You decide to take a solo boat trip for a vacation. While contemplating the Universe, you lose track of your location. Fortunately, you have some astronomical tables and instruments, as well as a UT clock. You thereby put together the following description of your situation:
It is the day of the summer solstice.
The sun is on your meridian at an altitude of 67° in the south.
The UT clock reads 01:00.
What is your latitude and longitude? Explain how you know.