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Encyclopedia Britannica



INVERSION (Lat. invertere, to turn about)

This article appears in Volume V14, Page 722 of the Encyclopedia Britannica.

Encyclopedia Britannica - Main :: INV-JED
INVERSION (Lat. invertere, to turn about) , in
chemistry
 , the name given to the
hydrolysis
  of cane
sugar
  into a mixture of
glucose
  and fructose (invert
sugar
 ) ; it was chosen because the operation was attended by a
change
  from dextro-rotation of polarized light to a laevo-rotation. In mathematics,
inversion
  is a geometrical method, discovered jointly by
Stubbs
  agd Ingram of Dublin, and employed subsequently with conspicuous success by Lord Kelvin in his electrical researches. The notion may be explained thus: If R be a circle of centre 0 and radius r, and P, Q be two points on a radius such that OP.OQ = r2, then P, Q are said to be inverse points for a circle of radius r, and 0 is the centre of
inversion
 . If one point, say P, traces a curve, the corresponding locus of Q is said to be the inverse of the path of P. The fundainental propositions are: (I) the inverse of a circle is a line or a circle according as the centre of inversion is on or off the circumference; (2) the
angle
  at the
intersection of two circles or of a line and a circle is unaltered by inversion. The method obviously affords a ready means for converting theorems involving lines and circles into other propositions involving the same, but differently placed, figures; in mathematical physics it is of
special
  value in solving geometrically electrostatical and optical problems.


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