1 arcminute = 1/60th of a degree = 1 nautical mile of latitude
1 arcsecond = 1/60th of an arcminute
To answer your question about distances, at this latitude, 1 arcminute = ~cos(77deg) = .22 nautical miles of longitude. Somebody slap me if get any of this wrong.
I find degrees-minutes-seconds to be a very painful way to express location, so let’s convert it to decimal degrees.
77 deg 38′ 36.9″ *S* 166 deg 45′ 58.5″ E
77 + (38 + (36.9/60))/60 = 77.643583 degrees South
166 + (45 + (58.5/60))/60 = 166.76625 degrees East
So what’s there? Nada.
It’s not Cape Evans — 77.633333S 166.4E (77 38′ 10″S 166 24′ 60″E) It’s not Turks Head Ridge — 77.64177184S 166.6535647E — although that’s close. It lays somewhere on the slope of Mt. Erebus, on the glacier face between Turks Head Ridge and Cape Evans, perhaps near the “Tech Crags” mentioned before. I have some very nice pictures of huge crevasses there. This also jives with what Google Earth shows, at least for me.
Perhaps the original latitude has an error in it? I only suggest this because the longitude is almost precisely the same as that of New Zealand’s Scott Base, (77°55’03″S 166°45’45″E, or 77.85S 166.762778E).