C EXPLANATION OF SOURCE AND USE OF TABLES. 



Tables 7 and 8 are taken from " Smithsonian Meteorological Tables " (the 

 first volume of this series). Their mode of use will be apparent from the follow- 

 ing example : Required the sine and tangent for 28° 17'. 



sine 28° 10', Table 7 



Proportional part for 7' (7 X 2.6) 



sine 28° 17' 0.4738 



0.4720. 

 18. 



Tabular difference = 26. 



tangent 28° 10', Table 8 

 Increase for 7' (7 X 3-8) 



tangent 28° 17' 



0-5354. 



27. 



0.5381. 



Difference for i' = 3.8. 



Table g is a copy of a similar table published in " Professional Papers, Corps 

 Engineers," U. S. A., No. 12. It has been checked by comparison with other 

 tables in general use. This table is useful in computing latitudes and departures 

 in traverse surveys wherein the bearings of the lines are observed to the nearest 

 quarter of a degree, and in other work where multiples of sines and cosines are 

 required. Thus, if L denote the length and B the bearing from the meridian of 

 any line, the latitude and departure of the line are given by 



LcosB and Zsin^^ 



respectively; the " latitude " being the distance approximately between the paral- 

 lels of latitude at the ends of the line, and the " departure " being the distance 

 approximately between the meridians at the ends of the line. As an example, let 

 it be required to compute the latitude and departure for Z = 4837, in any unit, 

 and B = 2,G° 15'. The computation runs thus : — 



Latitude. 



For 4000 3225.77 



800 645.16 



30 24.19 



7 5-63 



4837 Zcos^= 3900.77 



Departure. 



2365-23 



473-05 



17-74 



4-14 



Zsin^= 2860.16 



Tables 10 and 11 give the logarithms of the principal radii of curvature of the 

 earth's spheroid. They were computed by Mr. B. C. Washington, Jr., and care- 

 fully checked by differences. They depend on the elements of Clarke's spheroid 

 of 1866. The use of these tables is sufficiently explained on p. xlv-xlix. 



Table 12 gives logarithms of radii of curvature of the earth's spheroid in sec- 

 tions inclined to the meridian sections. It is abridged to 5 places from a 6-place 

 table published in the " Report of the U. S. Coast and Geodetic Survey for 

 1876." Its use is explained on pp. Ixi-lxiv. 



Tables 13 and 14 give logarithms of factors needed to compute the spheroidal 

 excess of triangles on the earth's spheroid. No. 13 is constructed for the Eng- 

 lish foot as unit, and No. 14 for the metre. These tables were computed by Mr. 



