Solar Phys (2011) 270: 347–363 DOI 10.1007/s11207-011-9749-y Flattening Index of the Solar Corona and the Solar Cycle Mykola I. Pishkalo Received: 2 November 2010 / Accepted: 5 March 2011 / Published online: 15 April 2011 © Springer Science+Business Media B.V. 2011 Abstract The photometrical flattening index of the solar corona a + b is defined according to Ludendorff. In this paper we have investigated how the flattening index varies with respect to the phase of solar activity and the sunspot number. We have compiled 170 values of the flattening index using the data on 60 total solar eclipses from 1851 to 2010. We have found that the flattening index takes values from 0 to 0.4, and is anticorrelated with solar activity. The value of the flattening index at the beginning of solar cycle 24 was used as a precursor to forecast the amplitude of the cycle. It was found that the amplitude of solar cycle 24 will be about 95 in terms of the smoothed monthly sunspot numbers. Keywords Solar corona · Solar cycle 1. Introduction It is well known that the structure, shape, and brightness of the solar corona change sig- nificantly from eclipse to eclipse. Hansky (1897), after analyzing the material of 20 total solar eclipses from 1842 to 1896, first came to important conclusions about the dependence of the shape and brightness of the corona on yearly sunspot numbers. In a sunspot number maximum, the corona forms an entire radiance around the Sun. In a sunspot number mini- mum, the corona stretches more along the equator, and its brightness is weaker. Naegamvala (1902) compared drawings of the solar corona during 21 total solar eclipses with sunspot activity and confirmed Hansky’s (1897) results. Lockyer (1903, 1922, 1931) in a number of papers attempted to find a relationship between the shape (and structure) of the corona and solar prominences. However, these investigations were rather qualitative. A quantitative analysis of the shape of the solar corona was first made by Ludendorff (1928). He analyzed isophotes of coronal images and defined the averaged flattening of the M.I. Pishkalo ( ) Astronomical Observatory of Kyiv National Taras Shevchenko University, 3, Observatorna vul., Kyiv 04053, Ukraine e-mail: pish@observ.univ.kiev.ua