Distribution of estimated umbral areas of sunspots. Top: the area distribution for 1831−1867. The solid curve shows the log-normal fit. The dashed curve and dash dot curve are the fit curves form Bogdan et al. (1988) and Kiess et al. (2014), respectively. The horizontal bars show the widths of the bins. The error margins on the distribution values are all smaller than the symbols. Bottom: the area distribution of spots for ascending phases, descending phases, cycle minima and maxima of all cycles within 1831−1867. The lines show the log-normal fits for the corresponding area distributions.