APPENDIX. 



CONSTANTS. 



Numerical Constants. 



Base of natural (Naperian) logarithms, 

 Log e, modulus of common logarithms, 

 Circumference of circle in degrees, 

 " " " in minutes, 



" " " in seconds. 



Circumference of circle, diameter unity, 

 Number. Logarithm. 



277 = 6.2831853 0.7981799 



e- 

 M. 



TT : 



TT 



1. 0471976 0.0200286 



— = 0.3183099 9.5028501 - 10 



7r 



7r2 =9.8696044 0.9942997 

 The arc of a circle equal to its radius is 



in degrees, P° = iSo/tt 



in minutes, p^ = 60 P° 



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 i^'' = i/f>'' 



Geodetical Constants. 



Number. 



2.7182818 



0.4342945 



360 



21 600 



I 296000 



3.14159265 



0.1013212 



1-7724539 



—^ = 0.5641896 



1.4142136 

 1.7320508 



57-29578 

 3437.7468^ 

 206 264.8'''' 



0.017 4533 

 0.000 2909 

 0.00000485 



l/7r2 



I 



v/3 



Logarithm. 



0.4342945 

 9.6377843 - 10 

 2.5563025 

 4-3344538 

 6. 1 1 26050 

 0.4971499 



9.0057003 — 10 

 0.2485749 



9.7514251 - 10 



0.1 505 1 50 

 0.2385607 



1. 7581226 



3-5362739 

 5.3144251 



8.2418774 — 10 

 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, 



... a2 _ ^2 

 (Bccentncity)2 = 



Flattening = 



a — b 

 a 



a2 



a =i 20926062. 



a = 3963-3 

 b = 20855121. 



b =^ 3949-8 



e' = 0.0067 6866 



£ = 1/294.9784 



= 24859.76 

 = 24 901.96 

 =r 196940400 



= 5.576 ±0.016. 

 =: 2.56 zfc 0.16. 



7.3206875 



3-5980536 

 7.3I92I27 

 3-5965788 



7.8305030 - 10 



miles. 



square miles. 



Perimeter of meridian ellipse, 

 Circumference of equator. 

 Area of earth's surface. 



Mean density of the earth (Harkness) 

 Surface density " " " 



Acceleration of gravity (HarknESS) : 



£-4, (cm. per second) = 980.60 (i —0.002662 cos 2 <p) for latitude <j) and sea level. 



g-, at equator = 977.99 ; g, at Washington = 980.07 ; £-, at Paris = 980.94. 



g-, at poles =983.21; g, at Greenwich =981.17; 

 Length of the seconds pendulum (Harknkss) : 



/ = 39.012540 + 0.208268 sin2 (f> inches = 0.990910 + 0.005290 sin* <f) metres. 



Smithsonian Tables. 



258 



