The theory of emrs uus developed by Gauss primarily in relation to the needs
of ustrrmmw-u urbd uufueyors, rrrukiny nither uccurute urryulur rrreu:cruurzrrsents.
Because of this accuracy at was appropriate to develop the thww in relation
to an infinite Pnear continuum, or, as multivariate errors mme into V ~ ~ U J ,
to a Euclideun ~ p c 0e1 the required diniensionalitp. The uctuul topologacd
framework of such measurements, the surface of a sphere, is ignowd in the
theory a.9 developed, eutth u certain yuin in airrrplicity.
It is, therefore, of some little mathenaatical interest to consider how the
theom uwdd have had to he developed if the observations under discussion
hud in fact ivswolved errors YO large thut the actual topologg lbud had to be
taken into account. The question is not, however, entirely auadenaic, for there
a= in nutwe iiectors with such la y e riuturul disper.uioria.