APPENDIX. 



CONSTANTS. 



Numerical Constants. 



Base of natural (Napierian) logarithms, 

 Log e, modulus of common logarithms, 

 Circumference of circle in degrees, 

 " " " in minutes, 



" " " in seconds. 



Circumference of circle, diameter unity, 



Number. 

 ZT = 6.2831853 



*= 1.047 1976 

 3 



-= 0.3183099 



IT 



■k"- = 9.8696044 



Logarithm. 

 0.7981799 



0.0200286 



9.5028501 — 10 

 0.9942997 



The arc of a circle equal to its radius is 



in degrees, p° = i8o/ir 



in minutes, p' =6op° 



in seconds, p" = 60 p' 

 For a circle of unit radius, the 



arc of 1° = i/p° 



arc of i' = i/p' 



arc (or sine) of l"= i/p" 



Geodetical Constants. 



Number. 



= <? = 2.7182818 



= M = 04342945 

 = 360 



= 21600 

 = I 296000 



= IT =3.14159265 



l/ir2 = 0.1013212 



V^ = 17724539 



-r4= = 0.5641896 



V IT 



^7= 1.4142136 

 ^3"= 17320508 



= 57.29578° 

 = 34377468' 

 = 206264.8" 



= 0.0174533 

 = 0.0002909 

 = 0.00000485 



Logarithm. 



0.4342945 

 9-6377843 — 10 

 2-5563025 

 4-3344538 

 6.1 1 26050 

 0.4971499 



9.0057003 — 10 

 0.2485749 

 9.7514251 — 10 



0.1 5051 50 

 0.2385607 



1.7581226 



35362739 

 5-3144251 



8.2418774 — ID 

 6.4637261 — 10 

 4.6855749—10 



Dimensions of the earth (Clarke's spheroid, 1866) and derived quantities. 



Equatorial semi-axis in feet, 



in miles, 

 Polar semi-axis in feet, 

 in miles, 



^2 1)2 



(Eccentricity)^ = ^ 



„. . 3 — 1> 

 Flattening = 



= a = 20926062 

 = a= 3963.3 



= d = 20855121. 

 = d= 3949-8 



«2 = 0.00676866 



7.3206875 



3-5980536 

 7.3192127 

 3-5965788 



7.8305030—10 



=/= 1/294.9784 7-5302098 — 10 



= 24859.76 miles. 

 = 24901.96 " 

 . =: 196940400 square miles. 



= 5.576± 0.016. 

 = 2.56 ±0.16. 



Perimeter of meridian ellipse. 



Circumference of equator, 



Area of earth's surface. 

 Mean density of the earth (Harkness) 

 Surface density " 

 Acceleration of gravity (Harkness) : 



g (cm. per second) = 980.60 (i — 0.002662 cos 2<p) for latitude <p and sea level. 



g, at equator = 977-99 ; g, at Washington = 980.07 ; g, at Paris = 980.94 ; 



^, at poles =983.21 ; j^, at Greenwich =981.17. 

 Length of the seconds pendulum (Harkness) : 



/ = 39.012540 + 0.20826S sin2 (p inches = 0.990910 + 0.005290 sin^ <p metres. 



Smithsonian Tables. 



171 



