TOPOGRAPHICAL SURVEYS 107 



tants' of many places to Munich to obtain necessary details. 

 Notes for a portion of his survey have survived, mainly lists 

 of angles observed. We may therefore picture him, riding 

 through the countryside in the summer months, with two 

 companions, and periodically halting to ascend a convenient 

 church tower or hill with his diopter, compass and notebook 

 and to take angles to all prominent features in the surrounding 

 countryside. From his notes it appears that, in an area of 

 approximately 25 kms. X 35 kms. he observed at twenty-eight 

 stations, taking in all 200 sights. Some of his rays were quite 

 long, even by modern standards, up to fifty kilometres. The 

 winter months were spent in working up his observations and 

 drawing the map, and also in eliciting details from experienced 

 countrymen. 



The basis of Apian's map was his calculations of the latitude 

 and longitude of a number of important towns, the latitudes 

 being obtained from the observation of the passage of circum- 

 polar stars. As for the longitudes, Peter Apian had advocated 

 the use of lunar distances, but these observations were not 

 accurate; his son therefore calculated longitudes from the 

 differences in latitude and the direct distance between two 

 places. These positions were entered in the map net and 

 served as centres for the detail collected by Apian on his 

 peregrinations. 



It has been shown that he kept mainly to the valleys, and 

 that the intervening plateau or mountain was sketchily re- 

 presented, and often served to absorb the accumulated errors. 

 He seems occasionally to have measured approximately the 

 side of a triangle as a check on his observed angles; this was 

 probably calculated from riding time between the two points, 

 for he expressly states that one hour's riding equalled one 

 German mile. 



By these methods, he attained to a considerable degree 

 of accuracy, at least within the area of his direct observation, 

 and his work remained the basis of all maps of Bavaria for 

 more than two centuries. His angles in general were accurately 

 observed, but errors in his determination of latitudes affected 

 the system of coordinates. 



It will be noticed that Apian appears to have entered the 



