EXPLANATION OF SOURCE AND USE OF TABLES. CI 



Charles H. Kummell. Their use is explained on p. Iviii. The following example 

 will illustrate their use : — 



Latitude of vertex A of triangle 48° 08' 



" " B " 47 52 



" " C " 47 04 



Mean latitude 47 41 



Angle C^ 51° 22' 55" log sin C 9.89283 — 10 



log a (feet) 5.64401 



log b (feet) 5.58681 

 log factor, Table 13, for 47° 41' 0.37176 



Spheroidal excess = 31. "290, log i. 49541 



Tables 15 and 16 give logarithms of factors for computing differences of lati- 

 tude, longitude, and azimuth in secondary triangulation whose lines are 12 miles 

 (20 kilometres) or less in length. These tables were computed by Mr. Charles 

 H. Kummell. Table 15 gives factors for the English foot as unit, and Table 16 

 for the metre as unit. The use of these tables is illustrated by a numerical exam- 

 ple given on pp. Ix and Ixi. For lines not exceeding the length mentioned, the 

 tables will give differences of latitude and longitude to the nearest hundredth of 

 a second of arc, using 5-place logarithms of the lengths of the lines. 



Table 17 gives lengths of terrestrial arcs of meridians corresponding to lati- 

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

 to arcs less than 1°. The unit of length is the English foot. The table was 

 computed by Mr. B. C Washington, Jr. 



The length corresponding to any latitude interval is the distance along the 

 meridian between parallels whose latitudes are less and greater respectively than 

 the given latitude by half the interval. Thus, for example, the length corre- 

 sponding to the interval 30' and latitude 37° (182047.3 feet) is the distance along 

 the meridian from latitude 36° 45' to latitude 37^^ 15'. 



By interpolation, we may get from this table the meridional distance corre- 

 sponding to any interval. The following example illustrates this use : Required 

 the distance between latitude 41° 28' 17. "8 and latitude 41° 39' 53."4- The 

 difference of these latitudes is 11' 35."6, and their mean is 41° 34' o5."6. The 

 computation runs thus : — 



Latitude 41°. 

 10' 60724.60 feet 



i' 6072.46 " 



30" 3036-23 " 



5" 506.04 " 



o."6 60.72 " 



^ X 12.41 7-05 " 



Distance = 70407.10 " 

 When the degree of precision required is as great as that of the example just 



