Proper Use of a Refractometer

I noticed I may have been using my refractomer incorrectly. I simply used my thermometer as a dip stick but never really dipped it in deep into the wort. Then, i smeared the sample onto the refractometer and, after letting it cool, I took the measurement. For my last brew, I did the same except that I really stirred around the boiling wort and then quickly stuck in the thermometer much deeper than normal into the wort and again smeared the sampling onto the refractometer, let it cool and then took a measurement. While these were two entirely different beers making any gravity comparisons between the two meaningless, I am getting the sense that the later method (the stir and deep dipping method for the lack of a better term) is probably the way to go. (Why? Because I got the answer I wanted using the latter method in that I was much more satisfied with my gravity reading!)

Two questions:

First. Is the latter method the proper way of using a refractometer?

Second. I know any answer to this question would be totally speculative (and inadmissible in court, but the rules of evidence don't apply to this forum), what would the gravity reading be using the latter method, assuming that that is the proper method of using a refractometer, if a gravity reading of 1.061 was achieved by using the former method (the quick and shallow dip stick smear)?

Thanks fellow brewers!

No gravity reading should ever be taken without completely stirring. End of story.