Refinement of the Gnevyshev-Waldmeier Rule Based on a 140-Year Series of Observations

The Gnevyshev-Waldmeier rule relating the lifetimes of sunspot groups and their areas has been verified on an interval of approximate to 140 years, which exceeds the one used by M.N. Gnevyshev by a factor of 6. The range of lifetimes of recurrent groups under study has been extended from 40 to almost 90 days. The linear form of the Gnevyshev-Waldmeier rule has been confirmed. A more accurate expression for this law is shown to be A(max)= (13.0 +/- 1.1) LT, where LT is the lifetime of a group in days and A(max) is its maximum area in the time of observation measured in millionths of the solar hemisphere. Thus, the conversion factor from the lifetimes to the maximum areas of sunspot groups turns to be larger than that in Gnevyshev (1938) by a factor of approximate to 1.3.