S U R 



distance of two objects was there found by calculation to be 6574,4 feet, 

 find, by actual admeasurement, the distance was found to be 30574,3 feet, 

 differing very little more than an inch from the computed distance. 



We shall close this necessarily imperfect article with the methods of 

 finding the difference of longitudes and difference of latitudes of places 

 upon the earth's surface, as practiced in the late government survey of 

 this country. 



Difference of Longitude. 



Let P be the pole, L G the circle described by the 



G 



pole star, A and B the two places. Take by the in- 

 strument the /_ GAB / contained by B and the 

 pole star when at its greatest azimuth ; then knowing 

 P A, P G, we may find PAG the greatest azimuth, 

 which added to GAB gives P A B ; hence in the 

 spherical A P A B, we have PA, P B and / P A B to 

 find /_ A P B the difference of longitude. Hence if A 

 be Greenwich, the longitude of B is known. 



N.B. For four minutes either before or after the pole star's greatest 

 elongation, it moves only about a second in azimuth; h.nce a good 

 pocket watch gives the time of greatest a/iniuth with sufficient accuracy 



Difference of Latitude. 



In finding the difference of longitude above, the latitude was i 

 known j this was found by geometrical admeasurement thus, 



Let A, B, and C be three places, A F the 

 meridian of A. Find the / B A D zz supple- 

 ment of / P A B in the former figure (and 

 which may be found, if A 'a latitude ia known, 

 as was shewn ia the last Article) ; and find by 

 observation A B. B C, and / A B C; then ia 

 the A A B D we can find A D in feet, and ' 

 (knowing the dimensions of the earth) in second,, which gives the dif- 

 ference of latitudes of A and * Again,!, the A C B E, w! hT.e C B Q 

 the supplement of ABC and GBE (.BAD) and .'. CBE; hence 

 BE may be found, and /. A F, = difference of latitude of A and C 



s , h r r!^ ! h r u any ** * ** A be G^: 





tan^alpt^^ ff 



The tetitude. thus determined are more accurate than thoso dtfuoe* 



