HARMOI^IC AISTALYSIS AN^D PREDICTIOIN' OF TIDES. 165 



for this argument given in Table 3, the elements of the formulas 

 being functions of N, which are given in Table 6. The u's of com- 

 ponents L, and Mj are functions of both N and P. The w of Lj == 

 u of M2 - (R from Table 8) and the u of M^ = ^ (u of M3) + {Q from 

 Table 10). For any time between the years 1900 and 2000 the it's 

 of L2 and Ml may be conveniently obtained from Table 13. 



Table 12. Log factor F for each tenth degree of I. — This table is 

 based upon the formulas for factor Fin Table 3. The factors for Lj 

 and Mj being functions of both / and P are not included directly in 

 the table. These may be obtained from the following formulas : 



log F (L2) =log F (M.,)+ (log J2a from Table 7) [See (186) p. 49.] 

 log F (MJ =log F (O,) + (log Qa from Table 9) [See (206) p. 53.] 



For any time between the years 1900 and 2000 the factors for Lj and 

 Ml lasij be conveniently obtained from Table 13. It will be noted 

 that the above formula for log F (Mj) accords with the factor gen- 

 erally used in practice rather than the theoretically correct factor, as 

 indicated in Table 3 (see p. 52). 



Table 13. Values of u and log factor F for components Lj and 

 Ml- — This table includes the values of u and log F for components 

 Lj and M^, for each 5° of N for the years 1900 to 2000, inclusive. 

 The values are based upon the following formulas : 



uoi'L, = 2^-2v-R = {uoiM,)-R p. 48. 



u oiM.i = ^-v + Q = ^iu oiM2)+Q p. 51. 



F (L,) = F (MJ X i?a (186) of p. 49. 



F (MJ = F (0\) X Qa (206) of p. 53. 



The values of u of M2 may be taken from Table 11, i^ (M,) and 

 F (Oi) from Table 12, R from Table 8, Q from Table 10, R^ from" Table 

 7, and Q^ from Table 9. The factors F of M^ represented in this table 

 are those which have heretofore been in general use (see p. 52) . For 

 the corrected F (MJ the tabular logarithms should be increased by 

 0.1523, which is the logarithm of the correcting factor 1.42. 



Table 14. Factor f for middle of each year 1850 to 1999. — The factor 

 / is the reciprocal of factor F. The values for the years 1850 to 1950 

 were taken directly from the Manual of Tides, by R. A. Harris, and 

 the values for 1951 to 1999 were derived from Tables 12 and 13. 



Table 15. Equilibrium argument {Vo + u) for beginning of each year 

 1850 to 2000. — The equilibrium argument is discussed in section 10. 

 The tabular values are computed by the formulas for the argument 

 in Table 3, the Fo referring to the value of V on January 1, hour 

 Greenwich mean civil time, for each year, and the u referring to the 

 middle of the same calendar year; that is, Greenwich noon on July 

 2 in common years and the preceding midnight in leaf) years. The 

 value of the T of the formulas is 180° for each midnight, and the 

 values of the other elements for the V may be obtained from Table 

 4. The u of the argument may be obtained from Tables 11 and 13 

 after the value of N has been determined for the middle of each year 

 from Tables 4 and 5. In constructing Table 15 the values for the 

 years 1850 to 1950 were taken directly from the Manual of Tides, by 

 R. A. Harris, and the values for the years 1951 to 2000 were computed 

 as indicated above. 



Tables 16, 17, and 18. — These tables give the differences to adapt 

 Table 15 to any month, day, and hour, and are computed from the 



