:

PAC, 1981, *53*, 1805*
(Assignment and presentation of uncertainties of the numerical results of thermodynamic measurements (Provisional))
* on page 1822

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Cite as:

IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook.

IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook.

Last update: 2014-02-24; version: 2.3.3.

DOI of this term: doi:10.1351/goldbook.L03492.

Original PDF version: http://www.iupac.org/goldbook/L03492.pdf. The PDF version is out of date and is provided for reference purposes only. For some entries, the PDF version may be unavailable.