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Lars,

      My result is 03:39:07, which is pretty close to yours. I too like you and Antonie, did not trust both altitudes and relied soly on the measured distance and a selected AP,as Frank himself has described the figure as being "accurate to the nearest tenth of a minute of arc." 

       However,there are the problems with assumed positions and LD rate of change,thanks to Antonie's detailed elaboration. Antonie has come up with an LD rate of change of about 0.1′ per 32s at a predetermined AP, that is the averaged rate for a ten-minute interval between 03:35 and 03:45, he's trying to get to the actual LD rate at 03:37 as close as possible. The LD rate of change itself is obviously irratic and would definitely vary between different positions and at different times. Since Frank did not provide a set of specific coordinates, it's practically impossible to yield the specific LD rate of change. Everyone would come up with their own rate of change,which would only applie at their assumed positions.

       If one were to use a rate of change that is directly based on lunar distance tables, then he has to understand that this rate only applies when an observer is being physically at the geocentric point. (l used a rather coarse and straightforward hourly rate,between 0300hrs and 0400hrs,derived from Frank's LD table). 

       One condition that will put yourself come close to the geocentric point is what Antonie has described as being a "moving observer",one has to travel along your latitude line at an angular speed of 15° per hour, by doing so, he would literately remain stationary with the geocentric point. But the instant and averaged LD rate would still vary from table to your location at the hemisphere. The instantaneous rate would be greater if moon stays at your zenith（closest to moon）,and slower if at your horizon.

      Therefore,If I were to use the LD rate from the LD tables or other means that were calculated from the geocentric point,the assumed position consequently has to shift westwardly with time. I have deduced a UTC of 03:39:07 base on an LD hourly rate of 21.6′/ assumed time 03:37:00/assumed position 47°10′N 9°32′E). The position has to shifted westwardly to (47°10′N 9°0.3′E, travelling for 127 seconds at 0.25′/Sec) at 03:39:07 in order to best-suite that table-calculated rate. Did not check the maps so I have no idea if the new location are still within Liechtenstein territory.