282 Mr. Riddle on the new Methods qfjinding the Longitude. 



Table I. 



Azim. 



10° 



20° 1 30° 



40° 



50° 



60° 



70° 



80° 



Lat. 

 10° 



Error in Hour Angle for 1' error in Latitude. 



5' 46" 



2' 47" 



1' 46" 



1' 13" 



0' 51" 



0' 35" 



0' 22" 



0' 11" 



20 



6 2 



2 55 



1 50 



1 15 



54 



37 



23 



11 



30 



6 33 



3 10 



2 



1 22 



58 



40 



25 



12 



40 



7 24 



3 35 



2 16 



1 33 



1 6 



45 



28 



14 



50 



8 49 



4 16 



2 41 



1 51 



1 18 



54 



34 



16 



60 



11 20 



5 30 



3 28 



2 23 



1 41 



1 9 



44 



21 



70 



16 35 



8 2 



5 4 



3 29 



2 27 



1 41 



1 4 



31 



80 



32 40 



15 49 



9 59 



6 52 



4 50 



3 22 



2 6 



1 1 



Table II. 



Azim. 



10° 



20° 



30° 



40° 



50° 



60° 



70° 



80° 



Lat. 



Error in Hour Angle for 1' error in Altitude. 



10° 



5' 51" 



2' 58" 



2' 2" 



1' 35" 



1' 19" 



1' 10" 



1' 5" 



1' 2" 



20 



6 7 



3 7 



2 8 



1 39 



1 23 



1 14 



1 8 



1 5 



30 



6 39 



3 22 



2 18 



1 48 



1 30 



1 20 



1 14 



1 10 



40 



7 31 



3 49 



2 37 



2 2 



1 42 



1 30 



1 23 



1 19 



50 



8 58 



4 33 



3 7 



2 26 



2 2 



1 48 



1 39 



1 34 



60 



11 31 



5 51 



4 



3 7 



2 37 



2 19 



2 8 



2 2 



70 



16 50 



8 33 



5 51 



4 33 



3 49 



3 23 



3 6 



2 58 



80 |33 10 



16 50 



11 31 



8 58 



7 31 



6 39 



6 7 



5 51 



Now we shall suppose as an example, that the sun and the 

 moon are the objects observed, the latitude of the ship being 

 one minute uncertain, and the altitude of each object also one 

 minute uncertain ; that the latitude of the ship is about 50°, 

 the azimuth of the sun 40°, and of the moon 50°. Then in 

 Table I. we have the uncertainty in the solar horary angle 

 arising from the uncertainty in the latitude, 1' 51", and the 

 uncertainty in the lunar horary angle arising from the same 

 cause, 1' 18". And in Table II. we have the uncertainty in the 

 same angles resulting from the uncertainty in the altitudes, 

 2' 26" and 2 r 2" respectively. Hence the sum of these four 

 arcs, or 7' 37", is the uncertainty in the difference of the right 

 ascensions arising from an uncertainty of only one mile in the 

 ship's latitude, and one minute in the altitudes of the objects. 

 This in a general way would render the longitude uncertain 

 to about 3°f. 



In 



