▁for ▁him ▁the ▁prize ▁of ▁the ▁Berlin ▁Academy ▁in ▁ 1 8 3 0 , ▁and ▁a ▁mem oir ▁on ▁com et ary ▁dist urban ces ▁was ▁crown ed ▁by ▁the ▁Paris ▁Academy ▁in ▁ 1 8 5 0 . ▁ ▁In ▁ 1 8 3 8 ▁he ▁published ▁a ▁revision ▁of ▁the ▁lun ar ▁theory , ▁entitled ▁Fund ament a ▁nova ▁investigation is , ▁& c ., ▁and ▁the ▁improved ▁T ables ▁of ▁the ▁Moon ▁(" H ansen ' s ▁L un ar ▁T ables ") ▁based ▁upon ▁it ▁were ▁printed ▁in ▁ 1 8 5 7 , ▁at ▁the ▁exp ense ▁of ▁the ▁British ▁government , ▁their ▁mer it ▁being ▁further ▁recognized ▁by ▁a ▁grant ▁of ▁£ 1 0 0 0 , ▁and ▁by ▁their ▁ad option ▁in ▁the ▁N aut ical ▁Al man ac ▁as ▁from ▁the ▁issue ▁for ▁the ▁year ▁ 1 8 6 2 , ▁and ▁other ▁E ph emer ides . ▁A ▁theoretical ▁discussion ▁of ▁the ▁dist urban ces ▁emb od ied ▁in ▁them ▁( long ▁familiar ly ▁known ▁to ▁lun ar ▁exper ts ▁as ▁the ▁Dar leg ung ) ▁appeared ▁in ▁the ▁Ab hand lungen ▁of ▁the ▁Sax on ▁Academy ▁of ▁Sciences ▁in ▁ 1 8 6 2 – 1 8 6 4 . ▁ ▁At ▁the ▁time ▁of ▁publication ▁of ▁Hans en ' s ▁T ables ▁of ▁the ▁Moon ▁in ▁ 1 8 5 7 , ▁astronom ers ▁generally ▁believed ▁that ▁the ▁lun ar ▁theory ▁was ▁at ▁last ▁complete ; ▁ ▁but ▁within ▁about ▁a