156 U. S. GOAST AND GEODETIC SURVEY 
Therefore we have the following relations which may be used in com- 
puting the values of J, v, and é in the table: 
cos [=cos 7 cos w—sin 7 sin w cos N 
—(0,91370— 0.03569 cos N 
cos 4(w—12) 
tan 3(N—£-+») > Gis SE) 
tan 3N=1.01883 tan $N 
_ sin 3(w—1) 
sin 3(w +1) 
For the computation of v’ and 2»v’’, formulas (224) and (232) on 
pages 45-46 may be used. The tabular values themselves were taken 
from the preceding edition of this work where they were based upon 
formulas differing slightly from those given here but any differences 
arising from the use of the latter may be considered as negligible. 
Table 7. Values of log R, for amplitude of constituent Ly.—Values 
in this table are based upon formula (213) on page 44. 
Table 8. Values of R for argument of constituent L,—Values in 
this table are derived from formula (214) on page 44. 
Table 9. Values of log Q, for amplitude of constituent M,—Values in 
this table are based upon formula (197) on page 41. 
Table 10. Values of Q for argument of constituent M,—Values in 
this table are derived from formula (203) on page 42. 
Table 11. Values of wu for equilibrium arguments.—This table is 
based upon the u-formulas in table 2 and includes values for the 
principal lunar constituents for each degree of N. The w’s of L, and 
M,, which are functions of both N and P are given separately in 
table 13 for the years 1900 to 2000. 
Table 12. Log factor F for each degree of I—The factor F is the 
reciprocal of the node factor f to which references are given in table 2. 
The values in table 12 are based upon the formulas for these factors 
and are given for all the lunar constituents used in the tide-predicting 
machine, excepting values for L, and M, which are given separately 
in table 13. 
Table 13. Values of u and log F for Ly and M,.—From a com- 
parison of the u’s of constituents L,, M;, and Mz in table 2, it will be 
noted that the following relations exist: 
tan 4(N—é—p) tan 4N=0.64412 tan 3N 
u of Ly»=(u of M,)—R 
u of M,=i(u of M2) +Q 
Also, the following relations may be derived from formula (215) on 
page 44 and formula (207) on page 43 since the factor F' is the recip- 
rocal of the node factor f: 
log F(L,)=log F(M2)+log R. 
log F(M,) =log F(O;) +log Q, 
The values for table 13 were computed by the above formulas, the 
component parts being taken from tables 7 to 12, inclusive. The 
values for log F(M,) in this table are in accord with Darwin’s original 
