Rights and wrongs of the temporal solar radius variability

From time immemorial men have strived to measure the size of celestial bodies. Among them, the diameter of the Sun was a source of curiosity and study. Tackled by Greek astronomers from a geometric point of view, an estimate, although incorrect, has been first determined, not truly called into question for several centuries. One must wait up to the XVIIth century to get the first precise determinations made by the French school of astronomy. Gradually, as the techniques were more and more sophisticated, many other solar diameter measurements were carried out, notably in England, Germany, Italy and US. However, even with instruments at the cutting edge of progress, no absolute value of the solar diameter has been provided yet, even if the community has adopted a canonical radius of 959''̣63, given in all ephemeris since the end of the XIXth century. One of the major difficulties is to define a correct solar diameter. Another issue is the possible temporal variability of the size of the Sun, as first advocated at the end of the XIXth century by the Italian school. Today, this question is just on the way to being solved in spite of considerable efforts developed on ground-based facilities or on board space experiments. We will here give a review of some of the most remarkable techniques used in the past, emphasising how incorrect measurements have driven new ideas, leading to develop new statements for the underlying physics. On such new grounds, it can be speculated that the roundness of the Sun is not perfect, but developing a thin “cantaloupe skin” in periods of higher activity, with departures from sphericity being inevitably bounded by a few kilometers (around 80 km or 10 to 15 mas)