CONTENTS. IX 



13. Solution of Spheroidal Triangles Ivii 



a. Spherical or splieroidal excess Iviii 



14. Geodetic Differences of Latitude, Longitude, and Azimuth Iviii 



a. Primary triangulation Iviii 



b. Secondary triangulation 'x 



15. Trigonometric Leveling Ixi 



a. Computation of heights from observed zenith distances . . . Ixi 



b. Coefficients of refraction Ixiii 



c. Dip and distance of sea horizon Ixiii 



16. Miscellaneous Formulas Ixiii 



a. Correction to observed angle for eccentric position of instrument Ixiii 



b. Reduction of measured base to sea level Ixiv 



c. The three-point problem Jxiv 



17. Salient Facts of Physical Geodesy Ixv 



a. Area of earth's surface, areas of continents, area of oceans . . Ixv 



b. Average heights of continents and depths of oceans .... Ixv 



c. Volume, surface density, mean density, and mass of earth . . Ixv 



d. Principal moments of inertia and energy of rotation of earth . Ixvi 



ASTRONOMY. 



1. The Celestial Sphere. Planes and Circles of Reference . Ixvii 



2. Spherical Co-ordinates Ixvii 



a. Notation Ixvii 



b. Altitude and azimuth in terms of declination and hour angle . Ixviii 



c. Declination and hour angle in terms of altitude and azimuth . Ixix 



d. Hour angle and azimuth in terms of zenith distance .... Ixix 



e. Formulas for parallactic angle Ixix 



f. Hour angle, azimuth, and zenith distance of a star at elongation Ixx 



g. Hour angle, zenith distance, and parallactic angle for transit of 



a star across prime vertical Ixx 



h. Hour angle and azimuth of a star when in the horizon, or at the 



time of rising or setting Ixxi 



i. Differential formulas \\x\i 



3. Relations of Different Kinds of Time used in Astronomy . Ixxii 



a. The sidereal and solar davs Ixxn 



b. Relation of apparent and mean time Ixxui 



c Relation of sidereal and mean solar intervals of time .... Ixxiii 



d. Interconversion of sidereal and mean solar time Ixxiii 



e. Relation of sidereal time to the right ascension and hour angle 



of a star Ixxiv 



4. Determination of Time Ixxiv 



a. By meridian transits Ixxiv 



b. By a single observed altitude of a star Ixxvi 



c. By equal altitudes of a star Ixxvii 



5. Determination of Latitude Ixxvu 



a. By meridian altitudes Ixxvu 



b. By the measured altitude of a star at a known time .... Ixxviii 



c. By the zenith telescope Ixxix 



