Cii EXPLANATION OF SOURCE AND USE OF TABLES. 



given, it will be more convenient to use formulas (2) on p. xlvi. Thus, in this 



example, — 



log. 

 A<f> = 695."6 2.8423596 



</> = 41° 34' 05. "'6, p„ (Table 10) 7.3196820 



cons't 4-6855749 



Length = 70407.10 feet 4.8476165 



Table 18 gives lengths of terrestrial arcs of parallels corresponding to longi- 

 tude intervals of 10", 20", . . . 60", and 10', 20', . . . 60', or lengths corresponding 

 to arcs less than 1°. The unit is the English foot. This table was computed by 

 Mr. B. C. Washington, Jr. 



The method of using this table is similar to that applicable to Table 17 

 explained above. For the computation of long arcs it will in general be less 

 laborious to use the formulas (i) on p. xlix than to resort to interpolation from 

 Table 18. 



Tables 19-24 give the rectangular co-ordinates for the projection of maps, in 

 accordance with the polyconic system explained on pp. liii-lvi, for the following 

 scales respectively : — 



Table 19, scale ^^^ 



250000 

 I 



■*"' 1^000 



21' " i2ikr (2 "^iles to i inch) 

 22, " ^ (i mile to I inch) 



> unit = English inch. 



033U0 

 _! 



2000UO 



^' 80000 



23, 



unit = millimetre. 



These tables were computed by Mr. B. C. Washington, Jr. 



The use of these tables and their application in the construction of maps may 

 be best explained by an example. Suppose it is required to draw meridians and 

 parallels for a map of an area of 1° extent in longitude, lying between the paral- 

 lels of 34° and 35°. Let the scale of the map be one mile to the inch, or 1/63360, 

 and let the meridians and parallels be 10' apart respectively. Draw on the pro- 

 jection paper an indefinite straight line AB, Fig. 4, to represent the middle me- 

 ridian of the map. Take any convenient point, as C, on this line for the latitude 

 34°, and lay off from this point the meridional distances CD, CE, CF, . . . CI, 

 given in the second column of Table 22, p. 114.* Through the points D, E, E, 

 ... I, thus found, draw indefinite straight lines perpendicular to AB. By means 

 of these lines and the tabular co-ordinates, points on the developed parallels and 

 meridians are readily found. Thus, for example, the abscissas for points ten 

 minutes apart on the parallel 34° 20' are 9.53, 19.06, and 28.59 inches. These 

 distances are to be laid off on iWV in both directions from AB. At the points 

 Z, AI, tV, Z', M\ N', so determined, erect perpendiculars to NJV' equal in 

 length, respectively, to the ordinates corresponding to the longitude intervals 



* The meridional distances and the abscissas of the points on the developed parallels in Fig. 4 

 are one twentieth of the true or tabular values. The ordinates of points on the developed paral- 

 lels are the tabular values. 



