Mnenth,
Perhaps you should read the supporting link. Gilliland actually confirmed the periodicity that Crashfrog mentions, or did your cite not mention this to you? What he did claim was
the possibility of a very small net shrinkage over 265 years. However the data is inconclusive, even Gilliland was cautious, suggesting that the data
allowed for a 0.1 arc second per century over the last 265 years. Parkinson (J. H. Parkinson, "New Measurements of the Solar Diameter," Nature 304,518 1983), however, confirmed "that there is no evidence for any secular changes in the solar diameter, with a reduced upper limit". The tiny variation was within the limits of accuracy & is considered uninformative by astronomers today.
Just to put Gilliland's possible shrinkage into perspective. The sun increased diameter by 0.3 arc seconds per annum between 1967-1980. So even had Gilliland been correct his 265 year shrinkage would have been wiped out in under a year between the above dates, & not only that but exceeded by the same for every year thereafter until 1980.
I would also like a cite that your source used "much more complete data set". Given that my cite uses measurements
from when records began, I find this a little unlikely.
Mark