Hard to believe a professional astronomer wrote this. A long time ago I took photos of the sun in UV and in visible light, close enough to the horizon that there were ground objects for relative scale. When you look at the sun in visible light, you see a yellow-white ball with a sharp edge against the blue-sky surrounding. In UV the sun had a fuzzy edge, the brightness tapers off as you look farther from the center, but the blasted-out bright area on the UV film was at least twice as large in diameter as the visible disc. The sun's corona, extending far beyond the visible disc, radiates very strongly in the UV spectrum.
Contrary to Ms. Winterburn's statement, at least in the UV spectrum, the sun is vastly brighter at totality than any full moon. When you stare at the sun with your eyes, your pupils crank down to their smallest aperture (unless you're full of LSD!) and even then the brightness makes you flinch away after a couple of seconds. But if you look at a fully-eclipsed sun, to your eyes it seems dark and you don't experience immediate discomfort, nor do your pupils contract. While the part emitting visible light is fully obscured by the moon, more than half of the area emitting UV extends past the edge of the moon, so while you stare with opened pupils for the entire duration of the obscuration (if you don't know better, that's what you'd do naturally) though you're not aware at the moment your eyes get a dangerously large, possibly permanently damaging dose of UV light.
Light from an arc welder is brighter in the UV than in the visible spectrum, so a welder's helmet's lens is more opaque to UV than it is to visible light. You can buy replacement lenses for a mask where you get welding supplies. If you want to stare at a full eclipse, that's the stuff to look through.
Maybe I should have posted this yesterday...
Yours WDK - WKiernan at concentric.net