Butter a nine-inch cake pan and place a neat circle of parchment or wax paper on the bottom, covering it completely. If wax paper is used, butter it. If parchment is used, it is not necessary to butter.
Chop both the chocolates into fine pieces and set aside.
Combine the water with one cup of the sugar in a heavy two quart saucepan. A large copper saucepan is ideal for this. Bring to the boil over high heat and cook about four minutes or to a temperature of 220 degrees.
Remove the saucepan from the heat and immediately add the chocolate pieces; stirring until they are melted and smooth. The mixture may seize but that is alright; it will blend when the butter is added. Immediately start adding butter, stirring gently until all of it is used.
Place the eggs and remaining sugar in the bowl of an electric mixer. Start beating on high speed and continue until they are quite thick and pale yellow, and tripled in volume. This may take about 15 minutes. It may be useful to place a dishcloth over the mixer and bowl to prevent splattering.
Start mixing the eggs and sugar mixture on slow speed. Add the chocolate mixture, stirring only until it is fully incorporated. Do not overheat. This would cause air bubbles to form.
Spoon and scrape the mixture into the prepared cake pan. Set the pan in a slightly larger pan and pour boiling water around it. Do not allow the sides of the pans to touch.
Place in the oven and bake 25 minutes. Insert the sharp point of a knife into the center of the cake; if it comes out clean, the cake is done. If it does not come out clean, continue cooking for up to 10 minutes. Do not cook longer than a total of 35 minutes.
Let cool in the pan for 10 minutes. Run a sharp knife around the edge of the cake and unmold onto a cookie sheet. Invert a serving plate over the cake and turn it right side up onto the serving plate.