X CONTENTS. 



6. Determination of Azimuth Ixxix 



a. By observ^ation of a star at a known time Ixxix 



b. By an observed altitude of a star Ixxxi 



c. By equal altitudes of a star Ixxxi 



THEORY OF ERRORS. 



1. Laws of Error Ixxxiii 



a. Probable, mean, and average errors Ixxxiv 



b. Probable, mean, average, and maximum actual errors of inter- 



polated logarithms, trigonometric functions, etc Ixxxv 



2. The Method of Least Squares Ixxxvi 



a. General statement of method Ixxxvi 



b. Relation of probable, mean, and average errors Ixxxviii 



c. Case of a single unknown quantity Ixxxix 



d. Case of observed function of several unknown quantities . . xc 



e. Case of functions of several observed quantities xciii 



f. Computation of mean and probable errors of functions of ob- 



served quantities . ^ xcv 



EXPLANATION OF SOURCE AND USE OF TABLES. 



Tables i and 2 xcix 



Table 3 . xcix 



Table 4 xcix 



Tables 5 and 6 xcix 



Tables 7 and 8 c 



Table 9 c 



Tables 10 and 11 c 



Table 12 c 



Tables 13 and 14 c 



Tables 15 and 16 ci 



Table 17 ci 



Table 18 cii 



Tables 19-24 cii 



Tables 25-29 ciii 



Table 30 ciii 



Table 31 . . civ 



Tables 32 and 7,^ civ 



Tables 34 and 35 civ 



Tables 36 and 37 civ 



Table 38 civ 



Table 39 civ 



Table 40 civ 



Table 41 cv 



Table 42 cv 



