  This article proposes a mathematical model of an inverted analemmatic
sundial, provides formulas for calculating the coordinates of their hour
markers. On the example of the Belogorsk sundial, a method is described for
determining the accuracy of time measurement using an inverted analemmatic
sundial, in which cup marks are used as hour markers. The obtained value of the
accuracy of time measurement with the help of the Belogorsk sundial is 5 - 6
minutes and is quite good for a measuring instrument of the Bronze Age, and is
also higher than the accuracy of time measurement with the help of a water
clock. As a result, it is concluded that the hypothesis is confirmed that the
invention of the sundial was associated with the need to improve the accuracy
of time measurement using a water clock.
