We compiled 77 values of the geometrical flattening index H (according to Nikolsky) of the solar corona for total solar eclipses from 1860 to 2010. It is found that the index H takes values from 0.9 to 2.5 and anti-correlates with solar activity: maximal values are observed in a cycle minimum and minimal values are seen in a cycle maximum. In addition, we investigated a correlation between the H index and photometrical flattening index a+b according to Ludendorff and extension of polar ray systems.