190 



ASTRONOMY. 



10. — Elements for mavMng parallels^ &c. — Continued 



PARALLEL 31'= 47'. 



na o 



s ° 



a 



tc 



.3 



bo 



o 



1 



10 

 13 

 20 

 25 



35 

 49 

 45 



50 

 55 

 60 



Length of oiiset (= differ 

 ence of latitude,) 



In arc. 



If 



0.004 



0.102 



0.408 



0.918 



1.632 



2.550 



3.673 



5.000 



6.530 



8.265 



10.203 



12,346 



14.692 



In feet. 



0.4 

 10.3 

 41.9 

 92.7 



164.9 

 257.6 



371.1 

 505.3 

 659.8 

 835.0 



1030.9 

 1947.4 

 1484.4 



Log. N in feet. ....... 



Lo^. (1 -|- e* COS. »L) 



Log.2sinl" 



Log. sin 1" 



1° of parallel , 



10' of parallel 



V of parallel'. .,...•. 

 l^'of paralleL. •,..., 

 l"of parallel 



Latitude at the 

 end ot any dis- 

 tance on the 



tausent. 



Azimuth of the tan- 

 gent at any dis- 

 tance hearing 



North East. 



« / // 

 31 47 00.00 



46 59.90 



59.59 



69.08 

 58.37 



57.45 

 56.33 

 55.00 

 53.47 

 51.74 

 49.80 

 47.65 

 45.31 



o I ff 



89 59 43.0 

 57 18.9 

 54 37.8 

 51 55.7 

 49 15.5 

 46 34.5 

 43 53.0 

 41 12.2 

 38 31.2 

 35 50. 

 33 09.0 

 30 08.0 

 S7 47.0 



Longitude of the 

 point of the par- 

 allel determined 

 by each offset. 



1 01.17 

 5 05.88 

 10 11.75 

 15 17.63 

 20 23.50 

 25 29.37 

 30 25.24 

 35 41.11 

 40 46.97 

 45 52.83 

 50 58.68 

 56 04.53 

 61 10.37 



7,3210287 

 0.0021098 

 4,9365049 

 4.6S55749 



L 



7_.-n» tang. L(l + e» cos L) 

 * — ^ N» 2 sin 1" 



Z = 90 



104,069.2 yds. 



17,344.87 « 



1,734.487 " 



28.908 '« 

 86,724 feet. 



1 1 



Biff. long. ==: D ^--^^, ^Sn 



D = distance in feet, measured on tangent 

 L =^ lat- of points of beginning of ditto. 

 / =lat. of any point o( tangent. 

 Z =c= azimuth"^ of tangent line at any point. 



Log. (L - = 

 Log. 2 sin 1'^ = 



Log. sin 1" 



= Iog. (D'') + 0.1579209 

 = 4.9866049 

 4.6855749 



MEMORANDA. 



One hundred miles of parallel of 31° 47' 



Longitude of initial point of parallel on Eio Bravo, (by survey from Frontera.) ,. 



Longitude of terminal point of parallel 31^ 47' 



Longitude of terminal point of parallel 31==* 20', (by treaty) 



1 41 57, 55 



lOG 31 26.50 



108 13 24.05 



111 00 00.00 



// 



Length of parallel 31° 20'— in arc 



do ^- in yards 



do in feet 



Do 



Do 



Do » do -. in miles and feet 



One degree of parallel of latitue Sl*^ 47' 



One minute of do 



do 



One second of do do 



Or in feet 



One degree of parallel of latitude 31° 20' 

 One minute of do ^-do.- 



One second of --.do do 



Or in feet 



From parallel 31=3 20' to 31^ 47' = 27' 



One degree of meridian (taiddle latitude being dl^ 3^) 



One minute of .-.-do.* do ,. do.-. 



One gfetond of do do.-* do-_. 



Or in feet .--*. .... -^ — 



2 46 35. 95 



288964. 03 

 866892. 10 

 164 miles + 972 feet, 



103, 670. 85 yards. 



1,726.18 " 

 28.77 " 

 86.310 



104,069,2 yards, 



(C 



(4 



1,734,487 

 28. 908 

 86. 724 



31 miles -f 5. 37 feet, 

 121,248.43 yards. 



2,020.807 

 33. 680 

 101.04 



CI 



ii 



